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THESIS

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'2 COI

This is to certify that the
thesis entitled

LAND OWNERSHIP PARCELIZATION AND FOREST FRAGMENTATION IN
THREE FORESTED COUNTIES IN NORTHERN LOWER MICHIGAN

presented by

Scott A. Drzyzga

has been accepted towards fulfillment
of the requirements for

M. A. degree in Geography

 

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LAND OWNERSHIP PARCELIZATION AND FOREST FRAGMENTATION IN
THREE FORESTED COUNTIES IN NORTHERN LOWER MICHIGAN

By

Scott A. Drzyzga

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of

MASTER OF ARTS

Department of Geography

2000

ABSTRACT

LAND OWNERSHIP PARCELIZATION AND FOREST FRAGMENTATION IN
THREE FORESTED COUNTIES IN NORTHERN LOWER MICHIGAN

By

Scott A. Drzyzga

This research assesses historic landscape configurations of private land
ownerships and forest habitats in Crawford, Grand Traverse, and Kalkaska
Counties, in northern Lower Michigan. This study builds on previous research
that has produced quantitative indicators of parcelization (changing average
parcel sizes). This study also produces quantitative indicators of regional forest
areal extent and fragmentation over a twenty-year period. Spatial and temporal
patterns of land parcel subdivision are analyzed using digitized plat map data,
while patterns of forest cover and forest cover change are assessed using digital
remote sensing data. Changes in land parcel subdivision and forest cover are
observed at multiple spatial scales. Examinations of changing spatial structure
are used to determine whether or not evidence exists to support a hypothesized
link between these phenomena. The purpose of this research is to provide
information that may lead to land use planning and forest management
strategies that are sensitive to land ownership patterns and their influence on

forest structures.

Copyright by
SCOTT A. DRZYZGA

2000

ACKNOWLEDGEMENTS

I would like to thank my committee, Dr. Daniel G. Brown, Dr. Bruce Wm. Pigozzi,
and Dr. J. Michael Vasievich for helping me to complete this thesis. Also, I
extend a special thank you to Dr. Brown for his role in advising me, editing the

many drafts of this text, and showing me how to ask interesting questions.

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1: INTRODUCTION
1 .1 Introduction.
1 .2 Background.
1.3 Statement of problem.
1.4 Research questions.
1.5 Basic definitions.

1.6

CHAPTER 2:
2.1

2.2

2.3

CHAPTER 3:
3.1
3.2
3.3
3.4
3.5
3.6
3.7

CHAPTER 4:
4.1
4.2
4.3

1.5.1 Land ownership parcelization and parcelization.

1.5.2 Forest fragmentation and fragmentation.
Research objectives.

STUDY AREA

Introduction.

2.1.1 Selecting a time frame.

2.1.2 Selecting an area frame.
Description.

2.2.1 General geomorphology.

2.2.2 General hydrography.

2.2.3 Forest cover characteristics.
2.2.4 Forest ownership characteristics.
Summary.

LITERATURE REVIEW
Introduction.

Population studies.
Agricultural land use changes.
Parcelization pressures.

Land consumption theory.
Other concerns.

Summary.

METHODS
Introduction.

Scales of analysis.

Parcel data.

4.3.1 Collection.

4.3.2 Classification.
4.3.3 Temporal analysis.
4.3.4 Location analysis.

viii

5.

VQQU'IU'IOD—F-‘d

10
13
13
15
17
20
23

24
24
26
33
34
39
41
43

45
45
46
49
49
50
55
60

4.4

4.5

4.3.5 Spatial analysis.

Forest data.

4.4.1 Collection.

4.4.2 Image processing.

4.4.3 Image classification.

4.4.4 Temporal analysis.

4.4.5 Landscape patterns and metrics.
4.4.6 Location analysis.

4.4.7 Spatial analysis.

Summary.

CHAPTER 5: RESULTS

5.1
5.2
5.3
5.4
5.5
5.6

5.7
5.8
5.9
5.10
5.11
5.12
5.13

5.14

Introduction.

Scales of analysis.

Parcel data - hypothesis l.

Parcel data - hypothesis II.
Parcelization - location analysis.
Parcelization - spatial analysis.

5.6.1 Townships.

5.6.2 Sample sites.

5.6.3 Survey sections.

Forest cover.

Forest cover - hypothesis III.

Forest cover - hypothesis IV.

Forest cover - hypothesis V.

Forest fragmentation - hypothesis VI.
Forest fragmentation - location analysis.
Forest fragmentation - spatial analysis.
5.13.1 Townships.

5.13.2 Sample sites.

5.13.3 Survey sections.

Summary.

CHAPTER 6: DISCUSSION

6.1
6.2
6.3
6.4
6.5

6.6
6.7

Introduction.

Influences of scale on results and their implications.

Changes in ownership parcelization.

Urban sprawl.

Forest cover change.

6.5.1 Forest parcelization.

6.5.2 Forest fragmentation.

The link between parcelization and fragmentation.
Conclusions.

vi

63
67
67
68
70
72
74
77
78
79

81
81
81
83
86
90
95
97
101
105
109
112
117
118
122
124
127
127
131
135
140

142
142
142
145
155
160
161
164
170

APPENDIX A: PARCEL DATABASE

APPENDIX B: SATELLITE IMAGE DATABASE

APPENDIX C: ISODATA CLUSTERING ALGORITHM PARAMETERS
APPENDIX D: HISTORICAL AERIAL PHOTOGRAPH DATABASE
APPENDIX E: ACCURACY ASSESSMENTS

APPENDIX F: CORE FRAGMENTATION (CF) METRIC
LITERATURE CITED

vii

175
177
180
181
185
194

205

LIST OF TABLES

Table 2.1: Population counts and changes. 12

Table 2.2: Vegetation changes within the study area. 18

Table 2.3: Forest ownership by class. 21

Table 4.1: Population growth rates - 1970-1990. 59

Table 5.1: Average parcel size estimates for political sampling 84
units (ha).

Table 5.2: Summary of parcel size changes for small sampling units. 85
Table 5.3: Average parcel size changes for all scales (ha). 85
Table 5.4: Average annual parcelization rates for political units (ha/yr). 88

Table 5.5: Decadal summary of parcelization rates for small sampling 89

units.
Table 5.6: Parcelization rates and changes for all scales (ha/yr). 89
Table 5.7: Average parcel sizes for concentric bands around 93
Traverse City (ha).
Table 5.8: Spatial autocorrelation results: township values of APS. 98
Table 5.9: Spatial autocorrelation results: township parcelization 100
ra es.

Table 5.10: Spatial autocorrelation results: sample site values of APS. 103

Table 5.11: Spatial autocorrelation results: sample site parcelization 104
rates.

Table 5.12: Spatial autocorrelation results: survey section values 106
of APS.

Table 5.13: Spatial autocorrelation results: survey section 107

parcelization rates.

viii

Table 5.14:

Table 5.15:

Table 5.16:

Table 5.17:

Table 5.18:
Table 5.19:

Table 5.20:

Table 5.21:
Table 5.22:

Table 5.23:

Table 5.24:

Table 5.25:

Table 5.26:

Table 5.27:
Table 5.28:

Table 5.29:

Table 5.30:

Table 6.1:

Landscape metrics describing forest patch and core
distributions.

Average percent of private land as forest and changes
for all scales.

Percent forest summary for small sampling units.

Summary of percent private land as forest for political
units.

Average annual forest change rates for all scales.
Forest fragmentation changes for all scales.

Summary of forest fragmentation for small sampling
units (%).

Summary of forest fragmentation indices for political units.

Forest fragmentation rates and changes for all scales

(CF/yr).

Summary of forest fragmentation rates for political units
(CF/yr).

Fragmentation indices for concentric bands around
Traverse City.

Spatial autocorrelation results: township CF indices.

Spatial autocorrelation results: township fragmentation
rates.

Spatial autocorrelation results: sample site CF indices.

Spatial autocorrelation results: sample site fragmentation
rates.

Spatial autocorrelation results: survey section CF indices.

Spatial autocorrelation results: survey section
fragmentation rates.

Correlations between township growth and parcelization
rates.

110

112

113

115

117
118

119

121
122

123

125

128

129

132

134

136
138

147

Table A1 :
Table B1:
Table C1:
Table D1:
Table D2:
Table D3:
Table D4:
Table E1:

Table E2:
Table E3:

Table F1:

Parcel plat map book dates.

NALC Imagery metadata.

ISODATA clustering algorithm parameters.
Aerial photograph metadata legend

Aerial photograph metadata: 1970.

Aerial photograph metadata: 1980.

Aerial photograph metadata: 1990.

Post classification training sets accuracy assessment
results.

Stratified random sampling accuracy assessment results.

Wall-to-wall accuracy assessment results.

CF metric - observed components.

175
177
180
181
182
183
184

188

190
192
198

Figure 2.1:
Figure 2.2:
Figure 2.3:
Figure 2.4:
Figure 3.1:
Figure 4.1:
Figure 4.2:
Figure 4.3:
Figure 4.4:

Figure 5.1:

Figure 5.2

Figure 5.3:
Figure 5.4:
Figure 5.5:
Figure 5.6:
Figure 5.7:
Figure 5.8:
Figure 5.9:
Figure 5.10:

Figure 5.11:

LIST OF FIGURES

Selected counties.

Elevation model.

General hydrography.

Early settlement vegetation.

Seasonal homes.

Spatial scales of analysis.

Minor civil divisions.

Illustrated example of the parcel classification scheme.
Frequency distributions of parcel areas.

Theoretical land consumption function.

Actual land consumption functions for Traverse City.
Spatial correlograms: township values of APS.
Spatial correlograms: township parcelization rates.
Spatial correlograms: sample site values of APS.
Spatial correlograms: sample site parcelization rates.

Spatial correlograms: survey section values of APS.

Spatial correlograms: survey section parcelization rates.

Map of the Stephan Bridge Road Fire.
Forest fragmentation functions for Traverse City.

Spatial correlograms: township CF indices.

xi

11
14
16
19
32
47
48
54
56
91
91
98
100
103
105
108
108
116
126

128

Figure 5.12:
Figure 5.13:
Figure 5.14:
Figure 5.15:
Figure 5.16:

Figure 6.1:
Figure 6.2:
Figure 6.3:

Figure 6.4:

Figure 6.5:
Figure 6.6:
Figure 6.7:
Figure 6.8:
Figure 6.9:
Figure B1:
Figure E1:
Figure F1:
Figure F2:

Figure F3:

Spatial correlograms: township fragmentation rates.
Spatial correlograms: sample site CF indices.

Spatial correlograms: sample site fragmentation rates.

Spatial autocorrelation results: survey section CF indices.

Spatial correlograms: survey section fragmentation rates.

Temporal frequency distribution of private parcels.
Temporal percentage distribution of private parcels.

Map of parcelization rates for the period between 1970
and 1980.

Map of parcelization rates for the period between 1980
and 1990.

Temporal APS values in the Traverse City area.
Temporal CF values in the Traverse City area.

Forested parcel size frequency distributions.

Map of fragmentation changes between 1973 and 1985.
Map of fragmentation changes between 1985 and 1991.
Geographic coverage of NALC imagery.

Location of reference aerial photograph mosaics.

1973 Forest cover - Whitewater Township.

CF metric calculations.

CF Index representation.

xii

130
132
134
135
139
149
149

153

153

158
159
163
169
169
178
187
196
199

203

CHAPTER 1: INTRODUCTION

1.1: Introduction.

We, meaning humans, have converted natural land cover patterns into
fragments of natural vegetation within a matrix of human dominated land uses in
many places. Fragmentation of natural land cover patterns affects plant and
animal habitats, plant and animal biodiversity, and primary productivity (Fox and
Macenko, 1985). These changes can limit the natural ability of a landscape to
provide resources on a sustained basis and therefore, deteriorate the long-term
environmental quality of landscapes (Cawrse, 1994) and resident ecosystems.
The State of Michigan and land management agencies within the state are often
faced with the task of balancing competing interests that advocate maintaining
sustainable forest resources and those that seek to develop forested lands.
However, the issue is not simply limited to optimizing the amount of woodland
dedicated to each use, but includes many complexities inherent in the spatial

patterns and inter-Ieaved distributions of each land use.

1.2: Background.

In Michigan, land use planning is a local decision process that is directed by local

(city, village, or township) legislation. Under the County Rural Zoning Enabling

Act (Ml PA 183 of 1943) and the Township Zoning Enabling Act (Ml PA 184 of

1943) township planning boards are given authority to develop ordinances to
provide for regulation of land uses, protection of natural resources, and an ability
to limit congestion of human populations. Since basic land-use regulation occurs
at the township level, townships are important organizational units for land and

ecological planning.

A large portion of idle or abandoned farmland is naturally regenerating into
young forests in Michigan’s northern Lower Peninsula (NLP). These new forests
may become incorporated into proximate forest habitats or may exist as island
habitats within a sea of human modified land covers. If these newer forest areas
are subjected to development pressures or are overlooked by local forest
managers, then monies spent on conservation efforts may not be efficiently
applied. Also, development on forested lands may ultimately destroy the natural
amenities that make such lands attractive to new property owners. Participation
among township entities is necessary if public, private, and protected forest
areas are to coalesce into a biologically meaningful ecosystem and a self-

sustaining economic base.

Federal and state forest managers have traditionally managed protected areas
as independent entities. However, recent research and conservation efforts
have recognized habitat sustainability and diversity are also dependent on the
character and quality of landscape features adjacent to protected areas

(adjacency facilitates the transfer and interaction of nutrients, energy, and

organisms between forested areas [Turner and Gardner, 1991]). Hence, tools
and models that explicitly accommodate spatial proximity should prove valuable
to planning organizations. Geographic information systems (GIS) and remote
sensing technology (R8) are tools that can provide local and regional planners
the ability to model spatially explicit data, which can represent complex

landscape systems.

1.3: Statement of problem.

Forests become fragmented when forested lands are developed for agriculture,
logging, or residential settlement purposes. Previously expansive forested
landscapes become insular blocks, or fragments, separated by industrial sites,
roads, railroads, town sites, and tree harvesting operations (Bell, 1995). Such
forest cover changes have been shown to negatively affect timber production
(Birch, 1983), wildlife habitat (Hill, 1985), and ecosystem biodiversity (lida and

Nakashizuka, 1995).

Subdivision of large land parcels under a single ownership into smaller parcels
under diverse ownerships in various stages of development or use greatly
reduces the effectiveness of coordinated management strategies dealing with
wildlife habitat, profitable agriculture, and timber production. In Northern
Michigan, “public forest managers have recently observed that the influx of new

woodlot owners often inhibits their ability to manage State and Federal Forest

timber resources” (Potter-Witter, 1995:29) in a manner that satisfies the public
policies set forth to utilize and protect said resources. Hence, State and Federal
officials are concerned about forested areas in Michigan that are affected by

parcel subdivision.

Brown and Vasievich (1996), Bell (1995), Vogelmann (1995), and Saunders et
al. (1991) have suggested a link exists between increased land ownership
subdivision and increased forest fragmentation. Although such a relationship is
implicitly understood to exist, as evidenced by Michigan’s public forest managers’
concerns (Potter-Witter, 1995:29), the literature is lacking definitive explanations
of the spatial and temporal relationships between the two phenomena.
Understanding how parcel changes manifest as physical changes in terms of
forest cover is important because some forest cover changes can negatively

affect finite supplies of natural resources.

The Michigan Society of Planning Officials (MSPO) explicitly stated a need for
research on “the impact of local, regional, and statewide land fragmentation on
natural resources” (Warbach and Norberg, 19952A-3). This analysis responds
to the MSPO’s stated need for quantification of the spatial and temporal
components of land parcel subdivision and forest cover change within a forested
region in Michigan. This thesis is intended to fill the mentioned knowledge gap
and to provide information that may lead to better land use planning and forest

management strategies.

1.4: Research questions.

I posed four questions in order to determine how the influx of new land owners
and subsequent parcel changes have manifested as physical landscape
changes, in terms of forest cover:
1. What changes occurred in ownership parcelization within a forested
region in Michigan?
2. What changes occurred, if any, in forest cover and forest
fragmentation within the same region in Michigan?
3. How were the relative changes in forest fragmentation related to
relative changes in land parcelization?
4. At what scale(s), if any, do patterns of change in either phenomenon
suggest processes acting on the landscape?
I selected a single, yet representative study area because the time and size
requirements necessary to gather detailed data representing parcel ownerships
and forest covers for all forested regions within the State of Michigan were too

cumbersome.

1.5: Basic definitions.

The terms fragmentation (Brown and Vasievich, 1996; Theobald, et al., 1996)

and parcelization (Barlowe, 1978; Erickson, 1995) have been used

synonymously in past research to mean the division or subdivision of land

ownership in a landscape. However, their meanings are different and must be
made specific for use in this study if the results are to be applied to future
research or policy decisions. Therefore, I have listed several terms and their

definitions below.

1.5.1: Land ownership parcelization or parcelization.

Land ownership parcelization is the division or subdivision of a finite landscape,
over time, into smaller, individual ownership parcels. In general, land subdivision
is evidenced through history by the surveying of land into states, states into
counties, counties into townships, townships into sections, and ultimately
sections into individual ownership parcels. Parcelization refers to the subdivision
of land under a single ownership into smaller parcels under a diverse ownership.
For this study I consider private land ownership changes only in terms of parcel
boundaries and areas. The term parcelization includes all divisions, exempt
splits, and subdivisions of parcels and tracts as defined by the State of

Michigan’s Land Division Act (Ml PA 87 of 1997).

1.5.2: Forest fragmentation or fragmentation.

The term forest fragmentation has been used in the landscape ecology literature

to represent static habitat conditions (Hargis et al., 1998). According to Forrnan

(1995), fragmented landscapes can be characterized by having relatively large

edge densities and relatively small interior habitat areas. Unfragmented

landscapes can thus be characterized by having relatively small edge densities

and relatively large interior habitat areas. In this research, is the term forest

fragmentation is defined as a static forest condition and it represents the degree

to which the amount of interior core area of a forested area differs from its

maximum potential habitat area.

1.6: Research objectives.

The objectives of this study are to:

1.

Select a forested region in Michigan that has been affected by high
population growth rates and is expected to continue to be affected by
its population growth trend into the future,

describe the character of land ownership parcelization within the
region at multiple scales,

describe the character and pattern of forest cover change within the
region at multiple scales,

test specific hypotheses, arising from the research questions,
regarding the spatial and temporal relationships between land
ownership parcelization and forest cover change,

and provide information that may lead to better land use planning and

forest management strategies.

CHAPTER 2: STUDY AREA

2.1: Introduction.

The first objective is to select an appropriate region for study. Selection criteria
include identifying a sufficiently forested area that has been affected by high
population growth rates, and is expected to continue to be affected by population

pressures into the future.

2.1.1: Selecting a time frame.

The period from 1970 to 1990 should be useful for studying land ownership
parcelization and forest cover changes in Michigan because various stages of
population growth, parcel subdivision, and forest cover change may be
observed. For example, non-metropolitan Michigan exhibited a positive
population growth trend that started during the 1970’s (US. Department of
Commerce, 1960 - 1990) and is expected to continue into the year 2020
(Warbach and Norberg, 1995). Demographic and economic researchers have
characterized the observed trend as a “rural renaissance” (Beale, 1977). While
this trend is not unique to Michigan‘, the rural renaissance is important because

most of Michigan’s forested lands are located in these growing rural areas.

 

‘ Johnson (1989) reported the rural renaissance to have been in effect
throughout the entire United States.

Recent forest inventories and analyses of the northern Lower Peninsula, which is
generally considered to be a rural area, have indicated a six percent increase in
total forest land area and an eight percent increase in total timberland area
(Leatherberry, 1994) between the years 1980 and 1993. Leatherberry (1994)
cautions readers of his report, however, that comparisons between inventories
should be kept in general terms because changes have been made in the way
forested areas have been sampled and reported from one inventory to another.
Yet, even in general terms, such increases are noteworthy because previous

inventories have indicated modest declines in forest area within the same region.

The specific twenty-year time frame is also unique to Michigan’s landscape
evolution because the Subdivision Control Act (SCA) of 1967 (Ml PA 288 of
1967) was in effect and enforced during this periodz. The significance of the SCA
and its effect on parcelization has been well documented by Norgaard (1984)
and Wyckoff and Reed (1995). In brief, the SCA provided for an expensive
platting process to be imposed on landowners that subdivided land into parcels
10 acres in size or smaller. According to Norgaard (1984), the statewide
response to the SCA has been a proliferation of parcels just larger than 10 acres
in size. Negative by—products of the proliferation of newly created 10+ acre
parcels are higher infrastructure-per-capita costs and land cover fragmentation

(Grand Traverse County Planning Commission, 1997).

 

2 The Land Division Act (Ml PA 87 of 1997) has since repealed and replaced
significant portions of the SCA and has begun a new era of state zoning
legislation.

The period from 1970 to 1990 is a time frame that is appropriate for this study.
During this time, the northern Lower Peninsula (NLP) experienced a significant
rural population growth trend, undewvent forest fragmentation due in part by
landowners responding to a particular piece of state zoning legislation (Wyckoff,
1995), and yet, exhibited signs of forest regrowth and succession (Leatherberry,

1994). These trends are counter-intuitive and worth research.

2.1.2: Selecting an area frame.

The MSPO asserts that urbanization will catch up with the current trend of forest
recovery (Warbach and Norberg, 1995). The critical junction is expected to
occur first in the northern portion of Michigan’s Lower Peninsula. The MSPO
assertion is seemingly based on the assumption that developing human
settlements and self-sustaining forests are mutually exclusive phenomena.
Given the above mentioned population growth trend and the concern of local
planners, attention should be focused on a forested region within the northern

Lower Peninsula (NLP).

Grand Traverse, Kalkaska, and Crawford Counties (see Figure 2.1) have been
selected as suitable areas for study for several reasons. First, the three counties
are representative of an extreme case in northern Lower Michigan as each has
experienced substantial population increases over the last twenty years,

although not concurrently. The three counties are also expected to incur

10

 

State of Michigan

Legend

   

W/A Grand Traverse County
- Kalkaska County
m Crawford County

339:3 Northern Lower Peninsula
Southern Lower Peninsula

- Eastern Upper Peninsula

5 Western Upper Peninsula

 

Figure 2.1: Selected counties.

11

continued population growth through the next twenty years (Grand Traverse
County Planning Commission, 1997; Warbach and Norberg, 1995). Table 2.1
highlights the population growth trends for the three-county region, the NLP, and
the State. The %CHANGE figures in Table 2.1 demonstrate that p0pulation
growth has occurred more rapidly in the NLP than in the state. In turn, the three

selected counties have grown more rapidly than all northern Lower Michigan.

Table 2.1: Population counts and changes.

 

County £70 1990 Change %CliANGE
Crawford 6482 12260 5778 89
Grand Traverse 39175 64273 25098 64
Kalkaska 5272 13497 8225 156
Region 50929 90030 39101 77
NL Michigan 383965 538534 154569 40
State 8881826 9295287 413461 5

Source: US. Department of Commerce: 1972, 1992a.

Second, Brown and Vasievich (1996) have already documented in their sample
study of the Upper Midwest that Crawford and Grand Traverse Counties have
undergone parcelization from 1960 through 1990. Their study examined 136
sample sites across seventeen counties. Each county, including Crawford and
Grand Traverse, was characterized by decreasing average parcel sizes. Lastly,
Crawford, Grand Traverse, and Kalkaska counties were selected because the
counties constitute one contiguous region, and land cover change phenomena

may be studied at scales both larger and smaller than the county scale.

12

2.2: Description.

In order for the reader to become better acquainted with the study area, several

general descriptions are provided in this section.

2.2.1: General geomorphology.

Michigan’s land characteristics, along with the number of lakes that speckle the
landscape, are residuals of glacial processes that occurred during the
Pleistocene epoch (Sommers et al. 1984). Areas of higher elevation tend to be
moraines that were formed by the Wisconsin age ice advance. The inland areas
of lower elevations and flatter slopes tend to be sandy outwash plains created by
glacial runoff and deposition. Most coastal areas (eg. the Old Mission Peninsula
of Grand Traverse County) are fringed by Iacustrine plains that surfaced after
glacial lakes (e.g., Glacial Lake Algonquin) receded. The remaining shorelines
now outline the modern Great Lakes. All of these features are represented in
the study area (see Figure 2.2) and they exist along an elevation gradient that
tends to increase from west to east. Morainic features dominate portions of
Crawford and Kalkaska Counties while much of Grand Traverse County can be
characterized as plains. However, local topography and landforms are varied

throughout the region.

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2.2.2: General hydrography.

Three main rivers provide natural drainage for the region: (1) the Boardman
River receives runoff from the west-central portion of Kalkaska County and the
central and southern portions of Grand Traverse County, (2) the Manistee River
collects water from the central and southern portions of Kalkaska and Crawford
Counties, and (3) the Au Sable River drains the northern and central portions of
Crawford County. The remaining areas within the region are drained by

subsurface water flows toward Lake Michigan (Sommers et al. 1977).

While the Au Sable, Boardman, and Manistee Rivers are important ecological
infrastructures, several large inland lakes, along with adjacent Lake Michigan,
prove to be the physically dominant hydrologic features within the region (see
Figure 2.3). The lakes not only store vast amounts of fresh water but also have
many recreational uses (Sommers et al. 1984). Lakes Bear, Duck, Green, Long,
Manistee, Margerethe, Spider and others provide the area with over 100
kilometers of lakefront shoreline, mostly in Grand Traverse County. The Lake
Michigan coastline that runs along Grand Traverse County and neighboring
counties constitutes another 100+ kilometers of freshwater access. In a recent
survey of seasonal homeowners, proximity to such water features was identified
to be a significant determinant in seasonal home development (Stewart, 1994;

Stynes et al., 1997).

15

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2.2.3: Forest cover characteristics.

Michigan forests have undergone several dramatic changes within the last 175
years. Almost every forest stand has been disturbed by tree harvesting activities
of the late nineteenth century. Due to subsequent erosion of northern Lower
Michigan’s sandy soils, second growth forest compositions and structures do not
reflect the composition and structure of forests that existed before the logging

boom (Sommers et al. 1984).

During Michigan’s first years of statehood (late 1830’s), public lands had to be
surveyed before they could be offered for private purchase. Hence, a general
land survey was conducted. The purpose of the general land survey was to
locate and divide the land into Jeffersonian townships and sections, and to
record detailed information about lakes, streams, and trees (Stearns, 1997).
Since then, the written recordings of witness trees, those trees located nearest to
surveyed section corners, have been studied in order to quantitatively recreate
the spatial pattern of pre-settlement vegetation (Brown 1998a, Brown 1998b, and
Comer et al., 1995). These recreated patterns are often used as a baseline with

which past and present changes are compared (Stearns, 1997).

The US Forest Service (1997a), in their Great Lakes Assessment Project, have

classified both the digital map of interpreted nineteenth century survey notes

(Comer et al., 1995) and recent remotely sensed imagery in order to

17

quantitatively identify changes in vegetation type distributions in the Upper
Midwest, over the last 175 years. Using their publicly available data, which was
stored in a geographic information system file format, I was able to subset each
data set by “clipping” the data by my study area boundary (see Figure 2.4). I
was then able to quantify and compare temporal similarities and differences in
regional vegetation cover types. Table 2.2 highlights the proportional conditions
of vegetation types and changes between the early settlement and post-

settlement classifications for my study region.

Early settlement vegetation (circa 1830) can be characterized as dominated by
the maple, beech, birch, and aspen forest type. The white, red, and jack pine
type was abundant while the spruce and fir type was present in lesser
proportions. Post-settlement vegetation (circa 1991) can also be characterized
by a maple, beech, birch, and aspen forest type majority but, it exists as a lesser

proportion of the total. Pine types and non-forested areas cover similar extents.

Table 2.2: Vegetation changes within the study area.

 

1mg %EarIy-settlement" %PosLt-settlement" Change
Elm, ash, and cottonwood 0.2 0.0 -0.2
Maple, beech, birch, and aspen 45.3 36.7 -8.6
Oak and hickory 0.0 12.3 12.3
Spruce and fir 10.2 0.0 -10.2
White, red, and jack pine 34.7 28.4 -6.3
Non-forested 9.5 22.6 13.1

Sources: US. Forest Service, Department of Agriculture: 1997a*, 1993“.

