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This is to certify that the

dissertation entitled

Studies Related to the Concept of Pest - Crop System Design:
1) Adult Parasitoid Activity and Its Relation
to Biocontrol and 2) Forest Harvesting
and the Spruce Budworm

pummuaiby

Jan Peter Nerp

has been accepted towards fulfillment
of the requirements for

Ph.D. . Entomology
degmxin

 

 

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STUDIES RELATED TO THE CONCEPT OF PEST - CROP SYSTEM DESIGN:
1) ADULT PARASITOID ACTIVITY AND ITS RELATION
TO BIOCONTROL AND 2) FOREST HARVESTING

AND THE SPRUCE BUDWORM

by

Jan Peter Nerp

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Entomology

1982

ABSTRACT
STUDIES RELATED TO THE CONCEPT OF PEST-CROP SYSTEM DESIGN:
1) ADULT PARASITOID ACTIVITY AND ITS RELATION TO BIOCONTROL AND
2) FOREST HARVESTING AND THE SPRUCE BUDWORM
BY

Jan Peter Nyrop

Damage to crops from pest organisms can be controlled two ways. First,
the structure of the crop production system can be accepted as is and the pest
organisms controlled in some fashion. Second, the structure of the crop
production system can be manipulated so that pest damage is minimized. In this
thesis the latter concept is explored in two studies.

In the first project, the temporal and spatial dynamics of an adult

parasitoid (Glypta fumiferanae Vierick) were assessed and related to the theory

 

of parasitoid-host dynamics. This was done because adult parasitoids and factors
influencing them may be objects of control for system management.

Field data on adult parasitoid activity was used to construct a model
relating activity to weather. Historical data were then examined to determine if
weather induced changes in parasitoid activity were reflected in changes in
parasitism. I concluded cool, wet weather inhibited parasitoid host seraching and
attack.

Observations of g. fumiferanae attacking hosts suggested the parasitoid

 

does not forage optimally. An experiment was conducted to determine whether
light and/or temperature influenced parasitoid foraging behavior. The

experiment indicated this was the case.

The empirical studies were related to parasitoid-host theory which was
then revised. This revision consisted of redefining the attributes of a successful
biocontrol agent to be one which has a high searching efficiency but need not
aggregate in areas of high host density.

In the second project, the use of forest harvesting was explored as a way to
change the structure of the spruce budworm/forest system and thereby improve
system control. A theoretical basis for the strategy was developed, an economic
analysis was made and the strategy was field tested. Results from the field test
did not substantiate the theory on the effect of partial harvesting on budworm

dynamics. As a result, the test was inconclusive.

to Jessica Erin

ii

ACKNOWLEDGEMENTS

I wish to express my sincere thanks to Gary Simmons for serving as my
advisor, for providing intellectual stimulation, encouragement, and for being a
friend. To my committee, Drs. Dean Haynes, Lal Tummala, Stuart Gage and
Gary Fowler I extend my appeciation for their guidance and patience during my
graduate training. Special thanks go to Dr. James Bath who, as Department
Chairman, has provided an atmosphere condusive to professionalism and at the
same time enjoyable to work in.

A large group of people assisted in collecting data for this thesis. I thank
them all. I especially wish to thank Marcia McKeague for her involvement in the
early stages of the forest harvesting study and James Pieronek for his help in
constructing an environmental chamber.

Finally, I wish to thank Jerryvonne Nyrop fo her help in data collection and

manuscipt preparation.

iii

TABLE OF CONTENTS

IntrOduction .0.........CIOOOOIOOOOOO0.0... ..... 0...... ......... 0.. 1
Adult Parasitoid Activity and Its Relation to Biocontrol . ..... .... 3
IntrOduction O0.0.0.000.........COOOOOOOOO...... ........ O ..... O 4
Methods and results ........................... ........ ........ 6
Field studies of adult parasitoid activity ............... 6

Sampling methods .................................... 6

Analysis ............................................ 14
Laboratory studies of host searching behavior ............ 26
Experimental design ................... ........ ...... 26
Analysis ............................................ 30
Historical data on parasitoid-host interactions .......... 33
Description of data ................................. 33

Analysis ............................................ 35
Discussion .................................................... 40

Relation to other studies ......................... ..... .. 40
Parasitoid-host models and biological control ....... ..... 42

A revised parasitoid-host model ....... ..... .............. 46
Attributes of a successful biocontrol agent . ............. 54
Conclusions ................................. ................ .. 55
Forest Harvesting and the Spruce Budworm ..... ..................... 58
Introduction ........................................... ..... .. 58

Strategies for controlling budworm damage ................ 59

A theoretical basis for partial forest harvesting ............. 61
Previous studies ......................................... 61
Mathematical analysis .................................... 66
Implementation and assessment of partial cut strategy ......... 78
Description of study areas ............................... 78
Feasibility analysis ............................. ..... ... 80
Economic considerations ...................... ...... . 85
Biological response of the system ................... 91

Dispersal loss of budworm ...................... 92

Predation and parasitism ... ..... ............... 96
COHClUSionS ....O.....O.......OOCOOOOOOOOOOOOOOO ...... 00.0.0... 102
Conclusions .................. ..... ...... ..... . ............. ....... 104

Appendices ........................................................ 106
Appendix 1: Distributed delays as models of insect life stages . 106
Appendix 2: Temperature controller for environmental chamber .. 108
Appendix 3: Mathematical methods for analysis of parasitoid-

host models ................... ...... .............. 109

iv

Appendix
Appendix
Appendix
Appendix
Appendix
Appendix
Appendix

Literature Cited

4
5
6
7
8
9
1

Computer program listings ............... ..... ..... 111
Analysis of the economics of partial cuts ......... 122
Form sent to loggers to determine cost and returns . 124
Bird census data .................................. 126
Additional malaise trap data and analysis ......... 130
Spruce budworm population data ............. ....... 135

0: Voucher specimen sheet ..... ...................... 143

....... ...... . ...................... . .......... . 145

TABLE

10.

LIST OF TABLES

 

 

PAGE
Models used to predict the temporal distribution of malaise
trap catch of female Glypta fumiferanae. ........ ............. 20
Distribution of attacks by Glypta fumiferanae on spruce
budworm larvae in balsam fir trees (n = 16). The exterior
of the tree denotes the first 18 inches of the canopy. . ...... 28

Total time and time spent in attack and non-attack behavior
by Glypta fumiferanae in different environmental regimes. .... 31

Julian dates for the degree day interval 428 - 584 (base

8.89 0C) and precipitation during this period in the years

1950 to 1957 at the Green River field station, New

Brunswick. ........................................ ..... . ..... 36

Equilibrium points and eigenvalues of a parasitoid host
model linearized about these points. ......................... 50

Comparison of species composition of live trees and tree
condition parameters for spruce budworm host trees by
treatment in stand 1. ...................... .. ................ 81

Comparison of species composition of live trees and tree
condition parameters for spruce budworm host trees by
treatment in stand 2. ..... ...... ...... ....................... 82

Comparison of species composition of live trees and tree
condition parameters for spruce budworm host trees by
treatment in stand 3. .... .................................... 83

Costs and revenues incurred by logger in harvesting stand 3. . 89

Dates and degree days (base 5.56 0C) for five sampling

periods during which spruce budworm densities were

determined in three stands. Peak 3rd instar occurs at c.

167 dd, peak 6th instar at c. 416 DD and initial emergence of
male moths at c. 472 DD. ................................ ..... 91

vi

TABLE

11.

12.

13.

14.

15.

PAGE
Density per m2 balsam fir foliage of various life stages
of the spruce budworm in 1981 and percentage mortality
due to parasitism and unknown causes in stand 1. ....... ..... 93
Density per m2 balsam fir foliage of various life stages
of the spruce budworm in 1981 and percentage mortality
due to parasitism and unknown causes in stand 2. ...... ..... . 94

Density per 1112 balsam fir foliage of various life stages
of the spruce budworm in 1981 and percentage mortality
due to parasitism and unknown causes in stand 3. ............ 95

Defoliation of balsam fir by spruce budworm in three stands
in which part of the stand was partially harvested and the
other part served as a control. .................... ......... 101

Malaise trap catch of female glypta fumiferanae from two

plots and weather data in 1982. One trap was located in

24 jack pine in each plot. Twelve traps were in the upper

crown and 12 in the lower crown. ..................... ....... 133

 

vii

LIST OF FIGURES

FIGURE PAGE

1. Location of study plots in Michigan's Upper Peninsula ....... 7

 

2. Details of a malaise trap designed for placement in tree

crows .0... OOOOOOOOOOOOOOOOOO O ..... ......OOOOOOOOOO0.0.0....8
3. Catch of female Glypta fumiferanae from 14 malaise traps

located in balsam fir trees in stand 1 during 1980 .... ...... 10

4. Catch of male and female adult Glypta fumiferanae from 13
malaise traps located in balsam fir trees in stands 2 and 3
during 1981 OOOOOOOOOOOOOOOOOOOOOOO ...... O OOOOOOOOOOOOOOOOOOO ll

 

5. Bi-hourly trap catch of female Glypta fumiferanae from 13
malaise traps located in balsam fir trees in stand 2 and the
temporal distribution of temperature and rainfall ... ........ l3

