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This is to certify that the

thesis entitled

A COMPUTER SIMULATION NDDEL FOR THE STUDY
OF DEER-ASPEN FOREST INTERACTIONS

presented by

Philip John Mello

has been accepted towards fulfillment
of the requirements for

M. S. degreein FiSherieS & WIIdI'ife

MM,

Major professor

Date February 22, 1983

0-7839

 

 

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Place in book drop to
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stamped below.

 

 

 

 

MAY 2 8 2000

 

 

 

A COMPUTER SIMULATION MODEL FOR THE
STUDY OF DEER-ASPEN FOREST INTERACTIONS

By

Philip John Mello

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Fisheries and Wildlife

1983

ABSTRACT

A COMPUTER SIMULATION MODEL FOR THE
STUDY OF DEER-ASPEN FOREST INTERACTION

BY
Philip John Hello

A computer simulation model was developed which re-

presents the interactions of white-tailed deer (Odocoileus

 

virginianus) population with an aspen-type (Populus spp.)

 

forest community. This model can be used by biologists as
a simulation of deer responses to manipulations and as

a teaching tool by instructors in wildlife and habitat
management. It will aid students in the understanding of
population dynamics and the effects of wildlife and habitat
management policies on wildlife populations.

The aspen stand is described by such parameters as
stand age, basal area, mean diameter breast height (dbh)
and total tree numbers. Stand information is further
broken down into dbh classes, height classes and the number
of trees within each class. The dynamics of the stand
are modeled with above ground biomass and tree numbers as
a function of tree height, number of trees, and season of
the year. Deer numbers within specified sex and age classes

are used to describe the deer population. Deer population

Philip John Mello

dynamics are modeled with age specific natality rates and

3 categories Of mortality; miscellaneous mortality,

harvest mortality, and starvation. Deer-aspen interactions
are represented by algorithms which represent the effects
of deer foraging on aspen growth and mortality, and the
effects of food supply on deer mortality (starvation) and
natality.

Management options for the user are deer harvest and
tree harvest. The user is able to manipulate deer harvest
by specifying the proportion of antlered and antlerless
deer to be harvested for each year of the simulation.
Logging operations can be simulated by specifying the size
of the clearcut and the rotation period.

Several computer experiments were performed. Popu-
lations with high antlered harvest rates (50 to 70 percent)
were able to reach higher peak densities than unexploited
populations. Responses of populations to antlerless harvest
were dependent on the rate of harvest and the response
potential Of the population. Logging intervals of 10 years
caused significant declines in deer numbers while 5 year
logging intervals showed no such declines. LOw density
populations, however, showed an immediate increase following
a clearcut.

Sensitivity analyses were run on winter severity,

vegetative energy content, and deer maintenance requirements.

Philip John Mello

Sensitivity analysis of winter severity suggests that
winter severity is a major limiting factor under conditions
of abundant summer food supply. The model was highly
sensitive to deviations in vegetative energy content and
deer maintenance requirements. This suggests the need for

more accurate and precise quantification of these variables.

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to
my major professor, Dr. Jon Haufler, for his assistance
and guidance throughout the study and for accepting me
as his graduate student. Sincere appreciation is also
given to my committee members, Dr. Carl Ramm and Glenn
Dudderar, for their much needed assistance and to Dr.
Stanley Zarnoch for helping initiate this study.

Special thanks go to Connie Myers, for reviewing the
text and providing helpful suggestions; to Heidi Grether
for helping with the flowcharts; and to Rique Campa and
Dave Woodyard for their advice and sharing their know-
ledge. I would also like tO thank all those who extended
their good wishes and words of encouragement.

This study was funded by the Michigan State University

Agricultural Experiment Station.

TABLE OF CONTENTS

LIST OF TABLES ......................................
LIST OF FIGURES .....................................
INTRODUCTION ........................................

METHODS .............................................

Model Structure .................................
Initial Inputs ..................................
Forest Dynamics .................................
Deer Dynamics ...................................
Management Options ..............................
Computer Experiments and Sensitivity Analyses

RESULTS .............................................

Winter Severity' .................................
Pattern Responses ...............................
Harvest Experiments .............................
Vegetative Energy Content .......................
Maintenance Energy Requirements .................

DISCUSSION ..........................................

Winter Severity .................................
Pattern Responses ...............................
Harvest Experiments .............................
Vegetative Energy Content .......................
Maintenance Energy Requirements .................
Clearcuts .......................................
Further Research ................................
Precautions .....................................
Validation ......................................

CONCLUSIONS .........................................
APPENDIX A ..........................................
APPENDIX B ..........................................

iii

10
17

24
37
38

LIST OF TABLES '

Number Page

1 Initial weights (kg) of deer for different
age and sex classes .......................... 11

2 Initial parameters describing aspen
stands at different ages ..................... 14

3 Yearly deer numbers (deer/kmz) under varying
antlered harvest levels (antlerless
harvest equal to 0) .......................... 43

4 Yearly deer numbers (deer/kmz) under varying
antlerless harvest levels (antlered
harvest equal to 70 percent) ................. 51

5 Yearly deer numbers (deer/kmz) of a low
density deer population subjected to a 25
percent antlerless harvest ................... 55

6 Yearly deer numbers (deer/kmz) under con-
ditions of varying metabolizable energy
content of cedar browse ...................... 57

7 Yearly deer numbers (deer/kmz) under con-
ditions of varying metabolizable energy
content of aspen browse ...................... 61

8 Some typical simulated deer weights (kg) in
year 5 of the simulation under conditions
of varying maintenance energy requirements ... 63

9 Yearly deer numbers (deer/kmz) under con-
ditions of varying maintenance energy
requirements. Changes are reflected by
deviations of the multiple of baseline

metabolism. ................................... 65
10 Some equations and coefficients used in aspen

growth Subprogram (USDA 1979) ................ 115
11 Equations and coefficients used to estimate

the proportion of aspen available as browse ..116

iv

Number

12

13

Page
Equations and coefficients used in esti-
mating total biomass (kg) for an aspen
sucker stand less than 4 years old ......... 117
Equations and coefficients used in esti-
mating total biomass (kg) for older
aspen stands .............................. 118

LIST OF FIGURES

Number Page

1 Sequence of computations in 1 year of a

simulation run of the model ................... 9
2 dbh distribution of a 4 year old aspen

stand (Pollard 1971) .......................... 15
3 The effect of deer browsing on aspen growth ... 20
4 Deer metabolic rates throughout the year

with a graphical estimation of deer main-

tenance requirements .......................... 27
5 Weight patterns of male and female deer from

birth to maturity (Moen 1978) ................. 29
6 The probability of a deer dying as a function

of percent weight loss ........................ 34
7 Fawn/doe ratio as a function of female winter

weight loss ................................... 35
8 Simulated response of deer densities to

varying winter severity ....................... 41
9 Pattern lresponse. Population decline

followed by an increase to original peak

densities ..................................... 43
10 Pattern 2 response. Population decline

followed by the eventual dying out of the

population .................................... 44
11 Pattern 3 response. Population decline

followed by a slow increase in number. The

population is unable to reach peak densities .. 45
12 Simulated effects of different antlered

harvest levels on deer densities

(antlerless harvest equal to O) ............... 47

vi

Number

13

14

15

16

17

18

19

20
21

22
23

24

25

Simulated effects of different antlerless
harvest levels on deer densities (antlered
harvest equal to 70 percent)

Simulated effects of different antlerless
harvest levels with clearcuts performed

in 5 year intervals ..........................

Simulated effects of different antlered
harvest levels with a 25 percent antler-
less harvest on deer densities

Simulated effects of varying metabolizable
energy content of cedar browse on deer
densities

Simulated effects of varying metabolizable
energy content of cedar browse, on
initially low density deer populations.
Clearcuts were performed in 5 year
intervals

Simulated effects of varying metabolizable
energy content of aspen browse on deer
densities

Simulated effects of changes in maintenance
energy requirements on deer densities.
Changes are reflected by deviations of the

multiple of baseline metabolism ..............

The main program .............................

Subroutine ADVANC. Advances tree data to
next age class. Called every 10 years of
the simulation

Subroutine AGESEX.

Subroutine BROWSE. Computes amount of aspen
consumed by individual deer per month.
Allocates consumed browse to height classes

Subroutine CHOOSE. Computes amount of
aspen browse available in each stand and

chooses feeding area .........................

Subroutine DIST. Initializes tree data for

a 4 year old aspen stand .....................

vii

Initializes deer matrix ...

50

52

53

56

59

6O

64
86

87

88

89

9O

91

Number Page

26 Subroutine FEED. Calculates individual

deer demand, deer growth, and probability

of starvation ............................... 92
27 Subroutine MORTAL. Calculates miscel-

laneous and harvest mortality ............... 93
28 Subroutine NATAL. Calculates fawns per doe

and adds fawns to the population ............ 94
29 Subroutine NORM. Initializes tree

matrices .................................... 95
3O Subroutine PRINT. Prints relevant deer

data ........................................ 96
31 Subroutine SUM. Calculates monthly deer

herd demand for aspen and cedar ............. 97

32 Subroutine TALLY. Tallies the number of
deer, harvest mortality, and starvation
mortality per age/sex class. Removes dead

deer from the population .................... 98
33 Subroutine TRECUT. Removes clearcut and

adds area to 1 year Old stand ............... 99
34 Subroutine TREGRO. Computes percent browse

consumed in each height class. Calculates
yearly tree growth and mortality. Prints

relevant tree stand data .................... 101
35 Subroutine YARD. Computes amount of cedar
browse consumed per month ................... 102

viii

INTRODUCTION

One of the major problems facing forest and wildlife
management professionals today is evaluating the impact of
forest management policies on wildlife populations. Modern
foresters and wildlife managers realize that a more holistic
view of the forest ecosystem.must be taken to assure proper
management of both forest and wildlife resources. Un-
fortunately, this approach involves a complex set of
interactions which make it increasingly difficult to fore-
lcast the outcome of a set of management decisions.