18

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19

The largest differences between the historic and modern forest covers is the
measured loss of the maple, beech, birch, and aspen type, the loss of several
coniferous types, and the large increase in non-forested areas. Although
changes induced by growth, mortality, and fire disturbances can and do occur
naturally, the large increase in non-forested areas, when taken together with the
aforementioned regional population increases, lends support to Harman’s (in
Sommers et al. 1984) assertion that human settlements have expedited forest
alterations to degrees and extents far greater than would have occurred

naturally.

2.2.4: Forest ownership characteristics.

Federal agency, state and county agency, forest products industry, and non-
industrial private are the primary institutions that own and manage regional
forested lands (Leatherberry, 1994). Table 2.3 highlights the distribution of
forest ownerships for the selected three county region, northern Lower Michigan,
and the State. The distributions of public and private forests vary
disproportionally from region to region because the distribution of public land in

Michigan is concentrated in the northern portions of the State.

Federal ownership within the region, specifically the Huron National Forest,

originated from state authorized acquisitions of abandoned agricultural land for

20

the creation of national forests (Weeks Law of 1911 [36 Stat. 961]). Federal

forests are currently managed for multiple uses and sustainable ecosystems.

Table 2.3: Forest ownership by class.

 

County Federal State/County lndustm Private
Crawford 13.1 52.4 0.0 34.5
Grand Traverse 0.0 43.9 0.0 56.1
Kalkaska 0.0 53.9 0.0 46.1
Region 5.2 50.9 0.0 43.8
NL Michigan 12.6 27.9 0.1 59.4
State“ 13.8 21.8 10.9 53.4

Sources: Leatherberry, 1993226 and *MacKay and Ellefson, 1997279.

Typical forest outputs include timber products, recreation, and preserved natural
habitats. Within the range of outputs, National Forests in Michigan tend away
from commodity outputs and toward recreation and natural habitat conditions
(Webster, 1997). Perhaps this tendency is the result of a voting public’s
perception that recreational uses benefit a greater number of people than do

timber harvests.

State ownership, specifically the Pere Marquette and Au Sable State Forests and
Hartwick Pines State Park, is the dominant ownership class within the study
area. State forests originated from abandoned agricultural lands and other lands
that reverted back to state ownership via property tax forfeitures. State forests,

like federal forests, are also managed for multiple uses and multiple outputs.

21

Such outputs include timber goods, recreation, and natural habitat sustainability.
Since state ownership is more localized than federal ownership, these lands tend
to play a more dominant role in regional economic development (Webster,

1997). For example, the State Forest Products Industry Development Council
(Ml PA 451 of 1994, formerly Ml PA 150 of 1984) was initiated in order to
develop forest product industries so that Michigan’s economy would become
more diversified and less dependent upon the automobile industry (Webster,
1997). Michigan State Forest resources have also become tied to tourism based
economic development. According to Chappelle (1997, p. 228), “efforts to attract
additional visitors, and to provide improved facilities” to forested areas are “the
core of resource based economic development efforts” within the region.
Because recreation and forest product economies are often viewed as
competing economies (as one requires forest accessibility and the other requires
forest cutting, respectively), forests in these areas require management practices
that synchronize the needs of each economy in order to optimize the outputs of
both. Should parcelization occur within these areas, efforts to synchronize
developments of multiple economies, which will include multiple new

landowners, would become increasingly difficult.

Private forest owners are the smallest ownership class individually and the
second largest in aggregate (see Table 2.3). Parcel sizes range from less than
one hectare to thousands of hectares with the majority of parcel sizes skewed

toward the low end of the range. According to Webster (1997), private forests

22

tend to be more productive than publicly owned and managed forests for a
“simple historic reason” (p. 256); most public lands came into existence by being
poor farmland with poor soil qualities. Subsequently, these poor farmlands
reverted into state ownership and prime lands with good soil qualities remained
in private ownership. The forest resources on private lands also serve many
different purposes. As private lands undergo parcelization and are further
developed, Michigan’s most productive forest land could be replaced by more

human dominated land covers and uses.

2.3: Summary.

The area selected for study has been shown to exhibit characteristics both
similar to and different from other forested areas in Michigan. Grand Traverse,
Kalkaska, and Crawford Counties contain common topographic, geologic, and
hydrologic features found in the NLP. Also, the region contains forested lands
that are owned by each of the dominant ownership institutions found in Michigan.
However, what sets the selected study area apart from the NLP and the rest of
Michigan has been its strong population growth trend, parcel subdivision trend,
and the expectation that this region will be the first region in Michigan to

experience a reversal of the current forest recovery trend.

23

CHAPTER 3: LITERATURE REVIEW

3.1: Introduction.

The Michigan Territory was granted statehood and admitted into the Union in
1837. In order for the new state to generate funds for operation and self-
improvement, government officials offered public lands for private purchase
(Warbach and Norberg, 1995). As described in Chapter 2, all such lands were
surveyed and reported according to the Jeffersonian-style public land survey
system. New landowners immediately recognized the market value of large
timber stands that existed on their properties and, as a result, began harvesting

timber to generate funds for their own benefit and improvement.

Timber harvesting in Michigan was a boom economy by 1840. The state
became the nation’s leading timber producer in 1870 and held that claim through
1890 (Sommers et al. 1984). For almost eighty years, timber was harvested in a
wave that enabled Michigan’s economy to flourish and yet, left a cleared and
impoverished landscape in its wake. Unfortunately, Michigan’s forest resources
were severely over—estimated and by the early 1900’s, the state was left with
almost no remaining timber (Warbach and Norberg, 1995). In addition to losses
attributed to logging, approximately 2 million acres of forest were destroyed by

fire (Warbach and Norberg, 1995).

24

During the 1920’s, State of Michigan officials began to recognize certain natural
resources, including forests, to be of some benefit to the public good. Poor and
marginal agricultural lands were bought or reclaimed by the state and were
appropriated for either State or National Forest designation. During the 1930’s,
the Civilian Conservation Corps replanted and reforested many of these lands

(Warbach and Norberg, 1995).

Subsequent to the Great Depression, the State of Michigan reclaimed an
additional 2.2 million acres of land via tax forfeitures and purchase programs and
was ultimately in charge of approximately 4.5 million acres by the early 1940’s
(Warbach and Norberg, 1995). While some of the reclaimed lands were later
sold back into private ownership, many were put into either the state or federal

forest systems and left to naturally regenerate into young forest conditions.

The United States Congress signed into law the Multiple Use Sustained Yield Act
in 1960 (74 Stat. 215; 16 U.S.C. 528 et. seq.) and the Forest and Rangeland
Renewable Resources Planning Act of 1974 (88 Stat. 476; 16 U.S.C. 1600 et.
seq). The federal legislation mandated the creation of compartments or zones
within public areas for the sake of developing natural resources and for the
preparation of multiple-use plans. The legislation also improved the existing
standard by mandating additional local involvement and management. The
Michigan Forestry Planning and Development Committee was later created so

the renewed forest inventory could be efficiently managed in order to “use

25

Michigan’s forest resources for enhanced economic development plus
diversification to enhance recreational opportunities and protect natural values”
(Warbach and Norberg, 1995:2-7). Hence, Michigan’s young forests today serve
a variety of vaguely stated interests. Such interests include: some development,
managed timber production for wood and wood pulp, recreation and tourism, and

protection of several plant and animal species (e.g., the Kirtland’s Warbler).

According to the United States Department of Agriculture Forest Service
(Leatherberry, 1994), twenty-one percent (3.8 million acres) of Michigan forested
lands are owned by state agencies and another fourteen percent (2.6 million
acres) are owned by the Federal Government. Since the State of Michigan holds
such a large amount of forested land, it has earned its claim to having the largest
state forest system in the continental United States. Yet, despite the state’s
sizable forest assets, private owners control property rights to the majority of
Michigan’s forest resources. Over fifty-three percent, approximately 9.8 million
acres, of all forested lands are held by thousands of private individuals while

another eleven percent are owned by private industry (Potter-Witter, 1995).

3.2: Population studies.

As mentioned above in Section 2.1.1, demographic and economic studies in

Michigan have characterized a “rural renaissance” (Beale, 1977) that was in

effect during the 1970’s. For nearly the first time in Michigan’s history the

26

population growth rate in non-metropolitan areas exceeded the growth rate in
metropolitan areas. Throughout the 1980’s and 1990’s, Michigan’s non-
metropolitan populations have continued to grow (US. Department of
Commerce, 1970; 1980; 1990). Public forest managers have become
concerned that development associated with continued population growth has
caused observed increases in forest fragmentation. Such concerns have given
rise to the MSPO’s stated need for research on the characterization and

quantification of such landscape changes.

In order to characterize landscape changes, historical land use and land cover
change analyses have often been grounded in Malthusian philosophy
(McPherson, 1982). Population growth was attributed the singular responsibility
for causing landscape change within any observed area (Leibenstein, 1957;
Vanderpol, 1963; Scheer, 1963; Wolf, 1966; Holmberg and Dobyns, 1969; Grigg,
1974 and Todaro, 1981). The logic behind these population growth studies
seemed intuitive: the greater the number of people moving into and settling on a
finite area, the greater the demand for natural resources and, hence, the greater
the subsequent landscape fragmentation and change. For example, Leibenstein
(1957), in his global summary of agricultural areas asserted that land “holdings
are continually subdivided as the population on the land increases” (p. 41).
Scheer (1963) argued in his study of Netherlands” agriculture that “a very serious
consequence of the population pressure” is “the splitting up of a great number of

farms into scattered parcels of small and impractical size” (p. 519).

27

In 1963, Papageorgiou published his article on Greece’s agricultural problems
and succinctly described the “conditions which greatly facilitate progressive
fragmentation” to be “the growing population and the existence of the right of
landowners to transfer and alienate his right in the land freely and, in particular,
the right to subdivide or add to existing holdings” (p. 546). By recognizing the
rights of individuals to transfer property rights, other researchers expanded
landscape change analysis to include examinations of inheritance systems
(Wolf, 1966; Grigg, 1974). However, such analyses were just simple extensions

of the population growth and limited carrying capacity arguments.

Many other landscape and land cover analyses were conducted with an
overwhelming majority focused on the effects of farmland subdivision on primary
productivity. In a series of working papers for the Harvard Institute for
lntemational Development, McPherson (1982; 1983) reviewed over 120 different
studies on agricultural land fragmentation and most were cited to conclude that
either population growth, local inheritance structures, or a combination of the two

were the primary drivers of landscape change.

Vesterby and Hiemlich (1991) examined landscape change as a result of several
interacting socio—economic factors and high levels of population growth. A
minimum rate of population growth, coupled with a minimum number of persons,
was used to select a set of developing areas within the United States.

Urbanization was then characterized by land conversion to urban uses and

28

increasing population densities. The most notable portion of the authors’
analysis indicated that changes in land use were most dramatic during the earlier
stages of urbanization rather than during the later. The authors specified the
building of infrastructure and critical services at the onset of development as
reasons for the trend they observed. Vesterby’s and Hiemlich’s (1991) findings
also serve to suggest the importance of understanding initial landscape
conditions at the onset of landscape change research. Without an
understanding of initial landscape conditions, researchers may find interpreting
subsequent landscape analyses difficult because relationships determined to

exist at one stage of development may not exist at another.

Vogelmann (1995) commented on his surprise at finding a strong relationship
between forest fragmentation and increasing population densities within a
forested region in New England. The author statistically compared the spatial
concurrence of mapped population data with mapped forest cover fragmentation.
Township population data were gathered from published US Census reports and
forest cover and forest fragmentation data were measured from classified
remotely sensed imagery. Both data sets were georeferenced and analyzed
using a GIS. In his discussion of results, the author tried to recognize
“government policy and fiscal incentives” as “significant determinants of land-
cover change” (Vogelmann, 19952445). However, his regression results
highlighted only increasing population density as the dominant factor contributing

to forest fragmentation. Vogelmann (1995) also indicated that the strength of the

29

relationship he observed diminished above and beyond a particular population
density threshold. This population density threshold supports, in part, Vesterby’s
and Hiemlich’s findings. Both studies suggest that processes identified to affect
landscape change may be dependent upon the set of initial conditions specified
at the beginning of analysis. Therefore, in landscape change research, the set of
initial conditions cannot be chosen arbitrarily without an effort to understand a

priori the limitations they may impose on subsequent research findings.

As evidenced so far, many researchers have studied the effects of growing
human populations and the landscapes on which they settle and develop.
McPherson’s (1982,1983) work emphasizes just how many have contributed to
such research. In all of the agricultural analyses discussed above, research
findings seem to have reaffirmed the notion that landscape changes are linked to
increases in resident populations. However, the last two studies (Vesterby and
Hiemlich, 1991; Vogelmann, 1995) show that the relationship between

population growth and land cover change is neither perfect nor direct.

I have already illustrated recent population growth trends in both the NLP and
the study area (Table 2.1). Because the study area is considered to be rural and
has exhibited a strong resident population growth trend, it might seem logical to
some to apply a test of population growth theory to the region. However, I do not
believe that such an application can be easily accomplished given the traditional

source of United States population data - US. Census Bureau reports.

30

Stewart (1994) has reported the significant impacts of seasonal homes and
seasonal populations on local industries and regional economies. In related
research Stynes et al. (1997) wrote the population of a Great Lakes county, like
any one in the study region, can be six or seven times the official resident
population because official census counts do not include seasonal homes or
seasonal home owners in their population totals. Also, because the proportions
of seasonal homes (see Figure 3.1) and seasonal populations vary across the
region, it is reasonable to assume that the impacts of resident populations,
relative to total populations, also vary across the landscape. Therefore, given
the extensive nature of seasonal home development within the region, the non-
uniform distribution of seasonal homes throughout the region, and inconsistent
temporal reporting of seasonal home data in US Census publications, a simple
analysis of residential population growth and landscape change is not

appropriate for this region.

31

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32

3.3: Agricultural land use changes.

Since the 1970’s, Michigan has been in a period of agricultural decline. Many
Michigan counties have experienced either small farm aggregation into fewer
and larger farms or losses in both the number of farms and total acreage farmed
(US. Department of Commerce, 1992b). According to a press release issued on
October 23, 1996 by the Michigan Department of Agriculture:

“Between 1982 and 1992, over 854,000 acres of Michigan

farmland was lost, almost 10 acres of every hour of every

day, representing an annual loss of over $100 million in local

farm revenue. As the population spreads out from the cities

into more rural areas, productive farmland is often carved

up into large building lots and taken out of production.”

To a lesser areal extent, decreases in agricultural production have also been

reported (US. Department of Commerce, 1992b) for the selected study area.

Erickson (1995), in her analysis of the River Raisin Watershed of Southeast
Michigan, used a GIS and regression techniques to demonstrate urbanization
and population growth alone, between the years 1968 and 1988, do not serve to
predict forest cover change “as might be expected” (p. 230). Her original
hypothesis stated urbanization and agricultural decline simultaneously effected a
net decrease in forested area. Instead, agricultural decline was shown to have a
significant positive relationship with forest cover change. The authors concluded
that agricultural land decisions, along with agricultural mechanization and
economics, were also useful for explaining forest cover changes. Such a

conclusion demonstrates that processes other than population growth can be

33

used to explain land cover change. However, the authors maintained that their
quantitative description captured only a snapshot of the iterative relationship

between human decision making processes and physical landscape conditions.

3.4: Parcelization pressures.

Increased accessibility, recreation and tourism development, and urban spillover
were general reasons cited by Hart (1984a) for the population turnaround, or
rural renaissance, in rural areas of the Upper Midwest. Hart (1984b) also
suggested that regions attract development for many reasons including
accessibility to a variety of natural features. Rural areas in northern Michigan
have attracted recreational development because of access gained from new
highway construction, the presence of extensive forests, and accessibility to
many lake front areas (Stewart, 1994). Since northern Michigan’s tourist
economy has expanded to meet the demands of such recreational and tourism
development, in the form of additional service-oriented businesses and
accelerated seasonal home construction, pressures have become even greater
on proximate forested lands. In other words, forested areas have become the

focus of development pressures because of their aesthetic qualities.

Land use patterns on developing private lands affect forest resources located on
both private lands and adjacent public lands. In a series of working papers

published by the Michigan Society of Planning Officials Trend Future Project, the

MSPO has clearly stated their concern about the impacts of land use practices
on forested lands:

“Land use patterns on private land continue to affect the

quality and sustainability of the forest base. Private forests

are the focus of development pressures and public forests

are the focus of pressures for more varied uses. As a result

of changes in the composition of forests, there are changes

in wildlife populations and the visual character of the forest.

With the fragmentation of the forest into smaller blocks,

edge species of plants and animals have proliferated, and

deep forest species have declined” (Warbach and Norberg,

19952iv).
In their conclusion, the MSPO went on to argue that if current land use trends
continue they. ..

“...can result in significantly less land in a cohesive natural

condition thereby reducing wildlife habitat and a biologically

diverse range of species” (Warbach and Norberg, 1995:4-6).
Negative attention has fallen on land ownership parcelization and its current and
future impacts on a young and vulnerable forest base. While parcelization
certainly results in the fragmentation of land ownership, parcelization may also
partition the land into different land uses. Should new adjacent landowners
decide to utilize their lands in many different ways, the resulting landscape could
ultimately assume the appearance and durability of a poorly woven quilt.
Continued parcelization and development of lands adjacent to forested lands
can; limit the abilities of forest managers to manage forests, limit the abilities of
forest production efforts to meet an increasing demand for timber products, alter

a delicate mix of plant and animal species, and cause a loss of wildlife from

existing ecosystems to occur.

35

Brown and Vasievich (1996) examined land ownership parcelization in Michigan,
Minnesota, and Wisconsin. Attention was focused on socio-economic and
locational factors that contributed to parcel sizes and parcel changes. Multi-
scaled analyses were conducted for three time periods; the 1960’s, 1970’s, and
1980’s. Brown and Vasievich (1996) reviewed relevant work on regional
ecological factors (Stewart, 1994), economic factors (Fuguitt et al. 1989), social
and demographic factors (Hart, 1984a), and institutional factors (Kufuor, 1981
and Norgaard, 1994). The authors gathered sampled parcel information from
published parcel plat maps in order to measure parcelization for the region as a
whole, between counties, and within counties. Also, variables were selected to
represent each of the examined factors with a generalized linear model. The
authors tried to determine whether or not the spatial pattern of parcelization
could be predicted by the spatial pattern of complex and interacting factors.
Brown and Vasievich (1996) stated that their generalized linear model results
provided “explanation of spatial variation in parcel fragmentation” (p. 1207). In
their conclusion, the authors discussed the moderate predictive ability of their
model (R2 = 0.30, pF = 0.000) but were satisfied with its statistical significance.
The authors also discussed the possible effects of ownership parcelization on
plant and animal habitats, plant and animal biodiversity, and primary productivity
and wondered about the ability of ecosystems to sustain themselves in the future

given the current trend of land subdivision.

36

In continued research, Brown (unpublished manuscript) documented statistical
and spatial analyses of his parcel data and found that parcelization “tended to
peak or lag slightly behind” county population growth rates when they “reached
their highest levels” (p. 25). After reviewing spatial autocorrelation and other
statistical test results, Brown concluded that the relationship between population
growth and parcelization “on a coarse scale, supports a link between the
movement of people and impacts on the landscape” (p. 25). Given the results of
his previous work, coupled with this latest evidence, Brown suggested a link
between parcelization and its implications on land cover types and patterns. To
suggest such a link seems reasonable since parcelization has been shown to be
associated with a complex set of landscape pressures (population, social,
institutional, and ecological), each of which has been identified independently as
a possible driver of physical landscape change. Therefore, parcelization should
be useful for representing a set of many driving factors in landscape change
research. Also, the opportunity exists to expand this research to include and test
continuous data representing the complete landscape because Brown and
Vasievich (1996) and Brown (unpublished manuscript) used only sampled data

to represent counties within the study area.

Even though the research reviewed above has shown promise, not everyone is
in favor of associating parcel patterns with complex Iandcover change
processes. Theobald, et al. (1996), in their research on rangeland fragmentation

in the Colorado Mountains, cautioned that “unlike roading and building, which

37

result in physical fragmentation, parcel subdivision necessarily results in
ownership fragmentation, which may or may not entail physical landscape
change” (p. 413). However, while their advice may hold true at the time of deed
transfer and shortly thereafter, only a few land cover changes are necessary to
effect changes in the character of an entire landscape. For example, in the
same article, Theobald et al. (1996) mitigated their own cautions by reporting the
concern among residents within the study area about the loss of open spaces
even though less than a quarter of all subdivided parcels observed contained a
building. The authors’ recognition of such resident concerns reinforces, in part,
Vesterby’s and Hiemlich’s (1991) conclusion that the most dramatic land cover
changes occur during the earlier stages of development. Perhaps, even more
dramatic than the land use changes already observed within the Colorado
Mountain study area is the real potential for much greater landscape
fragmentation and loss of open spaces as the results of future development on

all remaining parcels.

The study of land ownership parcelization, while uncommon, is not new. Roche
reported his analysis of parcelization trends in nineteenth century France in
1963. Using historical land survey documents, Roche measured a 25 million
parcel increase over a twenty-five year period. He also reported that
parcelization varied across the country as did the agricultural inefficiencies he
associated with it. Roche concluded that parcelization was detrimental to

agriculture because “the average size of a parcel” in some regions did “not allow

38

efficient mechanical farming.” The conclusion reached by Roche is, in effect, the
same argument being put forth by forest managers in Michigan today; breaking
large forested parcels into many smaller ones is ecologically inefficient.
According to Potter-Witter, small forested parcels are ecologically inefficient
because wildlife "rely on contiguous ecosystems of certain minimum size for

travel corridors and territorial requirements" (Potter-Witter, 1995118).

3.5: Land consumption theory.

The Consumption Theory of Land Rent (CTLR) (Thrall, 1987) provides a model
of land consumption around a central market or central business district (CBD).
The CTLR is based upon the idealized relationship between the maximum
“magnitude of happiness” (Thrall, 1987211) or welfare a household can attain
and its distance from the CBD. Many assumptions are needed to operationalize
the CTLR. The list of assumptions includes, but is not limited to: (a) a perfectly
malleable and isotropic landscape surrounding the CBD; (b) socioeconomic
homogeneity of all households within the landscape; (o) perfect information on
market conditions available to and used by all households; (d) the existence of
urban and non-urban land uses (a concept developed by Von Tht’inen [1842] in
his original work on agricultural land location); and (e) the attainment of equal

welfare by all households having the same income (Thrall, 1987).

39

The CTLR can be operationalized by evaluating the rent per unit of land with
respect to the equilibrium of household welfare in space as constrained by the
household budget. Since income and the composite price of goods are
considered exogenous variables, and thus are held constant, the price per unit of
land is allowed to vary with distance from the CBD. According to Thrall (1987),
the results of the CTLR can be stated as several principles. Several of those
principles I have deemed relevant to this research are:

“Principle 2.2 Land rent adjusts thereby compensating households

from locating in places that have relatively inferior access to central

locations. In general, rent per unit of land decreases with a

reduction in access to the central location, all other things being

equal

Principle 2.3 The consumption of land is inversely related to the
households’ access to the central location.

Principle 2. 7 The spatial equilibrium quantity of land consumed
increases at an increasing rate, and hence population density
decreases at an increasing rate with increasing distance from the
city center.” (Thrall, 1987:23-25).
Thrall (1987) summarized his review of the CTLR by stipulating that, in order for
remote households to compensate for the cost of transportation to and from the

CBD, “land rents are less and consequently households can consume more

land” (Thrall, 1987226).

The CTLR has relevance to this research because of the rural nature of the
study area and the presence of Traverse City, which is located in the northwest
portion of the region at the base of the peninsula, had the highest population

density of any minor civil division within the area during the 1970’s and 1980’s,

40

and can be considered a CBD despite observed population decreases over time
(see Table 4.1). Also, the several townships adjacent to Traverse City had
relatively high population densities while many of those located in Crawford
County had much lower densities. Such a spatial gradient of population density
is similar to the gradient suggested to exist by the CTLR. Although this particular
landscape does not meet most of the requisite assumptions of the CTLR
(including the lack of “roadways or rivers ...... or features built by nature and
humankind” (Thrall, 1987210)), the opportunity exists to compare the study region
to an idealized one. By substituting the term parcel size for the term
consumption of land, one might expect parcel sizes to increase with increasing

distance from Traverse City if one makes the same assumptions.

3.6: Other concerns.

Some of the issues discussed in this chapter have also been reviewed in the
MSPO Trend Future Project reports and were used to support their stated need
for research on “the impact of local, regional, and statewide fragmentation on
natural resources” (Warbach and Norberg, 1995:A-3). The logical next step is to
conduct a landscape change study of land ownership and forest cover in order to
characterize the proposed relationship between parcelization and fragmentation.
However, landscape studies are often fraught with difficult quantitative problems.
Issues of spatial and temporal scales are common in the Iiteratures provided by

landscape ecologists and conservation biologists and are expected during this

41

analysis. Allen and Starr (1982) developed hierarchy theory to help analyze how
processes and determinants shift in relative importance across multiple scales.
Meentemeyer (1989) and Turner (1990) have continued to developed hierarchy
theory, but within the vernacular of landscape ecology. Regardless of discipline,
each author has suggested the need for landscape research to be conducted at
multiple scales so that the effects of space and time can lead to a better

understanding of observed landscape processes.

Landscape ecology acknowledges many interrelationships between humans and
nature. According to landscape ecologists, landscapes are characterized in
terms of matrices, patches, and corridors, and are often done so with respect to
a specific species of interest (neo-tropical songbirds are typical in the literature).
Patches are considered the basic landscape unit (Forman, 1995) and are further
characterized by descriptions of size, shape, quantity, interior core areas, and
connectivity. The strength of landscape ecology lies in its fundamental use of
spatial concepts to measure the structural abilities of landscape patches to
distribute energy, materials, and species throughout a given area (Forrnan and
Godron, 1986). Since landscape ecology emphasizes both an understanding of
complex systems and the use of spatial principles, I have reason to believe some
of the tools used in landscape ecology research will be appropriate for use in this

study of land parcelization and forest fragmentation.

42

Perhaps the reason for the lack of large scale parcelization research, Brown and
Vasievich (1996), Kleiman and Erickson (1996), and Roche (1963) not
withstanding, has historically been the daunting task of observing thousands of
parcels and thousands of forest patches over a period of time. The requirements
for gathering, storing, and analyzing such data were, until recently, virtually
impossible. However, GIS and RS technologies have systematically mitigated
each of the above data requirements and offer researchers and planners
effective tools for recording and analyzing landscape data. Parcel maps can be
digitized and analyzed, and remote sensing technology allows us the ability to

gather detailed data about land covers from space.

3.7: Summary.

Reviewing the above research has helped me to gain additional perspectives on
both the potential strengths and weakness of my proposed study. The foremost
challenge that exists for this research is to deal with the degree of complexity
that exists within the study area. I have reviewed historic and current variations
in regional geology, hydrology, and vegetation type patterns - variations that can
influence forest distributions independently and co—dependently. Also, I have
reviewed variations in regional population growth trends, land ownership
institutions, ecological determinants, and a few planning ordinances - variations
that can influence parcel subdivision independently and co-dependently. While

all the intricacies of landscape change cannot be accounted for in a single study

43

of parcelization and forest fragmentation, perhaps enough will be accounted for
so that I may achieve a better understanding of the way forests and humans

relate to each other.

This literature review has also prompted me to be aware of the fact that any
relationship(s) I might find to be significant may have existed only during the
period from 1970 to 1990. Since relevant processes and determinants can shift
in relative importance through time (Allen and Starr, 1982; Vesterby and
Hiemlich, 1991) my results may also be dependent upon the set of initial
conditions that existed before the year 1970. However, instead of viewing such
questions as potential limitations, I believe they provide me an opportunity to
question and identify the effects space and time on the proposed relationship
between land ownership parcelization and forest cover fragmentation. By
organizing my investigation into multiple spatial and temporal scales, I will not
only be able to test whether the proposed relationship exists, but, if it does, I will

also be able to characterize how it has changed.

44

CHAPTER 4: METHODS

4.1: Introduction.

The general approach I adopted to quantify land ownership parcelization
included; converting published parcel plat maps into a digital GIS polygon format,
classifying each parcel by ownership type, and using a GIS to aide in the
calculation of average parcel sizes at several levels of spatial aggregation.
Spatial distributions of average parcel size and annual rates of parcelization

were examined with basic and spatial statistical techniques.