 

6. General structure of the model used to analyze the temporal
’ distribution of malaise trap catches of Glypta fumiferanae.
Elis a vector of weather variables and a is a prOportionality
parameter ......... . ............... . ....... . ............ ..... l6

 

7. Observed combined emergence of adult male and female Glypta
fumiferanae in stand 2 and predicted emergence of female Q;
fumiferanae as a function of degree days base 8.890 C ....... 19

8. Predicted and actual malaise trap catch of adult female
Glypta fumiferanae in stand 2 and the theoretical, relative
temporal distribution of adult females. Malaise traps were
located singly in 13 balsam fir trees ...... . ................ 22

9. Predicted and actual malaise trap catch of adult female
Glypta fumiferanae in stand 3 and the theoretical, relative
temporal distribution of adult females. Malaise traps were
located singly in 13 balsam fir trees . ........... v... ....... 24

10. Temporal relationships between the density per 10 m2 foliage
of second instar (L ) spruce budworm, the density of adult
female Glypta fumiferanae and the percentage of third and
fourth instar (L3-L4) budworm parasitized by Q; fumiferanae
in three plots at the Green River field station, New
Brunswick ................................................... 38

 

11. Parasitism of spruce budworm larvae by Glypta fumiferanae
as a function of the ratio of hosts to parasitoids and
rainfall during the period of adult parasitoid activity ..... 39

 

viii

FIGURE

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

PAGE
Net recruitment for an insect pOpulation preyed upon by
a constant density of predators which exhibit a sigmoidal
functional response I.COO.....0.........OOOOOOOOOOIOO0.0 ..... 48

Influence of parasitoid aggregation with respect to host
density on the stability region of a parasitoid host model .. 52

Influence of parasitoid host searching efficiency on
the stability region of a parasitoid host model ............. 53

The relationship between the rate of increase of spruce
budworm populations (solid line) and different levels of
predation and parasitism (dashed lines) ................ ..... 63

The influence of different levels of dispersal loss and
predation on the rate of change of spruce budworm numbers ... 68

The influence of spruce budworm defoliation on the survival
Of host trees ............OOOOOO-OOOOOO...... ..... ......OOOOOO 74

Influence of spruce budworm on the physiological condition
Of host trees OOOOOOOOOOOOOOOO0.0000000000000000000000000.... 77

Layout of cut and control areas in stands 1, 2 and 3 ........ 79

Relationship between the mean annual increment and the
current increment in timber volume growth ................... 84

The density per m2 foliage of various life stages of the
spruce budworm in the cut and control areas of stand 3 ...... 98

The density per 1112 foliage of various life stages of the
spruce budworm in the cut and control areas of stand 2 ...... 99

The density per m2 foliage of various life stages of the
spruce budworm in the cut and control areas of stand 1 ...... 100

Circuit diagram for temperature controller of an environmental
chamber. The portion to the right of the dashed line is
replicated for each group of heating elements .......... ..... 108

Proportion of total malaise trap catch of female Glypta
fumiferanae for 7 time intervals within a day. The sample

period was 6 days (7-19 to 7-24). One trap was located in

48 jack pine trees. Twenty four traps were located in the

upper crown and 24 in the lower crown ..... .................. 132

ix

FIGURE

26.

PAGE

Malaise trap catch of female Glypta fumiferanae from

two plots in relation to degree days base 8.9 0C in 1982.
One trap was located in each of 24 jack pine in each plot.
Twelve traps were in the upper crown and 12 in the lower

crown ....................................................... 134

INTRODUCTION

An inherent aspect of most crop production systems is the necessity to take
into account the influence of crop damaging organisms. Two different, though not
mutually exclusive, approaches can be adopted. First, the structure of the crop
production system can be accepted as is and pests can be controlled in some
fashion. The structure of a system refers to the physical and institutional
properties of the system and policies which, once implemented, usually cannot be
changed. The structure of crop production systems involves a number of diverse
factors such as crop variety, crop spacing and mixing, the genetic makeup of plants
and pests, crop markets, and society's expectations of crop consumption. With the
first approach, chemical toxicants are most often used to either drive a pest
species as close to extinction as possible or preserve the integrity of the host plant.

Increasing social and economic costs of chemical pesticides, reports of their
deleterious effects, and the significant rate at which they fail to prevent crop
damage make it apparent that the application of pesticides can no longer be an
exclusive pest control policy. With the advent of integrated pest management,
inputs of pesticides have been reduced in some crop production systems. For the
most part, however, this has been accomplished by improving the decision making
process of when and how much of a pesticide to apply as opposed to reducing
reliance on pesticides as a control tool.

The second approach, which might also be considered the second phase of
pest management, is to consider pests and factors which influence pest dynamics as
an integral part of the crop production system and design a system structure so

that the effects of pest organisms are minimized (Haynes e_t a_l. 1980). This will be

a formidable task. As in the design of an electronic amplifier, it will necessitate
the wedding of theory (often couched in terms of mathematics) and empirical
observations. However, unlike the amplifier, pest crop systems are "badly defined
systems" (Beck 1981, Young 1978). With such systems, g pri_or_i theory usually
cannot predict the nature of the system and design cannot come about from theory
alone. Furthermore, planned experiments with these systems are often difficult
and may at times be impossible to implement. Even _ig §it_u data of the "normal
operation" of the system may be difficult to acquire.

Although the obstacles to this approach seem insurmountable, it must be
pursued vigorously if pest management is to become what the name implies. In this
thesis, I present the results of two projects which were motivated by the concept
of design. In both, an effort is made to make use of theory and empirical data in
an effort to propagate the concept of system design and to develop principles
appropriate to each area of study. In the first project, the temporal and spatial
dynamics of an adult parasitoid of the spruce budworm were investigated. This was
done to develop methods for sampling this important life stage of parasitoids and
to develop concepts appropriate to design-mediated biological control. In the
second project, the use of forest harvesting was explored as a way to change the
structure of the spruce budworm/spruce fir forest system and thereby improve
system control. No pretense existed of actually being able to meet this entire
objective. However, the project was pursued in hopes of establishing a basis for

further study in this area.

Adult Parasitoid Activity and

Its Relation to Biocontrol

Introduction

Actions taken to achieve or improve control of crop damaging insects using
parasitoids fall into three endeavors: importation of exotic parasitoids, augmen-
tation of established exotic or endemic parasitoids, or management of existing
parasitic insects. Management entails any action taken to improve the effec-
tiveness of a parasitoid as a control agent. When applicable, management should
be the first action taken. Furthermore, when management can be implemented,
it will likely be more cost effective than importation or augmentation.

Knowledge of factors which influence the life system of a parasitic insect
and information on how these factors may be manipulated are prerequisites for
successful parasitoid management. One of the most important aspects of the
life system of parasitic insects is host searching since the maximum number of
progeny that can be produced by a generation of parasitoids is determined by
their host searching efficiency. Therefore, the adult female parasitoid and
factors which influence the number and distribution of hosts attacked by the
female may be important objects of control in any management effort.

Numerous theoretical investigations have examined the relationships be—
tween the host distribution, parasitoid host searching behavior and resultant
dynamics of parasitoid-host systems. Based on these studies, the characteristics
of successful biological control agents have been advanced (Beddington e_t g.
1978). In all of these studies the only factors influencing parasitoid host
searching are the density and distribution of hosts. However, factors other than
the host influence parasitoid searching behavior. Few field studies have been

undertaken to elucidate these factors. This is in part because such studies should

focus on the temporal and spatial dynamics of the adult parasitoid. These
organisms are small, highly mobile and most often few in number and as such are
difficult to sample. Even fewer studies have sought to juxtapose empirical
observations of the adult parasitoid and the theory of parasitoid—host systems.
Investigations of this type are necessary though if the chasm between empirical
observations and parasitoid-host theory is to be bridged and, concurrently, our
ability to manage parasitoids broadened.

In this paper we present the results of an investigation of the spatial and

temporal dynamics of adults of the parasitoid Glypta fumiferanae Vierick. Q.

 

fumiferanae is a common, specific, univoltine parasitoid that attacks first and

 

second instar spruce budworm (Choristoneura f umiferana (Clemens)). It over-
winters in the budworm larvae and emerges from either fifth or sixth instar
hosts. It then spins a pupal case in the tree and emerges as an adult at
approximately the time when budworm eggs are eclosing. Details of the biology

of Q. fumiferanae are provided by Brown 1946, Wilkes gt 31. 1948, Dowden 91 a}.

 

1948, and Miller 1960.
The paper consists of three sections. First, information on the temporal

and spatial dynamics of adult g. fumiferanae is presented. Data was obtained

 

through field studies of the activity patterns of the parasitoid and through a
laboratory investigation of host searching behavior in a gradient of abiotic
environments. Second, the relationship between the temporal dynamics of the
adult parasitoid and its searching efficiency is examined using historical data of
the interaction between 9. fumiferanae and its host. Finally, the general
implications of our findings are assayed. This is done by relating our observa-
tions to established parasitoid-host theory and to extensions of this theory which

we have developed.

Methoch and Results
Field Studies: Data was collected on the temporal and Spatial activity

patterns of adult _q. fumiferanae during 1980 and 1981 in northern Michigan.