One result of this new philosophy is the recent appli-
cation of systems analysis and computer simulation modeling
in forest and wildlife management. Jeffers (1978) listed
3 reasons for using systems analysis in ecological research.
These were: 1) the inherent complexity of ecological
relationships; 2) the characteristic variability of living
organisms; and 3) the apparently unpredictable effects
of deliberate modification of ecosystems by man. For
these reasons, and the dynamic nature Of the interactions
which occur in a natural ecosystem, the conventional

procedure of controlled laboratory or field experiments

often provides only fragmented information which, in many
cases, is insufficient to develop a clear understanding
of the interrelationships of an ecosystem.
Simulation models are tools which unify existing in-
formation and provide the user with a means to analyze
the system under study and evaluate various management
strategies while retaining to some degree the complexity
and variability that is found in natural ecosystems.
Because of the greater ease of measurement, the use
of modeling in forestry is both older and more sophisti-
cated than modeling efforts in wildlife management (Bunnell
1974). Many models have been developed which simulate
the growth of various types of forest stands and allow
the user to examine the effects of various timber management
strategies on the stand (Leuschner 1972, Fries 1974,
Perala 1979, USDA 1979). The primary goal of these models
was to predict the amount of merchantable timber produced
under various timber management plans. In these models,
forest growth is modeled as a function of some charac-
teristic Of the stand itself with no consideration of
the effects of wildlife on forest growth. Other forest
growth models have been developed which examine deer browse
production in a stand, although again, the effects of
wildlife on growth are not incorporated into the model

(Myers 1977, Cooperrider and Behrend 1982).

This same approach has been taken in many models of
ungulate populations (Lomnicki 1972, Walter and Gross 1972,
Anderson et a1. 1974, Fowler and Barmore 1976, Roelle and
Bartholow, unpubl. rep. 1977, Short 1979). In these
models, environmental factors are represented indirectly
as density dependent natality and mortality rates. This
type of model has been referred to as a complicated steady-
state model (Watt 1968). Models of this type are the most
commonly used type in wildlife management today. These
models are considered appealing because fewer parameters,
which can be measured and compared with simulation results,
are dealt with, simplified assumptions are used, and many
parameters which are difficult to measure are omitted.

The results of these models are considered potentially

less precise but more realistic than more complex and pre-
cise models (Pojar 1981). The major drawback of this type
of model is the assumption that environmental conditions and
the density dependent relationships within the system re-
main constant throughout the simulation. Therefore models
such as these cannot be used for long range prediction.
Also, since there are no environmental factors incorporated
in the model, these models are obviously unable to evaluate
the effects of habitat manipulations on wildlife populations.

Medin and Anderson (1979) developed a mule deer
(Odocoileus hemonius) model that incorporated environmental

influences on deer natality rates. This was done by a

3 step process which related forage nitrogen yield to pre-
cipitation, deer fat reserves to forage nitrogen yield and
then modified the mean age-specific birth rate of deer as
a function of fat reserves. This approach is useful in
that it provides the user with more long range predictive
power. However, it is limited by its inability to mani-
pulate habitat and by the unreliability Of many difficult—
to-measure parameters.

Still another approach has been introduced (Moen 1973,
Mautz 1978) which calculates the carrying capacity of an
area based on the nutritional requirements of an animal and
the amount of energy or protein available in the area.
Models of this type have been developed for deer (Wallmo
et al.1977, Spalinger 1980) and elk (Cervus elaphus)

 

(Swift et al. 1976, Hobbs et al 1982). A more complex model
developed by Bobek (1980) also incorporated this approach.
The value of these models is that they provide a link
between range conditions and deer numbers. Therefore, as
habitat conditions change, the maximum number of animals
an area can support can be calculated and appropriate
management strategies can be initiated depending on
management goals. These models, however, are not dynamic
and can only be used on a year to year basis.
The next step in model complexity is a model which links

both habitat dynamics and populations dynamics. Such models

can help predict the long range effects of various wildlife
and habitat strategies and also provide useful insights
into the interrelations of the system under study. Very
few models of this type relating ungulate populations and
forest vegetation have been developed. Davis (1967) de-
veloped a model which allowed the user to make decisions
on both wildlife and timber management strategies. Another
model which combined vegetation dynamics and population
dynamics was developed by Walters and Bunnell (1971).
The primary purpose of this model was to devise a management
game to be used as a teaching aid. Both of these models
were very generalized and used simplified assumptions
which made them difficult to apply to specific ecosystems.
Cooperrider (1974) developed a model which represented
the interactions of a deer population with northern forest
vegetation. This model was designed specifically for the
Huntington Wildlife Forest in the central Adirondack re-
gion of New York, though the author suggested it may be
applicable to other areas of similar vegetation composition.
This model enabled the user to determine the effects of
various habitat and wildlife management techniques and,
through sensitivity analysis, identify inputs and para-
meters which have the greatest effect on the system. Ad-
ditional models of this type dealing with different species

or ecosystems are needed.

One such system involves white-tailed deer (Odocoileus

 

virginianus) interactions with an aspen (Populus spp.)

 

forest community. A close association exists between white-
tailed deer and aspen in the Lake States region. Aspen

has been found to be the preferred summer habitat of

deer in Wisconsin (McCaffery and Creed 1969) and Minnesota
(Kahn and Mooty 1971). Studies in Michigan have shown that
a major proportion of deer harvested each year were taken
in areas where aspen is the most frequently occurring
forest type (Byelich et a1. 1972). Aspen, in Michigan, is
considered the most important deer producing cover type

and maintaining and treating this type is given first
priority in its deer habitat improvement program (Byelich
et a1. 1972, Bennett et a1. 1980).

The purpose of this study was to create a computer
simulation model which represents the interaction of a white-
tailed deer population with an aspen-type forest community.
The model can be used by biologists as a simulation of
deer responses to manipulations and as a teaching tool by in-
structors of forestry and wildlife management courses. The
value of computer modeling as a teaching aid has been dis-
cussed (Walters and Bunnell 1971, Zarnoch and Turner 1974)
and is viewed as a tool which allows the user to develop
an intuitive understanding of the ecosystem dynamics and
provides simulated field experience in the application of

management techniques. Paulik (1976) felt the use of

simulated resource management games provides students with
the type of learning experience normally acquired through
several years in a responsible management position. such
games allow students to "test their analytical skills as
well as their decision-making abilities in realistic manage-
‘ment situationsf' Therefore, by using this model, the user
is expected to develop an understanding of the effects of
manipulating various management options on deer-aspen
interactions and devise a management plan which will meet

previously specified management goals.

METHODS

Model Structure

The sequence of events for a simulated year is dia-
grammed in Figure 1. More detailed flow diagrams of the
main program and subroutines are shown in Appendix A.

The model was written in FORTRAN IV computer language for

a CDC 170 Model 750 computer. System dynamics were modeled
using a set of difference equations. This type of model
has been classified as a finite difference model (Lassiter
and Hayne 1971).

Data for this model were obtained from a literature
review of past studies in aspen and deer research. Thus
no field work was performed for this study. Data were
gathered primarily from published studies from.Michigan
and other areas of the Lake States region. Therefore,
this model is considered a generalized model of deer-aspen
interactions in the Lake States region and does not simu-
late the interactions of any 1 aspen stand in particular.

Simulation begins in November of the first year. This
was done because the information used to derive the age
structure of the deer population was obtained from the

deer harvest. There are 3 main components of the program:

 

SET INITIAL ASPEN dbh I
DISTRIBUTIONS AND DEER
AGE-SEX DISTRIBUTION.

 

 

Joriuory MOVE DEER TO CEDAR swAMfl

March ALLOCATE BROWSE CONSUMED TO
.dbh CLASSES. CALCULATE NEW ASPEN
GROWTH. PERFORM CLEARCUT IF
SCHEDULED.

 

 

 

 

 

April REMOVE DEER FROM CEDAR
SWAMP. CALCULATE NEw FAWN CROP.

 

.Iune ADD FAWNS TO DEER POPULA-
TION.

CALCULATE BRowSE AVAILABLE AND 1
CHOOSE FEEDING AREA.

 

- w
EALCULATE DEMAND OF THE DEER POPULATIOIfl

 

J A
LREMOVE BROWSE CONSUMEDI
. 1 *
LCALCU LATE DEER CRowTH]

 

November REMOVE HARVESTED DEER
FROM THE POPULATION.

L_lREMOVE MISCELLANEOUS AND STAT-NATION]

 

MORTALITY FROM THE DEER POPULATION.

Figure 1. Sequence of computations in 1 year of a
simulation run of the model.

 

10

l) forest dynamics; 2) deer population dynamics; and

3) deer and forest management options.

Initial Inputs

The initial deer population is created by the user
by assigning values for the total number of deer in the
population, the mean age of males and females, and the pro-
portion of males in the population. The total number of
males and females is calculated by multiplying the total
number of deer by the appropriate proportion. The age
distribution for each sex is then computed using a negative
exponential distribution with the appropriate mean age
(Cooperrider 1974).

All information on an individual deer is stored in a
600 by 5 matrix. Therefore, the model is unable to handle
more than 600 deer in a population. The statistics which
are kept on a deer include sex, age, weight, critical weight,
and the number of fawns dropped.

Initial weights for males less than 8 years old and
females less than 5 years old were obtained from.MOen's
(1978) sine wave curve (Table 1). It is assumed that male
deer reach their maximum.weight at 7 years of age and female
deer at 4, as has been reported for mule deer (Bandy et al.
1970). Therefore, initial weights for male deer older than
7 years of age were set equal to the initial weight of a
7 year old buck. Similarly, initial weights of older fe-

males were set equal to the initial weight of a 4 year old

doe.

11

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No.mw No.mm No.mw No.mw No.mm mm.mn Hm.wo om.om «o.m mamaom

mm.oma mm.mma H¢.~ma mw.qNH oN.oHH o~.ooa qo.qm mm.mm o~.m mam:

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mwd

¥.mmmmmao Now mnm owe DDOHOMMHm How Hemp mo wav munwwo3_amHuHcH .H OHnNH

12

The critical weight is used to compute the probability
of death due to starvation for a deer and the number of
fawns a doe will bear. This is set equal to the initial
weight at the beginning of the program. The number of
fawns dropped is set equal to O for all deer at the be-
ginning of the program. The program ignores this value
in the winter months for female deer (and all year round
for male deer) since the number of fawns a doe is carrying
has little significant effect on a doe's metabolism at
this time of year (Moen 1973). Since the program begins
in November, any arbitrary value could have been chosen
for this parameter.

After the initial deer population has been established,
the deer matrix is sorted by age and sex. First, deer are
sorted by age with the oldest deer occurring in the first
position in the matrix and the youngest occurring in the
nth poSition for a population of n deer. Deer of the
same age are sorted according to sex with males occurring
before females. The matrix is sorted in this manner to
represent deer social organization with older males having
greater access to browse than older females and both
having greater access to browse than fawns (Ozoga 1972,
Townsend and Bailey 1981).