Forested landscape patterns were measured using classified remotely sensed
imagery. Each sample image, a Landsat Multi-spectral Scanner (MSS) scene,
was classified using a consistent process of unsupervised classification
techniques. Three resulting maps, each representing a historical land-cover
landscape, were tested for accuracy with several common assessment
techniques, including the use of historical aerial photographs as ground truth
references. Quantitative measures of historic forest cover and forest
fragmentation were calculated for several levels of aggregation. Spatial patterns
of forest fragmentation and annual rates of change were also examined with

basic and spatial statistical techniques.

45

Ultimately, both static and dynamic patterns of parcelization and forest cover

fragmentation were compared at each spatial and temporal scale.

4.2: Scales of analysis.

Measures of average parcel size, parcelization, percent forest cover, and forest
fragmentation were quantified and described at five spatial scales. Figure 4.1
illustrates the different scales used to sample each landscape data set. I
selected region, county, and township (minor civil division) as three of the five
levels of analysis because policy decisions in Michigan are made and
implemented at each respective level. Figure 4.2 has been included so that the
location of individual minor civil divisions can be identified by name. A fourth
scale, which I call the sample site, was used to measure landscape variation at
frequencies and with a spatial regularity greater than the township analysis could
provide. Sample sites are defined as nine square mile blocks consisting of nine
survey sections, each site with three sections to a side. Brown and Vasievich
(1996) used three-by-three section units in their study of parcelization and such a
sample unit was proven adequate for parcel area and statistical analyses. Slight
adjustments to several sample site boundaries were made in order to
accommodate a dominant presence of open water in some areas. For example,
the land portion of Tier 28, Range 10, Section 13 was appended to sample site
#281026 because 90 percent of the original sample site to which the section

belonged existed undenrvater as part of the East Bay.

46

 

Scales Used for Spatial Sampling

Region
( n = 1 )

 

 

Counties
( n = 3 )

 

 

Townships
( n = 33 )

 

 

 

 

 

 

 

 

 

 

Sample sites
( n = 186)

Survey sections
( n = 1678 )

 

 

Figure 4.1: Spatial scales of analysis.

47

.mco_m_>_n :20 .655. Ne 65ml

 

.2232...
98m .62....

 

 

 

 

 

 

 

 

 

chcsuwm .4.”wa 22.80
8.32.60 826
Illll $2.0 9.6..
@5380 30m @668
2.82”. o
2.26.. a march ”fl «Rama

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m:o_m_>=u :20 .652

 

 

48

The fifth level of analysis was conducted using public land survey sections as
sample units and it provides the most detailed look at the regional landscape.
Each survey section is approximately 259 hectares (one milez) in size. This
smallest sampling unit uncovers the greatest variation in the distributions of

average parcel size and forest fragmentation.

4.3: Parcel data.

In Section 3.4, l summarized reasons for conducting an investigation of land
ownership parcelization, rather than of population pressure, and its potential
effects on the regional forest base. Since so little work has been done regarding
the collection of parcel data and quantifying land parcel changes on a large
scale, I had few examples to follow. However, Brown and Vasievich (1996) have
provided the most detailed, concise, and reasonable approach to doing such

research. Therefore, my methods are similar to theirs in many respects.

4.3.1: Collection.

I collected plat map books (Rockford Map Publishers Inc. 1969-1991) for each of
the selected counties for the approximate years 1970, 1980, and 1990. When
plat map books were unavailable for the exact dates, the closest available date
was used as a surrogate. Appendix A includes metadata descriptions of the plat

map books used and the final digital data sets. County plat map books contain

49

detailed maps that show the various parcels in townships as they are located
geographically. Each parcel is labeled with the name of the parcel owner and, in
some cases, the approximate size of the parcel. Roads, schools, cemeteries,
and civil division boundaries are also illustrated. Patterns of land ownership and
parcel boundary changes were developed by digitizing each parcel plat map into
a GIS database using Arc/Info (ESRI lnc., Redlands, CA) software. Each
digitized parcel map was registered and georeferenced to the UTM coordinate
system given ground control coordinate information obtained for survey section

corners (MIRIS, 1978).

4.3.2: Classification.

After digitization, l classified all polygons in the parcel data into one of five
categories. The categories included privately owned large parcels, privately
owned small tracts, public lands, open water, and other. Descriptions of each
parcel category are listed below:
1. Privately owned large parcels.
Such parcels are individually mapped in the plat map books.
Private ownerships were maintained by either individuals, groups of
individuals, or corporations. Ownerships maintained by schools,
government entities, incorporated cities, or villages were not
classified as private. The size of each parcel was determined to be

equal to its area.

50

2. Privately owned small tracts.
Small tracts are collections of small parcels of private land that
share a common mapped boundary. These small parcels were not
mapped individually, but rather, were mapped as a single block.
Small tracts are usually subdivisions, blocks of cottages, and/or
seasonal residences. Parcel ownerships are maintained by
individuals, groups of individuals, or corporations, but specific
ownerships within a small tract polygon are unknown and usually
include many different individuals, groups, and/or corporations.
Because the distribution of parcel areas within blocks of small
tracts could not be discerned from the plat maps, an assumed
average parcel size within these areas was used. Average parcel
sizes within each block of small tracts were assumed to be equal to
0.20 hectares (0.5 acres). According to Kufour (1984) the average
size of parcels within such small tract areas tended between 0.12
and 0.20 hectares (0.3 and 0.5 acres) in size between the years
1970 and 1980. Kufour (1984) also noted that such small tract
areas tended to be larger, (0.41 hectares (1.0 acres» during the
1950’s and 1960’s. Because several of these older small tract
areas remain throughout the landscape, I thought it appropriate to
use the larger, average estimate. If actual average parcel sizes
within small tract areas were less than or greater than 0.2 ha, then

measures of parcelization will be underestimated or overestimated,

51

respectively. This assumption was necessary because, as
mentioned above, actual parcel sizes within these areas were not
discernable from the plat map books and no better estimate was
available.

3. Public lands.
These parcel types included ownerships maintained by public
schools and government entities. Public lands also included all
county, state, and national parks, lakeshores, forests, and wildlife
reserves.

4. Open water.
Open water areas were permanent inland water features, such as
lakes, reservoirs, and ponds. In Michigan, open water areas that
are legally determined to be navigable (Article IV, Northwest
Ordinance of 1787) are held in the public trust. Because it is not
possible to divide fairly the surface area of a lake or stream among
adjacent owners in proportion to their land ownership, or by the
projection of their property boundaries that reach the water at
varying angles, the courts have held that all riparian owners share
an equal right to a reasonable use of the entire surface area of the
lake or stream. Therefore, open water areas were classified

independently of private land ownerships.

52

5. Other.
Any parcel that did not fit directly into any above stated ownership
group was classed into the “other” category. These parcels
included mostly ownerships maintained by incorporated cities,
villages, utility companies, and all military lands. These ownership
entities can and do exert unique pressures on a physical landscape
(i.e., powerline construction and heavy artillery maneuvers) and
therefore, were classified separately so as not to be included in this

particular analysis and earmarked for future study.

The three parcel data sets are relatively large and difficult to illustrate within the
confines of this document. Therefore, a single township, Whitewater Township,
has been arbitrarily selected to graphically represent the data. Figure 4.3

illustrates the classified distribution of 1970 parcel data for Whitewater Township.

53

 

Land ownership parcels +

Whitewater Township - 1 970
Grand Traverse County

Locator map

 

 

 

 

Legend
‘ Private large parcels

11:! Private small tracts

.. Public lands

- Open water

22”“; Other

Scale (meters)
1000 0 2000
III-:1

 

Figure 4.3: Illustrated example of the parcel classification scheme.

4.3.3: Temporal analysis.

Average parcel sizes were calculated for each sampled area using an average
parcel size index (APS) similar to that used by Brown and Vasievich (1996). The

APS index is a measure of average parcel size within a given area.

The geometric mean, instead of the arithmetic mean, was used to calculate the
average of large parcel areas because the distribution of large parcel areas was
positively skewed. A natural log transformation of area values used in the
calculation of the geometric mean attempts to normalize the distribution of areal
data for further use in common statistical techniques. By transforming each
sample distribution of parcel sizes into a normal distribution, subsequently
calculated means can be compared and easily tested for significant differences.
Figure 4.4 shows the frequency distribution of 278 parcel areas and the
frequency distribution of log transformed parcel areas in Whitewater Township
for the year 1970. The untransformed distribution, illustrated on the left, can be
described with a Pearson’s skewness value of 0.844 and a kurtosis value of
12.349, which implies a positively skewed and leptokurtic distribution. The
transformed distribution, illustrated on the right, approximates a normal
distribution and can be described with a Pearson’s skewness value of -0.262 and
a kurtosis value of 0.920. The use of normal distributions is often a prerequisite
of common statistical techniques so, log transformed parcel areas were deemed

more suitable for analysis than untransformed areas.

55

 

Histogram of Parcel Areas Histogram of Transformed Parcel
Areas

 

 

160

 

 

 

 

 

 

160
140 4» 14o ..
120 J- 120 ..
E 100 1 Q 100 ..
8 so 1 3 so ..
E 60 4~ 9? 60 4»
“- 4o .- LL 4o 4
20 1» 20 .
0 ~ 0 - .
VF or.) (\‘I v.- 0 v- N ('0 v g V 6.) 0.! v- 0 ‘- N 0") V g
2 2
2 Score 2 Score

 

Figure 4.4: Frequency distributions of parcel areas.

The APS index is derived using the following equation:

ZlnA

 

«nun )+(pm-In2000))
APS = (e “'9’ ) I 10000
where:
purge = the proportion of private land area classified as large parcels
Psmall = the proportion of private land area classified as small tracts
_Z_|n_A
"m“ = the mean of natural log transformed large parcel areas (m2)

2000 = the assumed size (m2) of all parcels in small tracts
10000 = a constant used to convert meter2 to hectares
The calculated geometric mean of large parcels, and the assumed geometric
mean of small parcels within small tracts, are weighted according to the
proportion of private land area each class covered within a sample unit and then
summed into a single measure. Large values of APS are associated with larger
average parcel sizes and, conversely, small values are associated with smaller

averages.

56

Land ownership data were summarized with summary statistics for each
approximate date (1970, 1980, and 1990) and annual rates of parcelization were
calculated for both ten-year intervals and the entire twenty-year period. Average
parcel sizes were compared in order to answer the question: Have average
parcel sizes changed over time and if so, how?
Three results are possible for each scale of analysis:
a. average parcel sizes have decreased over time.
b. average parcel sizes have not changed over time.
c. average parcel sizes have increased over time.
Brown and Vasievich (1996) reported estimates of average parcel sizes that
decreased over time in their study of the Upper Midwest. Because their study
area included Crawford and Grand Traverse Counties, detecting increased
average parcel sizes during this analysis seemed unlikely. However, Brown and
Vasievich (1996) sampled only portions of each county whereas I analyzed each
completely. Thus, the possibility of uncovering a parcel aggregation trend still
remained provided Brown and Vasievich (1996) did not sample appropriately.
However, I hypothesized similar decreases in parcel size over time in my study
area based on their results. My first formal hypothesis was stated as follows:
Hypothesis l
H1: average parcel sizes have decreased over time
Ho: average parcel sizes have not decreased over time
This hypothesis was tested between decades and at all spatial scales. Matched

pairs ttests were used to test for significant mean difference between values of

57

APS. Should significant test results indicate the null hypothesis be rejected, the
trend of declining average parcel sizes would serve to support Michigan public

forest managers’ concerns (Potter-Witter, 1995).

Table 4.1 lists population growth figures for the region, three counties, and 33
townships. For almost every case, greater population growth rates were
calculated for the 1970’s than for the 1980’s. The two notable exceptions were
the City of Grayling and Traverse City. Both urban areas exhibited higher rates
of declining total population during the 1970’s than during the 1980’s. The
observed decline in urban populations during this time period follows the rural
renaissance trend described by Beale (1977). According to Brown and
Vasievich (1996), the majority of counties observed in their study had peak
parcelization rates in a decade that corresponded to the decade of peak
population growth. Given Brown’s and Vasievich’s (1996) results, taken together
with the peak population increases outlined in Table 4.1, l hypothesized higher

parcelization rates existed during the 1970’s than did during the 1980’s.

My second hypothesis was:
Hypothesis ll

H1: the rate of parcelization during the 1970’s was significantly
greater than the rate of parcelization during the 1980’s

Ho: the rate of parcelization during the 1970’s was not

significantly greater than the rate of parcelization during the
1980’s

58

Table 4.1:

County

M9
Region totals

Crawford
BeaverCreek
Frederic
City of Grayling
Grayling
Lovells
Maple Forest
SouthBranch

Grand Traverse
Acme
Blair
East Bay
Fife Lake
Garfield
Grant
Green Lake
Long Lake
Mayfield
Paradise
Peninsula
Traverse City
Union
Whitewater

Kalkaska
Bear Lake
Blue Lake
Boardman
Cleanrvater
Cold Springs
Excelsior
Garfield
Kalkaska
Oliver
Orange
Rapid River
Springfield

1970

50929

6482
523
697

2143

2252
117
217
533

39175

1662

1677

3356
638

4917
507

1206

1584
651

1434

2642

18048
57
796

5272
186
238
310
884
321
232
214

1964
136
258
249
280

Population

1980
75316

9465
745
1142
1792
4019
316
355
1096
54899
2909
4613
6212
1056
8747
676
2997
3823
806
2117
3833
15516
185
1409
10952
433
300
903
1531
942
580
366
3544
241
792
581
739

59

Population growth rates - 1970-1990.

1990
90030

12260
1175
1287
1944
5647

420
407
1380

64273
3447
5249
8307
1344

10516

745
3677
5977

967
2508
4340

15116

255
1825

13497

639

378
1076
1959
1073

714

596
4269

291

885

746

871

Mean annual growth rate
1970 -1980 1980 -1990

4.8

4.6
4.2
6.4
-1.6
7.8
17.0
6.4
10.6
4.0
7.5
17.5
8.5
6.6
7.8
3.3
14.9
14.1
2.4
4.8
4.5
-1.4
22.5
7.7
10.8
13.3
2.6
19.1
7.3
19.3
15.0
7.1
8.0
7.7
20.7
13.3
16.4

2.0

3.0
5.8
1.3
0.8
4.1
3.3
1.5
2.6
1.7
1.8
1.4
3.4
2.7
2.0
1.0
2.3
5.6
2.0
1.8
1.3
-0.3
3.8
3.0
2.3
4.8
2.6
1.9
2.8
1.4
2.3
6.3
2.0
2.1
1.2
2.8
1.8

This hypothesis was tested between decades and at all spatial scales. One-
tailed matched pairs ttests were used to test for a significant mean decrease
between values of annual rate of change in APS. If the average rate of
parcelization was significantly greater during one decade than the other, then it

should be interesting to see if changes in forest cover followed the same trend.

4.3.4: Location analysis.

Determining the urban extent of a city is useful because it can provide insight
into how a parcel of land may be used given its location with respect to the city.
For example, a parcel of land located within the urban extent of a city (e.g., near
to the city center) will tend to be used for urban purposes (i.e., commercial).
Conversely, a parcel of land located beyond the urban extent of a city (e.g.,
farther away) will tend to be used for non-urban purposes (i.e., forest land).
Lands used for urban purposes are usually more developed than non-urban
lands and are often associated with higher population and road densities, and
thus are more accessible to goods and services. Such higher densities are, in
turn, associated with land covers that replace or displace natural cover types.
Therefore, areas that become urbanized over time may exhibit decreases in
natural land covers and increases in human dominated land covers. According
to Thrall (1987), the urban extent of a city can be characterized by a useful rule-
of-thumb, such as a specific population density. Those areas above a specific

population density threshold can be considered urban areas while those below

60

can be considered either non-urban or transitional. A rough estimation of the
urban/non-urban interface can also be made by substituting parcel size for
population density, which in this case assumes (1) one household exists per
parcel, and (2) areas with smaller average parcel sizes are associated with
higher population densities. For example, areas with average parcel sizes above
a specified threshold can be considered non-urban while those areas with

averages below the same threshold can be considered urban.

In order to characterize land consumption around Traverse City, I divided each
parcel landscape into several distance bands of equal width and calculated an
APS index value for each. Each band radiated from the geometric center of
Traverse City. The spatial pattern of land consumption radiating from Traverse
City can be visualized by plotting calculated index values against the middle

distance value of each band and interpolating index values between points.

In order to estimate changes in the extent of urban land uses around Traverse
City, I compared each APS value to a threshold value of 4.047ha (10 acres). l
arbitrarily chose a parcel size threshold value of 4.047ha because this value has
been used by Michigan lawmakers to distinguish lands available for development
from lands unavailable (Ml Plat Act of 1929 and MI PA 288 of 1967). Starting
from the center of the city and moving outward, the urban extent is marked at the

first distance at which average parcel size values exceed the threshold value.

61

Movement of the urban extent can be tracked over time by plotting this
relationship for several successive dates and observing changes in the

calculated intersection.

Should results indicate the urban extent of Traverse City increased over time,
those areas that came under urban pressures may have experienced decreases
in forest cover and increases in forest fragmentation. Conversely, should the
urban extent of Traverse City have decreased over time, those areas
relinquished from urban pressures may have experienced increases in forest
cover and decreases in forest fragmentation. Population figures reported for
Traverse City from 1970 to 1990 (see Figure 4.1) indicate a negative population
growth trend. So, given this trend and the decreasing population densities
associated with it, I suspect the urban extent of Traverse City decreased over

time and subsequently, fragmentation decreased in the relinquished areas.

As stated in Section 3.5, the study area does not meet all of the assumptions
required by the CTLR. Therefore, graphs that describe the radial distribution of
average parcel sizes and the urban extent of Traverse City are used only to
characterize change on the landscape. No formal hypothesis was made during
this portion of analysis because no effort was made to control the effects that

unsatisfied assumptions would have on subsequent results.

62

4.3.5: Spatial analysis.

According to Brown (unpublished manuscript), the spatial patterns of average
parcel sizes and parcelization rates across the region can reveal...

“...(a) spatial organization in the relative degree of parcelization on

a regional scale; and / or (b) the influence that space has on the

process of parcel subdivision. Such information can be used to

form spatially explicit hypotheses about the causes of regional-

scale patterns of parcelization and changes in parcelization”
Brown’s (unpublished manuscript) observations are relevant to my research
because I have also been interested in determining the influence that space has
on both land ownership parcelization and forest cover fragmentation. Should
estimates of parcelization and forest fragmentation exhibit similar spatial
structures such a spatial coincidence might serve to further support a link
between the two phenomena. Also, if the coincidence of spatial structures is
examined at multiple scales, strong correlations between structures observed at

one scale, relative to others, may indicate at which scale(s) landscape processes

were operating.

The spatial structure of parcelization was examined using spatial autocorrelation
techniques. Spatial autocorrelation is a measure of the similarity of objects or
phenomena that are separated by a specified distance. An object or
phenomenon can have a least two types of descriptive elements; aspatial and
spatial attributes. For this study, spatial autocorrelation measures the

relationship between the values of the aspatial attributes (average parcel size

63

and annual rate of parcelization) of townships, sample sites, and sections at
specified distances between townships, sample sites, and sections, respectively.
Spatial autocorrelation indices are useful in this analysis because a single value
is used to describe spatial distributions of parcel sizes and parcelization rates.
The Moran statistic (Moran, 1948), also known as Moran’s I, was used to
measure spatial autocorrelation within the data. Moran’s l represents spatial
autocorrelation along a continuum from -1 to 1. Values approaching 1 indicate
positive correlation meaning places near to each other are more similar than
places far from each other. Values approaching -1 indicate negative correlation
meaning places near to each other are more dissimilar than places far from each
other. Values of zero or near zero indicate that the aspatial variable is not
spatially distributed in a manner significantly different from random. The strength
of the Moran statistic can be tested for statistical significance by comparing the

calculated value to the mean and variance of a critical sampling distribution.

Brown (unpublished manuscript), in his spatial analysis of parcel size changes,
suggested that spatial autocorrelation. ..

“...might be expected in the pattern of parcelization at short
distances, because the same characteristics that make one site
more favorable for parcel subdivision might be expected to hold for
a nearby site. Furthermore, the favorability of a site might have
more spillover effects on nearby sites. For example, if a site has a
large lake in it that attracts parcel subdivision, then a nearby site
might also experience increased parcel subdivision because it is
near, but not on, that lake. Decreased autocorrelation might be
expected to accompany increasing distance separation, or lag,
between sites as such spillover effects are diminished. Aside from
this simple relationship between spatial autocorrelation and
distance, the actual form of the correlogram can yield useful

information about the scale of the process (i.e., at what distances
does autocorrelation become insignificant?) and the underlying
cause of the pattern.”

The same observations hold true for the data in this study as well as the

landscapes they represent.

A correlogram can be calculated by partitioning the range of distances
separating sampled units into distance bands. By plotting the calculated values
of Moran’s l for each distance band against the values of the midpoint of each
band, the spatial structure of parcelization can be visualized. In this technique,
the Moran statistic is not necessarily indicative of similarities between values
near or far but, rather, between values separated by a specific range of

distances.

Brown (1997) constructed correlograms in his analysis of sampled parcel data.
He reported specific autocorrelation values that described the spatial distribution
of average parcel size for sample sites separated by distances up to 600
kilometers apart. Although Brown (1997) was able to identify a regional spatial
structure that included an initial diameter of 60 kilometers, he was unable to
observe structures at finer scales due to his sampling strategy. My research
design allows for spatial structures of parcelization to be examined of scales finer
than Brown’s (1997), and equal to and finer than the basic political units charged

with land use planning, zoning, and development responsibilities.

65

Spatial correlograms were calculated in order to describe the influence of
distance, without respect to direction, on the similarity of sampled units in terms
of average parcel sizes and annual rates of parcelization. By utilizing a multi-
scaled approach, I had hoped to identify at which scale, perhaps, at which
political scale, the pattern of parcelization was most evident. Rather than
formally testing the existence of a specific spatial lag, l constucted correlograms
in order to explore and summarize the overall existence of pattern in my attribute
data. I wanted to answer three basic questions regarding each parcel dataset
and the temporal changes between them. The three questions were:

a. At what distance did spatial autocorrelation become insignificant?

b. Did estimates of average parcel size and parcelization exhibit any

periodic structure or particular spatial lags?

c. If a periodic structure did exist, at what scale(s) was it most evident?
If I could identify at what distance and at what scale changes in parcelization
formed patterns on the landscape, I might then be able to use such clues to infer

what landscape process(es) operated during that time.

Spatial autocorrelation techniques are subject to many rules governing statistical
appropriateness. Due to the lack of appropriate sample sizes necessary for
variance-based statistical analysis (n 2 30) (McGrew Jr. and Monroe, 1993) at
the region (n=1) and county (n=3) levels, spatial autocorrelation indices were
calculated only for the township (n=33), sample site (n=186), and section

(n=1678) level analyses

66

4.4: Forest data.

Satellite data are commonly used for forest classification and mapping. By
superimposing satellite images taken at different dates, land cover change can
be detected and rates of change calculated (lverson, et al. 1989). When such
satellite images are also incorporated into a GIS, lengths, areas, spatial
coincidences, and proximities of natural features can be derived (Johnson,
1990). Using a GIS to manipulate satellite data allows users the ability to
efficiently sample landscapes at multiple scales in order to gain insight into

landscape processes.

4.4.1: Collection.

I collected three pairs of available satellite imagery that cover the study area for
the approximate years 1973, 1985, and 1991. Each satellite image has been
registered, georeferenced, and distributed as part of the North American
Landscape Characterization (NALC) data set at a spatial resolution of 60 meters
(Lunetta, et al., 1998). Slight registration errors were detected and corrected
using PCI lmageWorks (PCI, Richmond Hill, Ontario) workstation software and
known UTM coordinate system information obtained for regional road networks
stored in vector GIS format (MIRIS, 1978). Appendix B includes a metadata

description of the satellite images used for this analysis.

67

4.4.2: Image processing.

Two options are generally available for classification of areas larger than or more
than one satellite image. In one method, each scene is classified individually
and resulting class maps can then be mosaiced. This method can produce
abrupt boundaries between mapped classes as an artifact of the seam joining
the two original images. Such abrupt boundaries can be problematic during
calculation of common landscape indices. (Landscape indices and metrics are
discussed later in this chapter.) Boundaries between land cover types are
thought of as important ecological features in the landscape ecology literature
(Forman and Godron, 1986). Therefore, false edges in landscape data can bias
subsequent ecological analysis. The second method, and the one chosen for
this experiment, results in a seamless class map by mosaicing raw image pairs

prior to classification.

The histogram matching method of mosaicing adjacent images compares a
‘slave’ image to an adjacent ‘master’ image (Jensen, 1996). This method has
been used in recent research (Homer et al., 1997; Vogelmann et al., 1998) and
its ease of use and reasonable results makes histogram matching an efficient
option. In the process of histogram matching, regions of spatial overlap are
selected and the distribution of brightness values in the slave image is
normalized to match the distribution of brightness values in the master image.

This normalization, or matching, is carried out for each spectral band.

68

Before each pair of scenes could be matched and mosaiced. however, all clouds
and cloud shadows needed to be removed. Clouds and cloud shadows often
produce extreme brightness values in visible light bandwidths. Such extreme
values are statistical outliers and can perturb the histogram normalization
process by exaggerating the observed distribution of brightness values within
each visible light image band. Clouds were identified and removed through on-
screen polygon digitizing according to their popcorn shapes and corresponding
displaced shadows. The cloud and cloud-shadow polygons were then used to
“mask” the images, thus removing pixel values associated with these features.

In an effort to further reduce the amount of non-essential variation between
corresponding histograms, each individual scene was clipped by the areal extent
of the study area plus a one-mile buffer zone. This clipping discarded unwanted
variations in brightness values representing waves in Great Lakes Huron and
Michigan, as well as those variations induced by real landscape changes outside

of the area of interest.

After each pair of masked and clipped images were histogram matched and
mosaiced. a composite cloud mask, which was generated by aggregating all
clouded areas within all six images, was used to mask the three resultant image
mosaics. This masking was done in order to maintain a consistent area of

analysis throughout the experiment.

69

4.4.3: Image classification.

My primary remote sensing task was to identify and distinguish all forested areas
from non-forested areas. I used Vogelmann’s (1995) research, which made use
of Landsat MSS data to identify forested areas in New England, to guide my own
classification scheme. My target classification scheme included five classes:

forested areas, not forested areas, open water, clouds, and background.

The ISODATA clustering algorithm (Tou and Gonzalez, 1977) was used to
identify statistically homogenous areas within each landscape mosaic. Like
other unsupervised image classification techniques, this numerical operation was
used to search for “natural groupings of the spectral properties of pixels”
(Jensen, 19962231) that I could ultimately label into land cover classes of
interest. The ISODATA algorithm is an iterative technique that partitions
n-dimensional image space into homogenous groups, or clusters, along
calculated mean vectors by averaging digital numbers in each cluster across
several spectral channels. For all iterations past the initial seeding, each mean
vector is statistically adjusted by reassigning each pixel to the nearest cluster
mean in n-dimensional space. Several pre-specified parameters, like cluster
size and separability, control the pixel assignment and iteration processes.
Then, each cluster is recalculated. The process continues until changes within
the cluster set fall below a set of pre-determined tolerances. At that point, the

algorithm converges upon a final cluster solution. In this experiment, four image

70

bands, plus a fifth Normalized Difference Vegetation Index (NDVI) band, were
used as inputs for each image. The NDVI, a mathematical combination of MSS
bands 2 and 4 (Jensen, 19962181) has been found to be a sensitive indicator of
the presence of green vegetation (Lillesand and Kiefer, 1994:506). Vegetated
areas, like trees and forest canopies, will generally yield higher NDVl values than
bare soils, urban surfaces, water, and clouds. The parameter values used to
control the ISODATA algorithm are outlined in Appendix C. Each process

converged on a solution set of 72 clusters.

Subsequent to cluster analysis, I used three sets of sixteen aerial photograph
mosaics (each set was obtained for the approximate dates 1970, 1980, and
1990) to aide me in cluster identification and accuracy assessment. The photos
had already been scanned into digital form, georeferencd, and mosaiced into
three-mile by three-mile images corresponding to the sample areas in Crawford
and Grand Traverse Counties used by Brown and Vasievich (1996). l divided
each temporal set of photographs into two subsets of eight by maximizing the
geographic extents covered by each. The first subset for each date was used to
identify and classify clusters and assign them to historic land cover types. The
second subset was set aside for use in testing the quality of my final
classification maps. By digitally ‘linking’ each photograph to its corresponding
ISODATA output image, I could be confident about the positional accuracy of
land covers identified in the photographs and the image clusters that were

spatially associated with them. Appendix D includes a metadata description of

71

the three sets of sixteen aerial photograph mosaics used. Also, Appendix E has
been included to provide the reader with a review of common accuracy
assessment techniques and quantitative descriptions of my classified images.