 

One forest stand was sampled in 1980, and two stands were sampled in 1981 (fig.
1). The study area used in 1980 was not used in 1981 because it was cut for
timber.

Based on previous sampling of adult parasitoids (Julliet 1963, Price 1971,
Reardon _e_t _a_1_. 1977, Ticehurst and Reardon 1977, Simmons unpubl. data), malaise
traps were selected as the principal tool for measuring the activity patterns of
adult Q. f umiferanae. Malaise traps are ideally suited for this task because they
are passive traps and snare actively flying insects. The traps were designed and
constructed for placement in tree crowns and on the forest floor; this way trap
catch could be easily inspected. Details of trap design and construction are
given in figure 2.

During early July 1980, 14 of these traps were placed in the mid to upper
crowns of 14 balsam fir (_A£ie_s balsamea (L.) (Miller)), and 14 were placed on the
forest floor in stand 1 (fig. 1). Traps were placed on the forest floor because it

was hypothesized that 9. f umiferanae might use this habitat when foraging for

 

food. The forest floor provides a habitat for many plants which produce nectar
and pollen. These plant products have been cited as food for adult parasitoids by
many authors (Chermokova 1960: Leuis 1960, 1961a, 1961b, 1963, 1967; Shahja-
han 1974; Simmons e_tal. 1975; Syme 1966, 1975; Thorpe and Caulde 1938).

Stand 1 consisted of 93. 60% mature balsam fir. Trees in which traps were
placed were selected on the basis of ease of access for trap placement and good

crown condition. Traps were positioned in the trees so that one open side of the

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Figure 2.

A MODIFIED MALAISE TRAP

FOR PLACEMENT IN
TREE CROWNS

  

 

 

 

 

 

 

----L---+

 

 

 

 

 

 

 

 

 

 

 

Details of a malaise trap designed for placement in tree crowns.
Trap volume is 1 m3. The frame is cbnstructed of PVC pipe and
the screening of Saran 20 mesh screening. The intermediate
and final collection jars and the face plate are plastic. The
final collection jar is affixed to a nylon cord which passes
through a threaded pipe which is in turn attached to the inter-

mediate collection jar. Trap catch is inspected by lowering the
final collection jar.

trap was tangent to the tree crown. Q. fumiferanae pupal density per m2 balsam

 

fir foliage was 7.61 (5:10.02, n=48). Traps were emptied each morning between
10 July and 10 August. In total, 39 females were trapped in the trees (fig. 3),
and none were caught on the forest floor.

We felt that the low trap catch in 1980 may have been due to the
orientation of the traps in the tree crowns. Therefore, in 1981 the traps were
oriented so that the Open sides were perpendicular to the crown. Thirteen traps
were located in balsam fir and 13 on the forest floor in stands 2 and 3 (fig. 1).
Stand 2 was 10096 mature balsam fir and stand 3 ca. 5096 mature balsam fir. The
density of Q. fumiferanae pupae per m2 balsam fir in stands 2 and 3 was 10.45
(8:11.28, n=40) and 9.87 (s=9.03, n=40). Traps were emptied each morning
between 2 July and 15 August. During the peak flight of females, traps in stand
2 were emptied bi-hourly from 800 to 2200 hours for 3 days. In total, 125 males
and 294 females were trapped in trees in stand 2, and 72 males and 182 females
were trapped in trees in stand 3 (fig. 4). Clearly, the orientation of the traps in
the trees during 1981 was superior and indeed necessary for capturing significant

numbers of g. fumiferanae. N o parasitoids were trapped on the ground.

 

The flight activity as measured by trap catch of both males and females in
stands 2 and 3 during 1981 are remarkably similar (fig. 4). Hence, we
hypothesized that weather was a major determinant of flight activity. This
hypothesis was supported by the bi-hourly trap catch data for females in stand 2
(fig. 5). This data indicated that parasitoid flight activity was strongly depressed
by rain. On 17 July rain began ga. 1500 hours resulting in a decline in female
activity as measured by trap catch. Activity also followed the daily temperature

profile.

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425 450 475 600 525 660 676 600 626

Degree days - Bose 8.89‘C

Figure 3. Catch of female Glypta fumiferanae from 14 malaise traps
located in balsam fir trees in stand 1 during 1980.

 

11

Figure 4. Catch of male and female adult Glypta fumiferanae from 13
malaise traps located in balsam fir trees in stands 2 and
3 during 1981.

 

12

 

 

 

 

 

 

 

 

 

 

Degree doys - Bose 889°C

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Degree doys — Bose 889°C
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son 2400 coo '7 2430 060 ' 2430 Hours
| 7-10 | 7-17 | 1-10 Days

 

 

 

Figure 5. Bi-hourly trap catch of female Glypta fumiferanae from 13
malaise traps located in balsam fir trees in stand 2 and
the temperal distribution of temperature and rainfall.

14

In order to examine the influence of rainfall and other possible weather
factors more extensively, a model was constructed so that the relationship
between weather and the time series of trap catches could be examined. A
modelling approach was adOpted because conventional statistical methods could
not be used in analyzing this relationship. This is because trap catch in the
absence of any other influencing factors would be proportional to the density of
adult parasitoids. This density was unknown. However, with the assumptions
outlined below, an index of this density could be derived from the trap catch
data.

In the model, predicted trap catch (TC) of Q. fumiferanae was expressed as

 

a function of adult density (Ad) and adult activity (Aa). In addition, the activity
of the adults was related to a set of weather variables (W). These relationships
are concisely written as:

TC = f(Ad, As) (1)

Aa = f(W)

The time-specific adult density, Ad(t), is not known. However, it is a
function of the emergence, dispersal and death processes Operating until time t.
With the assumptions that dispersal into and out of an area balance and that
either a constant or no external mortality operates on the adult population, Ad(t)
is a function of the emergence rate and physiological time interval between
emergence and death. With these assumptions, our modelling methodology can
be outlined as follows: 1) specify a function for the change in adult density
through physiological time, 2) specify a function relating trap catch to adult
density and weather, 3) parameterize a model based on these functions through

the use of a nonlinear Optimization algorithm, and 4) evaluate model fit by

15

comparing predicted trap catch to the data with which the model was
parameterized and to an independent data set. Physiological time was
approximated with degree days (DD) (base 8.8900), and the model was
parameterized with the data collected from stand 2.

The general structure of the model is given in figure 6. Ad(t) is the
integral of the difference between the emergence and adult mortality rates.
Each of these rates was modelled as a distributed delay. These delays can be
used to model aggregate processes which are made up of entities in which each
entity has an output related to its input via a pure time delay. In this case the
emergence of a parasitoid is related to some initial time point and its death is
related to its emergence via two physiological time delays (PTD).

For a population of parasitoids, a PTD is a random variable. It can be
shown that the distributed delay is based on the probability density function (pdf)
of a PTD (appendix 1). If f(t) is the pdf of the physiological time delay between
emergence and death, and p(t) and m(t) are the emergence and mortality rates,
then:

m(t) = I}, p(v)f(t-—v)dv where t = physiological time.

The adult density is given by:
Ad(t) = I}, p(v)-m(v)dv
The parameters for the emergence rate were estimated from data on the

cumulative emergence of _G_. fumiferanae collected in stand 2. Those for

 

mortality were estimated jointly with other model parameters from the trap
catch data. The gamma density function with an integer shape parameter (k)
was used for f(t). The shape parameter was determined by initially selecting a

value based on the shape of the distribution of p(t) and Ad(t) and then adjusting it

l6

 

T—

_Emergence

 

Dlstrlbutedl Rate Distributed Mortality
_ Delay J Delay _’ Rate

 

 

Intlal Input

 

 

 

Trap Catch I

 

Figure 6. General structure of the model used to analyze the temporal
distribution of malaise trap catches of Glypta fumiferanae.
Elis a vector of weather variables and a is a proportionality
constant.

 

17

prior to determining the other model parameters until a best fit was obtained. k
was estimated independent Of the Optimization because it must be an integer and
the Optimization algorithm used requires continuous decision variables. The
mean Of PTD (£112) and k are sufficient statistics for f(PTD).

Variables in the set 11 included rainfall, relative humidity, temperature,
and barometric pressure. Hourly measures Of these variables were averaged over

800 tO 2200 hours, which was the period 53. fumiferanae was active. The values

 

Of W and TC used in the model are constant for a given day while Ad changes
continuously according tO the degree days accumulated on that date. Therefore,
the value Of Ad midway through a day was used in the function TC = f(Ad, Aa).

TO estimate model parameters, a linear form Of (1) was adopted. Predicted
trap catch is therefore given by:

TC" = (a + 9W) 0;“ p(v) - f;’l‘(tn-z)p(z)dzdv)
where: n is a daily index, tn are degree days accumulated on day n, and
underlined variables denote vectors. The parameters a, Q and 3TB of the
mortality rate were estimated using the complex nonlinear Optimization algo-
rithm due to Box (Kuester and Mize 1973). The Objective function for the
Optimization is given by:

Minimize F = 2:1: 1 (T6,, - T0,”)2
With this Objective function, the value assigned to the parameters Of a particular
model minimizes a sum Of squares about the Observed trap catch.