The initial aspen forest is created simply by assigning
the proportion of the total area for a specific aged stand.
A maximum.of 7 age classes can be assigned with initial

ages ranging from 1 to 61 at 10 year intervals; Values for

13

mean diameter breast height (dbh), total number of trees/
ha, and Standard deviations for each stand are Specified
within the program (Table 2). Values for total number

of trees/ha in a stand greater than or equal to 20 years
of age were obtained from Perala (1977). The value for
the number of suckers/ha in a new stand was obtained from
Graham et a1 (1963). Scant information on 10 year old
aspen stands could be found in the literature. Therefore,
the initial number of trees/ha was estimated from the
program by running the forest submodel separately for a
period of 10 years.

Diameter breast height distributions for aspen stands
of various mean dbh's have been reported by the Lake
States Forest Experiment Station (1933). Chi-square goodness
of fit tests performed on these distributions showed
all stands, with the exception of the 7.62 cm stand, were
normally distributed. To be consistent, all stands greater
than or equal to 11 years of age (mean dbh i 5 cm) were
assumed to be normally distributed. These mean dbh's
and standard deviations were then assigned to different
stands such that the mean dbh was approximately equal to
reported mean dbh's for stands of different ages in the
Lake States region (Perala 1977).

The youngest dbh distribution which could be found in
the literature was for a 4 year old stand (Pollard 1971).

The distribution of a 4 year old aspen stand (Figure 2)

14

 

 

No.q wN.NN «ma Ho
om.q om.mH oom Hm
o~.¢ qe.qa mom Ha
mm.m N~.~H and an
em.m mH.n own HN
mm.H ow.¢ mqoa HA
0 o oaoa H
mm M m£\mOOHH Ow<

 

ABS 5%

 

.mowm DEOHOMMHm mo museum comma wcHnHHomom mnouoamumm HmHuHcH

.N maan

15

FREQUENCY

 

DBH (CM)

Figure 2. dbh distribution of a 4 year old aspen stand
(Pollard 1971).

16

contained a greater proportion of trees in the smaller dbh
classes. As the stand ages, many of the smaller trees will
die due to competition for sunlight with larger overstory
trees and the distribution will approach normality.

Initial information on a tree stand included dbh,
number of trees within a dbh class, and tree height. The
interval for the initial dbh classes is 0.25 cm. The mid-
point of these intervals is designated as the initial dbh
of the tree. The number of trees within a dbh class is
calculated by multiplying the initial total number of trees
within a stand by the probability that a tree will occur
in that dbh class. This probability is computed by a
function subprogram listed in Kossack and Henschke (1975)
which calculates the area of an interval under a specified
curve. The initial height of a tree is then computed as a
function of its dbh.

Values for tree height, dbh, and number of trees with-
in a dbh class are stored in 3 respective 120 by 7 matrices.
Each column of the matrix represents a stand (the 1 year
old stand in column 1 and the 61 year old stand in column
7) while each row represents a dbh class. This allows for
a maximum of 120 dbh classes within a stand.

All values for the 1 year old stand are set equal to
0 since trees in this stand are not distributed to dbh
classes until the fourth year of the simulation. When a

stand reaches.4 years of age, the process described above

17

for assigning dbh and height values, and calculating the number
of trees within a dbh class is used. In this case, however,
the curve shown in Figure 2 is used rather than the normal
curve.

In addition to these parameters, the user must specify
the size of the area to be modeled, choose from 3 levels
of winter severity (mild, normal, and severe) and designate
various deer and habitat management plans. The method
for implementing these plans will be discussed in the

section titled management options.

Forest Dynamics

There are 3 food sources available to deer in the
model: aspen browse, cedar browse, and herbaceous vege-
tation. Neither cedar browse nor herbaceous vegetation are
modeled dynamically in the program” A fixed amount of
herbaceous material and cedar browse is supplied to the
deer at the appropriate times of the year for each year
of the simulation. This assumes that deer browsing has
no effect on cedar or herbaceous production and that a
fixed amount of cedar and herbaceous vegetation will be
produced each year regardless of the intensity of browsing
in the previous years.

Aspen growth is modeled as a dynamic process using a
simplified version of a model developed by the North

Central Forest Experimental Station (USDA 1979).

Growth and mortality coefficients have been developed for
various pure and mixed stand forest ecosystems of the Great
Lakes region. Yearly forest growth is summarized in the

following equations (Leary 1979):

AY - . —
E — F1(D, CR, 51) * NT ~k 1720:, NT)
where

AY = change in the sum of tree diameters in
a year

F1 = the potential growth function

F2 = the modifier function of potential
growth actually occurring

D = mean dbh

CR = mean crown ratio

SI = site index

Y = sum of the tree diameters

NT

number of trees

The potential growth function is designed to estimate
how rapidly the mean tree would be growing in dbh if it
were not interacting with any other trees (Hahn and Leary
1979). This number is then multiplied by the number of
trees in the stand to give the potential change in the
sum of tree diameters in the stand. The modifier function
reduces the potential change to what has been observed
from permanent growth plots (Leary and Holdaway 1979).
The equations used and the coefficients for aspen are listed

in Appendix B, Table 10.

19

Change in dbh for an individual tree is then calcu-
lated using what is termed the "allocation rule” (Leary
et al. 1979). This rule calculates change in dbh as a
function of its proportion to the total growing stock in
the stand. Change in height growth is then calculated
using the regression equation which relates the tree height
tx> tree dbh. This value is then modified (Figure 3)
to represent the effect of deer browsing on aspen growth.
This modified change in height growth is then converted
back to a modified change in dbh. If height growth is
negative or, in other words, if a tree is shorter than it
was the previous year, diameter growth is set equal to O.
The probability of a tree dying is then computed as a func-
tion of its diameter growth (Buchman 1979).

Since there is no distribution for a stand younger
than 4 years old in the literature, stands of these ages
are described in the model simply by mean height, mean dbh
and total numbers of trees. Due to a lack of data on average
tree heights of a young aspen stand, site index curves for
the Lake States region were used to estimate this value
(Lundgren and Dolid 1970). This method will most likely
result in an overestimation of mean stand height. This.
value is then modified mashow the effects of deer browsing
in the same manner as an older stand. Tree mortality,
however, is computed as a function of stand age and the

number of trees in the stand (Perala 1973).

20

 

120
100
80
E
U
8
H
00
F, 60-
né *
U
58
H
(DU-1
o 40
4.)
$3
0)
U
H
0)
D...
" 20.
1
o

 

 

25 50 73 100
Percent Browsed

Figure 3. The effect of deer browsing on aspen growth.

21

For a stand less than 4 years old, available browse
for deer is calculated simply as a function of mean stand
height and total number of trees (Westell 1954). First
the total biomass of aspen in a stand is computed. This
value includes leaves in the spring, summer and early fall
months (April to October) but only woody vegetation in the
late fall and winter. The percent of the total biomass
available to deer as browse in the appropriate season is
then calculated as a function of mean stand height.

For an older stand, the process of computing available
browse is much the same with slight modifications. The
total above ground biomass of an individual tree is esti-
mated using equations developed by Young and Carpenter
(1967). Again, this includes or excludes leaves depending
on the season. Available browse per tree is then computed
by multiplying the percent of woody material available
as browse (computed as a function of individual tree height
(Westell 1954)) by the total biomass and then adding the
total biomass of leaves per tree. This value is then
multiplied by the number of trees of equal dbh and height
to give the total available browse per dbh class.' This
process is repeated for each dbh class. The sum of these
values equals the total aspen browse available within a
stand. The equations and coefficients used for estimating
browse availability are listed in Appendix B, Tables 11—
12.

22

For both young and old stands, 2 values for browse
availability are calculated. One value assumes deer will
browse aspen stems and twigs to the 0.64 cm diameter as
is the case under light browsing conditions, while the
other assumes deer will browse to the 1.27 cm diameter.
Heavy browsing to the 1.27 cm diameter usually occurs when
deer populations are large and food is scarce (westell
1954).

The model assumes that a tree greater than 3.34 meters
in height will provide no woody browse to an adult buck.
Trees out of reach of adult does are assumed to be those
which are greater than 3.1 meters, while trees greater
than 2.7 meters are assumed out of reach of fawns. How-
ever, the leaves on these trees were provided to deer under
the assumption that they will fall in early autumn and be-
come available to deer.

Prior to calculating yearly growth of aspen, the total
amount of aspen consumed in each stand in the previous year
is allocated to the tree height classes. Three possibilities
exist when comparing the amount of aspen consumed to the
amount available: 1) the browse consumed is less than the
browse available to the 0.64 cm diameter; 2) all available
browse is consumed; 3)the browse consumed is greater than
the browse available to the 0.64 cm diameter but not all
available browse is consumed. If the first possibility

exists, the amount of browse consumed is proportionally

23

allocated to each height class. That is, if height class
X makes up Y percent of the total browse available, then
Y percent of the total browse consumed is allocated to
height class X. If all available browse is consumed, the
amount of browse consumed in each height class is set equal
to the amount available.

In the case of the third possibility, the following
equation illustrates how browse is allocated to each height

class:

BA6 + ((BA - BA6) x TBC ' T36 )

BC TBA - TBA

where,
BC = browse consumed per height class
BA = browse available per height class

BA6 = browse available to the 0.64 cm diameter
per height class

TBC = total browse consumed
TBA = total browse available

TBA6

total browse avalable to the .064 cm
diameter

First, the proportion of browse greater than 0.64 cm in dia-
meter that was consumed is calculated. This value is then
multiplied by the amount of available browse greater than
0.64 cm in diameter in a height class to give the amount

of consumed browse greater than 0.64 cm in diameter. The
total amount of browse consumed in a height class is then

calculated by adding the amount of available browse less

than 0.64 cm in diameter to this value. This process is

repeated for each height class.

Deer Dynamics

The major food source for deer in this model is aspen
browse. In the summer and fall from June to November,
herbaceous vegetation is provided to supplement the deer's
diet. For 3 months during winter, no aspen browsing takes
place and deer are provided with a specified quantity of
cedar browse. This represents the behavioral adaptation
of northern deer to gather in coniferous swamps which pro-
vide maximum thermal protection during winter months.
Winter severity is represented by the quantity of cedar
supplied to deer during the winter with higher amounts
supplied during mild winters and smaller amounts in severe
winters.

In the model, deer yarding season occurs during a
3 month period from January to March. A deer yard is as-
sumed to provide 184 kg/ha of browse on the average (Ryel
1953). The size of the deer yard in the model is equal to
one-tenth of the total aspen area. The size of the area
in which a deer herd will cover is then further reduced
for each.month of the yarding season to represent the re-

duction of deer mobility due to severe winter conditions.

The magnitude of this reduction is dependent on the severity

of the winter.