A water mask was created using published 1:100,000 Digital Line Graph
hydrography data (US. Department of the Interior, 1993) in order to remove
pixels associated with water from each classified image. I concede that, in
reality, open water boundaries are rarely static in nature - even over geologically
short ten and twenty year periods. However, I assumed constancy of the
presence and extent of open water within my study area in order to isolate

changes only in forested and non-forested land covers.

4.4.4: Temporal analysis.

Forest cover data were necessarily partitioned into private and non-private land
cover categories because the APS index is a measure of parcel subdivision on
private lands only and one of my objectives was to compare relative changes in
parcelization to relative changes in forest fragmentation. For this experiment, all
references to changes in forest cover and forest fragmentation are limited to
changes observed on only privately owned lands. Classified imagery was
converted from PCI image (raster) to Arc/Info polygon (vector) format. Percent
forest cover estimates were calculated from each classified coverage for sample
units at all spatial scales. Percentage forest cover is defined as the sum of

privately owned forest polygon areas divided by the sum of all non-water and

72

non-cloud, private areas. Changes in percent forest cover were calculated for
each decade and the entire eighteen-year period. I note here that the amount of
land as private remained very stable over the entire time frame. Therefore,
calculated changes in percent forest cover can be attributed to changes in
forested area (the numerator) and not to changes in the amount of land as
private (the denominator). Percentages and rates of change were examined in
an effort to answer the question: Has privately owned forest cover changed over
time and if so, how?

Three possible results for each scale of analysis are:

a. the extent of privately owned forest land has decreased over time

b. the extent of privately owned forest land has not changed over time

c. the extent of privately owned forest land has increased over time
As stated in Section 2.1, a recent forest inventory analysis reported a six percent
increase in total forest land area between the years 1980 and 1993 for the NLP
(Leatherberry, 1994). Conversely, as reported in Section 3.3, Michigan planning
officials have expressed concern about observed occurrences of forest
fragmentation (Wyckoff, 1995). I tested the data to uncover what had really
happened because each of these sources has advocated seemingly different
views of recent forest changes. My third and fourth hypotheses were:

Hypothesis lll

H1: the average percentage of private lands as forested changed
over time

Ho: the average percentage of private lands as forested did not change
over time

73

Hypothesis IV

H1: the annual rate of change in percent forest cover has changed
over time

Ho: the annual rate of change in percent forest cover has remained
the same over time

These hypotheses were tested between decades and at all spatial scales. Two-
tailed matched pairs ttests were used to test for significant difference between
mean values of percent forest cover at each time and for significant difference
between the mean values of annual rate of change in percent forest cover ever

each time step.

4.4.5: Landscape patterns and metrics.

The use of landscape metrics or landscape indices is common for quantifying
landscape patterns. Landscape ecology is based upon the premise that
landscape patterns are indicative of ecological processes (Forman and Godron,
1986; Turner, 1989; Gustafson, 1998) and quantitative metrics allow measurable

links to ecological processes to be determined (F rohn, 1998).

In the landscape ecology literature, spatially distinct contiguous areas within a
landscape class are referred to as patches. Patches can be quantitatively
described in terms of size, shape, interior core area, and complexity. Much
research has been done that has utilized several or many such landscape

metrics (McGarigal and Marks, 1995; Ritters et al., 1995; Li and Reynolds, 1993;

74

Baker and Cai, 1992; Milne, 1991; Turner and Gardner, 1991; and Forrnan and
Godron, 1986).

Studies of forest fragmentation often use metrics to describe interior core areas
and edge effects (Fahrig and Merriam, 1994: Merriam and Wegner, 1992:
Villard, 1992). Interior core areas, sometimes referred to as interior habitat
areas, are internal patch areas where some natural species and ecosystems can
function independently and better sustain themselves. These interior areas
contain requisite energy, nutrients, materials, and gene pools necessary for self-
perpetuation. Edges are portions of an ecosystem (forest patch) near the
perimeter where influences of surrounding areas prevent natural interior
environmental conditions (Forman, 1995) and can be considered habitat by other
species. Those forest areas influenced by the effects of non-forest edges are
often called disturbed forest areas. Thus, patch size and shape can influence
population dynamics and survival as two patches of the same area but with
different amounts of edge may effect core areas of differing quality and species

composition (Saunders et al., 1985; Saunders et al., 1991).

Gustafson (1998), however, is critical of the current set of landscape metrics
often used in the landscape ecology literature and of the lack of any means to
interpret them consistently. He stated, “[t]here is seldom a one-to-one
relationship between index values and pattern (that is, several configurations

may produce the same index value)” (p.150). In the same paper he argued...

75

“[v]ery few pattern indices produce values that are useful by
themselves. Their most instructive use is in comparing alternative
landscape configurations, either the same landscape at different
times or under alternative scenarios, or different landscapes
represented by using the same mapping scheme and at the same
scale” (p.152).
So, I have found it necessary to construct a landscape index of my own that
could be (1) useful by itself, (2) useful for describing conditions of forest
fragmentation, and (3) have a direct relationship with degrees of fragmentation.
The core fragmentation (CF) index can be derived with the following equation,
which is expressed here in condensed terms:

COREma! “ COREQbs
CF = CORE"...x

The CF index can be interpreted as the proportion of the potential core area

(COREmax) of a patch that is not core area (CORE...ax - COREobs) because of

shape induced edge effects. The index is constrained between zero and one,
has a direct relationship with core area fragmentation, and is useable on its own.
Calculated CF values approaching a value of one indicate a highly fragmented

landscape with all forest areas being influenced by edge effects. Urban forests,
with few core areas would generally fit into this category. Calculated CF values
approaching zero indicate an unfragmented forest area subjected minimal edge
effects. Such areas would include the interior areas of very large forest stands.
Appendix F contains a detailed description of the heuristic used to calculate the

CF index.

76

As mentioned above, Michigan planning officials have hypothesized increases in
forest fragmentation. In order to test the validity of these observations, on a
regional scale, I posed my fifth and sixth hypotheses:

Hypothesis V

H1: Forest fragmentation has increased over time.

Ho: Forest fragmentation has not increased over time.

Hypothesis Vl

H1: The annual rate of change in forest fragmentation has
increased over time.

Ho: The annual rate of change in forest fragmentation has not
increased over time.

These hypotheses were tested between decades and at all spatial scales. One-
tailed matched pairs ttests were used to test for significant mean difference
between estimates of forest fragmentation and between estimates of annual rate

of change in fragmentation.

4.4.6: Location analysis.

In order to describe the distribution of forest cover and forest fragmentation with
respect to distance from Traverse City, I calculated percent forest cover and the
CF index for each of the distance bands radiating from Traverse City as specified
in Section 4.3.4. By plotting the calculated values of percent forest cover and
the CF index for each distance band against the value of the midpoint of each

band, the spatial structure of forest cover and forest cover change around

77

Traverse City can be visualized. The results of this exploratory experiment were
then compared to the results calculated for Section 4.3.4 in order to observe and

characterize any coincidence or dissimilarity.

As stated above, should results indicate that the hypothetical radial extent of
Traverse City increased over time, those areas that have become urban might
reasonably be expected to have exhibited decreases in forest cover and
increases in forest fragmentation as human dominated land covers replaced
more natural land covers. Conversely, should the radial extent of Traverse City
have decreased over time, those areas relinquished from urban pressures might
be expected to have exhibited increases in forest cover and decreases in forest

fragmentation as trees were allowed to regenerate.

4.4.7: Spatial analysis.

The spatial structure of calculated CF indexes and annual rates of fragmentation
were also examined using spatial autocorrelation techniques in the same manner
described in Section 4.3.5. Spatial correlograms were calculated and graphed in
order to describe the influences of distance on the similarity of sampled units in
terms of CF values and annual rates of change in CF values. I wanted to answer
three basic questions regarding each forest cover data set and the temporal

changes between them.

78

The three questions were:
a. At what distance did spatial autocorrelation become insignificant?
b. Did estimates of forest fragmentation exhibit any periodic structure or
particular spatial lags?

c. If a periodic structure did exist, at what scale(s) was it most evident?

Again, by utilizing a multi-scaled approach, I had hoped to identify at which
scale(s) the pattern of forest fragmentation is most evident. Since I had found no
theoretical or practical basis for the existence of a particular spatial lag, this
portion of my analysis was also exploratory in nature. Examining the spatial
structure of fragmentation is of interest because such an analysis has the
potential to reveal spatial patterns that may have been similar to those exhibited
by average parcel sizes and parcelization. Should the two phenomena be
similarly distributed across space with respect to time, such results would provide
additional evidence supporting the link between land ownership subdivision and

forest cover changes.

4.5: Summary.

I have outlined a detailed approach to quantifying land ownership parcelization
and forest cover fragmentation using basic and spatial statistical techniques.

Attention was paid to the collection and preparation of accurate and valid data
with respect to: (1) successful theories and methods found in the Iiteratures of

geography, remote sensing, and landscape ecology, (2) meeting the

79

assumptions of statistical appropriateness, (3) a basis in logic and common
sense, and (4) answering my five basic research questions. Geographic
information tools were used to capture and store the necessary data and to
provide an effective interface for querying and analyzing landscape states and
patterns of change. Quantitative methods were used to allow measurable links

to ecological processes to be determined (Frohn, 1998).

80

CHAPTER 5: RESULTS

5.1: Introduction.

This chapter presents results of basic and spatial statistical treatments of
digitized land parcel data and remotely sensed forest cover data for Crawford,
Kalkaska, and Grand Traverse Counties in Northern Lower Michigan.
Quantitative measures of land ownership parcelization and forest cover
fragmentation were calculated for three dates and analyzed at multiple scales.
Spatial patterns of parcelization and fragmentation were examined. Also,
images in this thesis are presented in color. However, most images should

withstand black-and-white duplication without loss of content.

5.2: Scales of analysis.

Five spatial scales were used to analyze landscape data. The five scales were
region, county, township, sample site, and survey section (see Section 4.2).
Each sampling unit at the region, county, and township scales contained large
areas of privately owned land and forested land covers. However, at the
smallest scales (i.e., sample sites and survey sections) some observation units
had to be removed from analysis because each lacked privately owned land
area. Further, other sampled units contained only a very small number of

parcels that, in aggregate, covered only a very small portion of the land area. In

81

order to prevent changes in any one small parcel from leveraging an observation
unit, I arbitrarily set a minimum threshold of 16.2 hectares (40 acres) of private
land. Any sample site or survey section containing less than 16.2 hectares of
privately owned land for any of the three dates was omitted from further study.
The effects of the threshold altered the sample size of sample sites from 186 to
168 and reduced the survey section sample size from 1678 to 1176. Sample
units that did not meet the minimum threshold criterion were generally located

within interior regions of large public land areas.

Matched pairs ttests were used to test for significant mean differences between
values measured for each set of sampling units for two dates. Changes
measured at the region scale were accepted as significant changes during all
hypothesis testing, therefore no tvalues were calculated for region level
analyses. However, significance testing of landscape data sampled at smaller
scales was done in order to ensure results and conclusions obtained from areal
analysis were commensurate with region scale results and not characteristic of
the units used to sample the landscape (Openshaw, 1984). A 95 percent
confidence interval was used to assess the significance of all statistical tests.
The significance of this interval meant that only a 5 percent chance existed to

falsely reject a null hypothesis due to random sampling error.

82

5.3: Parcel data - hypothesis l

l hypothesized that APS values had decreased over time based on results
published by Brown and Vasievich (1996). The APS index (see Section 4.3.3)
was used to estimate the average size of parcels for each sampled unit. Table
5.1 outlines APS index values calculated for each sample unit in the region,
county, and township level analyses. In all but one case, the City of Grayling,
APS values decreased over time. Review of the original plat map data revealed
that almost all small tract areas mapped within the City of Grayling city limits in
1970 had been cartographically reclassified by the publisher into polygons
associated with the incorporated city (the exceptions being public land areas,
water bodies, and utility corridors) by 1980. Subsequently, no small tract areas
were used in the calculation of the 1980 APS index and the resultant value did
not measure their influence. No APS values were calculated for the City of
Grayling and Traverse City for 1990 because all private parcels had been
reclassified into city-owned parcels by 1990. Hence, each respective value was

replaced with a 'NO DATA' entry in Table 5.1.

Because the number of cases in both the sample site and section level analyses
are too numerous to outline here, Table 5.2 is provided to summarize changes in
APS over time. As the numbers indicate in Table 5.2, many more areas

experienced parcel subdivision (decreases) than experienced parcel aggregation

(increases).

83

Table 5.1: Average parcel size estimates for political sampling units (ha).

County

Township

Region totals

Crawford

Beaver Creek
Frederic

City of Grayling

Grayling
Lovells
Maple Forest
South Branch

Grand Traverse

Acme

Blair

East Bay
Fife Lake
Garfield
Grant
Green Lake
Long Lake
Mayfield
Paradise
Peninsula
Traverse City
Union
Whitewater

Kalkaska

Bear Lake
Blue Lake
Boardman
Cleanlvater
Cold Springs
Excelsior
Garfield
Kalkaska
Oliver
Orange
Rapid River
Springfield

APS
1980
4.92

3.30
3.95
3.37
7.03
2.40
4.33
5.11
3.02
5.77
6.29
4.98
3.62
5.62
3.28
9.53
4.81
3.83
10.33
7.82
4.90
0.36
8.56
5.57
5.40
3.82
3.99
6.91
5.94
3.17
6.34
5.11
5.12
5.70
6.13
4.42
6.50

19

4.11

O

3.03
3.15
2.88

NO DATA

2.25
3.89
4.29
3.26
4.27
4.32
3.68
2.79
5.38
2.25
7.60
3.68
2.45
8.12
6.47
3.04

NO DATA

6.73
4.48
4.77
3.02
3.03
5.78
4.58
2.90
5.31
5.27
4.52
5.68
6.00
4.18
5.69

Table 5.2: Summary of parcel size changes for small sampling units.

 

Scale [1 % Increase % Decrease % No Change
Sample sites

1970 to 1980 168 6 94 0

1980 to 1990 168 15 85 0
Survey sections

1970 to 1980 1176 19 77 4

1980 to 1990 1 176 32 64 4

One-tailed matched pairs ttests were used to test for a significant decrease
between sets of APS values measured at different times. This test was applied

between dates and at all spatial scales. Table 5.4 highlights the test results.

Table 5.3: Average parcel sizes changes for all scales (ha).

1970 to 1980 1980to1990
530% L919 .128_0 __Q§%Chan 1969 .1_9_90 __m§°/oCha
Region 9.64 4.92 -49 4.92 4.11 -16
County 9.51 4.82 -49 * 4.82 4.02 -17
Township 10.29 5.20 -49 * 5.20 4.14 -20 *
San'ple 13.79 6.91 -50 * 6.91 5.78 -16 *
Section 18.05 10.85 -40 * 10.85 8.07 -26 *

* Denotes statistical significance with 95% confidence.

For all tests but one, mean estimates of average parcel size were significantly
less than those observed on the previous date. The regional average changed
from 9.64 ha in 1970 to 4.92 ha in 1980 - a 49 percent reduction over the ten-
year period. Average parcel sizes decreased again during the next ten years,

but exhibited only a 16 percent reduction. Township, sample site, and survey

85

section test results provided evidence to reject null hypothesis l for each of these
scales. In the single test that l was unable to reject null hypothesis l (county
level, 1980 to 1990) the calculated mean parcel size for 1990 (4.02ha) is less
than that calculated for 1980 (4.82ha) but, not at the 95 percent confidence level.
So, even though the county result could not meet the requirements for statistical
significance, I found no reason to mitigate the results obtained from the other
scales. Therefore, null hypothesis l was rejected. It can be stated that average

parcel sizes decreased over time within the study area.

I should indicate here that the set of mean APS values presented in Table 5.3
reveals a large range of average parcel sizes calculated for each date across the
different scales. For example, the 1970 section analysis produced a mean APS
equal to 18.05 ha, a value almost twice the value calculated for the county
average. Mean APS values appear inversely related to the size of individual

landscape sampling units, therefore indicating a scale effect exists.

5.4: Parcel data - hypothesis II.

I hypothesized higher parcelization rates existed during the 1970s than during
the 19805 because regional population growth rates peaked during the 19705
(see Table 4.1); Brown's ([unpublished manuscript] see Section 3.4) results
suggest higher parcelization rates occurred during the 1970‘s; and Stewart

(1994) indicated a strong seasonal home development trend existed during the

86

1970's. Average annual rates of change in APS were calculated between dates
and for all spatial scales. Linear rates of change between dates were assumed.
One-tailed matched pairs ttests were used to test for a mean decrease in

average annual parcelization rates over time.

Table 5.4 lists average annual parcelization rates for each sample unit in the
region, county, and township level analyses. Also listed in Table 5.4 are
rankings associated with each township. High ranks (i.e. 1,2,3...) indicate
relatively high parcelization rates. Conversely, low ranks (i.e. 30,31,32...)
indicate relatively low parcelization rates. In every case but one, rates of change
were greater during the 19705 than during the 1980s. Peninsula Township,
Grand Traverse County proved the exception as the parcelization rate of this

township increased slightly over time.

Individual cases used in both the sample site and section level analyses are too
numerous to itemize so, Table 5.5 is provided to summarize, using percentages,
how many sample sites and survey sections experienced the highest average
annual parcelization rate for each decade. More areas experienced higher rates
of parcel subdivision during the 19705 than during the 19805. For example, two
average annual parcelization rates were calculated for each sample site; one for
the 1970's and one for the 1980's. Of 168 sample sites sampled, 90 percent had

the highest average annual parcelization rate occur during the 1970's.

87

Table 5.42

County

Eugenia
Region totals

Crawford
Beaver Creek
Frederic
City of Grayling
Grayling
Lovells
Maple Forest
South Branch

Grand Traverse
Acme
Blair
East Bay
Fife Lake
Garfield
Grant
Green Lake
Long Lake
Mayfield
Paradise
Peninsula
Traverse City
Union
Whitewater

Kalkaska
Bear Lake
Blue Lake
Boardman
Clearwater
Cold Springs
Excelsior
Garfield
Kalkaska
Oliver
Orange
Rapid River
Springfield

1970 to 1980

Rate
-0.471

-0.261
-0.425
-0.315

0.406
-0.108
-0.276
-0.602
-0.284
-0.583
-0.409
-0.615
-0.320
-1.024
-0.323
-0.763
-0.555
-0.393
-1.161
-1 .337
-0.178
-0.031
-0.671
-0.561
-0.483
-0.315
-0.124
-0.424
-0.514
-0.306
-0.548
-0.399
-0.432
-0.507
-1.031
-0.415
-0.594

Rank

16
24
33
31
28

27
19
23
22
11
21
29
32
10
24
30
17
13
26
12
20
15
14

18

88

Average annual parcelization rates for political units (ha/yr).

1980 to 1990

Rate
-0.074

-0.023
-0.067
-0.041

NO DATA

-0.013
-0.036
-0.069

0.020
-0.150
-0.197
-0.130
-0.083
~0.024
-0.103
-0.193
-0.114
-0.138
-0.221
-0.136
-0.186

NO DATA

-0.183
-0.108
-0.057
-0.073
-0.088
-0.102
-0.123
-0.025
—0.093

0.014
-0.054
-0.001
-0.012
-0.021
-0.074

Rank

20
22

27
23
19
31

16
25
12

.5
#V—‘OOO’

AU!

18
15
13

24
14
30
21
29
28
26
17

Table 5.5: Decadal summary of parcelization rates for small sampling units.

% Having highest rate of change (ha/yr) in decade

Sale _r_i_ 1970's 1980's No Chame
Sarrple sites 168 90 10 0
Survey sections 1 176 70 27 3

Table 5.6 highlights the results of the one-tailed matched pairs ttests. For all
tests, mean parcelization rates were significantly greater during the 19705 than
during the 19805. Therefore, I rejected null hypothesis H for all scales and could
state that the study area exhibited higher parcelization rates during the 19705

than during the 19805.

Table 5.6 Parcelization rates and changes for all scales (ha/yr).

 

Scale 1970 t9 198_0 1980 to 1990 Mime
Region 0471 -0.074 -84
County 0442 -0.077 -83 *
Township 0471 -0.100 -79 *
Sample -0.673 -0.104 -85 *
Section 0684 -0.251 -63 *

* Denotes a statistically significant change with 95% confidence.

I note here that the set of average annual parcelization rates presented in Table
5.6 reveals a large range of values for each date and across scales. For
example, the 1970 to 1980 section-level analysis produced a rate equal to -0.684
halyr, a value much larger than the value calculated for the region (0471 ha/yr).

Average annual parcelization rates appear to be inversely related to the size of

89

individual landscape sampling units, therefore indicating a scale effect exists.

This scale effect is similar to the scale effect observed in Section 5.3.

5.5: Parcelization - location analysis.

According to Thrall (1987)1 and his CTLR, each additional increment in distance
from a city center should result in an increase (at a decreasing rate) in the
quantity of land consumed per household. Therefore, by assuming each
household exists on one and only one parcel on land, the radial pattern of land
consumption around a city can be represented by the theoretical function
graphed in Figure 5.1 (after Thrall, 1987). The shape of the theoretical function
can serve as a general baseline with which actual consumption functions can be

compared.

Actual land consumption functions were graphed for Traverse City by calculating
APS index values for a set of concentric bands radiating from the geometric
center of the City. The radial pattern of land consumption can be visualized by
plotting calculated APS index values against distance band midpoints and

interpolating index values between points (see Figure 5.2).

 

‘ Thrall (1987) is the latest in a series of researchers that have examined this
spatial relationship between land consumption and household economic
conditions (Alonso, 1964; Barlowe, 1978; Casetti, 1971; Muth, 1969; and Von
ThIJnen, 1842).

90

 

Land consumption (parcel size)

 

 

 

Distance from city center

Figure 5.1: Theoretical land consumption function.

 

18 1

16 1
’6 14 4 —-—ap51970
5
g 12 ->
75 +aps1980
3 10 -
as —o— aps1990
O.
8
9 - - - -4.047 ha (10 acre)
é” Threshold

 

 

 

 

TTTTT rle
990000009000
v-V-NC'O IO N002

Midpoint of distance band (km)
from Traverse City

Figure 5.2: Actual land consumption functions for Traverse City.

91

For this exercise I assumed 4.047 ha (10 acres) to be the largest parcel size
associated with the urban extent of Traverse City (see Section 4.3.4). By
comparing APS values calculated for all 1970, 1980, and 1990 distance bands to
the threshold value, I could determine the urban extent for each date. Table 5.7
lists APS index values for each band. Starting from the center of the city
(distance = 0) and moving outward, Figure 5.2 clearly shows that the first
distance at which average parcel size values exceeded the threshold value
increased over time. In 1970, the first intersection occurred between the first
and second bands. In 1980, the first intersection occurred between the second
and third bands. In 1990, the intersection occurred between the fifth and sixth
bands. Movement of this intersection away from the city suggests the urban
extent of Traverse City increased over time. This extent increased even though

Traverse City resident population decreased during the same period.

Also important are observable changes in slope of the land consumption function
over time. The general decrease in slope indicates that the parcel density
gradient around Traverse City became less steep and areas located farther away
from the city became more densely subdivided over time. This trend suggests
that places farther from Traverse City may have gained better access to the city
and its amenities, or that proximity to the city became less important to new land
owners over time. These reasons may explain why adjacent townships like
Acme, East Bay, and Garfield experienced increases in resident populations

during the same period that Traverse City experienced losses.

92

Table 5.7:

Band (km)

to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to
to

3

6

9
12
1 5
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
75
78
81
84
87
90
93
96
99

to 102

Average parcel sizes for concentric bands around Traverse City

(ha).

l97_0
0.339
5.363
9.347
7.707
8.487
13.287
12.821
17.274
13.433
11.002
10.484
12.890
10.064
11.152
10.295
5.225
5.925
4.974
8.224
8.216
6.033
6.750
5.086
5.295
6.748
5.510
3.244
4.079
2.684
5.665
9.962
4.662
10.159
2.692

1.9.8.9
0.727
2.476
4.319
3.567
4.226
5.960
5.649
7.218
7.438
5.795
5.417
5.373
5.149
5.373
4.796
3.388
3.691
3.203
5.191
3.555
1.793
3.720
3.419
3.153
3.588
3.373
2.446
2.239
2.112
3.163
5.921
3.212
5.306
3.131

93

Inspection of the APS-distance relationships in Figure 5.2 reveals two additional
and important trends. First, APS values tended to decrease with increasing
distance from the CBD beyond the 24 to 27 kilometer band. The basic CTLR
discussed by Thrall (1987) does not account for such decreases as the model
assumes (a) the existence of only one urban center within an isotropic landscape
and (b) land consumption per household increases infinitely from that one
center. Because average parcel sizes (a surrogate for land consumption) do not
increase infinitely from Traverse City, and because the study area does contain
other population centers (e.g., Village of Kalkaska and City of Grayling), the
trends observed beyond the 27 kilometer distance band could have been
produced by other central places operating on the landscape. And second,
several points along each graph consistently fall below the threshold value
through time, hence indicating lands used for urban purposes existed beyond the
urban extent of Traverse City. Review of the original plat map data revealed
several places that probably also serve as central places on this landscape.
Most obvious is the City of Grayling in Crawford County. The location of City of
Grayling, and the large military reserve surrounding it, explains the dip in
average parcel sizes observed between 57 and 76 kilometers. The Town of
Frederic is also located within this region - a town that nearly doubled in
population from 1970 to 1980. However, most interesting are the potential
central places that explain the dips between 45 and 54 kilometers, and 72 and
102 kilometers. Manistee Lake, a large inland lake, is located within the 45 to 54

kilometer region. Many small-tract areas surround this lake (and others near to

94

it) and have grown in number and extent over time, thereby explaining the dip
between 45 and 54 kilometers. Parcelization along the Au Sable River of
Crawford County may explain the dip between 76 and 102 kilometers. The
distance bands in this region contain many public land areas due north and
south of the river. Therefore, it is easy to attribute parcelization along the Au
Sable River to the observed dip in average parcel sizes because these areas

were the only areas able to exhibit significant changes in land subdivision.

These additional findings are important because they suggest the important role
natural features, like water bodies, play in attracting new landowners to an area.
This role of attraction has been traditionally attributed to urban places and the

human produced goods and services associated with them.

5.6 Parcelization - spatial analysis

Spatial autocorrelation statistics can be calculated to measure relations among
locations separated by different distances, or lags. A spatial correlogram can be
calculated as a series of autocorrelation statistics and “shows spatial
autocorrelation as a function of spatial lags and allows autocorrelation at

different spatial lags to be analyzed and compared” (Odland, 1988zp. 64).

Spatial correlograms illustrating the spatial patterns of average parcel size

distributions and the distributions of land ownership parcelization rates were

95

calculated. The correlograms describe the influence of distance, without respect
to direction, on the similarity of values at various spatial lags. Correlograms were
calculated for the township, sample site, and section level analyses. Individual
values of Moran’s I (a measure of spatial autocorrelation that is theoretically
constrained between +/- 1), which define points along each autocorrelation
function, were tested for statistical significance. Mean and variance estimates
were calculated for each sampling distribution (see Griffith, 1987 and Odland,
1988 for complete descriptions of mean and variance estimate calculations for
use in significance testing of the Moran statistic) and the calculated Moran
coefficients were compared to critical values associated with the 95 percent
confidence interval. Also, because “autocorrelation is a direct extension of
classical correlation” (Griffith and Annhein, 1991 :134) qualitative descriptions of
autocorrelation values are similar to descriptions of classical correlation values.
When individual Moran coefficients exceed +/- 0.7, then the relationship between
values can be described as strong. When Moran coefficients tend between —0.3
and 0.3, the relationship between values can be described as weak with values
near zero indicating no relationship. All other coefficients describe moderate

relationships.

Observed peaks and patterns in graphed autocorrelation functions were used to
describe the effects of distance on pattern at each time. Also, distances at which
spatial patterns were statistically indiscernible from random patterns were used

to infer the scale at which parcelization processes operated.