Owing tO the importance of the female parasitoid, the model was parame-
terized for female trap catch only. TO initiate parameter estimation, the initial
input (i.e., total number Of pupal female parasitoids) was arbitrarily selected.

This was done for two reasons. First, the absolute number Of pupal g.

18

fumiferanae in the trapping area was not known. Second, we were interested in

 

the qualitative aspects Of the model, and knowing this value was therefore
unnecessary. As a result, model parameters except 12 are scaled by the initial
input.

As stated previously, the emergence rate p(t) was determined from emer-
gence data. The rate Of adult female emergence was separated from the male
emergence rate by assuming that the initial trap catch of females indicated the
onset Of female emergence and that the shape Of the female emergence curve
was similar tO the joint male and female emergence curve. The first assumption

is based on the fact that g. fumiferanae was not collected in any habitat other

 

than the forest canopy. Hence, it is unlikely that females emerged at the same
time as males but initially used a habitat other than the trees containing
budworm in order to find food or alternative hosts. Parameters for the
distributed delay used to describe female emergence were selected so that
predicted emergence resembled the combined male and female curve but was
appropriately delayed in time (fig. 7).

Results Of the parameter estimation are given in table 1. Only models
which had some ability to predict trap catch are presented. Since the Objective
function for the Optimization process can be thought Of as a residual sum Of
squares, an R2 was computed for each model. A test Of significance cannot be
made, though, due tO correlation among variables within the model and because
the distribution Of the various sum of squares is unknown. The best prediction Of
trap catch was achieved with precipitation and temperature as independent
variables. Wet and cool weather was associated with declines in trap catch.

Reasonably large changes in the residual sum Of squares associated with the

Percent Emergence

l9

 

 

 

 

 

 

'T Ehnnbolluy' . c J b—
It — Recorded emergence Of d' and 9 / "“ ‘

J ¥ - 95% Confidence intervals * T ,9 r
0 - Predicted 9 emergence ”

-l I] I.

—l i 0 I.

-l u >-

4 -

..l u l—

X
.4 U E
o I m ' I I l l I I I
275 300 325 350 375 400 425 450 475 500 525 550 575

'Figure 7.

Degree days — Base 8.89°C

Observed combined emergence Of adult male and female Glypta

fumiferanae in stand 2 and predicted emergence Of female 9;

 

fumiferanae as a function of degree days base 8.89 00.

 

Table 1.

20

Mbdels used to predict the temporal distribution Of malaise trap
catch Of female Glypta fumiferanae. Variables used are:
TCn = predicted trap catch

T = average temperature between 800 and 2200 hours on day n

Rfin = average relative humidity between 800 and 2200 hours on
day n

R = rainfall in inches between 800 and 2200 hours on day n

A3 = a measure Of adult female density on day n

P = expected number Of degree days for emergence from pupae
p from an initial time point t

PTD = expected adult female life span in degree days
K , m = shape parameters Of gamma density function used to

p describe PTD

In allggpdels the emergence rate is given by a distributed delay
with PTD = 55.5, k = 4 and to = 388 degree days base 8.89°C.
The value of km wa 8.

 

 

 

 

 

 

 

 

 

Residual Sum

 

 

MODEL PTDm of Squares R

1 TC = .605 Ad 81 1300 .51
n n

2 TC = (.012 + .852 T ) Ad 84 1117 .58
n n n

3 TC = (1.24 - .892 RH ) Ad 76 1046 .61
n n n

4 TC = (154.6 - 1.89 R ) Ad 86 708 .74
n n n

5 TC = (.662 - .714 RH + .599 T ) Ad 87 982 .63
n n n n

6 TC = (.029 - 1.232 R + .9553 T ) Ad 87 546 .80
n n n n

21

stepwise inclusion Of each variable in this model ensured that the model was not
over-parameterized. The predicted trap catch and predicted temporal distribu—
tion Of adult females using this model and actual trap catch for stand 2 are
shown in figure 8. The predicted temporal distribution Of adults corresponds to
the index Of adult density.

As stated above, it was not possible tO evaluate the statistical significance
Of the relationship. between wet and cool weather and diminished trap catch.
Nonetheless, one is led to the conclusion that the relationship is not spurious for
two reasons. First, the probability Of Obtaining the relationship by chance is
very small. Based on the model-generated population index, adult female Q.

fumiferanae were most abundant between 450 DD and 560 DD. At the same

 

time, there were 3 days when trap catch was greatly reduced (517 DD, 522 DD,
560 DD) and 1 day when trap catch was somewhat reduced (484 DD).

The trap catch at 528 DD was not considered a reduced level even though
in stand 2 the number caught on this day (18) was approximately the same as that
caught at 484 DD (16). The reasons for excluding this date are twofold. First, in
stand 3 the number caught on this date is close to the average number trapped
during what we assume to be favorable weather conditions. Second, the trap
catch on this date followed a period of extremely depressed parasitoid activity
and the resumption Of higher levels Of activity may not occur immediately after
the restoration Of favorable environmental conditions.

During the four days Of reduced trap catch and only during these days was
precipitation recorded. In addition, for the three days with greatly reduced trap
catch the temperature was lower than the average for the 12-day period. For

the purpose at hand, these weather conditions will be classified as wet and cOOl.

Density Of 9 9. (mm

22

 

    

 

 

 

 

 

8‘
§
4 Symbol key L
e-l ‘.‘ a - COtCh Of 9 :9. Wm '-
4 - 3K - Predicted catch Of 9 :9. ml-
3.4 (D — Theoretical distribution Of *-
-I 9 3. WM l.
a— l-
t.
n—l l—
0
p—l _
N
L
'3 I.—
N
a —
0'.
g h-
:—l l—
l.
P
l-
L—
'3
in
7 I I I I I T T I
475 500 525 850 875 800 825 880 8V8

 

Degree days — Base 8.89°C

Figure 8. Predicted and actual malaise trap catch of adult female

 

 

Glypta fumiferanae in stand 2 and the theoretical, relative

 

temporal distribution of adult females. Malaise traps
were located singly in 13 balsam fir trees.

A measure Of the likelihood that no relationship exists between trap catch and
wet, cOOl weather can be computed by determining the probability that these
two sets Of events occurred on the same days by chance.

The number Of ways in which 4 depressed trap catches can be distributed
among 12 days without respect tO order is given by the binomial coefficient (12).
Suppose only the 3 days with greatly reduced trap catch are classified as low
catch days and the other as a normal catch day. There then occurred 3 wet and
cOOl days during which trap catch was reduced and 1 wet and cOOl day during
which no reduction in trap catch occurred. The probability of this happening by
chance is given by (g) (?)/(12) = .065. The probability Of either this event or the
more extreme event that all 4 days are classified as reduced is realized is then
given by .065 + (2) (3)/(li) = .067. In contrast, the most likely single outcome
would be for 1 reduced trap catch day to occur during the 4 wet and cool days
and the rest to occur during the other 8 days (p=.453). Clearly, the probability
that the partitioning Of wet and cOOl days with reduced trap catch occurred by
chance is very low. It is therefore likely that a relationship does exist.

The second reason for believing that the relationship between weather and
trap catch is not spurious is that the model closely predicts the actual trap catch
in stand 3 (fig. 9). Recall that the data from this stand was not used to
parameterize the model. In this case, the initial input Of pupal parasitoids was
set equal to the input from stand 2 scaled by the ratio Of estimated pupal
densities in stands 3 and 2. The close fit Of the model is not surprising
considering the similarity in the trap catch from stands 2 and 3. What the
relationship between the model and data from stand 3 does is reinforce the
important fact that the trap catch from structurally different and spatially

separated forest stands was strongly influenced by the same weather patterns.

24

 

Density Of 9 9. W
2? 3}

mbolkoy
t-cmwmoew— —
l-Prodtctodcatettotvs.p+.. a
O-Iheorectloaldletrlbutlonof —
99.9.1...qu .

[-

 

 

 

Figure 9.

l T l l l l I
350 375 400 425 450 475 500 525 550 575 600 625 650 675 700

 

I If I l l l 1

Degree days — Base 8.89°C

Predicted and actual malaise trap catch of adult female
Glypta fumiferanae in stand 3 and the theoretical, relative

 

temporal distribution Of adult females. Malaise traps were
located singly in 13 balsam fir trees.

25

We have established the fact that rainfall and cool temperatures reduce
the malaise trap catch Of 9. f umiferanae. An important question is whether the
reduced trap catch is indicative Of a reduction or cessation Of host searching.

Based on Observations Of g. fumiferanae's host searching behavior made in 1981,

 

the answer is yes. These Observations will be discussed more fully later;

however, two aspects are relevant here. First, very few g. fumiferanae were

 

Observed attacking hosts on cool, wet days. Second, the parasitoid frequently
flew from one part of the tree to another when searching for hosts. This was
especially evident when the parasitoids failed tO discover hosts in a particular
location. Since malaise traps are passive traps, trap catch will increase with
activity Of the parasitoid; in this case, activity is closely tied to host searching.

The estimated mean and variance Of the lifespan Of adult g. fumiferanae is

 

given by the mean and variance Of the gamma density function used to describe
the physiological time delay between pupation and death Of the adult parasitoid.
The mean is m = 87 DD and the variance is (LEV/k = 946 DD. The mean
corresponds tO g. 10.5 days in 1981. A similar lifespan was evident in 1980.
This conclusion is based on the fact that the degree day interval during which
female parasitoids were trapped in 1980 is approximately the same as that in
1981.