25

Each stand is assigned 2100 kg/ha of herbaceous material
in the month of June (Stormer and Bauer 1980). This is
assumed to be the total amount of herbaecous material avail-
able to deer during the summer and early fall. If there
is not enough aspen available to meet a deer's monthly
demand, its diet is then supplemented with herbaceous
material. The amount consumed is then subtracted from
the amount available and the process is repeated for each
deer.

'Many herbaceous species are preferred by deer over
aspen (Graham et a1. 1963, Stormer and Bauer 1980). How—
ever, it has been found, that a majority of the herbaceous
vegetation in an aspen stand consists of bracken fern

(Pteridium aquilinum) and grasses (Gramineae) which are

 

 

 

of low preference to deer (Stormer and Bauer 1980). For
this reason, the composite category of herbaceous material
in the model was given lower preference than aspen.

The amount of food consumed by a deer is computed as
a function of deer weight, the metabolizable energy of the
food, and the metabolic rate of a deer. The following
equation was used to compute the amount of forage a deer

will consume (Moen 1978):

(MBLM) 7o IFWKO‘75

DWFK = GEF DE c

where,

DWFK = dry weight forage in kilograms

26

MBLM = metabolic rate expressed as a multiple
of baseline metabolism

IFWK = ingesta-free weight (= .9*live weight)

GEFO = gross energy in forage

PDEC = digestible energy coefficient

MECO = metabolizable energy coefficient

Deer show a cyclic pattern of food consumption through—
out the year due to changes in metabolic rates (Figure 4).
The values for MBLM shown in this curve are the same for
adult deer of different ages since metabolic rate and

baseline metabolism increase by the same factor (Weighto'75

)
as the animal grows older and gains weight. The greatest
amount of food is consumed in the late summer and early
fall and the lowest in the winter months (French et al.
1955, Long et al. 1965, Moen 1978). This reflects the
deer's need to build up fat reserves to help survive the ap-
proaching winter and their behavioral adaptation of re-
stricting activity and conserving energy during the winter
months (Ozoga and Verme 1970). The model also incorporates
a decrease in food consumption by male deer in the month
of July (French et a1. 1955, Long et a1. 1965). A possible
explanation for this is deer decrease their activity at
this time due to the warm.summer temperatures (Short 1969).
Female deer not bearing fawns show a pattern similar

to male deer for metabolic rate with peak and minimum rates

occurring at the same time of year. However, the amplitude

27

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coaumEHumm Hmoflnamuw m nufl3 Hum» mnu uoozwsouzu mommy oflaonmumfi Home

zom<z .uma .pamm mzaw zom<=

moz<zw»z_<z
mom pzwzmm_=amm n.

35. 8.535: Ill!

.6 ouowwm

(51' 9x" 0; so 31d111nw)
alvu 311osv13w

28

of this change is smaller for female deer (Moen 1978).
Pregnant females, on the other hand, show a sharp increase
in metabolic rate in the spring, reaching a peak in July.
This is due to the increased energy requirements of a
female deer during the latter third of gestation and the
lactation period (Moen 1973).

Metabolic rates expressed as a multiple of baseline
metabolism were calculated separately for young fawns.
Examination of growth patterns of deer fed £9 1ibitum in-
dicate that young fawns do not exhibit the yearly cyclic
weight gain and weight loss of adult deer (Figure 5).
Rather, female fawns show a linear increase in growth during
the first 3 months of life before exhibiting adult growth
patterns. Male fawns show the same linear increase for
the first 3 months and then show an exponential relation-
ship between age and growth during the first winter of
life. This, combined with the fact that the metabolic ef-
ficiency of a small animal is less than that of a large
animal, suggests that the metabolic rate of a fawn in
relation to baseline metabolism may be greater than adult
deer.

This idea is supported in the literature. Robbins and
Moen (1975) reported newborn fawns consumed 369.48 Kcal/
day/Wkg of digestible energy as milk. This is equal to
302.93 Kcal/day/Wkg of metabolizable energy (digestible

energy x 0.82) which is 4.81 times baseline metabolism,

.Awmma noozv anounhmumé ou nuuwn Scum Hoop mamamm mam mama mo maumuuma unwwmz .m mummwm

   

to. +~ +H 25m mwa.
and cam nah nah can and Sam cam adh
. W, - 1 Hi £8:
N -.Qq M
3
I.
“5.25%, am.
.4
m
an
(
ow
3m:

-ONH

30

a value higher than any value reported for adult deer. In
addition, a t-test performed on data from Holter et a1.
(1977) showed a significant difference (P <.05) in meta-

bolizable energy intake (Kcal/kgo‘75

) during the fall
months in the first and second years of a deer's life.

Average monthly metabolizable energy requirements ex-
pressed as a multiple of baseline metabolism for fawns
were estimated in the following manner: For female fawns,
a linear relationship was assumed, with metabolizable
energy set equal to 4.81 in the first month and equal to
the adult female value in the fourth month. Adult values
were used when fawns reached the age of 4 months. For
male fawns, a linear relationship was established between
fawn age and metabolic rate using data from Holter et a1.
(1977). This line was used for male fawns aged 4 to 10
months. For young fawns another line was established
which connected the value for a 4 month old fawn and the
value 4.81 for a 1 month old fawn. Adult values for male
deer were used when the deer reached 11 months of age.

The choice of stand in which feeding occurs is based
upon the total amount of energy available to the deer
in the stands. In each month, the model calculates the
total amount of energy in each stand. These values are
then compared to each other and the stand with the highest
energy content is selected as the stand in which feeding

will occur for that month. This assumes that deer choose

31

feeding areas and select foods which maximize their energy
intake.

Once a stand has been chosen for feeding, it is assumed
all deer will feed in that stand for the entire month.

This is a simplistic assumption, as the possibility exists
that after a few days of feeding another stand might have
more available energy than the stand chosen at the beginning
of the month. However, because the program is constructed
in monthly time steps, the program is unable to deal with
any switching of feeding areas which might occur in a
shorter time interval.

After the feeding area has been chosen, the number of
deer-days in which the area can support the deer herd is
calculated by dividing the total supply of forage available
by the daily demand of the deer herd. If this value is
greater than the number of days in the month, it.is set
equal to the number of days in the month. The amount of
food consumed by each deer per month is then computed by
multiplying the daily demand of the individual deer by the
number of days in the month.

If the number of deer days the area can support is less
than the number of days in the month, this number is trun-
cated and then multiplied by the daily demand of the deer.
This value will be referred to as X. The extra fraction
of a deer day is then converted to available browse. This
is then compared to the daily demand of the deer. The

smaller value is added to X to give the amount of food

32

consumed by the deer in that month. The extra available
browse is then reduced and the process is then repeated for
each deer in the population.

This process was used because it is assumed that all
deer will meet their daily demand for at least X days. For
example, if the number of deer days equalled 205 then all
deer will feed for 20 days. On the let day only half the
herd will meet its daily demand. Since the deer matrix is
sorted first by age, only the older deer will feed on this
day.

Growth of adult and yearling deer in terms of weight

change is computed by the following equation:

0.005357 (C - M)N

AW = body weight change in kilograms

C = mean metabolizable energy consumed
in a month

M = mean energy requirements for maintenance
in a month

N = the number of days in a month

The slope of this line was derived from.Moen (1973).
Growth of fawns was computed using the same form of the
equation shown above. However, the slope was equal to
0.002349. This slope was derived from data reported in
Holter et a1. (1979).

33

Estimates of mean monthly energy requirements for main-
tenance were derived graphically (see Figure 4). A linear
relationship was assumed between maintenance requirements
and time of year with peak requirements occurring during
breeding and minimum requirements occurring in mid—winter.
For pregnant females, peak maintenance requirements occurred
during the lactation period (Moen 1973). A line was drawn
which intersected the metabolic rate curve at points where
deer fed Ed libitum began to gain weight in the spring and
lose weight in the fall (French et a1. 1955, Magruder et al.
1957, Long et a1. 1965). A second line was drawn which
connected peak and minimum requirements.

There are 3 types of mortality which occur in this model:
1) starvation; 2) miscellaneous mortality; and 3) harvest.
The probability of starvation is computed as a function of
percent weight loss (Figure 6). Miscellaneous mortality
is defined as all mortality which is not starvation or
harvest mortality (road kills, poaching, disease). This
rate is a constant throughout the simulation for each sex
and age class. This assumed density independence, though
in reality, all 3 are most likely density dependent. Deer
harvest is controlled by the user and will be discussed
further in the management options section.

The probability of a doe producing 0, 1 or 2 fawns is
a function of age (fawn, yearling or adult) and winter weight

loss (Figure 7). The nutritional condition of a doe is a

34

1.0
.8-
.6:
>.
4..)
-H
...;
-H
.o
m
.o
o
H
94
.4:
l
.2_

 

10 20 36 46 56
Percent weight loss

Figure 6. The probability of a deer dying as a function of
percent weight loss.

35

 

2.5
2.0 3+ years old
old
31.5
«H
m
p
m
o
'o
\
.5:
h.
1.0.l
0,5) 1 year old
‘ l
1
10 20 30 40

Percent weight loss

Figure 7. Fawn/doe ratio as a function of female winter
weight loss.

36

major factor affecting productivity (Cheatum and Severinghaus
1950, Whelan and Riffe 1966). Does which enter the spring
in poor physical condition, due to low nutritional diets
during the winter yarding season, will produce weaker fawns
with a low probability of surviving past the first few days
of life (Verme 1962, 1977).

The model computes the average fawn/doe ratio for specific
age classes and weight loss levels, and then calculates
the probability of each doe bearing 0, 1 or 2 fawns with the

following functions:

_ 1 - r r< l
f(0) - 0 r_>_l
_ r r<=1
f0”) — 2-r r'>'l
_ r - l r3;l
f(2) — 0 r<1

where,
r = fawn/doe ratio (0 1 r i 2)

For example, if the average fawn/doe ratio is 1.4 for

a doe, then the probability of that doe bearing 1 fawn
(assuming a doe will produce only 0, l or 2 fawns) is

2 - 1.4 = 0.6. The probability of bearing 2 fawns is

1.4 - l = 0.4 and the probability of not bearing fawns is
0. The total number of fawns produced is then tallied

and added to the population in the month of June. This
number reflects the number of fawns which survive to at

least 1 month of age.

37

Management Options

Management options for the user include deer harvest
and tree harvest. At the beginning of the program, the
user is able to assign a proportion of antlered and antler-
less deer to be harvested for each year of the simulation.
Antlered deer are defined as yearling and adult bucks while
antlerless deer include all does plus buck fawns.