96

5.6.1 Townships

An interdistanoe matrix was calculated for all pairs of townships using the
geometric center of each township as both a point of origin and destination.
Uniform distance bands of 12,000 meters were used in this particular analysis in
order to assure ample numbers of paired comparisons within each spatial lag.
The interdistanoe matrix was reclassified into a binary weight matrix for each
distance band. For example, all inter-township distances that fell between 0 and
12,000 meters were reclassified as 1’s (signifying contiguity) while all others
were reclassified as 0's (signifying no contiguity). The resultant binary weight
matrix was then used as the contiguity matrix during the calculation of Moran’s l
for connected townships in the 0 to 12,000 meter distance band. Next, all inter-
township distances that fell between 12,000 and 24,000 meters were reclassified
as 1’s (signifying contiguity) while all others were reclassified as 0's (signifying no
contiguity). The new binary weight matrix was then used as the new contiguity
matrix during the calculation of Moran’s l for connected townships in the 12,000
to 24,000 meter distance band. This procedure was iterated for all other

distance bands.

Table 5.8 lists calculated values of Moran’s I for each distance band for the
distribution of APS values. Figure 5.3 illustrates the results. Brown (unpublished
manuscript) suggests positive spatial autocorrelation might be expected at

shorter distances (see Section 4.3.5). The patterns depicted by functions

97

graphed in Figure 5.3 are consistent with this expectation. With respect to the

distribution of APS values, townships nearer to one another exhibited

significantly greater similarities in average parcel sizes than townships located

 

 

 

 

 

 

 

 

 

 

 

farther apart.
Table 5.8: Spatial autocorrelation results: township values of APS.
Confidence Interval Moran Statistic
_l‘_l Midpoint Um Lower 1970 1980 1990
30 6000 0.043 -0.112 0.547 0.404 0.517
33 18000 0.011 -0.073 0.037 -0.030 -0.008
33 30000 0.009 -0.071 -0.032 -0.051 -0.162
33 42000 0.017 -0.079 -0.113 -0.032 -0.153
33 54000 0.026 -0.089 -0.091 -0.073 -0.043
30 66000 0.042 -0.111 -0.373 -0.246 -0.161
22 78000 0.042 -0.137 -0.154 -0.115 -0.007
13 90000 0.092 -0.259 -0.125 -0.098 -0.022
1.0 1
l
_ 1 ------- Upper limit
53 Lower limit
5 +1970
5 +1980
——0— 1990
'1.0 l l I I T W 7 ii
5 5 5 5 5 5 5 5
Midpoint of distance band (m)
Figure 5.3: Spatial correlograms: township values of APS.

98

However, such similarity disappeared in the second spatial lag and an erratic
and near-random spatial pattern persisted into the last lag. The overall pattern
suggests that similarities between townships existed over only short distances.
These results suggest some sort of simple adjacency or spillover effect existed.
Also, negative autocorrelation that had existed within the 60 to 72 km distance
band in the 19705 steadily became less distinguishable from random over time.
As the lag within the 60 to 72 km band weakened, a new significant lag emerged
within the 24 to 36 km distance band. Because negative spatial autocorrelation
is associated with a spatial dissimilarity of values, one could infer dissimilar

township characteristics became separated by shorter distances over time.

With respect to average annual parcelization rates, results indicate (see Table
5.9 and Figure 5.4) that positive autocorrelation existed at short distances for
both time periods. The distance over which parcelization rates were positively
autocorrelated extended from the second lag (12 to 24 km) during the 19705 into
the third lag (24 to 36 km) during the 19805. Also, negative spatial
autocorrelation increased over time at greater distances as the spatial pattern of
dissimilar rates of parcelization increased from a single lag (60 to 72 km) to all
distances beyond 60 kilometers. However, when comparing values associated
with spatial lags greater than 60 kilometers, the reader should be aware that
such values increasingly reflect differences between Grand Traverse and

Crawford Counties rather than differences across the entire landscape.

99

Table 5.9:

Confidence Interval

Spatial autocorrelation results: township parcelization rates.

Moran Statistic

 

 

 

 

 

 

 

g Distance Upgr limit Lower limit 19705 19805
30 6000 0.043 -0.1 12 0.496 0.306
33 18000 0.011 -0.073 0.029 0.252
33 30000 0.009 -0.071 -0.050 0.167
33 42000 0.017 -0.079 -0.134 -0.011
33 54000 0.026 -0.089 -0.080 -0.317
30 66000 0.042 —0.1 11 -0.331 -0.290
22 78000 0.042 -0.137 -0.086 -0.383
13 90000 0.092 -0.259 -0.096 -0.612
1.0
0.5 1
:J, 0.0 . '- ------- Upper limit
C . .
9 Lower limit
2° 95* +1970 to 1980
+ 1980 to 1990
‘1.0 l I l I I I I
5585555
0 22 § 5 5 t8 :2
Midpoint of distance band
(It!)

 

 

 

Figure 5.4: Spatial correlograms: township parcelization rates.

100

Such a polar comparison exists because interior townships, those townships
located within Kalkaska County and geometrically centered within the study area,
were systematically removed from Moran coefficient calculations as spatial lags
were increased beyond 60 kilometers. Yet, these results are still useful as they
do suggest that townships associated with Grand Traverse and Crawford
County, respectively, became increasingly dissimilar over the twenty-year period.
They also indicate a regional east/west trend had existed in the parcelization
process. Visual inspection of the parcelization rate distribution revealed higher
rates tended to occur in Grand Traverse County and lower rates tended to occur
in Crawford County in both decades. These observations indicate a
parcelization rate gradient existed with higher values occurring in the west and

lower rates occurring in the east.

5.6.2: Sample sites.

An interdistanoe matrix was calculated for all selected sample sites (n=168)
using the geometric center of each site as both a point of origin and destination.
Binary contiguity weight matrices were constructed using the reclassification
procedure discussed above (see Section 5.6.1). However, because each
sample site was smaller than any township, l was able to partition the range of
distances separating sample sites into uniform distance bands of 6000 meters.
The use of shorter spatial lags provided for more detailed examinations of the

spatial patterns of APS values and annual parcelization rates.

101

Table 5.10 highlights values of Moran’s I calculated for each spatial lag. Figure
5.5 graphically illustrates the spatial correlograms calculated for each temporal
distribution of APS values. For 1970 and 1980 dates, adjacent sample sites
exhibited a significant similarity in average parcel sizes. Yet, such similarity
disappeared in the second spatial lag and erratic and near-random patterns were
observed into the last distance band. By 1990, the spatial pattern of average
parcel sizes became nearly indistinguishable from random for all spatial lags -
including the first lag where significant values were expected to have occurred.
The lack of any significant and moderate measure of negative autocorrelation
along the correlogram suggests no regional trend or periodicity in the parcel size

distribution was detectable, at least not with this scale of analysis.

102

Table 5.10: Spatial autocorrelation results: sample site values of APS.

Confidence Interval

Moran Statistic

 

 

 

 

 

 

 

 

fl Midpoint Upgr limit Lower limit 1970 1989
167 3000 0.007 -0.019 0.212 0.325
168 9000 0.001 -0.013 0.028 -0.015
168 15000 0.000 -0.012 -0.014 -0.015
168 21000 0.000 -0.012 -0.032 -0.011
168 27000 -0.001 -0.011 -0.009 -0.004
168 33000 -0.001 -0.011 -0.014 -0.009
168 39000 0.000 -0.012 -0.035 0.014
168 45000 0.000 -0.012 -0.029 -0.001
168 51000 0.000 -0.012 0.012 -0.006
168 57000 0.002 -0.014 -0.041 -0.008
165 63000 0.002 -0.014 -0.026 -0.016
148 69000 0.002 -0.016 0.008 -0.004
128 75000 0.002 -0.017 0.030 0.013
112 81000 0.003 -0.021 0.024 0.000
92 87000 0.004 -0.027 -0.013 -0.008
72 93000 0.004 -0.032 -0.020 -0.012
56 99000 0.006 -0.042 -0.032 -0.024
1.0
0.5 1 : ------- Upper limit
:5 s 1 Lower limit
§ 0.0 . +1970
2 + 1980
-0-5 4 i —o— 1990
I
-1.0 . ...... . ...... J
5 5 § § § § § 5 g
.— R 8 E3 3 3 S
Midpoint of distance band (m)
Figure 5.5: Spatial correlograms: sample site values of APS.

103

129;)
0.025
-0.009
-0.009
0.001
-0.008
-0.009
-0.007
0.001
-0.001
0.000
-0.003
-0.003
0.005
-0.004
-0.008
-0.020
-0.031

The distribution of parcelization rates exhibited no spatial pattern for either time
period. Table 5.11 outlines the results and Figure 5.6 illustrates both
correlograms. Even though a very weak positive autocorrelation coefficient did
emerge within the first lag during the 1980s, the strength of the relationship was
so weak that its presence provides little power to explain the pattern. I note here
that both temporal functions contain many significant coefficients. However,
because almost all coefficient values exist within a range between —0.05 and
0.05, each function can only be described as very weak. I believe these

correlograms collectively betray no interpretable spatial patterns or relationships.

Table 5.11: Spatial autocorrelation results: sample site parcelization rates.

Confidence Interval Moran Statistic

 

104

Q Midpoint Qgger limit Lower limit 19703 1980s
167 3000 0.007 -0.019 0.007 0.045
168 9000 0.001 -0.013 -0.019 0.006
168 15000 0.000 -0.012 -0.006 -0.003
168 21000 0.000 -0.012 -0.022 -0.002
168 27000 -0.001 -0.011 -0.007 -0.016
168 33000 -0.001 -0.011 -0.006 -0.025
168 39000 0.000 -0.012 0.026 -0.023
168 45000 0.000 -0.012 -0.035 0.001
168 51000 0.000 -0.012 0.012 0.032
168 57000 0.002 -0.014 -0.046 0.048
165 63000 0.002 -0.014 0.012 -0.001
148 69000 0.002 -0.016 0.029 0.010
128 75000 0.002 -0.017 0.003 -0.061
112 81000 0.003 -0.021 0.004 0.010
92 87000 0.004 -0.027 -0.054 -0.034
72 93000 0.004 -0.032 0.017 -0.066
56 99000 0.006 -0.042 -0.010 -0.072

 

1.0

 

0.5 -

Moran's I

 

0.0 W

 

 

PN

 

TTrIlII

555

Midpoint of distance band

I

5

------- Upper limit
Lower limit
+ 1970 to 1980
+ 1980 to 1990

 

 

Figure 5.6: Spatial correlograms: sample site parcelization rates.

5.6.3: Survey sections.

An interdistance matrix was calculated for all selected sections using the
geometric center of each section as both a point of origin and destination.
Uniform distance bands of 3000 meters were used to reclassify the interdistance
matrix into the appropriate set of binary contiguity weight matrices. Tables 5.12
and 5.13 highlight the autocorrelation results for APS values and parcelization

rates, respectively. Also, Figures 5.7 and 5.8 illustrate each set of correlograms,

respectively.

105

 

Table 5.12: Spatial autocorrelation results: survey section values of APS.

p
1172
1172
1169
1169
1168
1166
1164
1162
1160
1159
1157
1155
1153
1151
1149
1147
1146
1144
1142
1140
1106
1050
989
927
864
803
740
676
611
552
491
436
376
319
259
199
137
76

1500
4500
7500
10500
13500
16500
19500
22500
25500
28500
31500
34500
37500
40500
43500
46500
49500
52500
55500
58500
61500
64500
67500
70500
73500
76500
79500
82500
85500
88500
91500
94500
97500
100500
103500
106500
109500
112500

0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Confidence Interval
Midpoint Upper limit Lower limit

-0.003
-0.002
-0.002
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.003
-0.003
-0.003
-0.004
-0.004
-0.005
-0.005
-0.006
-0.008
-0.01 0
-0.01 5
—0.027

106

Moran Statistic

1919
0.245
0.098
0.087
0.058
0.038
0.029
0.013

-0.006
-0.013
-0.015
-0.018
-0.031
-0.027
-0.024
-0.010
-0.035
-0.042
-0.031
-0.029
-0.014
-0.024
-0.019
-0.028

0.000
0.008
0.009
0.016
0.001

-0.001

0.016

0.013
-0.013
0.006
0.003
-0.024

0.030
-0.010
-0.025

1.9.59
0.189
0.095
0.077
0.059
0.038
0.019
0.005
-0.015
-0.016
-0.011
-0.020
-0.022
-0.023
-0.022
-0.010
-0.029
-0.033
-0.025
-0.035
-0.013
-0.014
-0.018
-0.010
-0.019
0.008
0.002
0.024
0.008
-0.008
0.014
0.017
0.022
0.031
0.018
-0.028
0.000
0.013
-0.014

fig).
0.214
0.122
0.110
0.082
0.054
0.036
0.014
-0.016
-0.025
-0.032
-0.040
-0.039
-0.044
-0.047
-0.030
-0.037
-0.038
-0.030
-0.033
-0.004
0.009
0.010
0.003
-0.018
0.027
0.033
0.035
0.010
-0.014
0.015
0.019
0.020
0.017
0.004
-0.046
-0.019
0.029
0.002

Table 5.13: Spatial autocorrelation results: survey section parcelization rates.

p
1172
1172
1169
1169
1168
1166
1164
1162
1160
1159
1157
1155
1153
1151
1149
1147
1146
1144
1142
1140
1106
1050
989
927
864
803
740
676
611
552
491
436
376
319
259
199
137
76

1500
4500
7500
10500
13500
16500
19500
22500
25500
28500
31500
34500
37500
40500
43500
46500
49500
52500
55500
58500
61500
64500
67500
70500
73500
76500
79500
82500
85500
88500
91500
94500
97500
100500
103500
106500
109500
112500

0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Confidence Interval
Midpoint Upper limit Lower limit

-0.003
-0.002
-0.002
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.003
-0.003
-0.003
-0.004
-0.004
-0.005
-0.005
-0.006
-0.008
-0.010
-0.015
-0.027

107

Moran Statistic

1970s
0.016
-0.003
0.006
-0.001
-0.007
0.005
0.000
-0.001
0.007
-0.007
-0.004
-0.005
0.007
-0.010
0.006
-0.009
-0.014
0.013
-0.012
0.006
-0.006
-0.011
0.007
0.008
0.003
0.004
0.000
0.001
0.003
0.002
-0.002
0.001
-0.007
0.003
0.005
0.002
-0.009
-0.016

19805
0.063
0.025
0.001
-0.003
-0.004
-0.005
-0.004
-0.008
-0.002
0.006
-0.002
0.000
0.003
-0.003
-0.001
-0.010
-0.006
-0.002
0.001
0.005
0.005
0.006
0.006
0.007
-0.013
-0.009
-0.001
-0.007
-0.017
0.006
-0.012
0.007
0.001
-0.003
-0.008
0.007
0.008
-0.015

 

 

1.0

(L5

....... Upper limit
0.0 _, Lower limit
—-I— 1970

-0.5 .4 +1980
—0— 1990

 

Moran's l

 

 

 

-1-0 IIIII[IIIUIIUIIIIIIII’ITIUTT‘TVII‘IIII

555 55

Midpoint of distance band (m)

61500
85500

13500

 

 

 

Figure 5.7: Spatial correlograms: survey section values of APS.

 

 

....... Upper limit
Lower limit
+ 1970 to 1980
.05 .. +1980t0 1990

 

 

 

 

-1-0 [T1IIIIIfTTIIIIITIIIIIIIIIIIIIIIIIII
§ § :0 § § § § 8

ID ('0

N

1- N
O)
and

9
10950

s-NC‘OVCD

Midpoint of distance
(m)

5°
co
b

 

 

 

Figure 5.8: Spatial correlograms: survey section parcelization rates.

108

With respect to parcel sizes, positive spatial autocorrelation appears to have
existed at shorter distances for all three dates. Although first lag statistics
indicate only weak positive relationships, such patterns persisted into the
seventh spatial lag. Beyond the seventh spatial lag, the pattern becomes nearly
indistinguishable from random. No spatial pattern is observable within any
distance band beyond 21 kilometers for any date. As a whole, the correlograms
provide a slight indication of landscape periodicity but, Moran values associated

with lags beyond the first lag are so weak they command little attention.

With respect to annual rates of parcelization, a spatial pattern of positive
autocorrelation seems to have appeared during the 1980s within the first spatial
lag - a lag where no such pattern had been evident during the previous decade.
However, a coefficient value of 0.063 is very weak and does not imply a strong
pattern existed. Yet, the emergence of positive spatial autocorrelation within the
first lag can serve to suggest that sections near to one another exhibited slightly

stronger similarities between average rates of change than had existed before.

5.7: Forest cover.

The spatial extent of the study area is approximately 420 kha. Basic image

statistics have been extracted and examined to provide a foundation for this

analysis of forested land covers (see Table 5.14).

109

Table 5.14: Landscape metrics describing forest patch and core distributions.

Forest
Landscape
area (kha)

Forest area
(kha)

%Landscape
as Forest

% Forest as
Private

% Forest as
Public

% Forest as
other

Number of
patch areas

Mean patch
area (ha)

Patch area
std. dev. (ha)

Coefficient of
variation

 

1973 1985 1991
420 420 420
282 298 302

67 71 72
40 39 40
45 46 47
15 15 13
5899 4607 4890
19 25 25
163 205 221
8.5 8.1 8.9

Core Area

Landscape
area (kha)

Core area
(kha)

%Landscape
as Core

% Core as
Private

% Core as
Public

% Core as
other

Number of
core areas

Mean core
area (ha)

Core area
std. dev. (ha)

Coefficient of
vafiafion

 

1973 1985
420 420
111 168

26 40
34 33
51 52
15 15

3117 2314

12 24
60 105
4.9 4.4

191

420

160

38

35

53

12

2571

22

89

4.1

Mapped image classes (e.g. forested, non-forested, open water, clouds, and

background) and the distribution of their areas indicate each temporal landscape

was moderately heterogeneous. Descriptive statistics show forests were the

dominant land cover type and occupied no less than two-thirds of the landscape.

Private forest owners controlled approximately forty-percent of all forested areas
and public agencies, in aggregate controlled approximately forty—five percent.

The balance of forested lands was held by other ownership institutions.

Forest patches ranged in size from 0.36 ha (one satellite image pixel) to 54.9
kha, a maximum size observed on the 1985 landscape. Although mean patch
sizes tended near 25 ha, most patch areas (at least 63 percent) were less than 3
ha. These descriptions indicate the majority of forest patches were very small
while a majority of forested area existed as large contiguous blocks, hence
describing highly and positively skewed distributions of forest patch areas. Patch
area variation statistics (see Table 5.14) suggest variation among patch sizes

increased over the eighteen-year period.

Descriptive analysis of forest core areas indicate no more than 26 kha of interior
forest area (i.e., core area) existed after a 100 meter edge was removed from all
patches. No more than 56 percent of the all forest in the study area could have
been considered interior forest because nearly one-half of all forested areas
were disturbed by edge effects. Mean core area and coefficient of variation
statistics indicate the average size of core areas increased over time (albeit a
small decrease was observed from 1985 to 1991) while variation in core areas
decreased, respectively. These descriptions suggest the distribution of interior
forest areas, with respect to size and without respect to geography, tended

towards homogeneity over time. In summary, the numbers do not illustrate a

111

clear picture of forest area trends as variation in patch areas increased while

variation in core areas decreased during the same period. Also, both increases

and decreases were observed in patch and core areas even though forest

growth trends were observed between all three dates. These trends suggest

forest structure is not directly tied to the amount of forest present.

5.8: Forest cover - hypothesis III.

I tested for change in the amount of private lands as forest because Leatherberry

(1994) and Wyckoff (1995) presented conflicting views of forest cover. I used a

two-tailed matched pairs t test instead of a one-tailed test to test the hypothesis

that average percentages of private land as forested had changed over time

because I had no basis on which to build a directional argument. Hypothesis III

was tested between dates and at all spatial scales. Table 5.15 lists statistical

test results.

Table 5.15: Average percent private land as forest and changes for all scales.

19$
54.0
57.2
52.2
59.1
57.4

1973 to 1985
& Change
55.7 1.7
59.6 2.3
55.1 2.9 *
62.1 3.0 *
59.3 1.9 *

198.35
55.7
59.6
55.1
62.1
59.3

1985 to 1991
E1 @695
58.7 3.0
61.9 2.3
57.6 2.5 *
64.1 2.0 *
61.5 2.2 *

* Denotes a statistically significant change with 95 percent confidence.

The county level results, although indicating a trend of increasing forest cover,
failed to meet the requirements of statistical significance for each date.
Therefore, I failed to reject null hypothesis III at this scale. However, as each
forested landscape was examined with smaller sampling units and at greater
frequencies, matched pairs ttest results indicate a significant mean difference
exists between mean percent forest values. These results were significant at the
95 percent confidence level and null hypothesis III was rejected for each of these
scales. Forest growth trends can be inferred by comparing mean values of

percent forest cover over time at the township, sample site, and section scales,.

Table 5.16 summarizes the results of the sample site and section level analyses.
Both scales produced results that indicate more areas experienced forest growth
than forest loss, and no more than 35 percent of areas sampled showed signs of
forest decline. Contrary to Wyckoff's (1995) assertion that a trend of forest

decline is beginning, the number of areas in decline decreased over time.

Table 5.16: Percent forest summary for small sampling units.

Sglg p %lncrease %Decrease ° oNo Chang_e
Sample sites

1973 to 1985 168 68 32 0

1985 to 1991 168 71 29 0

1973 to 1991 168 74 26 0
Survey sections

1973 to 1985 1176 65 35 0

1985to1991 1176 68 31 1

1973 to 1991 1176 69 31 0

113

Table 5.17 outlines temporal percent private land as forest cover values for each
observation unit in the region, county, and township level analyses. In most
cases, trends of forest growth were observed over time. Townships such as
Bear Lake, Blue Lake, Union, and Fife Lake exhibited eighteen-year growth

trends. Only Grayling Township exhibited an eighteen-year trend of forest loss.

However, Grayling Township is the largest township in Crawford County and it
contains many large public land areas. l was surprised to see such a large
degree of forest loss in a township that contained so many managed areas.
Additional research revealed several large forest fires occurred in areas in or
around Grayling Township between 1985 and 1995 (USDA Forest Service,
1997b). Specifically, the Stephan Bridge Road fire of 1990 burned 2450 ha
(6000 acres) of private and public forest in Crawford County (Winter and Fried,
1997). Most forest loss associated with the Stephan Bridge Road fire occurred
in Grayling Township (see Figure 5.9) and thus, contributed to the loss trend
observed between the 1985 and 1991 satellite images. However, without more
spatially explicit information about other fire disturbances that occurred between
1973 and 1991, the possible extent of forest loss in Grayling Township (or any

other township) due to fire is unknown.

114

Table 5.17: Summary of percent private land as forest for political units.

115

County Percent
Township 19]_3 1185 19_1
Region totals 53.95 55.69 58.69
Crawford 74.08 77.56 75.56
Beaver Creek 69.49 75.25 70.19
Frederic 72.97 77.49 77.52
City of Grayling 28.34 36.42 23.71
Grayling 78.05 75.29 71 .93
Lovells 80.69 83.66 81 .70
Maple Forest 57.57 63.67 64.38
South Branch 74.33 84.17 83.00
Grand Traverse 43.75 40.24 44.18
Acme 31.64 26.03 34.05
Blair 41.01 36.64 39.58
East Bay 46.88 44.16 49.33
Fife Lake 48.94 55.59 58.24
Garfield 27.71 21.42 25.01
Grant 56.66 44.57 48.99
Green Lake 59.85 59.14 61.92
Long Lake 42.74 40.73 44.61
Mayfield 41.52 27.43 31.13
Paradise 46.24 48.21 49.82
Peninsula 29.22 25.05 27.45
Traverse City 16.35 27.49 24.55
Union 63.01 72.59 75.43
Whitewater 42.69 42.01 49.00
Kalkaska 53.83 60.89 65.89
Bear Lake 76.59 85.54 87.18
Blue Lake 72.56 76.06 79.91
Boardman 41.05 48.99 54.53
Clearwater 53.00 61 .90 66.50
Cold Springs 78.20 81.60 83.80
Excelsior 49.07 57.98 64.33
Garfield 54.70 60.45 64.41
Kalkaska 47.59 51 .98 59.64
Oliver 60.94 66.10 72.00
Orange 47.07 55.83 60.90
Rapid River 43.06 52.31 56.38
Springfield 43.94 52.06 59.22

 

Legend

Burn area
Forested .
Non forested . '
Open water a '
Clouds

Township
Boundary

  
 

E I I E} E

Scalein 3 0 3 6 9 12
Kilometers

 

Source: Fried (1999)

 

Figure 5.9: Map of the Stephan Bridge Road Fire.

All townships other than Grayling demonstrated some sort of fluctuation with
either gains or losses occurring during the first period followed by a reverse trend
during the second period. The region as a whole however, exhibited a

statistically significant forest growth trend over the entire eighteen-year period.

116

5.9: Forest cover - hypothesis IV.

I hypothesized the annual rate of change in forest cover had changed over time
within the study area. All two-tailed matched pairs ttest results (see Table 5.18)
indicate modest forest growth trends occurred between 1973 and 1991.
However, only the section level results for the period between 1985 and 1991,
derived using a very large sample (n=1176), met the requirements for statistical
significance. Notwithstanding, each calculated mean value was a positive value
and increased over time. Therefore, one can infer forest growth occurred at a

faster rate during the 1980s than during the 19706.

Table 5.18: Average annual forest change rates for all scales.

_Sqa_!§ 1973 to 1985 1985 to 1991 Cha_nge
Region 0.174 0.500 0.326
County 0.234 0.385 0.151
Township 0.287 0.417 0.130
Sample 0.297 0.329 0.032
Section 0.189 0.458 0.269 *

* Denotes a statistically significant change with 95 percent confidence.

Tables outlining the region, county, and township results or summarizing sample
site and section level results are not included in this section because hypothesis
IV was tested with a two-tailed test of differences, rather than a directional one-
tailed test of differences. The posting of individual values would not contribute to

an explanation of these test results.

117

5.10: Forest fragmentation - hypothesis V.

According to the Michigan Society of Planning Officials Future Trend Project
(Wyckoff, 1995), forest fragmentation has increased in Michigan. I tested this
hypothesis within the study area by using a one-tailed matched pairs ttest to test
for a significant mean increase between calculated CF values. Recall that CF
values are estimates of forest fragmentation and have values that range
between zero and one. Values near one indicate highly fragmented forest areas
and values near zero indicate unfragmented forest areas (see Appendix F for a
complete description). Hypothesis V was tested between dates and at all spatial

scales. Table 5.19 highlights the results.

Table 5.19: Forest fragmentation changes for all scales (CF units).

1973 to 1985 1985 to 1991
Scale 1973 1985 Chapgg 1985 1991 Chagge
Region 0.66 0.52 -0. 14 0.52 0.54 0.02

County 0.66 0.52 —0.137 * 0.52 0.54 0.02

Township 0.68 0.56 -0.12 * 0.56 0.58 0.02 *
Sample 0.65 0.50 -0.15 * 0.50 0.52 0.02 *
Section 0.65 0.52 —0.13 * 0.52 0.53 0.01 *

*Denotes statistically significant change with 95 percent confidence.

For all tests between sets of CF values calculated for 1973 and 1985 landscape
data, mean estimates of core area fragmentation were determined to
significantly decrease over time. These results were opposite of what was

hypothesized, therefore, I failed to reject null hypothesis V for all scales.

118

For tests between sets of values calculated for 1985 and 1991 landscape data,
mean estimates of core area fragmentation were determined to significantly
increase over time for all scales but county. Interestingly enough, this period
was the period during which the region experienced less rapid growth. I failed to
reject the null in the county example because calculated average CF values were
statistically determined not to be different. However, in the township, sample

site, and section level analyses, null hypothesis V was rejected.

Table 5.20 summarizes the results of both section and sample site level
analyses. According to the sample site results, the region experienced an
eighteen-year trend of decreasing forest fragmentation as evidenced by more
defragmented sites (80 percent) than fragmented sites (20 percent). However,
upon review of the results presented for each shorter time period, one can see
that between 1985 and 1991, more sample sites experienced forest

fragmentation (57 percent) than did forest defragmentation (43 percent).