In the laboratory, we found that adult female Q. fumiferanae died within 3

 

days if they were not fed. This implies that in the natural environment, adult _q.

fumiferanae dO indeed feed. They do not, however, use the vegetation on the

 

forest floor as a fOOd source. This assertion is based on two Observations. First,
although many parasitoids were caught in malaise traps on the forest floor, m g.

fumiferanae were snared. Second, extensive sweep-netting Of the ground

 

26

vegetation failed to reveal the presence Of g; fumiferanae. While it is evident

 

that the adult parasitoids do feed, they apparently do so in the forest canopy.
Futhermore, forest composition appears tO have no influence on the parasitoids‘
ability to secure food. This is founded on the equivalence Of the parasitoid
lifespans in stands 2 and 3, and the fact that stand 2 was exclusively balsam fir
and stand 3 a mixture Of balsam fir and other coniferous and deciduous trees.

Laboratory Study: In the laboratory, we sought to elucidate whether a

 

temperature and light intensity gradient influenced 9. f umif eranae's host search—
ing behavior. The study was catalyzed by the theory Of Optimal foraging and

information which indicated that _G_. fumiferanae searched for hosts in what

 

would appear tO be a non-Optimal fashion.

It is realistic tO assume that parasitoids adopt host searching behaviors
which maximize the number Of hosts parasitized at the end Of their lifetime.
Natural selection will favor those strategies which result in a reproductively
efficient distribution Of the parasitoids' Offspring among available hosts. Most
hosts Of parasitoids are distributed in a non-random fashion and Often in patches
Of variable density. Theoretical and laboratory investigations Of parasitoid host
searching (Royama 1970, COOk and Hubbard 1977, Hubbard and Cook 1978,
Waage 1979, Nachman 1981) and general foraging strategies (Charnov 1976;
Parker and Stuart 1976; Pyke, Pullman and Charnov 1977) have led tO the
principle Of Optimal patch use. Briefly, this means that all patches Of the
resource are reduced to some common harvesting rate. Thus, if a parasitoid‘s
rate Of encounter with healthy hosts is to be maximized over the period Of time
during which hosts are available, then the Optimal solution requires that when
presented with host patches Of different density, the parasitoid will reduce all

the areas it uses tO the same rate Of encounter between itself and healthy hosts.

27

The distribution Of 159 attacks by Q. fumiferanae on budworm Observed in

the field is given in table 2. Observations were made by individuals positioned in
tree crowns who recorded the activity Of individual female _G_. fumiferanae. The
length Of time that a particular parasitoid was Observed varied from 30 seconds
to over 45 minutes. More attacks were Observed in the outer portion Of the tree
crown than on the interior. This distribution may be biased since parasitoids in
different parts Of the trees may be more easily detected. However, because the
Observer was positioned within the tree crown, this bias should have deflated the
number Of attacks Observed in the exterior part Of the crown.

According tO an Optimal foraging strategy, an approximately equal distri-
bution Of attacks between the exterior and interior portions Of the crown would
be expected if the hosts were equally distributed in these two areas. This is not
the case, though. Lewis (1960) found that only 2596 Of the hibernating budworm
population were found on the terminal 15-inch twigs Of whole branches sampled
from balsam fir. He also found a trend Of increasing parasitism by g.

f umiferanae on the exterior Of the crown. Obviously, g. fumiferanae responds to

 

 

factors other than the host distribution when searching for hosts. The following
experiment was conducted tO determine if physical factors associated with the
interior and exterior Of the tree crown influenced the parasitoids' host searching
behavior.

A chamber was constructed in which: (1) a temperature and light gradient
could be generated and (2) parasitoids would be free tO range over this
environmental spectrum for hosts. The chamber was a rectangular tube Of
dimensions 80 x 10 x 10 cm and was manufactured from plexiglass 1.2 cm thick.
On the outside walls Of the chamber, 5 series Of two 25 watt, 725 Ohm heat

dissipating resistors were mounted and wired in parallel. A controller, which

Table 2.

28

Distribution of attacks by Glypta fumiferanae on spruce budworm
larvae in balsam fir trees (n = 16). The exterior Of the tree
denotes the first 18 inches Of the canopy.

 

 

 

Location of Attack

 

 

 

EXTERIOR INTERIOR
Bud Lichen Bark Flower Bud Lichen Bark Flower
Tip Scale Bract Tip Scale Bract
or or or or
Branch Needle Branch Needle
Fork Base Fork Base
ATTACKS
39 13 14 27 3 21 35 10
Total 93 69

57% 43%

produced pulses Of electricity whose duration were regulated by potentiometers,

was connected tO each set Of resistors. Pulses Of different durations were
distributed among the five sets Of resistors, resulting in differential warming Of
the chamber. A circuit diagram for the controller is provided in appendix 2.

The chamber was placed in a constantly cooled (10°C) and darkened room
and illuminated from above by two 30 watt flourescent bulbs. The experiments
were conducted in the cooled room in order tO Obtain the desired temperatures
within the chamber and so that the chamber would not have tO be recalibrated
due to changes in room temperature. The light intensity in selected portions Of
the chamber was regulated by placing a piece Of Saran“ 20-mesh screening over
these sections.

9. fumiferanae pupae were collected and males and females reared at

 

22°C and a 14 hour light/8 hour dark photoperiod. To provide hosts for g.

fumiferanae, budworm pupae were collected and reared, and adult males and

 

females were placed in small paper bags on which the females oviposited. Eggs
were collected and placed in a petri dish which was then covered with gauze and
Parafilm'. The dishes were placed in a paper sleeve in which an Opening was cut
to allow light to pass through the gauze and Parafilm. When the eggs hatched,
the photopositive larvae crawled onto the gauze and spun hibernaculae.
Parasitoids used in the experiment were between 3 and 6 days Old. This
age range was imposed to avoid confounding results with age-dependent behav-
ior. In addition, all experiments were conducted between 1100 and 1400 hours to
eliminate the possibility of die] periodicity as a source Of variation. Ideally, the
influence Of temperature and light on the behavior Of female 9. fumiferanae
should have been studied independently and then jointly. However, the short

time in which adult 9. f umif eranae were available precluded such an approach.

 

30

A temperature and light gradient was arranged so that there was a fully
illuminated warm environment, a shaded cOOl environment, and a spectrum
between these limits (table 3). Four patches Of gauze, each with five budworm
hibernaculae, were placed in two warm and light regions and two cool and shaded
regions. NO hibernaculae were placed in the center cell into which female
parasitoids were introduced. After the parasitoids moved at least one cell away
from the entry paint, their behavior was recorded for l to l-l/2 hours. This
consisted Of recording the time intervals each parasitoid spent in each environ-
ment searching for hosts, attacking hosts, and resting. The number Of oviposi-
tions in each cell was also recorded. Searching behavior consisted Of g.
fumiferanae probing and examining the gauze and surrounding areas with its
antennae in an effort tO locate hosts. Attack behavior consisted Of probing with
the ovipositor and oviposition. It was possible tO determine when oviposition
occurred, as the females, upon inserting the ovipositor in the host, remained
completely motionless for 93. 15 seconds. Resting behavior consisted Of
immobility, preening, and non-directed movement.

The average total time spent, average time spent attacking hosts, and
average time spent not attacking hosts in each Of the different environmental
conditions is given in table 3. Attack time consisted Of both attack and
searching behavior, when searching behavior occurred between attacks separated
by a short time interval. Attack time for the two warm-light and cool-shaded
environments were summed. This was done because few attacks occurred in the
cells at the extreme end Of the chamber and this result cannot be attributed tO
environmental conditions. It is just as likely that most attacks occurred in the

cells closest tO the entry because this is where hosts were first encountered.

Table 3.

31

Total time and time spent in attack and non-attack behavior by
Glypta fumiferanae in different environmental regimes. Time is

 

in minutes and tenths Of minutes. The variable W is the number
Of cases (0.) in which time spent in cell 4 is greater than that
in cell 2 when parasitoids were Observed in either Of these
cells. 4 is the probability that w 5 W given that W/ZCi = 0.50.
Attack times in cells 1 and 2 and in 4 and 5 are summed.

 

 

Environmental Conditiogs

 

 

 

 

 

 

Cell 1 2 3 4 5
Temperature °c 31 27 22 19 15

Lighting FULL/PARTIAL

Hosts present yes yes no yes yes 2C1 ¢
Total time n = 23

Mean 8.29 26.76 11.49 7.24 5.16

Std. Dev. 13.78 21.00 12.90 17.00 13.43

W 4 23 .001
Non-attack time n = 21

Mean 7.81 13.37 11.49 1.68 2.37

Std. Dev. 13.93 12.86 12.90 3.16 7.15

W 4 21 .004
Attack time n = 14

Mean 28.05 12.77

Std. Dev. 23.05 19.53

W 5 14 .212

 

32

Analysis Of the data is confined tO Observations from cells 2 and 4, except
for attack time in which the data is summed for cells 1 and 2 and for cells 4 and
5. Reasons for this restriction are as follows: The center cell (3) was not
included because hosts were not placed in this region. The cells at the ends Of
the chamber (1 and 5) were not included since the conditional probabilities for a
parasite tO enter these cells, regardless Of environmental influences, are not the
same as those for cells 2 and 4. This is a result Of the linear arrangement Of the
environments.