The probability of a deer in a particular category
(antlered or antlerless) being harvested is set equal to
the proportion assigned by the user. This assumes that all
deer in a category have an equal probability of being har-
vested and that hunters show no preference for a particular
age class within a category. This is, most likely, a sim-
plistic assumption, as studies have indicated hunter pre-
ference and greater vulnerability in certain age classes
(Maguireand Severinghaus 1954, Van Etten et a1. 1965,
Roseberry and Klimstra 1974). However, this relationship
is extremely difficult to quantify, and disagreement exists
as to which age classes are harvested at higher rates (Coe
et a1. 1980). Harvest mortality is calculated in November
and the number of deer harvested are removed at this time.

The only silvicultural treatment allowed in this model
is clearcutting. The user is able to specify the size of
the clearcut in acres and the stand age when the cut is to

occur. When a stand reaches this age, the number of acres

38

specified by the user is removed from that stand and added
to the 1 year old stand. The total number of suckers per
acre in the 1 year old stand is a function of the basal

area of the cut stand (Graham et al. 1963).

Computer Experiments
and Sensitivity Analyses

Several computer runs were performed under various
biological conditions. Due to the stochastic make-up of
the model, a total of 3 runs were made for each condition.
Computer experiments were performed to investigate the
effects of varying antlered and antlerless harvest rates on
deer populations. Clearcut intervals were also varied.

In addition, sensitivity analyses were performed on
such variables as winter severity (mild, normal and severe),
vegetation energy content (cedar and aspen), and maintenance
energy requirements. For the sensitivity analysis of
vegetation energy content, reported values of metabolizable
energy of cedar and aspen were used (Ullrey et a1. 1964,
1967, 1972) along with values computed as a function of
the proximate composition of the species using equations
derived by Mautz et a1. (1974). Mean monthly maintenance
energy requirements were changed by adding or subtracting
a factor of 0.1 or 0.2 to the multiple of baseline metabo-
lism. Each deviation of 0.1 from the multiple of baseline

metabolism was equivalent to a change in daily maintenance

39

energy requirements of 6.3 times the metabolic weight of

the animal.

RESULTS

Winter Severity

Initial conditions for these simulations included a
deer population of 8.4 deer/km2 consisting of 38 percent
males and 62 percent females. The average age of the male
segment of the population was 1.5 years of age while the
average age of females was 2.42 years old. The total

forest area simulated was 2.59 km2

consisting totally of
an aspen clearcut. No clearcuts were performed on these
runs.

Peak deer densities in severe winter conditions were
approximately 7 deer/km? while densities in normal con-
ditions were twice this amount (Figure 8). Densities
in mild conditions, however, were able to increase to
40 deer/kmz, an extremely rare occurrence in Michigan.
All populations showed a decline and eventual die out

following year 10 of the simulation. This is a result of

the aspen forest growing out of reach of deer.

Pattern Responses

The initial conditions for all the following runs

(unless stated otherwise) included a deer population of

40

Ierflmg

40

30

20

Figure 8.

 

41

_ Mild
Illlllll Normal
n“? Severe

Year of Simulation

Simulated response of deer densities to varying
winter severity.

20

42

9.39 deer/km2 with average ages and proportions of males
and females equal to these in the previous runs. The
aspen stand consisted of 5 age classes ranging from 1 to
41 with each class comprising 20 percent of the total area.
The total area simulated was 25.89 kmz. Normal winter
conditions were selected. In year 10 of the simulation,

a clearcut was performed on the 51 year old stand. Each
simulation was run for a period of 20 years.

Examination of yearly deer numbers revealed 3 distinct
patterns of deer response over a 20 year period (Figures
9-11). This variability in deer response is due, not only
to changes in some parameter of interest (as in the
sensitivity analyses) or management plans, but also, to
the stochastic nature of the model. This is reflected by
the fact that some runs under identical initial conditions
and management options showed different response patterns.

The pattern 1 response shows a deer population, at
first, oscillating at peak densities, followed by a sharp
decline in numbers due to the aspen vegetation growing
out of reach of deer. This is followed by a rapid in-
crease to peak densities after the clearcut, before a
second decline takes place. The pattern 2 response showed
an initial population decline of a lesser magnitude followed
by a slight increase or leveling off in numbers the next
year and then the eventual dying out of the population.

The pattern 3 response is similar to the pattern 1 response

43

20

15 /\,/°\/"° ...

O
O
N O
3 10
H
0)
Q)
Q
0
o O
5
O
I <“‘ 6"'
...-0’
i
1 5 10 is 20

Year of Simulation

Figure 9. Pattern 1 response. Population decline followed
by an increase to original peak densities.

44

20

 

'5 10 15 20
Year of Simulation

Figure 10. Pattern 2 response. Population decline followed
by the eventual dying out of the population.

45

 

20
15
O
“I .
3
H
o
m
C)
O
10'
5.

O

‘ I
o - 0,0

? 0’
i . oI-°"d"

to 15 20
Year of Simulation

    

Figure 11. Pattern 3 response. Population decline followed
by a slow increase in numbers. The population
is unable to reach peak densities.

46

except the magnitude of the decline is greater, the rate of
increase in the second half of the simulation is slower,
and the population is unable to restore itself to peak

density.
Harvest Experiments

Deer numbers were examined under buck harvest inten-
sities of 70 percent, 50 percent and no buck harvest. The
3 runs with a 70 percent buck harvest were the most variable
with all 3 pattern responses displayed. All runs with
a 50 percent buck harvest exhibited a pattern 1 response.
Two runs exhibited a pattern 3 response while a third
showed a pattern 2 response for runs in which no buck
harvesting occurred.

Deer populations with buck harvests ranging from 50
to 70 percent were able to reach densities of approximately
4 more deer/km2 in the first half of the simulation than
unexploited populations (Figure 12, Table 3). These popu-
lations were also able to maintain a larger number of
deer immediately following the decline period allowing
them to increase in the second half of the simulations at
a faster rate than those populations with no buck harvest.

The response of a deer population to antlerless har-
vest levels of 0, 25 and 50 percent (with a 70 percent
antlered harvest) was also examined. Two runs in which

there was a 25 percent harvest displayed a pattern 3 response

47

20

— 707. Harvest

llllllll 5070 Harvest
n“ No Harvest

N

 

Ex\ummn

Year of Simulation

Simulated effects of different antlered harvest
levels on deer densities (antlerless harvest

equal to 0).

Figure 12.

Yearly deer numbers (deer/kmz) under varying antlered harvest levels

(antlerless harvest equal to 0).

Table 3.

 

50% Harvest No Harvest

70% Harvest

Year

 

48

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+l+| l+l+l+l+l+l+l+l+l+l+l+l l+l+l+l+||

d’O‘NO‘flMMMOdNNMMx‘fOGd’m

GMONONHHQ’NCOOOOOOHH
r-h—h—h—h—h—h—l

Nd‘d’MHNLfiHquNNHv-dd’tnc

OOOOOOOOOOOc—CHNHOOH
I+I+l+l+|+l+|+l+l+l+l+l+l+l+l+l+l+l|
d’OHOHHNQ’wO‘wHMNNI-fix'f
mde’d’mNNNmmooHNd-dd'
u—h—h—h—h—h—I HHHH

+

+
<T

O"

14.2

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OOOOO$OOHOOHHNM¢¢H
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d’HHNNd'INMNOxNNMNr-INOHH
oxd'd'md-d’d'mmuHHHqu-mxom
v-h-h—h-h-h-h—l

Hmmd-mxorxoooxov-numc
o—h-h—h—h—i

 

49

while the third run showed a pattern 2 response. All runs
in which a 50 percent harvest occurred showed a steady de-
cline in numbers with little variability among runs.

Runs in which no antlerless harvest occurred were used
previously to compare the effects of antlered harvests on
deer numbers and were discussed earlier.

Under initial conditions a population with a 25 per-
cent antlerless harvest was able to reach the same population
level as a population with no antlerless harvest, al—
though more time was needed to reach that level (Figure 13,
Table 4). This is further substantiated in runs where
clearcuts were performed in 5 year intervals to prevent
any substantial declines in deer numbers (Figure 14).

In these runs, the population with an antlerless harvest
was able to consistently maintain numbers comparable to
the population with no antlerless harvest, once this
level was attained.

In none of the runs in which a 25 percent antlerless
harvest occurred were the populations able to rebound
after the decline and restore themselves to their original
numbers. This occurred regardless of the antlered harvest
rate (Figure 15). A series of runs were then made to
see if peak densities could be reached when more time was
allowed. Twenty year simulations were run with an initial
population of 1.08 deer/kmz. In addition, clearcuts were

performed in 5 year intervals to insure that browse

50

20‘

 

 

 

15 ' °\ (3
/ 0.040 n
- ¢
0 a
$9
6’
.\
‘9‘“ _ No Harve s t
9‘ .IIIIIIIII 25% Harvest
s n“ 50% Harvest
~
“5 1 0 i
\
H
o
o
a
6":
4‘ O
2. ./
‘0 o
v‘ | /
‘6 J‘ o\“\°“‘
4‘ .$‘\
b 0 “
0‘50 fi0§°"'lo‘“‘°‘
Year of Simulation
Figure 13.

Simulated effects of different antlerless
harvest levels on deer densities (antlered
harvest equal to 70 percent).

Table 4. Yearly deer numbers (deer/kmz) under varying antlerless harvest levels
(antlered harvest equal to 70 percent).

 

25% Harvest 50% Harvest

No Harvest

Year

 

51

d’qmd‘NNHOOHHHHHHr-IHO

OOOCO
+l+l+|+l+l+l+l+I+|+l+l+l+l+l+l+l+l+lI

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52

20
IIIIIIIII 257° HarVest
_ NO Harvest
“I O IIIOIIIIO|IIIO"'
15

O
/°\° 2“ 0‘0‘o\°uulo
o-Io ‘-blflo °

°'-o

 

Na 10
.24
\
H
m
(D
o
5.
1 '5 1'0 1'5
Year of Simulation
Figure 14.

Simulated effects of different antlerless harvest

levels with clearcuts performed in 5 year
intervals.

53

20

---70% Harvest
lllllllll 507.. Harvest
n“: No Harvest

    

Deer/km2

I
IIIIIIIIIIIIIIO IIIIII

5
O
O 0’0
I"
4‘3 6‘%
’0 ‘0 ‘:
’0‘ 0' 0
WHO’
"'O'lllo Ilo III-IIIOII 0 "'O"O" 0
l I l
5 10 15 20
Year of Simulation
Figure 15.