Table 5.20: Summary of forest fragmentation for small sampling units (%).

gale p %lncrease %Decrease %No Chapgg
Sample sites

1973 to 1985 168 16 84 0

1985 to 1991 168 57 43 0

1973 to 1991 168 20 80 0
Survey sections

1973 to 1985 1176 25 73 2

1985 to 1991 1176 48 49 3

1973 to 1991 1176 26 72 2

119

The section level analysis also reveals an eighteen-year trend of decreasing
forest fragmentation. A review of both shorter trends, however, indicates two
defragmentation trends, unlike the results posted for the sample sites. Yet, one
should note the large increase in the number of survey sections that undenivent
forest fragmentation during the second period (48 percent) compared to the

number that fragmented during the first period (25 percent).

Table 5.21 outlines CF values calculated for each observation unit in the region,
county, and township scale analyses. As the numbers indicate, no dominant
trend of fragmentation or defragmentation existed over the entire eighteen-year
period. Crawford and Grand Traverse Counties exhibited trends of
defragmentation from 1973 to 1985 and trends of fragmentation from 1985 to
1991. Most townships within these two counties, with exceptions like Blair, Long
Lake, and Union Townships, exhibited similar trends. On the other hand,
Kalkaska County demonstrated an eighteen-year defragmentation trend even
though townships like Clearwater, Excelsior, and Garfield exhibited increases in

forest fragmentation between 1985 and 1991.

In general, forest fragmentation appears to have decreased throughout the
landscape between 1973 and 1991. The general pattern however, is insensitive
to the shift from a period of defragmentation that existed between 1973 and

1985 to a period of forest fragmentation that existed between 1985 and 1991.

120

Table 5.21: Summary of forest fragmentation indices for political units.

County

Township

Region totals

Crawford

Beaver Creek
Frederic

City of Grayling

Grayling
Lovells
Maple Forest
South Branch

Grand Traverse

Acme

Blair

East Bay
Fife Lake
Garfield
Grant
Green Lake
Long Lake
Mayfield
Paradise
Peninsula
Traverse City
Union
Whitewater

Kalkaska

Bear Lake
Blue Lake
Boardman
Clearwater
Cold Springs
Excelsior
Garfield
Kalkaska
Oliver
Orange
Rapid River
Springfield

1973
0.662

0.597
0.620
0.555
0.710
0.543
0.636
0.607
0.631
0.728
0.792
0.723
0.724
0.713
0.862
0.611
0.605
0.762
0.779
0.710
0.848
0.957
0.691
0.694
0.647
0.601
0.525
0.805
0.591
0.454
0.682
0.690
0.729
0.567
0.706
0.609
0.713

CF Index

1985
0.524

0.405
0.439
0.376
0.600
0.441
0.368
0.497
0.310
0.662
0.699
0.670
0.684
0.549
0.870
0.601
0.541
0.730
0.770
0.627
0.855
0.992
0.508
0.576
0.501
0.313
0.538
0.614
0.487
0.399
0.419
0.530
0.608
0.365
0.501
0.521
0.576

121

191

0.543

0.461
0.534
0.421
0.715
0.509
0.435
0.544
0.339
0.669
0.752
0.654
0.691
0.563
0.867
0.607
0.552
0.715
0.784
0.618
0.870
0.978
0.506
0.607
0.492
0.295
0.506
0.606
0.491
0.367
0.439
0.535
0.578
0.364
0.502
0.512
0.550

5.11: Forest fragmentation - hypothesis VI.

I hypothesized the annual rate of forest fragmentation had increased over the
selected eighteen-year period. As one-tailed matched pairs ttest results indicate
in Table 5.22, the average rate of forest fragmentation increased over time for all
spatial scales. Table 5.23 is provided to list region, county, and township trends
in forest fragmentation rates as well as relative rankings over time. However, as
indicated above in Section 5.10, static measures of forest fragmentation indicate
a trend of decreasing forest fragmentation during the late 1970s and a trend of
increasing forest fragmentation during the late 19805. By comparing a previous
period of forest defragmentation to a later period of forest fragmentation, the rate
of forest fragmentation will, by mathematical definition, increase over time. So,
the test of hypothesis VI was most useful in determining the statistical
significance of the mean differences between fragmentation rates over time
rather than identifying a particular direction of change. In any case, the rate of

forest fragmentation had increased from 1973 to 1991.

Table 5.22: Forest fragmentation rate and changes for all scales (CF/yr).

 

_Sg|_e 1973 to 1985 1985 to 1991 Chapgg
Region -0.012 0.003 0.015

County -0.014 0.003 0.017 *
Township -0.012 0.002 0.014 *
Sarmle -0.014 0.003 0.017 *
Section -0.013 0.001 0.014 *

* Denotes a statistically significant change with 95 percent confidence.

122

Table 5.23: Summary of forest fragmentation rates for political units (CF/yr).

County

To_wr18_hi9
Region totals

Crawford
Beaver Creek
Frederic
City of Grayling
Grayling
Lovells
Maple Forest
South Branch
Grand Traverse
Acme
Blair
East Bay
Fife Lake
Garfield
Grant
Green Lake
Long Lake
Mayfield
Paradise
Peninsula
Traverse City
Union
Whitewater
Kalkaska
Bear Lake
Blue Lake
Boardman
Clearwater
Cold Springs
Excelsior
Garfield
Kalkaska
Oliver
Orange
Rapid River
Springfield

1973 to 1985

Change

-0.012

-0.016
-0.015
-0.015
-0.009
-0.009
-0.022
-0.009
-0.027
-0.006
-0.008
-0.004
-0.003
-0.014
0.001

-0.001
-0.005
-0.003
-0.001
-0.007
0.001

0.003
-0.015
-0.010
-0.012
-0.024
0.001

-0.016
-0.009
-0.005
-0.022
-0.013
-0.010
-0.017
-0.017
-0.007
-0.011

123

Rank

24
24
15
15
30
15
33

32

27
15
10
30
22
19
28
28
12
21

1985 to 1991

Change

0.003

0.009
0.016
0.008
0.019
0.011

0.011

0.008
0.005
0.001

0.009
-0.003
0.001

0.002

-0.001
0.001

0.002
-0.003
0.002
-0.002
0.003
-0.002
0.000
0.005
-0.002
-0.003
-0.005
-0.001
0.001

-0.005
0.003
0.001

-0.005
0.000
0.000
-0.002
-0.004

Rank

(DODODOOAODN

15
12
22
15
12
27
12
24
10
24
19

27
31
22
15
31
10
17
31
19
19
24
30

5.12: Forest fragmentation - location analysis.

Numerical results of the location analysis are listed in Table 5.24. The spatial
structure of forest fragmentation, with respect to distance from Traverse City, can
be visualized in Figure 5.10. Negative sloping trends observed at shorter
distances indicate a spatial gradient of forest fragmentation existed around
Traverse City. Areas closer to the city tended to be more fragmented than those
areas located farther from the city. This fragmentation gradient existed within a
48 kilometer radius and had become steeper over time. Erratic patterns of
increases and decreases in fragmented forest conditions were observed at

distances greater than 48 kilometers for all three dates.

Within the 48 kilometer radius, observed increases in negative slope indicate
decreases in forest fragmentation over time. Also, the effect of distance on
fragmentation conditions appears to have increased over time, meaning the
magnitudes of defragmentation increased with increased distance from Traverse
City. It is significant to note here that most of the change observed in the
fragmentation gradient occurred between 1973 and 1985. Little change was

observed in the gradient between 1985 and 1991.

124

Table 5.24: Fragmentation indices for concentric bands around Traverse City.

Band (km)
0 to 3
3 to 6
6 to 9
9 to 12
12 to 15
15 to 18
18 to 21
21 to 24
24 to 27
27 to 30
30 to 33
33 to 36
36 to 39
39 to 42
42 to 45
45 to 48
48 to 51
51 to 54
54 to 57
57 to 60
60 to 63
63 to 66
66 to 69
69 to 72
72 to 75
75 to 78
78 to 81
81 to 84
84 to 87
87 to 90
90 to 93
93 to 96
96 to 99
99 to 102

CF METRIC
.1_97_0 1_98_Q
0.959 0.996
0.781 0.794
0.794 0.786
0.805 0.756
0.691 0.608
0.671 0.612
0.740 0.674
0.724 0.647
0.665 0.559
0.725 0.594
0.674 0.565
0.777 0.633
0.704 0.593
0.666 0.472
0.559 0.463
0.537 0.328
0.552 0.401
0.657 0.413
0.469 0.335
0.646 0.484
0.744 0.535
0.457 0.353
0.627 0.393
0.553 0.381
0.652 0.518
0.615 0.434
0.467 0.457
0.442 0.421
0.533 0.389
0.688 0.354
0.601 0.334
0.664 0.277
0.750 0.304
0.322 0.145

1.99.0
0.991
0.785
0.796
0.757
0.629
0.606
0.688
0.641
0.564
0.576
0.548
0.620
0.585
0.481
0.474
0.316
0.360
0.379
0.336
0.444
0.552
0.427
0.431
0.464
0.570
0.503
0.499
0.524
0.429
0.460
0.360
0.315
0.329
0.124

125

 

1.00 _

 

 

0.75 -‘
.o
g 0.50 4 +CF1973
u. +c1= 1985
0 +CF 1991
0.25 -

 

 

 

0.00 IIUIUIIUIIIII'TTFFIIIIIFIUTIIIIIT

1.5 16.5 31.5 46.5 61.5 76.5 91.5
Midpoint of distance band (km)

Figure 5.10: Forest fragmentation functions for Traverse City.

As reported in Section 5.5, the parcel size distance functions observed for
Traverse City indicated the urban extent increased over time from the third
distance band in 1973 to include the entire study area by 1985. The area within
this large region was reasonably expected to exhibit signs of increased forest
fragmentation as urban pressures had come to influence forested lands.
However, as the distance functions in Figure 5.10 and Table 5.24 indicate, forest
fragmentation conditions decreased over the eighteen-year period, even though
small increases were observed between 1985 and 1991. This result does not
suggest forest fragmentation was directly related to urbanization or urban sprawl

but, perhaps, that the opposite is true.

126

5.13: Forest fragmentation - spatial analysis.

Spatial patterns of static forest fragmentation conditions and average annual
rates of forest fragmentation were measured using spatial autocorrelation
analysis. Spatial correlograms were calculated for the township, sample site,
and section level forest data analyses. Observed peaks and depressions in
graphed autocorrelation functions were used to describe the effects of distance
on pattern at each time. Also, distances at which spatial patterns were
statistically indiscernible from random patterns were used to infer the scale of
forest fragmentation. The same sets of binary contiguity weight matrices used
during parcel data analyses were used during forest data analysis with respect to

appropriate distance bands and sampling schemes.

5.13.1: Townships.

Uniform distance bands of 12000 meters were used to sample township level
forest data. Moran coefficients calculated for each distance band are listed in
Table 5.25. Moran coefficient values were plotted against distance band
midpoints and are presented in Figure 5.11. Moderate peaks of positive spatial
autocorrelation observed at shorter distances imply a simple adjacency effect
existed as nearby townships tended to exhibit more similar forest conditions than

did distant townships.

127

Table 5.25: Spatial autocorrelation results: township CF indices.

Confidence Interval

Moran Statistic

 

 

 

 

 

 

 

 

_l‘_l Midpoint Upper limit Lower limit 1973 1985 1991
30 6000 0.043 -0.112 0.515 0.659 0.686
33 18000 0.011 -0.073 0.323 0.442 0.441
33 30000 0.009 -0.071 0.133 0.194 0.108
33 42000 0.017 -0.079 -0.250 -0.133 -0.211
33 54000 0.026 -0.089 -0.482 -0.504 -0.577
30 66000 0.042 -0.1 1 1 -0.318 -0.399 -0.279
22 78000 0.042 -0.137 -0.474 -0.498 -0.328
13 90000 0.092 -0.259 -0.048 -0.569 -0.510
1.0
0.5 4
_ ------- Upper limit
'2 0.0 - """""""""""" Lower limit
(0
'5 -—-— 1973
2 43.5 ~ +1985
—0— 1991
-1.0 .
H8 0
55 55 5 5
Midpoint of distance band (m)

 

 

 

Figure 5.11: Spatial correlograms: township CF indices.

For all three dates, coefficient values declined as lag distances were increased
to 60 kilometers. Because zero autocorrelation can be inferred from Figure 5.11
at approximately 36 kilometers, the scale of static fragmentation conditions can

be considered to have been 36 kilometers. The consistent indirect relationship

128

between autocorrelation and distance suggests a stable spatial and temporal
landscape gradient existed between townships separated by distances less than
60 kilometers. Moran coefficients associated with distances greater than 60
kilometers suggest the spatial structure of fragmentation fluctuated over time at
greater distances. However, as higher order spatial lags were tested, fewer and
fewer townships representing Kalkaska landscape patterns were included during
analysis. As a result, observed fluctuations in Moran coefficient values
measured at distances greater than 60 kilometers cannot be discriminated
between those fluctuations induced by changes in sample size and those by real

differences in forest structure (see Table 5.25).

Analysis of average annual fragmentation rates revealed interesting distance
relationships. Table 5.26 outlines values of Moran’s I calculated for each spatial

lag and Figure 5.12 graphically illustrates the results.

Table 5.26: Spatial autocorrelation results: township fragmentation rates.

Confidence Interval Moran Statistic

p Midpoint Upper limit Lower limit 19705 19805
30 6000 0.043 -0.112 0.611 0.104
33 18000 0.011 -0.073 0.240 0.168
33 30000 0.009 -0.071 -0.001 0.051
33 42000 0.017 -0.079 -0.021 -0.294
33 54000 0.026 -0.089 -0.283 0.014
30 66000 0.042 -0.111 -0.074 0.011
22 78000 0.042 -0.137 -0.054 -0.641
13 90000 0.092 -0.259 -0.897 -0.761

129

 

 

 

_ ------- Upper limit
.3 Lower limit
g + 1973 to 1985
5 —.— 1985 to 1991

 

 

 

 

-1.o . . . I . t f

5 5 5 5 5 5 5 5

Midpoint of distance band
(m)

 

 

 

Figure 5.12: Spatial correlograms: township fragmentation rates.

In general, both functions yielded steep autocorrelation functions that signified
steep fragmentation rate gradients existed on the landscape over time. Positive
coefficients were measured at short distances and negative coefficients were
measured at greater distances. However, a peak in autocorrelation existed in
the earlier function between the 66 and 78 kilometer bands. This peak is
important because is represents a deviation from the general landscape trend.
The later function nearly mirrors the earlier function but, with two notable
exceptions. First, the level of spatial dependency associated with nearby
townships decreased sharply. The values of Moran’s I in the first spatial lag
dropped from a moderate 0.611 to a weak 0.104. This sharp drop implies rates
of fragmentation showed a weaker adjacency effect over short distances than

they did before. Second, the peak in autocorrelation shifted from the 66 and 78

130

kilometer lags to the 54 and 66 kilometer lags. This shift implies the deviation in
the landscape gradient could be observed over shorter distances and with
greater frequency. This deviation in pattern, is similarly located, with respect to
distance to the change in spatial pattern observed during township level parcel

analysis.

5.13.2: Sample sites.

Uniform distance bands of 6000 meters were used to sample forest data during
sample site autocorrelation analysis. Table 5.27 lists Moran coefficient values
calculated for each spatial lag. Values of Moran’s l were plotted against distance
band midpoints and are illustrated in Figure 5.13. For all three dates, each
correlogram indicates a negative sloping trend from moderate and positive
coefficients at short distances to moderate and negative coefficients at long
distances. Because these correlograms remained relatively stable over both
space and time, they provide further evidence to support the fragmentation
gradient identified in Section 5.13.1. Fluctuations in the spatial structure of CF
indices at distances greater than 51 kilometers are also consistent with those
observed at the township scale. From 1973 to 1985, forest conditions became
more dissimilar between dates, then rebounded towards randomness by 1991.

This fluctuation was most evident in the 60 to 72 kilometer lag.

131

Table 5.27: Spatial autocorrelation results: sample site CF indices.

Confidence interval

Moran Statistic

 

 

 

 

 

 

 

 

p Midpoint Upgr limit Lower limit 1973 1985
167 3000 0.007 -0.019 0.384 0.595
168 9000 0.001 -0.013 0.177 0.454
168 15000 0.000 -0.012 0.101 0.361
168 21000 0.000 -0.012 0.138 0.300
168 27000 -0.001 -0.011 0.139 0.270
168 33000 -0.001 -0.011 0.092 0.207
168 39000 0.000 -0.012 0.021 0.112
168 45000 0.000 -0.012 -0.059 0.004
168 51000 0.000 -0.012 -0.185 -0.224
168 57000 0.002 -0.014 -0.170 -0.330
165 63000 0.002 -0.014 -0.181 -0.315
148 69000 0.002 -0.016 —0.214 -0.291
128 75000 0.002 -0.017 -0.284 -0.442
112 81000 0.003 -0.021 -0.298 -0.573
92 87000 0.004 -0.027 -0.236 -0.714
72 93000 0.004 -0.032 -0.022 -0.782
56 99000 0.006 -0.042 0.034 -0.547
1.0

0.5 J ~ ------- Upper limit
_ Lower limit

5’ 0.0 5 ~ —I— 1973

g + 1985

5 415 - _._ 1991

‘1.0 l l l I I I I I f
55 5'5 5'5 5 5 5
Midpoint of distance band (m)

 

 

Figure 5.13: Spatial correlograms: sample site CF indices.

132

19.94
0.585
0.385
0.246
0.187
0.158
0.122
0.038

-0.033
-O.235
-O.320
-0.198
-0.088
-O.192
-0.338
-0.553
-0.655
-O.428

Sample site autocorrelation analysis of forest fragmentation rates also revealed
a general landscape trend existed over time. Table 5.28 outlines the calculated
set of Moran statistics and Figure 5.14 illustrates the correlograms. Again,
positive and significant coefficients were measured at short distances and
negative coefficients were measured at greater distances. However, finer
resolution distance bands had revealed peculiar changes in an othewvise stable
spatiotemporal gradient. The earlier function exhibited small peaks in
autocorrelation at the 45 and 75 kilometer lags, which signify two irregularities, or
deviations from the general landscape trend. Although these deviations were not
as large as those observed during township analysis, the general location along
the distance axis had remained about the same. The peaks in the pattern also
suggest a sort of ‘leap-frog’ effect as places characterized by higher (lower)
fragmentation rates existed between places characterized by lower (higher)
fragmentation rates. Yet, these deviations disappeared in the later correlogram.
In general, the changes observed over time imply a trend with distinct local
variations was transformed into a more general landscape trend. The later
pattern appears smoother and indicative of a broader spatial gradient of

fragmentation rates.

133

Table 5.28: Spatial autocorrelation results: sample site fragmentation rates.

Confidence Interval

Moran Statistic

 

 

 

 

 

 

(m)

 

 

p Midpoint Upper limit Lower limit 1970s 1980s
167 3000 0.007 -0.019 0.531 0.308
168 9000 0.001 -0.013 0.288 0.198
168 15000 0.000 -0.012 0.106 0.188
168 21000 0.000 -0.012 0.093 0.110
168 27000 -0.001 -0.011 0.068 0.076
168 33000 -0.001 -0.011 0.028 0.012
168 39000 0.000 -0.012 0.017 -0.040
168 45000 0.000 -0.012 0.073 -0.105
168 51000 0.000 -0.012 -0.058 -0.144
168 57000 0.002 -0.014 -0.155 -0.153
165 63000 0.002 -0.014 -0.106 -0.121
148 69000 0.002 -0.016 -0.024 -0.111
128 75000 0.002 -0.017 0.006 -0.145
112 81000 0.003 -0.021 -0.154 -0.185
92 87000 0.004 -0.027 -0.411 -0.202
72 93000 0.004 -0.032 -0.600 -0.179
56 99000 0.006 -0.042 -0.634 -0.122
1.0
_ ------- Upper limit
5 Lower limit

‘5“ + 1973 to 1985
5 + 1985 to 1991

'1.0 I T I I T I I I l I

5 5 5 5 5 5 ;

"’ g— R g «‘3 8 g E 8 !

Midpoint of distance band 1

i

 

 

Figure 5.14: Spatial correlograms: sample site fragmentation rates.

134

5.13.3: Survey sections.

Survey section forest data were sampled using uniform distance bands 3000
meters wide. Correlograms calculated at this scale provided the most detailed
look at the structure of spatially distributed CF indices. Graphed correlograms
are illustrated in Figure 5.15 and spatial autocorrelation test results are outlined
in Table 5.29. The inverse relationship between spatial autocorrelation and
distance characterized in the township and sample site analyses was also

evident in the section scale correlograms.

 

 

....... Upper limit
Lower limit
—I— 1973
+ 1985

I —0—1991
-1.0-

 

 

Moran’s l

 

 

 

‘— 1- N O") V E N co 0) ‘-
Midpoint of distance band (m)

 

 

Figure 5.15: Spatial autocorrelation results: survey section CF indices.

135

Table 5.29: Spatial autocorrelation results: survey section CF indices.

p
1172
1172
1169
1169
1168
1166
1164
1162
1160
1159
1157
1155
1153
1151
1149
1147
1146
1144
1142
1140
1106
1050
989
927
864
803
740
676
611
552
491
436
376
319
259
199
137
76

1500
4500
7500
10500
13500
16500
19500
22500
25500
28500
31500
34500
37500
40500
43500
46500
49500
52500
55500
58500
61500
64500
67500
70500
73500
76500
79500
82500
85500
88500
91500
94500
97500
100500
103500
106500
109500
112500

0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Confidence Interval
Midpoint Upper limit Lower limit

-0.003
-0.002
—0.002
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.003
-0.003
-0.003
-0.004
-0.004
-0.005
-0.005
-0.006
-0.008
-0.010
-0.015
-0.027

136

Moran Statistic

1573.
0.370
0.161
0.076
0.060
0.041
0.048
0.052
0.058
0.073
0.064
0.042
0.037
0.035
0.013
-0.017
-0.051
-0.080
-0.071
-0.079
-0.078
-0.087
-0.061
-0.079
-0.131
-0.146
-0.141
-0.166
-0.144
-0.118
-0.117
-0.022

0.007
-0.050
-0.070

0.013
0.029

-0.004
0.004

19.8.5
0.484
0.276
0.222
0.209
0.191
0.160
0.143
0.152
0.145
0.132
0.106
0.093
0.068
0.042
0.011
-0.036
-0.067
-0.111
-0.138
-0.142
-0.162
-0.157
-0.143
-0.168
-0.212
-0.265
-0.306
-0.356
-0.428
-0.533
-0.564
-0.579
-0.652
-0.624
-0.535
-0.357
-0.231
-0.108

L991
0.453
0.253
0.200
0.174
0.155
0.125
0.110
0.108
0.094
0.081
0.060
0.047
0.029
0.011
-0.016
-0.058
-0.074
-0.114
-0.134
-0.121
-0.107
-0.085
-0.043
-0.054
-0.089
-0.136
-0.170
-0.229
-0.293
-0.407
-0.447
-0.467
-0.527
-0.509
-0.430
-0.274
-0.176

0.060

Again, the spatial structure of the fragmentation gradient appeared relatively
stable over both space and time as the functions coincide at many distances.
However, the spatial patterns exhibited by the 1985 and 1991 CF distributions
are visibly different from the 1973 distribution in two important ways. First,
stronger positive autocorrelation coefficients and lesser instantaneous slopes
within the first twelve spatial lags suggest distance played a weaker role in the
fragmentation process over time. Given the forest growth trend that occurred
during this time period, coalescence between neighboring forest patches could
have reduced the amount of abruptness that existed, and subsequently relaxed
the distance decay effect. And second, much stronger negative Moran
coefficients were recorded for lags greater than 75 kilometers, which indicate a
steeper fragmentation gradient appeared at greater distances. Because those
sections separated by at least 75 kilometers represent sections located within
Crawford and Grand Traverse Counties, one could infer forest fragmentation
conditions within these counties changed over time and the two counties became

increasingly dissimilar.

Spatial autocorrelation analysis of average annual fragmentation rates revealed
spatial patterns similar to those revealed during township and sample site
analyses. Table 5.30 outlines values of Moran’s I calculated for each spatial lag

and Figure 5.16 graphically illustrates the results.

137

Table 5.30: Spatial autocorrelation results: survey section fragmentation rates.

p
1172
1172
1169
1169
1168
1166
1164
1162
1160
1159
1157
1155
1153
1151
1149
1147
1146
1144
1142
1140
1106
1050
989
927
864
803
740
676
611
552
491
436
376
319
259
199
137
76

1500
4500
7500
10500
13500
16500
19500
22500
25500
28500
31500
34500
37500
40500
43500
46500
49500
52500
55500
58500
61500
64500
67500
70500
73500
76500
79500
82500
85500
88500
91500
94500
97500
100500
103500
106500
109500
112500

0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Confidence Interval
Midpoint Upper limit Qwer limit

-0.003
-0.002
-0.002
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.003
-0.003
-0.003
-0.004
-0.004
-0.005
-0.005
-0.006
-0.008
-0.010
-0.015
-0.027

138

Moran Statistic

1970s
0.325
0.221
0.156
0.100
0.072
0.060
0.051
0.050
0.028
0.030
0.009
-0.008
-0.008
-0.018
-0.014
-0.023
-0.013
-0.044
-0.035
-0.042
-0.024
-0.016
0.007
0.024
0.044
0.032
-0.007
-0.044
-0.124
-0.189
-0.256
-0.380
-0.478
-0.571
-0.644
-0.619
-0.456
-0.183

1980s

0.143

0.084

0.062
0.059

0.050
0.062

0.052

0.040

0.038

0.029

0.011
-0.002
-0.017
-0.020
-0.034
-0.031
-0.036
-0.038
-0.032
-0.057
-0.051
-0.030
-0.048
-0.045
-0.040
-0.043
-0.061
-0.047
-0.053
-0.094
-0.043
-0.063
-0.112
-0.059
-0.124
-0.056
-0.065
-0.088

 

 

....... Upper limit

 

 

 

 

g Lowerlimit

5 +1973to1985

5 +1985 to 1991 .
-1-0 IYIWIIIIIITIIIIIIIIIT‘II'IITITIIIIII l

 

 

5.55555 555 l

9 co 9} 25 l
l

Midpoint of distance band I
(m) ,

 

 

Figure 5.16: Spatial correlograms: survey section fragmentation rates.

Section level autocorrelation analysis results support the existence of a general
landscape trend, or gradient, of forest fragmentation rates. Again, positive
coefficients were associated with shorter distances and negative coefficients
were associated with greater distances. The earlier function indicates a
disturbance in the gradient existed between the 67.5 and 76.5 kilometer bands.
Also, moderate negative values associated with the greatest distances indicate
one side of the region had fragmented at a much different rate than the other
side. Both the small peak and the large depression suggest a lot of localized
fragmentation activity had taken place between 1973 and 1985. However, by
1991 the landscape gradient appeared to have ‘calmed down’ as the peak and
the depression had both disappeared. All that remained was a gentle sloping

landscape gradient.

139

5.14: Summary.

Basic statistical analyses on digitized land parcel data and remotely sensed
forest cover data for Crawford, Kalkaska, and Grand Traverse Counties provide
evidence to support four basic trends; (a) average parcel sizes decreased over
time, (b) land ownership parcelization occurred at a faster rate during the 1970s
than during the 1980s, (c) forest cover increased by nearly 5 percent between
1973 and 1991, and (d) forest fragmentation decreased from 1973 to 1991,

although a small trend of increased forest fragmentation did appear after 1985.

Spatial autocorrelation analysis of temporal parcel data revealed spatial
relationships that existed over only short distances and imply a simple adjacency
or spill-over effect. For example, a piece of land undergoing parcelization may
have induced further parcelization in a nearby or adjacent area, but would have
had little to no effect on a more distant piece of land. Only the township level
analysis yielded evidence of a broader landscape trend. Review of the data
indicated land in Grand Traverse County parcelized faster than in Kalkaska
County, which in turn parcelized faster than in Crawford County. The landscape
trend identified at the township scale was an important finding because most
land use decisions are made at the township level. Therefore, this trend

suggests that land use and zoning policies may also exhibit a spatial gradient.

Spatial autocorrelation analysis of temporal forest data revealed spatial gradients

of both fragmentation indices and fragmentation rates that transcended all

140

scales. For example, Grand Traverse County was characterized by having the
least amount of forest cover, the most fragmented forests, and the lowest rate of
change over the eighteen-year period. Crawford County had the most amount of
forest cover, the least fragmented forests and the highest rate of forest change.
Kalkaska County was geographically and characteristically located somewhere in
the middle. Autocorrelation results also indicated irregularities in the forest
gradient occurred between 1973 and 1985. Although these irregularities were
marked by statistically insignificant Moran coefficients, they occurred in the same
general location along the distance axis as did the periodic trend observed in the
township level parcel trend, hence indicating a relationship exists between the
phenomena. However, the relationship between forest fragmentation and land
ownership parcelization should be posited as speculation only. I discuss my

reasons later in this document.