Since independence and normality assumptions could not be met, the
following method Of analysis was used. Let Ti be the time a parasitoid spends in
cell i. Let V: 1 ifT2>T4andv=0ifT4<T2. DefineWasm. ThenWis
distributed as a binomial random variable. If the time spent in cells 2 and 4 were
the same, then the parameter p Of this binomial distribution would equal 0.5.
The probabilities Of Obtaining the Observed or more extreme values Of W with the
hypothesis that p equals 0.5 are given in table 3. These probabilities are very
low for total time and non-attack time; hence, the null hypothesis is rejected.
The value Of a more extreme value Of W for attack time has approximately a l in
5 chance Of occurring, given p = 0.5. Hence, the null hypothesis cannot be
outright rejected; however, there is an indication that differences exist. A more
definitive analysis Of the allocation of attacks can be made by considering the
distribution Of ovipositions. In cells 1 and 2, 258 ovipositions were recorded; in
cells 4 and 5, 154 were recorded. If temperature and light produced no effect on
the oviposition distribution, the proportion Of attacks in cells 1 and 2 should be
0.5. The actual proportion was significantly different from this value (normal

approximation, at < .001).

33

The data suggests that the distribution Of attacks by Q. fumiferanae

 

Observed in the tree are a result Of the light and/or temperature differential
which exists between the interior and exterior Of the tree crown. If temperature
does play a role, it is due to increased radiant heat since only a very small
ambient temperature differential would exist between the interior and exterior
Of the crown.

Historical Data: Based on the field studies Of _q. fumiferanae's activity
patterns, we concluded that wet and cOOl weather would inhibit the parasitoid's
searching efficiency. In this section, this relationship is explored further by
examining historical data on the interaction between the parasitoid and its host.

Extensive data on this interaction was collected from 1950 tO 1958 during
the Green River Project in northwestern New Brunswick. Details Of the study
can be found in Morris (1963). This data has previously been analyzed by Miller
(1960) who also thought that rainfall might influence the attack efficiency Of Q.

fumiferanae. He did not, however, examine this in detail. Furthermore, Miller

 

employed a specific model to describe the attack dynamies Of the parasitoid. In
contrast, we have analyzed the Green River data without the encumbrance Of a
particular parasitoid attack model by exploring the relationship between the
ratio Of hosts tO parasitoids (H/P), rainfall, and percentage Of hosts parasitized.
In this case, this is a better approach since no 5 M assumptions about
parasitoid searching behavior are necessary. The influence Of temperature an
attack efficiency was not explored because the data lacked the resolution
necessary tO evaluate this factor.

Original data on spruce budworm densities and on the rate Of budworm

parasitism by Q. fumiferanae in the years 1950 tO 1958 at the Green River field

31,.

station was Obtained from the Maritime's Forest Research Center, Fredericton,

New Brunswick. The data from 3 plots (G2, G4, 65) were selected for use in the
analysis based on the plots having a data series spanning 5 or more years, having
budworm densities relatively constant, and having nO appreciable tree mortality.
The latter two criteria were established to minimize the possible influence Of
changes in the host's density and distribution and Of changes in the forest
environment on the parasitoid's searching behavior.

Parasitism rates had been determined by dissecting samples Of third and
fourth instar budworm. These rates were employed as an index Of the parasitism

Of second instar budworm, which is the host stage _G_. fumiferanae attacks. The

 

use Of this index, however, does introduce a potentially large bias into the
estimates Of parasitism. Between the second and third instars, budworm undergo
dispersal during which a large number Of insects die. The propensity for
dispersal is lower for parasitized larvae than for unparasitized ones (Lewis 1960).
As a result, depending on the differences between the dispersal rates Of
parasitized and unparasitized larvae, assessment Of parasitism in the spring will
be inflated over the true parasitism rate. This would not be a problem if this
inflation did not vary from year to year. Unfortunately, such an assumption
cannot be met.

Two factors influence the proportion Of third instars lost during dispersal:
stand composition and weather (Kemp _e_t g. 1980). Stand composition did not
change in the plots from which the data was collected. Weather, on the other
hand, was a dynamic variable. Results from a simulation model indicate that the
proportion Of third instars lost during dispersal might vary by as much as a factor
Of 2 between years as a result Of weather conditions during the dispersal period

(Kemp _e_t_ _a_l_. 1980). The net result is that the apparent parasitism rate may

35

change dramatically from one year to another while the actual rate changes
little. There is no way to determine this bias; however, one must be cognizant Of
the potential error.

An index Of the density per 10 m2 foliage Of female 9. fumiferanae was
computed by first assuming that the survival Of the parasitoid from the larval
stage located in the budworm to the adult stage was time invariant and that the

sex ratio Of g. fumiferanae was also time invariant. The index was then

 

determined by multiplying the density Of third and fourth instar budworm by one-
half the parasitism rate.

The index Of host density (second instars) was based on egg counts less egg
mortality and a constant dispersal loss Of first instars. An assumption Of a
constant first instar dispersal loss is supported by references contained in and
the simulation results Obtained by Kemp gt 91. (1980).

TO determine rainfall during the flight period Of the females, the appproxi-
mate calendar dates over which this activity occurred were determined by
assuming that the occurrence Of the female parasitoids flight activity with
respect to degree days would be the same in northwestern New Brunswick as it
was in Michigan. The time period Of activity in Michigan was determined from
the malaise trap catches Of 1980 and 1981. Minimum and maximum degree day
values for which females were caught for these two years were 388.44 and
662.88. However, the magnitude Of activity was not. uniform over this interval.
Hence, total precipitation for the interval 428 DD - 584 DD was computed since
it was during this period that peak activity occurred. The dates and precipita-
tion for this interval during the years 1950 tO 1957 in the Green River area are

given in table 4.

36

Table 4. Julian dates for the degree day interval 428 - 584 (base 8.89°C)
and precipitation during this period in the years 1950 to 1957
at the Green River field station, New Brunswick.

 

 

 

 

 

 

Precipitation
Year Julian Dates in inches
1950 215 - 244 2.87
1951 216 - 240 3.07
1952 203 - 221 2.57
1953 204 - 232 2.00
1954 214 - 241 5.87
1955 203 - 225 2.79
1956 221 - 248 3.00

1957 217 - 245 0.70

37

The data from each plot is presented in figure 10. Note that the
percentage Of hosts attacked in year i is plotted at year i + 1. This was done tO
preserve the temporal sequence in which the data was collected; the parasitoid
searched for and attacked hosts in late summer while the assessment Of this
attack was completed in early spring the following years. Of particular interest
is the year 1954. During this year the host density declined, the parasitoid
density increased, and parasitism declined dramatically in all three plots. This
decline in the parasitism rate is contradictory tO what would be expected.
However, during 1954, more precipitation fell than in any other year. Because
the decline in parasitism was evident in all three geographically separated plots,
it is logical to conclude that the decline was in fact related tO inordinate
rainfall.

A more complete picture Of the relatiorship between rainfall and parasi-
tism is Obtained by using the data from all 3 plots tO generate a parasitism
surface as a function Of the H/P ratio and rainfall (fig. 11). The pronounced
influence Of rainfall on the parasitism rate is readily apparent at both high and
low H/P ratios. There are, however, two unexplainable irregularities in the
parasitism surface. With moderate rainfall and high H/P ratios, a distinct valley
exists when the parasitism rate should either be nondecreasing or nonincreasing
with respect tO the independent variables. There is also a lack Of response in the
parasitism rate tO a decline in the H/P ratio when associated with a moderate tO
high rainfall. It must be remembered, though, that the data used in the analysis
is subject to a great deal Of potential bias. This bias may be due tO the affect Of
spring dispersal on the measured parasitism rate and also due to year-to-year

differences in the temporal sychrony between _G_. fumiferanae and the budworm

38

 

 

 

 

 

 

 

 

 

 

 

62 8 8
SYMBOL KEY .u -u
N u
a LOG I.
D
o LOG a. W9 ADULTS It} 8
D d N
”r l PERCENTAGE l. - 1.. PARASITIZED -g ;-_' ,;- ~a a;
H H
94 g '0‘ g
o a
or .3 L 9;“ l': a.
m I
t ‘9... g C to 0 I
s—c ... C o-o ...." C
a) b- u: g.
z O z z a z
w .:~ '2 8 .w .z- re ‘6‘
° .. :5 ° :5.
(D ..., ‘ 9‘
O o “- g a 0..
-’ _l
e- 9-
° no a -u
e e
s- s:
9 O
T I I I m I I I I I T I I I I r I I I I
11149 1960 1961 1962 1963 1964 1966 1966 1967 1966 1968 11149 1960 1961 1962 1969 1964 1966 1966 1967 1966 196?
YERR YEHR
a
as "
u-te
ea
0
m
0 N
'- I-O H
n N .—
H
.9“ m
" it
00-1 D“ C.
N on
I“
t: e. 0
H C. E
”’ z
z o m
“'57 P3t.)
‘3 15
t5 "2..
Cto “'
_l
0" -
o to
9
?-I
9
‘7 j I I I I I I u I
11149 1960 1961 1962 1969 1964 1966 1966 1967 1969 1963

 

 

YEflR

Figure 10. Temporal relationships between the density per 10 m2 foliage
of second instar (L ) spruce budworm, the density of adult
female Glypta fumiferanae and the percentage of third and
fourth instar (L3-L ) budworm parasitized by g; fumiferanae
in three plots at the Green River field station, New Brunswick.
(Data Obtained form Maritimes Forest Research Center
Frederiction, New Brunswick)

39

 

 

Ina

Parnltlnm RIM Incron

 

 

 

 

Figure 11. Parasitism of Spruce budworm larvae by Glypta fumiferanae
as a function of the ratio of hosts to parasitoids and
rainfall during the period of adult parasitoid activity.