Simulated effects of different antlered harvest
levels with a 25 percent antlerless harvest on
deer densities.

54

availability would not be a limiting factor. None of the
populations were able to increase to substantial numbers

in the time allowed (Table 5).

Vegetative Energy Content

Several runs were made to investigate the effects
of varying metabolizable energy content for cedar and
aspen browse on deer numbers. Harvest rates were set at
70 percent for antlered harvest and 0 for antlerless
harvest. All runs using a value of 1.88 Kcal/g for cedar
metabolizable energy content exhibited a pattern 3 re-
sponse although the rate of increase in the second half
varied considerably. Two runs using a value of 2.11 Kcal/g
showed a pattern 1 response, although, again, the rate
of increase varied in the second half of the runs. The
third run showed a pattern 3 response, although the
population was able to reach a peak of 11.12 deer/kmz.

The runs in which the value 2.47 Kcal/g was used are
the same runs that were used in the antlered harvest ex-
periments.

At peak densities, a difference of about 0.3 Kcal/g
resulted in an average difference of approximately 1
deer/km2 (Figure 16, Table 6). In addition, the overall
magnitude of the population decline increased as the energy
content of cedar decreased, although the opposite is true

when looking at the initial decrease in year 9 of

55

Table 5. Yearly numbers (deer/km2) of a low density deer
population subjected to a 25 percent antlerless

 

 

harvest.

Number
Year of deer

1 1.1
2 l.2:0.2
3 1.3:0.2
4 1.2:0.4
5 l.0:0.2
6 0.9i0.2
7 0.9:0.1
8 0.8:0.1
9 0.9:0.1
10 0.9:0.2
ll 0.9:p.2
12 0.9:0.2
l3 0.9:0.2
l4 l.2:0.0
15 1.410.1
16 l.3:0.1
l7 1.5:0.l
18 1.4:0.2
19 1.5:0.5
20 l.8i0.4

 

56
20

— 2 .47 Kcal/g
'Illlllll 2 . 11 Kcal/g
g“ 1 . 88 Kcal/g

Na
.2
\
H
a)
Q)

Q

 

15
Year of Simulation
Figure 16.

Simulated effects of varying metabolizable
energy content of cedar browse on deer densities.

Yearly deer numbers (deer/kmz) under conditions of varying metabolizable
energy content of cedar browse.

Table 6.

 

Metabolizable Energy (Kcal/g)

 

1.88

2.11

2.47

Year

 

57

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58

the simulation. Here, the runs with the highest energy
content showed the greatest decrease. The decrease the
following year, however, was slight where runs with a lesser
energy content showed a second substantial drop in numbers.
The metabolizable energy content of cedar browse did
not affect the rate of increase of a deer population at
low densities, however (Figure 17). No change in the
rate of increase was seen until year 6, when each popu-
lation was approaching its peak densities.
Runs in which the aspen metabolizable content was
set equal to 1.47 Kcal/g showed little variation in deer
numbers up to year 17 of the simulation. The runs in
which the value 1.57 Kcal/g was used were, again, the same
runs used in the antlered harvest experiments.
The model showed no sensitivity to different values
of aspen metabolizable energy for the first 8 years of
the simulation (Figure 18, Table 7). When aspen metabo-
lizable energy was set at 1.47 Kcal/g, the simulation showed
a greater decline in deer numbers than when the value

1.57 Kcal/g was used.

Maintenance Energy Requirements

All populations in runs where the multiple of baseline
metabolism was increased by 0.2 showed a continual de-
cline in numbers. For only 1 run, in which the multiple

of baseline metabolism was increased by 0.1, was the

59

20

—2 .47 Kcal/g

llllllll 2 . ll Kcal/g

In“ 1.88 Kcal/g

_ O
15 /° \ 0‘0
.-./,2). .\./ .4,
s o o o \'
«r 4&6 qz<§.cfzbvfivpfi> 5? ”W5
0,; ’0“ O 0 <0, 9" g
0“ o" ‘0', ‘0" fly“ 0"
04 10
3
$4
a)
m
D
O
.
5 ; o

 
     

10 15
Year of Simulation
Figure 17. Simulated effects of varying metabolizable
energy content of cedar browse on mitially low

density deer opulations. Clearcuts were
performed in year intervals.

60

20

15

— l . 57 Kcal/g
Illllllll l . 47 Kcal/g

  

i
N.

 

20
Year of Simulation
Figure 18. Simulated effects of varying metabolizable

energy content of aspen browse on deer densities.

Yearly deer numbers (deer/kmz) under conditions of varying metabolizable
energy content of aspen browse.

Table 7.

 

 

Metabolizable Energy (Kcal

 

1.47

1.57

Year

 

61

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62

population able to restore itself to peak densities. When
the multiple of baseline metabolism was decreased by 0.1,
the deer populations were able to restore their numbers

in 2 of the 3 simulations. The same situation occurred
when the multiple of baseline metabolism was reduced by
0.2.

The expected results of decreasing maintenance re-
quirements would be an increase in summer weight and a
decrease in winter weight loss with the opposite expected
from an increase in maintenance requirements. This would
be reflected by larger deer in simulations where maintenance
requirements were reduced and smaller deer where require-
ments were increased. Such was the case with deer showing
considerably different weights for each maintenance re-
quirement level (Table 8).

The model was quite sensitive to changes in main-
tenance requirements (Figure 19, Table 9). Peak densities
ranged as high as 21 deer per square kilometer in popu-
lations where the multiple of baseline metabolism.was de-
creased by 0.2 while populations showed a continual
decline to 0 in runs where the multiple was increased by
0.2. A decrease of 0.1 resulted in peak densities of
approximately 2 more deer per square kilometer, while an
increase of 0.1 resulted in approximately 3.5 fewer deer

per square kilometer at peak densities.

63

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64

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— 0
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Figure 19. Simulated effects of changes in maintenance energy
requirements on deer densities. Changes are
reflected by deviations of the multiple of
baseline metabolism.

+2

+1

Changes are reflected by deviations of the
Deviation

multiple of baseline metabolism.

 

Yearly deer numbers (deer/kmz) under conditions of varying maintenance

energy requirements.

 

 

Table 9.
Year

65

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66

The population decline period also differed as main-
tenance requirements were changed. The population de-
cline appeared 1 year earlier in runs where the multiple
of baseline metabolism was decreased by 0.2 as compared
to unaltered runs. Deer numbers in all of these runs
showed significant declines over a 3 year period with the
extent of the second and third declines dependent on
the magnitude of the preceding decline. The reverse
occurred in runs where the multiple of baseline metabolism
was increased by 0.1. Here, the population decline ap-
peared 1 year later than runs where the maintenance re-
quirements were not altered. A decrease of 0.1 resulted
in a population decline the same year as runs where
maintenance requirements were not altered, however the

magnitude of the decline was greater.

DISCUSSION

Winter Severity

The importance of winter severity to deer numbers in
the model is reflected by deer densities ranging from 7
deer/km2 in severe conditions to 40 deer/km2 in mild con-
ditions. his would indicate that winter severity is a
major factor in controlling deer numbers under conditions
of abundant summer food supply, although other factors
such as social stress cannot be discounted.

It was also shown that a young 2.59 km2 aspen stand
can support a substantial deer population for a period of
10 years. This conflicts with claims that deer densities
in excess of 17.5 deer per square kilometer will cause
extensive damage to an aspen stand (Graham et a1. 1963).
However, Graham simply compared deer census data and the
degree of damage to an aspen sucker stand. He did not
consider the size of the stand or the concentratiOn of
deer within the aspen stand. Therefore, the density of
deer feeding in the young aSpen stand examined by Graham
may have greatly exceeded 17.5 deer per square kilometer.

Another explanation for this conflict is that esti-

umtes of aspen browse may have been too high. However since

67

68

other deer foods such as grasses and forbs were not allo-
cated to deer in this model until aspen browse had been
consumed, it is. unlikely that the influence of deer on aspen

was underemphasized.

Pattern Responses

There are 4 main factors that determine which pattern
a deer population will follow: 1) the number and biomass
of deer in the year preceding the population decline;

2) the amount of browse available in the year preceding
the population decline; 3) the proportion of female fawns
in the fawn crop of the year preceding the population de-
cline; and 4) the proportion of females in the population
in the year preceding the population decline.

The magnitude of the population decline depended,
largely, on the degree in which the population demand ex-
ceeded the amount of available browse in the years of scarce
food supply. Populations in which the demand greatly ex-
ceeded the supply showed a large initial decline. Because of
this, however, the ratio of demand/supply was quite small
the following years and no further significant losses
were seen. Populations in which the demand exceeded the
supply to a lesser degree showed a smaller decline. In
most cases the demand/supply ratio would still be large
the following year and a second and sometimes third Sab-

stantial decline in numbers would result. In some cases,

however, the decline was large enough to allow a leveling
off or increase in number the following year. This resulted
in a large third year demand/supply ratio and a subsequent
catastrophic decline in numbers. In populations that
showed this response, the percent of females in the popu-
lation and the percent of female fawns in the fawn crop
were higher in the year preceding the decline than in the
previous case. As a result, more does were able to survive
and reproduce during the initial decline creating a fawn
crop that was large enough to increase or level off the
population the following year.

The rate at which the population recovered from the
decline was dependent mainly on the magnitude of the de-
cline. Populations which declined to smaller numbers
generally took longer or were unable to reach peak densities
than populations which showed a lesser decline. However,
populations which declined to similar numbers also showed
different rates of increase. Here, populations with a
larger percent of females in the population in the year pre-
ceding the crash showed the greatest rate of increase
following the clearcut. The reason for this was that, even
though total numbers were similar, more females were able

to survive and produce larger fawn crops.

Harvest Experiments

Populations with a 50 percent or 70 percent buck har-

vest were able to maintain higher peak densities than

70

unexploited populations because less winter mortality
occurred in these populations, particularly in the female
segment. The harvest of a large number of bucks meant
less competition for females for what little winter food
was available. Thus, they were able to consume a larger
proportion of their demand. This is important since the
loss of a doe represents not only the loss of 1 deer, but
also the loss of fawns she would potentially bear in future
years. Also, the does that do survive the winter are in
better physical condition than does in an unexploited
population and a higher fawn/doe ratio will result (Verme
1969).

Unexploited populations were also unable to restore
their numbers following the population decline. Although
initial declines were smaller than exploited populations
due to smaller demand/supply ratios, all populations showed
extremely low numbers in the year preceding the clearcut.

The high degree of variation in runs where a 70 percent
harvest occurred was due to a combination of factors.