141

CHAPTER 6: DISCUSSION

6.1: Introduction.

This discussion is intended to provide information that may lead to land use
planning and forest management strategies that are sensitive to ownership

patterns and their influence on forest structures.

6.2: Influences of scale on results and their implications.

Spatiotemporal land ownership and forest cover landscape data were partitioned
and analyzed five times, each time with more numerous and smaller-sized
sampling units. I calculated average parcel size (APS) and forest fragmentation
(CF) indices for each sampling unit. Values representing sample unit
characteristics were arithmetically combined into mean values to summarize
each landscape. Some test results suggest differences in spatial scale
influenced mean value calculations. For example, forest fragmentation results do
not to vary much with scale, but parcel size results do. Results that do not vary
with scale suggest that the methods used during analysis were not sensitive to
changes in scale. Alternatively, results that vary with scale suggest that the

methods used during analysis were sensitive to scale changes.

142

A review of mean CF values (see Table 5.19) reveals small ranges across spatial
scales thus suggesting spatial scale independence. For example, the 1973
section analysis produced a mean CF value of 0.65, a value similar to the 1973
regional average (0.66). Sample site, township, and county analyses also
produced similar mean magnitudes for the same year. These results show that
static levels of forest fragmentation were observable using all five spatial scales
and the method used to summarize fragmentation values was not sensitive to the
partitions used to sample the landscape. Fragmentation rate results (see Table
5.22) can be characterized in the same way. Therefore, I am confident that CF
values represent landscape conditions and not statistical influences associated

with scale changes.

Parcel size and parcelization rate results show strong evidence for scaling
effects. A review of mean APS values (see Tables 5.3 and 5.6) reveals large
ranges across spatial scales. For example, the 1970 section analysis produced
a mean APS of 18.05 ha, a value almost two times the regional average (9.64
ha) for the same year. As smaller sampling units were used, calculated mean
values increasingly exceeded the regional value. Stated another way, mean
APS values appear inversely related to sample unit sizes, thereby indicating the
method used to calculate APS indices was sensitive to changes in scale. Also,
although all parcelization results indicate the same direction of change (average
parcel sizes decreased over time with higher average annual rates of change

occurring during the 1970s), calculated values are not similar across scales (see

143

Table 5.6). These differences suggest that mean values calculated for finer
scales may not solely represent landscape conditions, but also statistical

influences associated with scale changes.

I attribute the scale effect on APS calculations to the method used to sample
large private parcels at different scales. Such parcels contributed greater
leverage over sample unit calculations as smaller sampling units were used.
Large parcel areas influenced measures of central tendency in two ways: first,
fewer parcels were included in each smaller unit calculation, which means each
large parcel had a relatively greater influence over mean values; and second,
large and extreme values biased the mean upwards. In some cases (section
analysis only), single large parcel areas contributed the only area value to
sample unit calculations. Therefore, when sample unit values were combined
into a single mean value, some large parcels assumed an entire degree of
freedom. I did not foresee this problem at the outset of analysis hence I did not
design a sampling scheme to mitigate it. Therefore, APS values associated with
smaller sampling units should be used only for relative comparisons and little
confidence placed on actual values. Values associated with larger sampling
units (i.e. counties and townships) can be used to summarize parcel sizes with

relatively greater confidence.

144

6.3: Changes in ownership parcelization.

Land ownership parcelization is a phenomenon that causes many planners
concern. Parcelization, especially when left unchecked, reduces viable
agricultural land, disrupts scenic landscapes, and can limit access to mineral or
water deposits (Wyckoff, 1995). Legislation, like the Subdivision Control Act of
1967 (SCA), has been used to preserve open spaces, agricultural land, and
scenic landscapes. However, such legislation has also contributed toward high
infrastructure per-capita costs, a high price for open spaces. Forest managers
are also concerned about parcelization because it retards their ability to manage

forested areas that extend over multiple parcel ownership boundaries.

A useful way to visualize land ownership parcelization is to compare published
plat maps for the same area for different dates. To find evidence of land
subdivision or ownership change, one can often identify blocks of small parcels
under diverse ownerships that were previously bounded under a single
ownership. Other observable possibilities include aggregated parcels as well as

parcels that did not undergo a change in either ownership or extent.

I analyzed digital representations of published plat maps using a geographic
information system in order to quantify the parcelization phenomenon in Grand
Traverse, Kalkaska, and Crawford Counties. A regional APS index value was

calculated for each date. APS values decreased over time from 9.64 ha (23.8

145

acres) in 1970, to 4.92 ha (12.2 acres) in 1980, and to 4.11 ha (10.2 acres) in
1990. Differences between values show the region experienced higher average
parcelization rates during the 19703 than during the 19805. These trends
coincide temporally with residential population growth trends. This temporal
coincidence might lead some people to believe the two phenomena are directly
related and infer changes in one phenomenon cause changes in the other to
occur. However, I believe this coincidence should not be interpreted in this
manner. Out of curiosity, I measured the relationship between township growth
rates (average number of persons per year) and parcelization rates (average
change in parcel size per year) with Spearman's rank-order correlation
coefficients.1 Resultant coefficients (see Table 6.1) indicate township
parcelization rates were statistically unrelated to residential growth rates.
Furthermore, correlation results of lagged township rates (19703 population
growth and 19805 parcelization) suggest changes in land subdivision were not
statistically related to earlier residential growth rates. Therefore, the two
phenomena, statistically speaking, were not directly related across time and
space. However, I speculate that weak coefficients presented in Table 6.1 do not
necessarily discount the role new resident populations played in the land

subdivision process, but imply other factors must have played a larger role.

 

‘ Only 31 of 33 townships were used in calculating correlations between 1980
and 1990 township data because City of Grayling and Traverse City parcelization
rates are undefined (see Table 5.5). All correlation results are statistically
insignificant using a two-tailed, 95 percent confidence interval.

146

Table 6.1: Correlations between township growth and parcelization rates.

Parcelization Rate

Growth Rate 1970 to 1980 1980 to 1990
1970 to 1980 0.086 0.230
1980 to 1990 - 0.185

Recall that seasonal populations are not accounted for in census counts, and
hence, were not accounted for in this simple test for correlation. Stewart (1994)
and Stynes et al. (1997) have shown how seasonal home development and
seasonal populations have contributed substantially to rural landscape

development in the Great Lakes region.

It is likely that seasonal homeowners who made new claims on the landscape
influenced the subdivision process. Local planners and planning organizations
should take interest in the results presented in Table 6.1 because they suggest
that a measured change in residential population alone may not serve as an
adequate indicator of land ownership change for this region. Again, Stynes et al.
(1997) demonstrated that the population of a Great Lakes county, like any one of
the three counties in the study area, can be six or seven times the official
resident population because official census counts do not include seasonal
homes or seasonal home owners in population totals. Yet, official census counts
are often used to describe landscape conditions and inform planning decisions,
probably because such data are readily available and often distributed free of

charge. For example, Wyckoff and Reed (1995) used census data to describe

147

past and project future demographic changes in Michigan. The authors then
used their projections to speculate about what landscape changes might occur
should current population trends continue. However, they paid little attention to
seasonal population trends or the impacts associated with them. Thereby,
Wyckoff and Reed (1995) probably underestimated the impacts that future

population changes will have on the landscape.

Given the importance of seasonal home populations to this region, I think an
effort spent to record, map, and monitor the spatial and aspatial characteristics of
seasonal homes, in addition to residential homes, would produce new and
valuable information. This information can be used to better inform our ideas

about land ownership and potential landscape change in this region.

Another useful way to visualize land ownership parcelization is to compare parcel
size frequency distributions for different dates. Changes between measured
frequencies and percentages can be used to infer changes on the landscape.
For example, Figures 6.1 and 6.2 illustrate temporal frequency and percentage
distributions of parcel areas for the region, respectively. At first glance, one can
see each distribution is positively skewed, is multi-modal, and has peaks

occurring in the 4, 8, 16, 32, and 65 hectare bins.

148

 

 

 

Frequency

 

 

 

 

 

 

 

 

31970 15555555535555
[I
l 1338 Parcel size (ha)

Figure 6.1: Temporal frequency distribution of private parcels.

 

 

 

Percent of total area

: ,rs
a

I‘l'l If". 1,. '. ‘J'n(

I '3' -. lull. III-Id-Iulill' '2 a

[11970 ovoomcoovaowggomonmrxvm
1- ‘- m

 

 

+
81980 NNNC‘O V'VV'IO (0608
I 1990 Parcel size (ha)

Figure 6.2: Temporal percentage distribution of private parcels.

149

I believe these peaks betray the effects of recursive halving and/or quartering of
Jeffersonian-style survey sections - a pattern typical of the post-colonial

American landscape.2

Figures 6.1 and 6.2 reveal large increases in the number and aggregate extent of
small parcels and coincident decreases in the number and aggregate extent of
large parcels over time. Numbers of small parcels were calculated by dividing
the total area classified as small tracts by 0.2 ha, the assumed average size of
parcels in small tract areas (see Section 4.3.2). In 1970, parcels smaller than 1
ha, in aggregate, consumed 11415 ha (6%) of private land, while parcels larger
than 65 ha consumed more than 43710 ha (19%). By 1990, parcels larger than
65 ha covered only 10620 ha in aggregate (4%), while parcels smaller than 1 ha
consumed 19740 ha (10%). Obviously, newly created parcels were carved out of
larger parcels given the finite amount of land. On this landscape however, many

newly created parcels seem to have been carved out of the largest large parcels.

 

2 Public land survey section are approximately 259 ha (640 acres) in size.
Typical section subdivisions produce parcel areas approximately equal to 65ha
(160 acres), 32ha (80 acres), 16ha (40 acres), 8ha (20 acres), 4ha (10 acres),
etc.

150

This finding will probably strike a nerve in local planners, forest managers, and
especially those interested in agriculture because I believe it represents, to some
extent, agricultural losses for this region. As stated in Section 3.3, Michigan
experienced trends of agricultural decline between 1970 and 1990. Grand
Traverse, Kalkaska, and Crawford Counties were not exceptions to these trends
(US. Department of Commerce, 1992b). Because agricultural land uses are
land-consumptive uses, it is likely that the measured loss of very large parcels
reported above represents agricultural losses. If these very large parcels do
represent past agricultural lands, then this study will provide evidence to support
claims made by the Michigan Society of Planning Officials that suggest urban

sprawl has occurred in this region (Wyckoff, 1995).

Figures 6.1 and 6.2 also reveal large increases in the number and aggregate
extent of parcels 4 to 5 hectares (10 to 12.5 acres) in size. These increases
likely reflect the influence the Subdivision Control Act (SCA) of 1967 (MI PA 288
of 1967) had on the parcelization process during this time. As described in
Section 2.1.1, the SCA was a piece of legislation that provided for an expensive
platting process to be imposed on landowners who subdivided land into parcels
smaller than 10 acres. According to Norgaard (1984), the observed statewide
response to the SCA was a proliferation of parcels just larger than 10 acres in
size. Increases in 10+ acre parcels represented in Figure 6.1 provide additional
evidence to support Norgaard's claim. Local and regional planners should pay

particular attention to these parcels for three reasons. First, so many parcels of

151

this size now exist; second, they accounted for a relatively large area in
aggregate (5%) in 1990; and third, I suspect that many land cover changes have
occurred on these parcels. For example, the possibility exists that large parcels,
perhaps once held in agriculture, were subdivided into these many 10+ acre
parcels. If this is true, then the likelihood exists that subsequent residential
development was concentrated on only a small portion of each 10 acre parcel,
thereby leaving the balance of each to regenerate from an open field condition
into a young forest condition. This scenario might serve as one possible
explanation for the forest growth trend reported in Section 5.7. Secondarily, this

scenario also attributes to the SCA of 1967 a positive by-product.

Summary values like the ones presented above are easy to calculate and useful
for describing general land ownership trends, however such values do not reveal
extant spatial variations in the data. Spatial variations in land ownership data
can be revealed by mapping land ownership characteristics and using small
sampling units. Mapping parcel size changes using survey section data is useful
for identifying relative "hot spots” on the landscape. Differences between maps
representing two dates or periods indicate changes in hot spot locations over
time. Figures 6.3 and 6.4 illustrate relative parcelization rate surfaces
interpolated from 1970s and 1980s section level results, respectively. Interior
areas not mapped with either purple or green hues represent non-private lands.

Areas mapped with a blue hue represent inland lakes.

152

 

 

 

Legend: Parcel Aggregation 13.1. E Parcelization

Figure 6.3: Map of parcelization rates for the period between 1970 and 1980.

 

 

 

 

Legend: Parcel Aggregation E , E! Parcelization

Figure 6.4: Map of parcelization rates for the period between 1980 and 1990.

153

Although a majority of private land areas undenrvent parcelization (purple hues)

during both time periods, interesting differences are worth noting.

First, relatively high rates of parcelization (represented by darker purples) appear
randomly distributed about the landscape during the 19703. Such randomness
is supported by fine-scaled spatial autocorrelation results that indicate the
distribution of parcelization rates exhibited no spatial pattern during the 19703
(see Tables 5.11 and 5.13). In contrast, relatively high rates of change occurred
in scattered clumps during the 19803. Slight clumping during the 19803 is
suggested by slight increases in spatial autocorrelation values at short separating
distances (see Tables 5.12 and 5.14). Obvious changes in spatial pattern are

evident in Kalkaska County and the southern portions of Grand Traverse County.

Many possible reasons exist to explain these changes, such as: a) land supply
tightened and therefore was limited to fewer locations, b) new landowner
preferences, in aggregate, became focused on a few areas, c) local townships
restricted random development with new zoning plans, or d) other reasons. At
this time, I am unable to specify with any certainty what actually caused these
spatial patterns to change, but perhaps a better understanding could be obtained

with additional research.

Second, although the focus of this paper is on parcelization, some areas did

experience parcel aggregation. A place of particular interest is located in the

154

northeast corner of Frederic Township, Crawford County (represented by the
dark green cluster on Figure 6.3). At some time between 1970 and 1980, several
parcels were merged to form a few very large parcels. However, by 1990, these
very large parcels were platted as subdivisions and subsequently chopped into
small tracts. This particular location is adjacent to several creeks and
surrounded by the Au Sable State Forest (due west), the Hartwick Pines State
Park (due southeast), and several large inland lakes (due north and just across
the county line). It seems likely that proximity and centrality to these recreational
features were factors that influenced the parcelization process in this location.
Interestingly, 1990 aerial photographs of this location clearly show the land was
roaded in order to accommodate scores of new homes. However, only a few
homes were actually built. Perhaps the developer experienced difficulties during

early stages of the project and was unable to complete it.

6.4: Urban sprawl.

According to the MSPO, urban sprawl is becoming the dominant land use pattern
in the Northern Lower Peninsula (Wyckoff, 1995). The MSPO characterizes
urban sprawl as a process that produces low-density home developments,
population densities lower than urban centers but greater than will permit
profitable agriculture, large infrastructure per capita ratios, and a diminished rural
character (Wyckoff, 1995). These negative by-products often provide grist for

articles and editorials in local newspapers.

155

The Encyclopedia of Community Planning and Environmental Management
offers a similar description of urban sprawl:

"[Urban sprawl is] an unattractive use of land and resources,

causing infrastructure costs related to extending utilities to remote

areas. It has also been accused of eliminating environmentally

important open space while leapfrogging developable parcels"

(Schulz and Kasen, 1984).
These descriptions explicitly identify a link between parcelization and urban
sprawl, and they suggest both phenomena are spatial phenomena because they
occur with respect to existing locations of open spaces and developable parcels.
It seems likely that urban sprawl is preceded by subdivisions of large parcels into

small parcels. Therefore, the concept of urban sprawl can be a useful way of

thinking about the consequences of parcelization.

Township level spatial autocorrelation analysis results support the idea that the
parcelization process is a spatial process, and indicate its extent is larger than
any one township. These results suggest that township level parcel patterns do
not occur independently of, but are influenced by, surrounding townships. For
example, significant Moran's l values in Figure 5.3 show APS values were
positively autocorrelated in space at short distances, and negatively
autocorrelated at distances greater than 66 kilometers. Also important, the
separating distance associated with negatively autocorrelated results decreased
from 66 km to 33 km from 1970 to 1990, thus indicating dissimilar 1990 parcel
characteristics were separated by half the 1970 separating distance. This

decrease in separating distance over time suggests that new landowners

156

leapfrogged developed areas as they bought and divided parcels of land. These
results, when considered together with the regional decreases in APS reported
above and Shulz and Kasen's (1984) description of urban sprawl, are evidence of
new landowners tending to locate not in closed urban spaces, but in open rural
spaces. Given this evidence, decision makers for each township may want to
consider coordinating planning efforts with other township planners - and not just
those that share a common border. These results indicate township planners
should plan at the scale of the process, and not just at the scale of the township,
if they want to be proactive and mitigate consequences associated with urban

sprawl.

Figure 6.5 represents the parcel size gradient within the 1990 urban extent of
Traverse City - a portion of the results presented in Section 5.5. Changes in
parcel size indicate average parcel sizes decreased in areas surrounding the city
and the urban extent increased over time. Also, the general slope of the trend
away from Traverse City (represented by the lines connecting point data in
Figure 6.5) decreased over time. This change in slope over time suggests that
the landscape, which at one time changed rapidly as one traveled away from the

city, became more homogeneous.

A person can visualize increasing population densities (decreasing parcel sizes)

that spread into areas surrounding the city by considering changes in the

average parcel size gradient in terms of population density. One can also

157

visualize these new densities, although high enough to be considered urban in
this example, to be low relative to the urban core. So, location analysis results
from this research can be used to support the claim that urban sprawl has

occurred in areas surrounding Traverse City.

 

14-
12«
7; +1970
5 10-
m ,-
.5 , +1980
5 8‘ “
a —o—1990
o. 65
(D
5’ 4 ----4ha(10acre)
a): T Threshold
<
2.
0 .

 

 

1.5 4.5 7.5 10.5 13.5 16.5

Midpoint of distance band (km) from
Traverse City

Figure 6.5: Temporal APS values in the Traverse City area.

Recall, however, that forest fragmentation results from Section 5.12 indicate
forest defragmentation occurred in these same areas (Figure 6.6 represents the
portion of the results presented in Figure 5.10 that fall within the 1990 urban
threshold). The areas around Traverse City were expected to show signs of

increased forest fragmentation if urban pressures had increased. They did not.

158

Thus, these results do not indicate a direct relationship exists between

parcelization and forest fragmentation.

 

1.0 a

0.8 -
g 0-6 - +1973
g +1985
5 0,4 . +1991

0.2 ~

0.0 I 1 I I I I

 

 

1.5 4.5 7.5 10.5 13.5 16.5

Midpoint of distance band (km) from
Traverse City

Figure 6.6: Temporal CF values in the Traverse City area.

Location analysis results seem counter-intuitive unless I assume parcelization
and subsequent development occurred on non-forested lands, but not on
forested lands. If low-density development occurred on non-forested lands, then
the possibility exists that areas not maintained as buildings or lawns succeeded
from open field conditions to young forest conditions. Such non-forested lands
may have been agricultural lands and were taken out of production, parcelized,

and subsequently developed for either residential or seasonal home purposes.

159

Such speculation seems quite reasonable, especially when one considers the
agricultural loss, resident population growth, seasonal home development, and

tourism development trends that distinguish this region.

6.5: Forest cover change.

Regional forest covers increased by almost five percent from 1973 to 1991,
although particular areas of forest growth and loss varied across space and time.
This increase seems reasonable because it is similar to the proportion published
by the United States Forest Service; Leatherberry (1994) reported a six percent
increase for the same region between 1980 and 1993 after a recent forest
inventory analysis. Differences between inventory dates and methods may

account for the measured difference between forest growth percentages.

In real numbers, forested area increased by 3072 ha from 1973 to 1985, and by
another 5602 ha from 1985 to 1991 (see Table 5.15). These numbers do not
confirm the idea that a reduction in forest cover occurs as population,
urbanization, and parcelization pressures increase. This finding may come as a
surprise to many local residents and planners, although probably not to area

forest managers.

160

6.5.1: Forest parcelization.

The Michigan Society of Planning Officials (MSPO) has raised concern about
land use practices on forested lands (Wyckoff, 1995). They describe forest
fragmentation as the result of forests being cut into configurations where "edge
species of plants and animals have proliferated" and deep forest habitats and
resident species have declined (Warbach and Norberg, 19952iv). This definition
explicitly links physical landscape changes to human activities. However, the
MSPO also describes forest fragmentation as a process of subdividing large
forested parcels into many smaller parcels under a diverse ownership. The
effect of this process does not necessarily involve a loss of habitat or scenic
area, but an impediment to forest management strategies. Forest management
strategies are difficult to construct and implement when many, rather than few,
landowner viewpoints must be considered. The second MSPO definition, unlike
the first, does not imply physical landscape change, but a political consequence.

The two definitions are not synonymous.

Additional confusion surrounds the term fragmentation because landscape
ecologists have used it to describe different kinds of structural habitat change.3

For example, Bell (1995) defined fragmentation as the "process of detaching or

 

3 In the English language the suffix -ion has three meanings associated with it
when attached to either a noun or a verb. It can be used to identify: a) an action
or a process, b) a result of an action or process, and c) a state or condition.
Accordingly, the term forest fragmentation has been attributed these three
meanings.

161

separating expansive tracts of forest into spatially segmented tracts." Saunders
et al. (1991) defined it as the results of a process that "produces a series of
remnant vegetation patches surrounded by a matrix of different vegetation and/or
land use." And third, Hargis et al. (1998) used the term to denote static habitat

conditions.

| used a single definition for forest fragmentation consistently throughout this
analysis in order to avoid any such confusion. For this research, forest
fragmentation means a static forest condition and it represents the degree to
which the amount of interior core area of a forest patch or class differs from its
maximum potential core area. This definition is concerned with physical
landscape change, not political consequences. However, I recognize that the
political connotation of the term fragmentation is very important to some planners
and planning agencies so, I have included a brief discussion of the phenomenon

I think should be called forest parcelization.

A useful way to visualize private forest parcelization is to compare forested
parcel size frequency distributions for different dates. I used a GIS to query
parcel and forest data in order to create histograms of forested parcel areas. For
this discussion, private parcels were considered forested if they contained at
least 0.4 ha (1 acre) of forest area. Figure 6.7 illustrates a temporal frequency

distribution of forested parcel areas for the region.

162

55874
89697
94936

 

 

 

 

 

 

 

2500a
> 20004
O
C
o
g 1500~
“- mood
500-
o- ' ' E
ovwseasaeseeeacsa+
a 1970 8
D 1980 .
. 1990 Parcel srze (ha)

Figure 6.7: Forested parcel size frequency distributions.

Each distribution displayed in Figure 6.7 is positively skewed, is multi-modal, and
has peaks occurring in the 4, 8, 16, 32, and 65 hectare bins, just like each total
private parcel distribution. In fact, forested parcel distributions (see Figure 6.7)
are similar to total parcel distributions (see Figures 6.1) because relatively few

parcels existed without some forest cover.

Changes between measured parcel-size frequencies can be used to infer
changes on the landscape. For example, Figure 6.7 reveals large increases in
the number and aggregate extent of small, forested parcels and coincident
decreases in the number and aggregate extent of large forested parcels over
time. In 1970, forested parcels smaller than 4 ha (n=57070) contained 8270 ha

(7%) of privately owned forest, while forested parcels larger than 65 ha (n=492)

163

contained more than 34970 ha (31%). By 1990, forested parcels larger than 65
ha (n=303) contained only 24330 ha (20%), while forested parcels smaller than 4
ha (n=99400) consumed 19430 ha (16%). Obviously, forests in this region
undenNent parcelization as thousands of new landowners gained control over
private forests. It is no wonder that forest managers are concerned about how to
best implement new management strategies, especially when so many different

forest owner viewpoints must be recognized and considered.

6.5.2: Forest fragmentation.

Changes in forest structure can disrupt or create new pathways for plant and
animal species, nutrients, and energy to disperse in forested landscapes. A
change in forest structure is implied by the term forest fragmentation. Increases
in forest fragmentation can increase the amount of edge-dependent species
while simultaneously stranding and extinguishing local populations of interior-
dependant species (Fahrig and Merriam, 1994). If enough local populations are
extinguished in one region, then a regional population may become extinct. lida
and Nakashizuka (1995) have shown how measured decreases in landscape
biodiversity, and subsequently forest health, are associated with increases in
forest fragmentation. These associations explain why forest fragmentation is
another concern for planners and resource managers in the region. The health
of regional tourism- and timber-based economies are linked to the health of

regional forest ecosystems.

164

Unfortunately, the results of this analysis do not help to paint a clear picture of
forest fragmentation trends in this region. In brief, forest fragmentation
decreased from 1973 to 1985 during a period of average forest growth, but then
increased between 1985 and 1991 during another forest growth trend. In
general, forest fragmentation trends are usually associated with forest loss
trends, and defragmentation trends are associated with growth trends. However,
these associations were not consistently evident between 1985 to 1991.
Complicating matters further, forest fires occured in the region between 1973 and
1991. Although the extent of the Stephen Bridge Road Fire (see Section 5.8)
has been well documented (Winter and Fried, 1997), the extent of other fires
have not been explicitly recognized or accounted for in this study. Thus, it is
impossible for me to ascertain the influence that forest fires had on my results.
Therefore, I cannot posit a single scenario that conveniently summarizes all

changes that occured on this landscape.

Yet, I can imagine a likely scenario that may explain forest trends between 1973
and 1985, assuming that data and methods used in this research are accuracte
and appropriate. I speculate that as farmland was abandoned, many forest
patches naturally extended beyond linear boundaries and into open spaces,
thereby allowing patches to grow and coallesse into fewer and larger patches.
Aforementioned agricultural trends and patch number, patch area, and core
areas statistics in Table 5.14 can be used to support this scenario. At the same

time, the possibility exists that some small and highly fragmented forest patches

165

were removed from the landscape in order to accomodate large construction
equipment, new home sites, and new roads. Therefore, it may be possible that
policies or economic conditions that contributed to agricultural land abandonment
and higher intensity development may have also resulted in forest growth and
defragmentation trends. According to lida and Nakashizuka (1995), such forest

structure changes are associated with increased biodiversity levels.

I can imagine two scenarios that can be used to explain the forest growth and
fragmentation trends that occured between 1985 and 1991. First, I speculate a
possibility exists that during the 19703, open land was heavily parcelized and
small portions of these parcels were developed. Further, undeveloped portions
were either landscaped or abandoned to natural succession processes. After
several years, many new small patches emerged in these undeveloped portions,
and exhibited many forest edges and few core areas. Second, and also
possible, several large forest patches may have been bisected by efforts to build
new roads, or perforated by new mineral well, logging, or home construction
efforts. These processes could have slowed the previous forest growth trend
and also resulted in increased fragmentation conditions. Patch number, patch
area, and core area statistics in Table 5.14 can be used to support these two
scenarios. According to lida and Nakashizuka (1995), such forest structure

changes are associated with decreased biodiversity levels.

166

Obviously, the above scenarios, although possible, are highly speculative and
were not tested. They cannot be confirmed by the data, methods, or results
described in this study. However, I included them because they are reasonable
and may provoke planners and forest managers to ask additional questions

about the relationship between humans and forest environments in this region.

Unlike the results of parcel analysis, spatial analysis of forest fragmentation
indices produced results that transcended all observed scales and consistently
indicated the existence of general trends. For each date and for each scale,
positive spatial autocorrelation decreased with an increase in distance. Such a
pattern indicates sampling units near to one another exhibited similarities in static
fragmentation conditions while units far from one another exhibited strong
differences. Sommers et al., (1984) and Stearns (1997) have described the
physical environments that support regional forest covers in terms of spatially
varying phenomena (i.e. elevation, hydrology, and soils) so, naturally, one would

expect forest conditions in this region to also vary along these spatial gradients.