4O

host. In addition, a large amount of sampling variability must be present,
although information on this variability is unavailable. Finally, temperature has
not been included as an independent variable even though it has been shown to
influence the activity of the female parasitoid. It is somewhat surpising that any
discernable relationship between rainfall and parasitism was produced. In fact,
in order to be visible, the relationship must be quite strong. When this
relationship is combined with the observation that rainfall impedes host search-
ing by the parasitoid, a conclusion can be drawn that excessive rainfall greatly

diminishes the attack efficiency of the parasitoid.

Discussion

Factors other than the host which influence the number and distribution of
hosts attacked by a parasitoid may be classified as being either controllable or
uncontrollable. Controllable factors are those which can be ameliorated or
accentuated by management actions. In this study we have identified two ways

in which uncontrollable factors affect _(_3_. fumiferanae. First, the attack effi-

 

ciency of the parasitoid is greatly diminished by excessive rainfall and/or cool
temperatures. This is because host searching by the parasitoid occurs at a

reduced rate during these weather conditions. Second, the spatial pattern of

 

host searching by 9. f umif eranae is influenced by light intensity and/or tempera-
ture. Similar types of phenomena have been observed for other parasitoids.
Temperature, sunlight, rainfall, and dew have been reported as influencing
the ability of parasitoids to locate and parasitize hosts. Klomp (1959) found that
the attack efficiency of the tachinid parasitoid, 9355113 2923, was correlated

with the amount of sunshine during the period of egg deposition. Burnett (1951,

41

1954, 1958) demonstrated that as the temperature declined, the number of
sawfly pupae attacked by a chalcid parasitoid decreased. This decrease was
attributable to a decline in the capacity of the parasitoid for oviposition and also
to a reduction of the number of hosts contacted by the insect. In field
experiments, he noted that parasitism was inhibited by rain and heavy dew.
Messenger (1968) found that temperature extremes affected the aphid parasitoid,
M exsoletum, by inducing a shif t in the proportion of ovipositional activities
relative to other activities engaged in by the females, and by reducing the
proportion of successful attacks. In laboratory studies of E3922 mellitor,
Barfield e_t _a_l. (1977) found that the parasitoid exhibited a narrow temperature
range in which total fecundity was maximized.

The spatial interplay between parasitoid host searching and abiotic factors
has also been observed before. Weseloh (1976) reviews a number of studies which
indicate that responses to humidity, light, and temperature are at least partially
responsible for the spatial distribution of parasitoids in forest habitats. Munster-
Swendsen (1980) has suggested that the aggregation of the parasitoid Apanteles
tedellae with respect to its host may be explained by an evolution of a similar
preference for physical conditions as opposed to a direct response to host
densities.

An important factor influencing adult parasitoids and, one that may be
controllable, is the availability of nutrients and moisture. These resources are
essential for the survival of many adult parasitoids (Townes 1958, Hassan 1967).
We found no evidence that a particular habitat was a better source of nutrients
or moisture for g. fumiferanae. Examples exist, however, which demonstrate
the importance of habitat in providing food sources for adult parasitoids (e.g.,

Syme 1975, Calderon 1977).

42

The importance of abiotic and biotic factors other than the host in
determining the number and distribution of hosts attacked is clear. As a result,
it is desirable to know, at least in a qualitative manner, how these factors
influence the dynamics of parasitoid-host systems and the capacity of a
parasitoid to act as a biological control agent. One way of elucidating these
influences is to incorporate these factors, in a general way, in the mathematical
models used to describe and study these systems. This is done below.

The dynamics of coupled parasitoid-host systems with discrete generations
have been extensively analyzed with the following model:

H =HtF(Ht)f(Ht’Pt) <2)

t+l

Pt +1 = Htu'fmt’Pt»
Because the basic structure of this model corresponds to many real-world

systems, it will serve as a basis for the discussion. In (2), H and Pt are host and

t
parasitoid densities, NIH) is the net rate of increase of the host in the absence
of Pt’ and f(Ht’Pt) is a parasitoid attack function. This function can be
interpreted as the probability of Ht hosts escaping discovery and subsequent
parasitization by Pt parasitoids.

Model (2) is nonlinear. As a result, analytical analysis is generally limited
to determination of the equilibrium states and stability properties of these
states. Equilibrium states are values of state variables which are either constant
or are periodic through time. Periodic equilibrium states are called limit cycles.
In (2), the state variables are the host and parasitoid densities. An equilibrium
point or cycle is stable if, when a state variable is perturbed from its

equilibrium, system dynamics drive the variable back to or asymptotically close

to this state. An equilibria is locally stable if the magnitude of the perturbation

is restricted to some neighborhood about the equilibrium. It is globally stable if
such a restriction is not necessary.

Limiting the analysis of (2) to determination of equilibria and stability of
these equilibria is not overly restrictive because these properties convey, within
the context of (2), the salient features of a successful biological control agent.
These features are that a parasitoid can depress and/or help maintain a host
population at a density well below the host's carrying capacity. This does not
imply that the parasitoid must singularly be able to do this, since F(Ht) may
contain complex density dependent relations. What is necessary is that all
mortality factors acting in combination are able to do so, and that in the absence
of the parasitoid, regulation would not be possible or would not be as strong. The
aim here is to examine the ties between factors which influence adult parasitoids
in their search for hosts and the equilibrium states and stability properties of (2).
This will be done by first relating the empirical observations to forms of (2) for
which equilibria and stability have been laid bare. An analysis is then made of a
variation of (2) which provides a different insight into the importance of factors
influencing adult parasitoid dynamics.

A sufficient condition for stability in simple one parasitoid—one host models
is that spatial or temporal incoincidence (or both) between the host and parasite
occurl (Hassel 1978, Nachman and Munster-Swendsen 1978). A stable system is

lStability can also be generated if: (1) F(Ht) 1s a nonlinear function such that the

host is limited by the carrying capacity of its habitat (Beddington_ et al.1975)
or (2) the host and parasitoid populations are comprised of cells and_ dispersal of
hosts and parasitoids occurs among these cells (Crowley 1981 and references
therein). However, (1) results in host equilibrium densities which are unrealis-
tically high (Beddington et al. 1978), and (2) might be considered as a
component of spatial and/or temporal incoincidence.

44

generated when either of these events is realized at appropriate intensities.
Stability transpires because the parasitoids do not overexploit the host resource.
Excessive incoincidence leads to runaway host papulations while too little
incoincidence leach to diverging oscillations in the host and parasitoid densities.
Here, attention is restricted to spatial incoincidence.

Two factors lead to spatial incoincidence: (l) contagiously distributed
hosts, and (2) parasitoids which forage in response to this patchy distribution and
possibly also in response to other biotic and abiotic factors. The essential
aspects of spatial incoincidence can be captured in (2) by incorporating non-
random host searching by the parasitoid. This has been done a number of ways
(Hassel and May 1974, Murdoch and Oaten 1975, Munster-Swendsen 1982). A
detail independent and analytically tractable method first pr0posed by Griffiths
and Holling (1969) and fully developed by May (1978) is used here.

May proved that the zero term of the negative binomial distribution

(1- ap/kf" (3)
could be used to model f(H,P) when the hosts are patchily distributed and the
parasitoids search randomly (i.e., do not discriminate previously attacked hosts)
within a particular host patch. This is a descriptive model unlike other models
which have been derived from the geometrical attributes of parasitism (Royama
1971). Nonetheless, it is adequate for our purposes because we are only
interested in being able to describe the outcome of the parasitoids' attack.