The population with the smallest demand/supply ratio also
had the largest percent of female fawns and total-females
in the year preceding the population decline. Thus a
small decline occurred the first year with.many females
surviving. This led to a large fawn crop and an increase
in numbers the following year and then a catastrophic de-

cline in numbers the year after. Conversely, the

71

population with the highest demand/supply ratio had the
smallest percent of female fawns and total females in the
year preceding the decline. This led to a large initial
decline which nearly decimated the female segment of the
population and the population was unable to recoVer from
this. The third population was an intermediate between
the two and showed a pattern 1 response.

The percent of females and female fawns in the year
preceding the decline was the main factor causing a pattern
2 response in 1 population where no harvesting occurred.
Demand/supply ratios were similar for all 3 populations.
However, the percent of females in the population was much
higher (50.0% compared to 43.4% and 41.0%) as was the per-
cent of female fawns (62.4% compared to 42.6% and 50.6%)
in the population which showed the pattern 2 response.

There was less variation in pattern responses in popu-
lations where an antlerless harvest occurred. The population
that displayed a pattern 2 response showed the same charac-
teristics as the population that displayed a pattern 2
response when no antlerless harvest took place. These were
a lower demand/supply ratio, and higher percentages of
females and female fawns in the year preceding the popu-
lation decline.

A great deal of controversy exists concerning the
feasibility of an antlerless deer harvest and its effects

on deer numbers. The modeled populations exhibited

72

different responses to a 25 percent antlerless harvest, de-
pending on the conditions in which they existed. At peak
densities, the population showed little response to the
antlerless harvest, except for smaller year to year fluctu-
ations in numbers. Moderate density populations were able
to withstand this harvesting pressure and increase to

peak densities, although at a noticeably slower rate.

None of the populations were able to increase after the
population decline, however.

Unlike populations with no antlerless harvest, this
inability to increase was not due to high starvation losses
or an insufficient number of remaining females following
the decline period. Populations with no antlerless harvest
which declined to comparable numbers were able to restore
themselves to peak densities. Rather, it was the antler-
less harvest rate which was preventing the populations
from increasing to substantial numbers in a reasonable
amount of time. In these populations, there were not
enough does left after the harvest to allow for a substan—
tial fawn crop the following year. The result was an
extremely low rate of increase. Thus the model indicates
that the response potential of the population should be a
major consideration when evaluating the desirability of

an antlerless harvest.

73

Vegetative Energy Content

The variation in the magnitude of the decline, in
runs where smaller energy values were used, appeared to
be related mainly to the demand/supply ratio. However,
since substantial declines in these runs appeared over a
2 year period, browse availability at both high and low
extremes in the year preceding the population decline caused
the same results, namely a greater overall decline in
numbers. The demand/supply ratio is low when a large
quantity of browse is available causing a relatively small
decline in the first year. This creates a high ratio the
following year and a major decline results. The converse
occurs when browse availability is 10W’With a major decline
the first year and a smaller decline in the following year.
Intermediate amounts of browse resulted in smaller over-
all declines. This suggests that under these conditions
some optimum demand/supply ratio exists which will minimize
deer losses during the period of population decline.

As the metabolizable energy content of cedar browse
decreased, the amount of available aspen in year 8 of the
simulation increased. There are 2 reasons for this. One
reason is there were fewer deer in runs with lower energy
values, but more significant was the fact that deer in
these populations weighed less than deer in populations
with higher energy values. This was due to the greater

weight loss of deer in the winter months. These 2 factors

74

led to a smaller demand for aspen browse and subsequently,
less was consumed.

Therefore, with a smaller demand and a greater supply
of aspen these runs showed a smaller initial decline.
Because of this, however, the demand of the herd the
following year greatly exceeded the supply and a second sub-
stantial decrease occurred. In summary, the magnitude
of the population decline was greatest when low cedar meta-
bolizable energy values were used and smallest when using
high energy values. However, this decline was extended
over a 2 year period.

Another interesting result of these sensitivity ana-
1yses was the fact that the model showed no sensitivity
to changes in aspen metabolizable energy content during
the first 8 years of the simulation. This same lack of
sensitivity to changes in cedar metabolizable energy
content was exhibited by low density populations. In both
of these cases, the browse supply was abundant in relation
to the demand during this period. This indicates that
the metabolizable energy content of browse is an impor-
tant factor in influencing deer numbers only in times
when the browse supply is limiting and has little, if any,

influence when browse is more abundant.

Maintenance Energy Requirements

As was the case when metabolizable energy contents

of browse were altered, the variation in pattern responses

75

and magnitudes of decline appeared to be related primarily
to the demand/supply ratio. In conditions where the de—
cline was extended over a period of years, intermediate
amounts of browse resulted in the smallest overall decline.
In conditions where lumjor decline in numbers ocCurred,

a positive relationship was seen between the demand/

supply ratio and the magnitude of the population decline.

Changes in maintenance requirements of deer affected
the deer population in a manner similar to changes in
energy values of browse, but to a much greater degree.

The immediate effect was a change in deer weights. This
increased or decreased the probability of a deer starving
during the winter months with the result being considerable
changes in peak densities of populations.

These weight changes and changes in peak densities
also had a considerable effect on the decline period.
Browse shortages occurred 1 year early when the multiple
of baseline metabolism was decreased by 0.2 as a result
of the excessive demand of a high number of extremely
large deer. This caused a decline which continued over a
3 year period. Conversely, when the multiple of baseline
metabolism was increased by 0.1, browse shortages did not
occur until I or 2 years later than runs where maintenance
requirements were not altered. Here, peak densities were
lower and deer were smaller, resulting in a lower demand,

and subsequently less consumption by the herd. The browse

76

shortage in runs where the multiple of baseline metabolism
was decreased by 0.1 was not drastic enough to bring about
an early population decline. However the magnitude of

the decline was greater than runs where maintenance require-
ments were unaltered. Thus, changes in maintenance re-
quirements had a considerable effect on peak density levels
and the pattern, magnitude and timing of the population

decline.

Clearcuts

The frequency of clearcuts had a definite influence
on the simulated deer populations. All but 2 populations
in which clearcuts were performed on 10 year intervals
showed an immediate increase the year following the clear-
cut. Populations which did not show an increase existed
in conditions which were too harsh for a population to
maintain itself, regardless of any habitat manipulation
schedule. The response of the populations which showed
an increase can be compared to Figure 8 where no clearcutting
occurred and the populations died out in the fourteenth
or fifteenth year. Additionally, populations, in runs
where clearcuts were performed on 5 year intervals, con-
tinued to increase or maintain peak densities and showed
no significant declines in numbers. Intervals of 5 to 10
years have been prescribed for aspen clearcuts when managing

for white-tailed deer (Perala 1977). The model indicates

77

that this rate of manipulation should be followed, as longer

intervals would result in an abrupt decline in deer numbers.

Further Research

One school of thought views the objective of computer
modeling as part of the accumulation of knowledge of the
‘ system under study (Hayne 1969). In this respect, an im—
portant aspect of modeling exercises such as these is to
point out areas which are ill defined and require more
investigation. As Hayne (1969) stated, "a successful
model dictates the kind of data required in the future."

One such area which should be more precisely defined
is the question of energy requirements of wild deer. Con-
siderable research has been carried out in this area
(Silver et al. 1969, Ullrey et al. 1970, Thompson et al.
1973, Moen 1973, 1978). However, results were often con—
tradictory and lacked the precision which the model needed
to accurately predict deer numbers'

There is little information in the literature regarding
deer growth as a function of energy consumption, par-
ticularly among adult deer. This is very important, as
the most important factor affecting the amount of browse
consumed is deer weight. This can be seen in Moen's
(1978) equation for estimating browse consumption. There-

fore a better understanding of the rate of increase of

\J
C3

deer weight as a function of energy consumption will lead
to better long range prediction of deer weights and ul-
timately, deer demands. More importantly, however, a
better understanding of the rate at which a deer loses
weight as a function of energy consumption will lead to
better predictions of losses due to malnutrition in times
of low food supplies.

The incorporation of other nutrients may be necessary,
however, to develop better growth rate estimates. Although
energy is considered the most critical factor in deer
nutrition, other requirements, such as proteins and minerals,
must also be met. It has been suggested that low protein
contents in foods may account for low productivity and
suboptimal growth (Murphy and Coates 1966). Holter et al.
(1977) was unable to find a close correlation between body
weight gain and energy deposition. In a further study
(Holter et al. l979),the use of multiple stepwise re-
gression techniques showed growth to be a function of
energy intake (digestible or metabolizable) and digestible
nitrogen intake. Verme and Ozoga (1980) concluded that
a protein rich diet was not vital, whereas small energy
deficiencies could be detrimental. However when energy
was not limited, the protein level became important for
optimal development.

The model was also sensitive to small changes in the

metabolizable energy content of both cedar and aspen

79

browse, particularly during the period of the population
decline. One reason the results of different studies varied
was that different parts of the plant were used. Some
studies used only the tips of branches while others included
more woody vegetation. A stratified sampling design could
provide more precise estimates of the metabolizable energy
content of aspen and cedar browse.

The conflict between the claims of Graham et al.

(1963) and the results of the model raises questions about
the accuracy of deer browse estimates in young aspen
stands. Also, scant information exists concerning aspen
growth response to deer browsing. High estimates of aspen
response could be a factor contributing to this conflict.
Further research is needed in both of these areas to help
answer these questions.

One of the major assumptions of this model is that deer
will feed in areas where the most energy is available.
However, a study using tame deer showed that deer used a
mature aspen forest and a clearcut equally in the month
of June (Stormer and Bauer 1980). One could conclude from
that that both stands had equal or adequate amounts of
available energy or that other factors play a major role
in selecting a feeding area. In either case, more infor-
mation on deer behavior and their choice of feeding areas

could have a significant impact on models such as these.

80

A major limitation of this model is its lack of con-
sideration of spatial distributions. This assumes that the
energy cost of moving from 1 place to another is negli-
gible. Other models have shown, however, that the area
a deer can forage in a day is quite critical in determining
deer densities (Cooperrider 1974). Moen (1978) found
that walking is one of the more costly activities for deer.
This suggests that the consideration of spatial patterns
could have a significant effect on these types of models.
Before this can be realistically incorporated into a
model, however, more research is needed regarding the
energy costs of different activities and the behavior of

wild free-ranging deer.

Precautions

Some precautions should be taken when applying this
model to specific situations. Although the model has been
described as a generalized model for the Lake States re-
gion, not all aspen forest will behave as this model does.
The site index for the model is set at 70 and the model
does not allow for changes in soil characteristics, water
levels or any other environmental factors which affect
aspen growth. Therefore, one should be sure that stand
characteristics are similar to those in the model.