When fragmentation results are interpreted with the original data, these general
trends can be better defined. For example, regional amounts of forest cover
tended to increase from west to east, and regional fragmentation rates tended to
increase from west to east. The forest cover trend represents common
knowledge about the area, Grand Traverse County is more populated and

contains fewer forested areas than Kalkaska County, which in turn is more

167

populated and contains fewer forested areas than Crawford County. However,
the second trend is interesting because it suggests that higher fragementation
rates occured in the county with lower populations and higher forest
concentrations. Perhaps this trend was unduly influenced by forest fires that
occurred in Crawford townships. These results may also suggest the same
conclusions made by Vesterby and Hiemlich (1991), Vogelmann (1995), and
Theobald, et al. (1996); landscape changes tend to be more dramatic during
earlier stages of development than during later stages. By comparison, Crawford
County was much less developed and urbanized than Grand Traverse County.
Therefore, more dramatic changes in forest cover were more likely to be
observed in Crawford County than in Grand Traverse County because Crawford
County was in an earlier stage of development. This finding has policy
implications. Forest managers in Crawford County may have a better opportunity
to apply new forest management strategies than those in Grand Traverse County
because fewer landowner viewpoints must be organized and considered during
decision making processes. Subsequently, forest managers in Crawford County
may have a better opportunity to mitigate dramatic forest changes than do forest

managers in Grand Traverse County.

Spatial variation in forest fragmentation data can be revealed by mapping
average annual fragmentation rates with small sampling units. Figures 6.8 and
6.9 illustrate relative fragmentation rate surfaces that were mapped from section

level results.

168

 

Legend: Defragmentation .57; .7: i:- Fragmentation

Figure 6.8: Map of fragmentation changes between 1973 and 1985.

a

 

'* .' - ‘
. ' fl
-..~' ‘ ‘
. ' 437‘
‘l "- -

 

Legend: Defragmentation E3 , j if.“ Fragmentation

Figure 6.9: Map of fragmentation changes between 1985 and 1991.

169

Figures 6.8 and 6.9 are useful for visualizing where relatively high and low rates
of fragmentation occurred. Interior areas not mapped with either red or green
hues represent non-private lands. Areas mapped with a blue hue represent
inland lakes. From 1973 to 1985, forests were fragmenting in the southeast
portion of Grayling Township, Crawford County, and in many places in Grand
Traverse County. Yet overall, most privately owned forests were defragmenting.
From 1985 to 1991, forest fragmentation occurred in many places throughout the
landscape. Relatively high rates are noticeable in every county. Note the many
sections in Crawford County that exhibited relatively high fragmentation rates.
The cluster located in the east-central portion in Grayling Township surely
represents structural damage caused by the Stephen Bridge Road Fire (see
Figure 5.9). Also note that many sections with high fragmentation rates were
located adjacent to inland lakes. This association is observable in both maps
and suggests that activities that occur near inland lakes may influence the

fragmentation process.
6.6: The link between parcelization and fragmentation.

Spatial distributions of average parcel size and forest fragmentation indices
appear to exist along spatial gradients that trend from Grand Traverse County to
Crawford County. In general, smaller parcel sizes are associated with higher
fragmentation indices. This spatial coincidence is reasonable because one

would expect small parcel and small tract areas to be dominated by dense

170

anthropogenic land covers. Location analysis results clearly realize this
expectation as forest fragmentation indices tended to decrease with an increase
in distance from Traverse City. Also, one would expect areas with many large
parcels to contain lower densities of anthropogenic land covers and open spaces
available for natural forest covers. Therefore, the spatial concurrence of the
average parcel size gradient with the static forest fragmentation gradient seems
to support the proposed link between parcelization and fragmentation (Brown
and Vasievich, 1996; Bell, 1995; Freedman et al., 1994; and Saunders et al.,

1991)

However, I found little evidence to continue to support the proposed link after I
visually examined spatially coincident distributions of parcel and forest changes.
In general, areas that exhibited high parcelization rates tended not to have high
fragmentation rates - although some specific locations did. In general, areas
that exhibited low parcelization rates tended not to have low fragmentation rates -
- although a few specific locations did. A simple interpretation would suggest that
forest defragmentation was associated with land subdivision, at least within this

particular study area.

These findings are very important because they suggest that parcelization and
fragmentation processes in this region were not associated in the same manner
as coincident patterns of static landscape conditions. This means that we cannot

use the relationship between static landscape patterns in this region as a proxy

171

for an understanding the relationship between landscape processes.
Furthermore, these findings demonstrate that a complexity exists between these
two phenomena that cannot be explained by a simple cause-and-effect
relationship. Therefore, these patterns and processes require continued

investigation.

6.7: Conclusions.

This research has assessed landscape configurations of private land ownerships
and forest habitats in Grand Traverse, Kalkaska, and Crawford Counties.
Quantitative analysis of landscape parcel data revealed average parcel sizes
decreased over time and land ownership parcelization occurred at a faster rate
during the 1970s than during the 1980s. Analysis of forest cover data revealed
forest covers increased by nearly 5 percent from 1973 to 1991, forest

fragmentation decreased from 1973 to 1985, and increased from 1985 to 1991.

Final interpretations of results suggest six basic conclusions. First, locations with
recreational amenities (e.g. inland lakes) seem to influence parcelization and
fragmentation patterns as do locations with urban amenities. Second, local
planners and forest managers have legitimate concerns about the impacts that
urban sprawl can have on the landscape and their abilities to manage forested
areas. Third, the Subdivision Control Act of 1967 had an impact on the way land

was subdivided, and perhaps, also facilitated some forest growth. Fourth, a need

172

exists for a better accounting of seasonal populations and impacts associated
with them. Fifth, parcelization and fragmentation patterns exist with spatial
extents larger than any one township in this region. This finding is very important
because land use planning in Michigan is a local decision process that is directed
by legislation at the township scale, but landscape patterns indicate processes
are operating at larger scales. And sixth, we cannot use an association between
static landscape patterns in this region as a proxy for understanding a dynamic
relationship between landscape processes. In summary, the relationship
between land ownership parcelization and forest cover fragmentation is very
complex. A need still exists for research results that will help us better

understand the ways human decisions and landscape processes interact.

173

APPENDICES

174

APPENDIX A: PARCEL DATABASE

I collected plat map books (Rockford Map Publishers, Inc., 1969-1991) that
contain cadastral maps representing the Crawford, Grand Traverse, and
Kalkaska County ownership patterns for the approximate years 1970, 1980, and
1990. When plat map books were unavailable for the exact target dates, the
closest available date was used as a surrogate. In any such case, the difference
between obtained date and target date was not greater than one year. Table A1
lists the dates for the set of plat map books used. All parcel maps were published
at an approximate scale of 1:51 ,000 with a consequent positional error in parcel

boundaries of about +/- 25.5 meters.

Table A1: Parcel plat map book dates.

Target Date
__teroun fl 1&9 &
Crawford 1970 1979 1991
Grand Traverse 1969 1980 1990
Kalkaska 1969 1980 1991

Parcel maps were digitized, registered, and georeferenced using Arc/Info
software (ESRI Inc., 1997) using known section corner locations (MIRIS, 1978)
stored in UTM zone 16 coordinates as positional control. All parcel maps were
oriented to the section corners with a positional root mean squared error (RMSE)
no greater than 12 meters. Individual map coverages were appended to create

region coverages for each target date. Region coverages were then edited to

175

remove unwanted sliver polygons, unattributed polygons, and non-existent parcel
boundaries. Each regional parcel coverage was topologically correct and

attributed consistently and completely with respect to the published source data.

176

APPENDIX B: SATTELITE IMAGE DATABASE

I collected three pairs of Landsat Multi-Spectral Scanner (MSS) scene data that
covered the study area for the approximate years 1973, 1985, and 1991. As
mentioned in Chapter 4, each image had been registered, geo-referenced, and
distributed as part of the North American Landscape Characterization (NALC)
Data set (Lunetta et al., 1998) at a spatial resolution of 60 meters (0.36 hectares
I 0.88 acres). Table B1 lists the path/row locations, acquisition date, reported
geopositional RMSE, and sun/sensor geometries for the set of images used.
Figure B1 illustrates the geographic coverage of the selected NALC data used

and the clipped area selected for study.

Table B1: NALC Imagery metadata.

Target date
_19_79 L980. 1_9__90

__Attribut&6 Wit Est West East W_;_est East
Path 22 21 22 21 22 21
Row 29 29 29 29 29 29
Acquisition date 6/9/73 811 I7 5 6/28/85 8/8/85 7/15/91 8/9/91
RMSE 0.56 0.49 0.85 0.72 0.33 0.31
Sun elevation angle 60 53 59 53 56 52
Sun azimuth angle 128 127 124 131 133 129

177

 

Figure B1: Geographic coverage of NALC imagery.

According to the Yuan et al., (Yuan et al., 1994) the NALC triplicate data sets
"constitute a unique data base with which to investigate multidisciplinary issues
related to land use/land cover issues, human interactions with the environment,
carbon cycling dynamics, and numerous land process studies" (p. 130).
Because the data are coregistered and were processed consistently using
standardized methods, the NALC data set provides a valuable temporal baseline
for regional analyses. However, the NALC data do contain imperfections that
pose limitations on some analyses. Major sources of problem are acquisition
conditions, changes in phenology, and sensor conditions (as two different

satellite sensors were used to gather the data used during this analysis). The

178

acquisition conditions include variations induced by different atmospheric
conditions and different levels of illumination (sun/sensor geometry). The sensor
conditions include variations between sensors primarily due to aging of each
sensor and slight differences in calibration. Because these fluctuations are
inherent in the NALC data and are difficult to quantify (Brown et al., in press), the
need for an accuracy assessment of any subsequent image classification is

greater.

179

APPENDIX C: ISODATA CLUSTERING ALGORITHM PARAMETERS

Table C1 lists the parameter settings used to instruct the ISODATA clustering

iterations in the PCI (PCI, 1997b) XPACE software module.

Table C1: ISODATA clustering algorithm parameters.

Qoflgn
Database input channels

Clustering result output channel
Area mask

Number of clusters desired
Maximum number of clusters
Minimum number of clusters
Seedfile

Maximum number of iterations
Movement threshold

Generate signatures file (yes/no)
Minimum sample threshold
Standard deviation

Lumping parameter

Maximum number of lumping pairs
Background grey-level value
Number of image pixels used in sample

Description of input
Bands 1 thru 4 (DNs) + NDVI band

((band4 - band2)/(band4 + band2))
Channel 6

Study area less cloud mask

30

255

10

blank (uses computers internal clock)
500

0.01

no

32

2

1

5

0

100,000

180

APPENDIX D: HISTORICAL AERIAL PHOTOGRAPH DATABASE
Table D1 lists the attributes used to describe each mosaic. Tables D2, D3, and
D4 contain metadata information for photos mosaics used to represent land

cover conditions for the years 1970, 1980, and 1990, resepctively.

Table D1: Aerial photograph metadata legend.

Site#: 1 thru 8 Within county identifier for airphoto mosaic
Classification: C Photo used for image classification
Accuracy: A Photo used for accuracy assessment
Tier/Range/Section: PLSS identifier of upper left comer of mosaic
Status: Done Photo mosaic completely covers site

Partial Photo mosaic partially covers site
Missing No photo exists for site for date

Date: Photo acquisition date
Type: B&W Black and white
CIR Color infrared
COLOR Color
Scale: Linear cartographic scale of original photo
Agency: ASCS Agricultural Stabilization & Conservation Service
BDR
MDSH Michigan Department of State Highways
and Transportation

NHAP National High Altitude Photography
USGS United States Geological Survey

181

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APPENDIX E: CLASSIFICATION ACCURACY ASSESSMENT

The accuracy of photo-interpreted satellite imagery is often accepted as correct
and without qualification. Congalton (1991; p.35) argues, however, "given the
complexity of digital classification, there is more of a need to assess the reliability
of the results." Meyer and Werth (1990) have addressed problems and issues
associated with digital classifications and were critical of decisions made based
on invalid and undocumented classification maps. The authors suggested that a
quantitative method of accuracy assessment would be most useful for qualifying
the usefulness of a particular classification map. According to Jensen (1996), in
order to perform classification accuracy assessment, two sources of information
must be compared: (a) the derived classification map and (b) accepted ground
truth information. Jensen (1996) adds that the relationship between these two

sets of information can be summarized and quantified in an error matrix.

An error matrix represents overall and categorical map accuracy together with
errors of commission and omission between derived and referenced classes.
Producer’s accuracy is a commonly used measure of omission error whereas
user's accuracy is a term used to describe errors of commission. Producer's
accuracy indicates the probability of a reference pixel being correctly classified
on the image and is calculated by dividing the "number of correctly classified
pixels in each category by the number of reference pixels in that category"

(Lillesand and Kieffer, 1994; p. 613). User's accuracy indicates the probability

185

that "a pixel classified on the mapfimage actually represents that category on the
ground" (Congalton, 1991 :37) and is calculated by "dividing the number of
correctly classified pixels in each category by the total number of pixels that were

classified in that category" (Lillesand and Kieffer, 1994; p. 613).

The Khat statistic is another measure of agreement or accuracy that is often used
to test whether of not the results presented in an error matrix are significantly
better than results obtained by random chance (Jensen, 1996). The Km. statistic
is an estimate of KAPPA used in discrete multivariate analysis. Jensen (1996)
maintains that where overall accuracy figures incorporate only proportions of
categories classified correctly, the Km statistic is more robust as it also

incorporates commission and omission errors.

For this analysis I utilized error matrices and the Km. statistic in order to evaluate
the accuracy of the three classification maps. Historical aerial photographs were
collected and used as ground truth references. Figure E1 illustrates the study
region with the geographic distribution of aerial photograph mosaics used for
image classification and accuracy assessment. Although this approach is
favored by Congalton (1991), the best method of comparing derived and
referenced data sets probably has yet to be determined. So, rather than pick one
method arbitrarily, I have chosen to assess the classified image mosaics

according to three common methods outlined by Lillesand and Kiefer (1994).

186

 
       

 
 

Ira-

. Grand Trgverse
E: E: 0..... I I

Sites used for Sites used for
D Study area D classification accuracy assessment

Figure E1: Location of reference aerial photograph mosaics.

The post-classification training sets method utilizes manually selected
homogenous areas representing derived land cover categories. Areas
representing forested and non-forested cover type are on-screen digitized from
each subset of aerial photographs, rasterized, and compared to the classified
images. Table E1 presents the post-classification training sets method results

obtained during this analysis.

187

Table E1: Post classification training sets accuracy assessment results.

 

REFERENCE AIRPHOTO DATA
1973 NF FOR ROW USER
NF 504 29 533 94.56

FOR 25 458 483 94.82
COL 529 487 1016

PROD 95.27 94.05 94.69
Khat = 89.35

1985 NF FOR ROW USER

NF 476 9 485 98.14

FOR 53 504 557 90.48

COL 529 513 1042

PROD 89.98 98.25 94.05
= 88.1 1

 

1991 | NF FOR ROW USER
NF 511 9 520 98.27
FOR 13 521 534 97.57
COL 524 530 1054

 

PROD 97.52 98.30 97.91
Khat = 95.83

For = Forested

NF = Not Forested

USER = Users Accuracy

PROD = Producers Accuracy

Khat = Kappa Statistic

The accuracy results presented in Table E1 suggest the cluster classification
process was quite successful for classifying all three image mosaics. The 1985
image mosaic produced the lowest relative scores with an overall accuracy of
94.05% and a Khat statistic equal to 88.11%. These numbers indicate 94 percent
of the pixels in the image were classified correctly and suggest I could be 88

percent confident that these results were better than a random classification.

188

However, Lillesand and Kiefer (1994) caution that results obtained from
assessments using homogenous training areas are often overly optimistic

because bounday pixels tend to be undersampled.

The stratified random sampling method is a process of randomly selecting pixel
locations within derived land cover areas that are also represented by historical
aerial photographs. This process is stratified so small but potentially important
areas within each area are not undersampled (Lillesand and Kieffer, 1994).
Next, all selected pixel locations are attributed with both image classes and
reference classes. Finally, an error matrix is used to compare the two sets of
classes for all locations. This method is often preferred to the post classification
training set method because the random method allows selection of pixels that
represent borders between adjacent land cover categories. In a study of forest
fragmentation, such borders between forested and non-forested land cover
categories are important ecological features and should be considered in any
accuracy assessment. The post classification training sets method tends to
avoid such boundaries as homogeneous areas are preferred. Table E2
highlights the results of the stratified random sampling method obtained during

this analysis.

189

Table E2: Stratified random sampling accuracy assessment results.

 

REFERENCE AIRPHOTO DATA
1973 NF FOR ROW USER
NF 284 59 343 82.80

FOR 81 440 521 84.45
COL 365 499 864

PROD 77.81 88.18 83.80
Khat = 66.52

1985 NF FOR ROW USER

NF 275 29 304 90.46

FOR 56 499 555 89.91

COL 331 528 859

PROD 83.08 94.51 90.10
Khat = 78.79

 

 

1991 I NF FOR ROW USER
NF 231 28 259 89.19
FOR 20 529 549 96.36
COL 251 557 808

 

PROD 92.03 94.97 94.06
Khat = 86.25

For = Forested

NF = Not Forested

USER = Users Accuracy

PROD = Producers Accuracy

Khat = Kappa Statistic

The results outlined in Table E2 are less optimistic than the results posted in
Table E1 as overall accuracies and Khat statistics were lower for all three dates.
However, despite the lower values, the numbers are still relatively high and
suggest the selected classification method did a good job of identifying forested
and non-forested areas on the regional landscape over time. One noticeable

trend is the increase in producers, users, and overall accuracy measures and the

190

Khat statistic over time. The 1973 image mosaic produced the least reliable
results while the 1991 image mosaic produced the most reliable results. Perhaps
this trend is a result of increasingly better technology used in newer satellite
sensors. However, such a suggestion is speculation only: the real reason behind
this trend is unknown and beyond the scope of this research. Regardless, the
numbers posted in Table E2 allowed me to be confident in the classifications

derived for each mosaic.

The wall-to-wall method compares every pixel in the classified image to every
pixel in an image with a reference source (Lillesand and Kiefer, 1994). This
methods avoids all the trappings of improper statistical sampling and class
representation but, because of the massive amount of reference data needed to
perform a wall-to-wall analysis during a regional analysis, this method is not
usually preferred. Further, according to Lillesand and Kieffer (1994; p. 614)
"reference land cover information for an entire project area is expensive and
defeats the whole purpose of performing a remote sensing—based classification in
the first place." However, in Michigan, such reference data are available to the
public for a single date - 1978 (MIRIS, 1978). Therefore, I used the Michigan
Resource lnforrnation System (MIRIS, 1978) land cover data to perform a wall-to-
wall accuracy assessment of the 1980 target image. Table E3 highlights the

wall-to-wall accuracy assessment results obtained during this analysis.

191

 

Table E3: Wall-to-wall accuracy assessment results.

1 985

NF

MIRIS DATA
FOR ROW USER

 

NF 230827 126704 357531 64.56
FOR 55436 705421 760857 92.71
COL 286263 832125 1 1 18388

 

PROD 80.63 84.77 83.71
MIRIS classes Image classes
Coniferous Forest

Deciduous Forest Forested
Forested Wetlands

All Others Non forested
For = Forested

NF = Not Forested

USER = Users Accuracy

PROD = Producers Accuracy
Khat = Kappa Statistic

Because wall-to-wall assessments make use of each entire image mosaic, Khat

statistics were determined unnecessary as no statistical sampling was performed

and little to no chance was involved. The producers, users, and overall

accuracies calculated during this assessment provide the least evidence to

support the validity of the 1985 mosaic classification. Forested areas tended to

be identified more consistently and more accurately than non-forested areas

even though these numbers suggest the classification method produced an

underestimation of forest cover for this region. Users could be 92% confident

that a forest pixel on the MIRIS map was classified as forest on the image map.

Regardless, although this wall-to-wall assessment produced lower accuracy

192

results, I felt confident enough that the 1985 image mosaic sufficiently
represented the larger forest stands contained in the MIRIS data and it probably
did a better job of identifying smaller forest patches because of the images had
better spatial resolutions and smaller minimum mapping units (one pixel).
Furthermore, the MIRIS data and the image data were gathered on non-
anniversary dates separated by at least 6 years. Because landscape change
can take place within a six-year period, the results from this analysis should be

used as only a general indicator of validity.

As mentioned above, the best method of comparing derived and reference data
sets probably has yet to be determined. All three methods described above are
commonly used, if any method is used at all, in the remote sensing literature to
characterize the validity of any particular classification. As might have been
expected, all three methods produced slightly different results but, all indicated
that the derived classifications were reasonably good in the context of the

subsequent analysis.

193

APPENDIX F: CORE FRAGMENTATION (CF) METRIC

Forest fragmentation is a “detaching or separation of expansive tracts of forest
into spatially segmented tracts” (Bell, 1995:45) and is associated with an overall
reduction of contiguous and homogeneous forest area. The end result of
fragmentation may resemble a patchwork of small, isolated, habitat islands.
Quantification of landscape fragmentation is difficult because landscape patterns

can be very complex.

Interior core areas contain requisite energy, nutrients, materials, and gene pools
necessary to allow forest patches and the plant and animal species associated
with them to proliferate in perpetuity. Interactions between interior core areas
and patch perimeters are also difficult to quantify because definitions of core
area, patch perimeter, and associated edge effects are not mutually exclusive.
However, many quantitative measures have been developed that try to measure
particular aspects of landscape heterogeneity in an effort to objectively link
landscape pattern to landscape process (Baker and Cai, 1992; McGarigal and

Marks, 1995).

As mentioned in Section 4.4.5, I found it necessary to construct a landscape
index of my own that could (1) be useful by itself, (2) be useful for describing
conditions of forest fragmentation, and (3) have a direct relationship with degrees

of fragmentation because no sufficient fragmentation metric existed. The core

194

fragmentation (CF) index can be derived with the following equation, which is

expressed here in condensed terms:

COREmaS " COREobs

CF = CORE"...x

The best way to explain the CF metric is to describe its components using a
series of illustrations. As I did in Chapter 2, I use the Whitewater Township

landscape data to guide this example.

Figure F1 shows the distribution of Whitewater Township forest cover as it
existed in 1973. The green areas represent forested land covers and yellow
areas represent non-forested covers. Areas colored with blue represent open
water areas. The outset map shows a close-up of one survey section. In it, one
can see that much of the land area is covered by forest, although several non-
forested fingers penetrate the forest from the east. Also, the land adjacent to the
open water area (northwest corner) is generally non-forested and exists between
water and forest boundaries. Interestingly enough, review of the original plat
map data revealed a small narrow subdivision existed in this particular non-

forested area.

Also illustrated in Figure F1 is the distribution of interior core areas (dark green).
These interior areas are areas that remained after a 100 meter edge effect was
removed from all forest edges. It is plain to see that the spatial extent of interior

core area is much less than the spatial extent of total forested area.

195

 

 

 

 

 

 

 

 

 

 

 

 

    

 
 

Area shown approximately
one square mil.

Scale 1:30000

Legend

Forested
Core Area

Non-forested
Water

Survey section
D lines

Scale 1 :160000

Figure F 1: 1973 Forest cover - Whitewater Township.

196

 

 

This difference between interior core area and total forest area is most noticeable
in locations where forest edges exist in close proximity to one another (see
eastern side of outset map in Figure F1). This edge effect represents the
disturbing influence that non-forested land covers have on forest edges and
isolated forest areas. Measuring the magnitude of this effect is a common
subject in the landscape ecology literature as some edge effects have been
determined to extend over distances less than 50 meters (Chen et al., 1992;
Vaillancourt, 1995) while others over distances greater than 500 meters (Skole
and Tucker, 1993; Robinson, 1992). In this research, a 100 meter edge depth
was used for calculation of CF indices; I considered 100 meters to be a
conservative estimate of the-forest edge depth environment. However, I must
note here that edge depth is a species or process-dependent characteristic and

should be changed accordingly to suit the analysis objectives (Gustafson, 1998).

The CF metric is designed to measure the relationship between the amount of
interior core area observed and the maximum amount of interior core area
possible should the total forested area exist in the least fragmented condition
possible: a circle is the shape with the largest area-to-perimeter ratio and is
therefore, the most compact patch shape subject to the least amount of edge
effect. In order to calculate the CF metric, several measurements must be made:
total forested area (Af), total interior core area (An), sum of all forest area
perimeters, which include both real edges and those imposed by the sample unit

boundary (E3), and sum of real forest area perimeters (Er). Common core area

197

metrics usually incorporate only E3 in metric calculations. However, the sum of
all forest area perimeters does not distinguish between those edges that induce
edge effects and those edges that are artificially created by sampling. Therefore,
metrics that use Es as the only estimation of forest edge will overestimate real
edge effects and subsequently, overestimate forest fragmentation. Table F1 lists
observed landscape measurements for the one square mile area highlighted in

Figure F1.

Table F 1: CF metric - observed components.

Variable Notation Value

Total land area as private A. 2140000m2
Total private land area as forest Af 1630000m2
Total interior core area Ah 690000m2
Sum of all forest patch perimeters Es 14200m
Sum of all real forest patch perimeters E, 11400m
Distance of edge effect d 100m

The following section outlines the heuristics used to calculate the CF index.
Figure F2 has been provided to illustratively guide the reader through the

calculation procedure.

198

 

 

Til-Mi: ‘

 

 

 

 

 

 

 

 

Figure F2: CF Metric calculations.

199

Section F2.1: The heuristics.

For a given sample unit area and a known edge effect represented by distance d.

Given: Af
Ah
Es
Er

d

Sum of land area as forested (Figure F2.a)

Sum of interior core areas

Sum of all forest patch perimeters (real and artificial)
Sum of real forest patch perimeters

Distance representing the edge effect.

The values for the example survey section have been provided in Table F1.

Let: Ac =
rf =
rc =
pa =
pn -.-

Geometric Assumption:

Maximum possible core area possible when Er = Es
Radius of a circular patch with an area equal to A:
Radius of a circular core area with an area equal to AC

Proportion of all forest edges as real forest edges

Proportion of all forest edges as artificial forest edges

For a given perimeter, a circle is the shape with the largest area. If a

forest patch is arranged as compactly as possible, then it would be in the shape

of a circle. The radius of such a circle would be equal to the following (see

Figure F2.b):

l'f =

\I(Af/T[)

\/(1630000m/1t)

\/ 518845m

720m

200

If we subtract the 100 meter edge effect from radius rf, then we can calculate the
maximum possible core area, first assuming E, = E8. The size of such a core
area can be calculated as follows (see Figure F2.c):

rc = rf‘d

720m - 100m

620m

lf rc > 0 then let Ac = nrcz, else let A.; = 0.

620 > 0 TRUE

Let Ac = 1: rc2
= 7r - 6202

= 1r 0 384400

1207628m2

Next, we calculate the proportion of all forest perimeters as real forest edges

(see Figure F2.d).

Let pe Er] Es

11400 / 14200

= 0.80

201

The proportion of forest perimeters not inducing an edge effect is easily

calculated by subtracting p9 from 1 (see Figure F2.d).

Let pn 1 " pg

1 - 0.80

0.20

The term pn represents the difference between real forest edges and total forest
edges and is used to correctly adjust the fragmentation estimate in order to

prevent sampled edges from biasing any calculations.

At this point we can combine terms in order to estimate the maximum possible
core area if the observed forest area was arranged as compactly as possible and
was influenced by the same proportion of negative edge effects. Such a
maximum core area can be calculated as follows:

COREmax = Ac 1' PnAr - PnAc

1207628 + 0.20 ( 1630000 ) - 0.20 ( 1207628 )

1207628 + 326000 - 241525

1292103

The third term, peAc (see Figure F2.e) represents the amount of overlap between

A; and peAf and is necessarily subtracted from the total in order to prevent

overestimation of COREmax (see Figure F2.f).

202

With all of the requisite pieces calculated, we can calculate the CF metric that
describes the proportion of potential core area that has been disturbed by
shaped-induced edge effects. The observed core area amount (see Figure F29
and related Figure F2.h) is subtracted from the maximum core area estimate.
The result is then divided by the maximum core area estimate. The CF metric is
calculated as follows (see Figure F3):
CF = ( CORE"...x - Ah ) / CORE"max

= ( 1292103 - 690000 ) / 1292103

= 602103 / 1292103

= 0.466

CF = 0.466

 

Figure F3: CF Index representation.

The value of the CF metric can be interpreted as follows (see Figure F3);
approximately 47 percent of the potential core area in the observed survey
section has not been realized because shaped induced edge effects have

fragmented these forest areas.

203

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