Another characteristic of the model which one should

take into account is that deer habitat is evaluated solely

81

on the basis of browse availability. Thus, the model would
indicate that areas with greater proportions of clearcuts
would support greater deer densities and that an optimum
deer habitat would be one that is totally clearcut. In
reality; however, optimum deer habitat requires a mix of
clearings and forested areas which are used for hiding,
thermal protection and fawning (Thomas et al. 1979).
Studies in Michigan have shown that areas in which 25
percent was clearcut received greater overall use by deer
than areas with more extensive treatments (Bennett et al.
1980). In addition, the size of a cleared area has a sig—
nificant bearing on its usage by deer. Studies have shown
that the greatest amount of use by deer occurred in areas
within 183tn of an edge (Reynolds 1962, 1966). Any

use beyond this point was insignificant.

The feeding habits of white-tailed deer have been
greatly simplified in this model. At times when aspen browse
was abundant, the diet of the simulated deer population
would consist of 100 percent aspen browse. However, diver-
sity is a very important aspect of a deer's diet (Rogers
et al. 1981). Deer will prosper more with a variety of
plants in their diet than with a diet of 1 preferred food
(Dahlberg and Guettinger 1956, Halls 1978). In reality,

a deer will maintain some degree of diversity in their diet,

even when a preferred food is abundant.

82

The assumption that aspen is a preferred food through-
out the non-yarding period also leads to an overemphasis
of the importance of aspen in deer diets. In the spring,
fresh green grasses and forbs are the most important deer
foods while grasses, acorns (if available), asters, fruits
and mushrooms equal or exceed aspen in importance during
the fall months (McCaffery et al. 1974, Rogers et al. 1981).
The primary effect of this simplification of deer food
habits on the model is a high degree of sensitivity of
deer numbers to aspen browse availability. This is reflected
by the large variability seen among simulations where
the initial conditions were identical.

The user should also be aware of the effect of short
rotation intervals on aspen productivity. Harvest intervals
of less than 10 years have been shown to have a deleterious
effect (hi the ability of an aspen stand to sustain its
production level (Berry and Stiell 1978). Since the model
does not account for this, long range simulation, using
intervals of less than 10 years, would result in over-
estimations of aspen browse availability in the latter
years of the simulation.

In the model, there is an indirect relationship be-
tween tree height and stand density. Height is calculated
as a function of dbh, which is affected by the density of
trees in a stand. In nature, however, height appears to

be related mainly to site index. Stand density has little

83

effect on tree height (Sorensen 1968). Therefore this re-
lationship is 1 source of error in estimating the amount
of aspen available to deer since browse availability is
affected mainly by tree height.

Since the model does not consider spatial distributions
it is unable to allow for the juxtaposition of clearcuts.
This is a very important consideration, however, when
managing for white-tailed deer. One must insure that all
vegetation or habitat types are provided by juxtaposing
clearcuts so that longer rotation periods are used, but new
forage areas are created every 5 to 10 years. In this
way, one can provide optimum deer habitat and sustain high
aspen productivity.

These limitations and simplified assumptions must all
be taken into account when evaluating the results of the
model. Therefore, the user must possess sufficient know-
ledge to supply his/her own expertise in areas which the
model is unable to address in order to devise a viable
management plan.

Validation

The subject of model validation has long been a pro-
blem area in system analysis and a subject of controversy
which remains unresolved to this date (Naylor and Finger
1967, Van Horn 1971, Goodall 1972). Some argue that the
validity of a model is determined by its purpose (Caswell
1976, VanKeulen 1976). That is, several models of a
system may exist and all may be valid, but aiming at dif-

ferent goals.

84

This problem is further compounded, in this case,
by the scarcity of sufficient deer data. Accurate censusing
of large deer herds continues to be a difficult problem
of deer research and management. Because of this, it may
be of greater use to consider relative numbers of deer
under different management conditions, rather than actual
numbers, when evaluating model results.

Shannon (1975) stated, "by far the most important
test for the validity of our model and the results obtained
should be the answer to the question, 'Does the model make
sense?’ " In this case, the question is, 'Are there
sound biological explanations for what is happening in the
model?‘ Using this criterion and considering the purpose
of the model and the current state of knowledge of deer-
aspen interactions, the model appears valid.

One should always keep in mind, however, the simpli-
fied assumptions and the limitations of the model and regard
results tenatively until more data are gathered and a
further understanding of deer and aspen ecology is de-
veloped. As more information becomes available, additional
complexity can be incorporated into future simulation
models of this type which will make them more realistic

and add to their validity.

CONCLUSIONS

At this time, the primary benefit of computer models
such as these is to synthesize existing information and
point out gaps where existing knowledge of the ecosystem
under study is lacking. This type of information is
of great assistance to researchers in setting priorities
and directions for future research. Currently, however,
the limitations of existing data place severe restrictions
on the use of models of this type in developing long range
deer management policies. However, there remains great
potential in this tool and modeling efforts should be con-
tinued.

The greatest practical use of this model in its current
state is as a teaching aid. Although the accuracy of
the estimations of peak densities and the magnitude of
the population responses is questionable, the trends which
the model exhibits appear realistic. Thus.the user will
be able to see immediately the beneficial or detrimental
effects of his/her management decisions. After repeated
trials, the user then can develop an understanding of the
effects of manipulating these options and devise a manage-
ment plan which will meet previously Specified management

objectives.

85

APPENDIX A

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The main program.

87

 

 

 

 

 

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Figure 21. Subroutine ADVANC. Advances tree data to
next age class.

88

 

 

 

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Figure 22. Subroutine AGESEX. Initializes deer matrix.

89

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Figure 23. Subroutine BROWSE. Computes amount of aspen
consumed by individual deer per month.
Allocates browse consumed to height classes.

9O

 

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Figure 24. Subroutine CHOOSE. Computes amount of aspen
browse available in each stand and chooses

feeding area.

 

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Figure 25. Subroutine DIST. Initializes tree data for
a A year old stand.

 

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Subroutine FEED.
demand, deer growth and probability of

starvation.

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Calculates individual deer

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Figure 27.

Subroutine MORTAL. Calculates miscellaneous
and harvest mortality.

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Figure 28. Subroutine NATAL.

Calculate fawns per doe and

adds fawns to the population.

95

 

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Figure 29. Subroutine NORM. Initializes tree matrices.

 

96

 

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Figure 30., Subroutine PRINT. Prints relevant deer data.

 

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Subroutine SUM.
demand for aspen and cedar.

L__.=_._....____._J

Calculates monthly

deer herd

- Ln.- 1. “W

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Figure 32. Subroutine TALLY. Tallies number of deer,
harvest mortality, and starvation mortality
per age/sex class. Removes dead deer from
the population.

99

 

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Figure 33. Subroutine TRECUT. Removes clearcut and adds
area to 1 year old stand.

 

 

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100

Figure 34. Subroutine TREGRO. Computes percent browse
consumed in each height class. Calculates
yearly tree growth. Prints relevant tree

stand data.

101

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Subroutine YARD. Computes amount of cedar

browse consumed by individual deer per month.

APPENDIX B

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LITERATURE CITED

Anderson, F. M., G. E. Connolly., A. N. Halter, and W; M.
Longhurst. 1974. A computer simulation study

of deer in Mendocino County, California. Ore.
Agric. Exp. Stn. Tech. Bull. 130. 71 pp.

Bandy, P. J., I. M. Cowan,, and A. J. Wood. 1970. Com-
parative growth in four races of black-tailed deer
(Odocoileus hemonius). Part I. Growth in body
weight. Can. J. Zool. 48: 1401-1410.

 

Bennett, Jr., C. L., E. E. Langenau, Jr., C. E. Burgoyne,
Jr., J. L. Cook, J. P. Duvendeck, E. M. Harger,
R. M. Moran and L. G. Visser. 1980. Experimental
management of Michigan's deer habitat. Trans. N.
Am. Wildl. Nat. Resour. Conf. 45:288-306.

Berry, A. B. and W. M. Stiell. 1978. Effect of rotation

length on productivity of aspen sucker stands. For.
Chron. 54: 265-267.

Bobek, B. 1980. A model for optimization of roe deer

gana egent in central Europe. J. Wildl. Manage. 44:
37- 4 .

Buchman, R. G. 1979. Mortality functions. Pages 47-55
iE.A generalized forest grOwth projection system
applied to the Lake States region. U.S. Dept.
Agric. For. Serv., North Cent. For. Exp. Stn. Gen.
Tech. Rep. NC-49.

Bunnell, F. L. 1974. Computer simulation of forest-
wildlife management in the Pacific Northwest. Pages
39-50 in_H. C. Clark, ed. Wildlife and forest
management in the Pacific Northwest. Oregon
State Univ., Corvallis.

Byelich, J. D., J. L. Cook, and R. I. Blouch. 1972.
Management for deer. Pages 120-125 in_Aspen:
symposium proceedings. U.S. Dept. Agric., For.
Serv., North Cent. For. Exp. Stn. Gen. Tech. Rep.
NC-l.

107

108

Caswell, H. 1976. The validation problem. Pages 313-325
in B. C. Patten, ed. Systems analysis and simu-

lation in ecology. Vol. IV. Academic Press,
New York.

Cheatum, E. L. and C. W. Severinghaus. 1950. Variations
in fertility of white-tailed deer related to range
conditions. Trans. N. Am. Wildl. Nat. Resour. Conf.
15: 170-190.

Coe, R. J., R. L. Downing, and B. S. McGinnes. 1980. Sex
and age bias in hunter-killed white-tailed deer.
J. Wildl. Manage. 44: 245-249.

Cooperrider, A. Y. 1974. Computer simulation of the inter-
action of deer population with northern forest
vegetation. Ph.D. Thesis, State Univ. of New York
College of Environmental Science and Forestry,
Syracuse. 220 pp.

Cooperrider, A. Y., and D. F. Behrend. 1980. Simulating forest

'gynggics and deer browse production. J. For. 78
5- .

Dahlberg, B. L. and R. C. Guettinger. 1956. The white-tailed
deer in Wisconsin. Wis. Conserv. Dept. Tech. Wildl.
Bull. 14. 282 pp.

Davis, L. S. 1967. Dynamic programming for deer manage-
ment planning. J. Wildl. Manage. 31: 667-679.

Fowler, C. W. and W. J. Barmore. 1976. A population model
of the northern Yellowstone elk herd. Pages 427-
434 in R. M. Linn, ed. Proceedings of the first
conference on scientific research in the National
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