In (3), the parameter (a) is an index of the searching efficiency of a
parasitoid within a patch and k is an index of its aggregation with respect to the
host distribution. Note that an unrealistic linear relationship between the

number of hosts available and number attacked is assumed. In general, the

45

number of hosts attacked by a constant density of parasitoids must reach an
asymptotic limit as host density increases (Holling 1959, Royama 1970). For the
present, this additional complexity is omitted, although it will be discussed later.
May has shown that a sufficient condition for stability of an equilibrium of
(2) employing (3) and allowing F(Ht) to be a constant is k < 1. This means that a
sufficient degree of aggregation must be realized for stability. Searching
efficiency (a) has no influence on the stability of the equilibrium in the one
parasitoid-one host model. It does, however, scale the equilibrium values.
Factors such as temperature, rainfall, and adult food sources which
influence the searching efficiency of a parasitoid can be incorporated in (2)
through the parameter (a). For instance, if adverse weather causes a reduction
or cessation of host searching activity, this can be incorporated by writing (a) as
(a't) where a' is an instantaneous index of searching efficiency and t is the
amount of time favorable weather occurs. Likewise, those factors which
influence the spatial distribution of parasitoids can be partially described in
terms of k. They can only be partially described since k can only incorporate the
influence of factors up to the point where the spatial distribution of parasitoid
attack is random and because a single statistical parameter can not capture all
aspects of a complex spatial pattern. Nonetheless, this simple model indicates
that it is essential that parasitoid aggregation with respect to the host
distribution not be interrupted by extrinsic factors if the parasitoid is to be an
effective biological control agent. The model also indicates that factors which
influence the searching efficiency of the parasitoid cannot alter system stability
but simply influence the equilbrium densities. Similar conclusions can be made
for all single parasitoid-single host models which incorporate non-random parasi-

toid search.

46

An important question is whether these models are representative of any
real—world situation. We feel that they may describe cases of introduced pests
and exotic parasitoids. Additional complexity is needed, though, to describe
other, more common parasitoid-host systems. As demonstrated below, these
added components dramatically alter the effect of factors that influence adult
parasitoids on the stability properties of a particular system.

Populations of many insects exist for long periods of time at low densities
and periodically erupt to high densities. This is most noticeable in temporally
continous and undisturbed ecosystems but may also occur in agro-ecosystems.
The underlying mechanism of such phenomena is density dependent mortality
which at first becomes more effective with increasing densities but whose
effectiveness then diminishes beyond some threshold density. This model, often
called a double equilibria population process, was proposed as an explanation of
population dynamics by Ricker (1954), Morris (1963), and Takahashi (1964), and
has been extensively reviewed by Holling (1973), May (1976), Royama (1977), and
Berryman (1978). The salient features of the models are two equilibrium points
or cycles, one at low densities which is locally stable, the other at higher
densities which is unstable. A population will reside in the low density state
until moved beyond the unstable point or until the unstable point is itself moved
below the existing population density. Because these types of population
processes are likely to be quite common, we have analyzed a form of (2) which
incorporates such processes along with a parasitoid.

Consider a situation where a host population is limited by a group of
factors which, when acting in combination, produce a double equilibrium popula-

tion process. To add substance, let this group consist of predators whose density

47

is constant and which display a sigmoidal functional response and a parasitoid.
The predation can be incorporated in (2) by writing F(I-It) as:

6exp [(WPth) / (a2 + Hf )1 <4)
The parameter (6) in (4) is the net rate of increase of H in the absence of
parasitism and predation by PD predators. The exponential function describes
the probability of H prey escaping predation by these predators. It is based on
Real's (1977) extension of models of enzyme kinetics for describing functional
responses. The parameter (y) is the maximum number of prey captured per
predator, and a is the density of prey at which the predator's consumption level
is 1/2 7.

The model obtained by incorporating (4) and (3) in (2) is:

Ht+1 = Ht5exP ['YPth / (o2 + Hfinu + aP/kf" (5)

Pt+1= Ht [1 - (l + aP/k)’k]

Predation is assumed to occur after parasitism and is complementary.

In order to analyze (5), numerical procedures had to be adopted. These
procedures consisted of: (l) evaluating equilibrium densities for a particular set
of parameters via Newton's method for determining the roots of a function, (2)
ascertaining the stability of these equilibria, and (3) determining a region of
stability about each equilibrium point by iteratively perturbing equilibria and
simulating system dynamics. Because numerical methods were necessary, it was
impossible to completely elucidate model behavior. However, the results do
indicate its qualitative properties.

Suppose that the predators by themselves are incapable of regulating the
prey population. That is, the net recruitment curve in the absence of parasitism

is greater than one for all prey densities (fig. 12). By incorporating a parasitoid

48

 

 

 

 

T 2.3- “T
2.4«
'11
I
\
3:
ta“;
*0
5200‘
S
“5
I.
O
. 0
G
.. 1.6 «
:‘z‘ 2 2
"1+1: sexpE-vPbllt/(a +11, )]11t
5:10
7Pb=3e7s
1.2% a = 1
i i 3
11
t l

 

 

Figure 12. Net recruitment for an insect population preyed upon by a
constant density of predators which exhibit a sigmoidal
functional response. H is the insect density, Pb is the
predator density, 6 is the rate of increase of H, 7 is the
maximum number of H consumed by a predator and a is the
density of H for which predator consumption is 7/2.

49

with an appropriate searching efficiency, a stable, low-density equilibrium can
be generated. The requirement placed on the searching efficiency is that the
host equilibrium falls in a particular region of the cusp of the recruitment curve.

The equilibrium densities of the parasitoid and host and eigenvalues of
model (5) linearized about the equilibrium points for 6 = 10, be = 3.75, a =l.0,
and various values of parasitoid searching efficiency and aggregation are
presented in table 5. The methodology for obtaining these values is outlined in
appendix 3. The eigenvalues indicate which equilibria are locally stable, since a
necessary and sufficient condition for local stability of an equilibrium is that the
real part of the eigenvalue has modulus less than 1.

The most noticeable aspect of this model is that aggregation is no longer
necessary for local stability. Even with random parasitoid search (k = a9), stable
equilibria exist. Moreover, one measure of system resilience, the speed with
which perturbed populations return to the vicinity of an equilibrium, is higher
with less aggregated parasitoid search. System resilience is the ability of a
system to absorb changes in state variables or parameters without abrupt
changes in system trajectory. Here, system resilience relates to the host
population remaining in an endemic phase. A system will be more resilient with
a faster return time since it will be less likely that disturbing effects in year i
and then again in year i + 2 will induce instability. The speed with which
perturbed populations return to the vicinity of an equilibrium is expressed in
terms of the largest eigenvalue (1.) of the linearized model by l/(l -|). I) for Ill
< l (Beddington, Free, and Lawton 1976). With strong parasitoid aggregation (k =
0.75), an equilibrium was stable or no equilibrium existed (a = 1.0). Nonexistence

of an equilibrium was first indicated by Newton's method; however, because this

Table 5.

50

Equilibrium points and eigenvalues of the following parasitoid-
host model linearized about Ehege points} -k

H = 5H exp -7P H (a +H ))(l+aP k)
, Ptii = H fl-(1+aP:/E)’k) t t
H is the host density, P is the parasitoid density, P is the
density of background predators, 6 is the rate of increase of H
‘Yis the maximum number of H consumed per predator, a is the

density of H for which predator consumption is 772, (a) is a

measure of the parasitoid's searching efficiency with efficiency

increasing with larger (a) and K is a measure of the parasitoid

's

aggregation with respect to host density with low k representing

strong aggregation. Values for parameters not given below are:
6 = 10.0, 1? = 3.75, a = 1.0.

 

 

 

d l
Equilibrium Points igenvalues
a H P 11
k = .75 +
3.0 .661 .290 .420 ; .6271
2.5 .734 .295 .509 ; .6081
2.0 .852 .310 .650 ; .5801
1.5 1.120 .399 .907 - .4901
1.0 * *
k = 2.0 +
3.0 .558 .283 .371 ; .7431
2.5 .627 .288 .444 $ .7051
2.0 .730 .295 .565 ; .6661
1.5 .918 .323 .780 ; .6221
1.0 1.539 .685 1.166 - .4791
k = 6.0 +
3.0 .513 .277 .365 I .8171
2.5 .582 .284 .429 ; .7631
2.0 .683 .291 .539 ; .7081
1.5 .859 .311 .742 ; .6571
1.0 1.325 .521 1.117 - .5801
k=¢o**
3.0 .489 .274 .363 i .3861
2.5 .558 .283 .425 $ .3621
2.0 .659 .290 .529 ; .3531
1.5 .831 .307 .726 - .3701
1.0 1.256 .475 1.096 f .3561

* No equilibrium point_ ound
** When k=ao'(l + aPt/k) as exp(-aPt) and parasitoid search is
random

51

procedure may not converge to a root of a function, extensive simulations were
also employed. The simulations failed to uncover either an equilibrium or a limit
cycle. It was also observed that as aggregation increased, the searching
efficiency where equilibria ceased to exist became larger (i.e., for k = 0.5, no
equilibrium could be found for a = 1.5).

The eigenvalue analysis of the linearized model provides an initial indica-
tion of the stability properties of the system. It is, however, of limited
usefulness because it only pertains to the immediate neighborhood about an
equilibrium point. Real-world populations are not restricted to "small" changes,
and local stability analysis may be quite misleading because parameters may
produce local stability; however, the region about the stable point where the
model remains stable may be extremely small. In order to determine the global
stability properties of (5), simulation was used to outline the boundaries of the
host and parasitoid densities for which the system remained stable.

The influence of decreasing parasitoid aggregation on the stability region
(i.e., the set of all host and parasitoid densities for which stability is maintained)
of the model is portrayed in figure 13. With k = 0.75 and k = 2.0, the stability
region is not closed. This is a result of truncating the analysis at a particular
parasitoid density. The region would eventually close with further increases in
parasitoid numbers. It is clear that while parasitoid aggregation is not essential,
it does improve the system's resilience to perturbation in host or parasitoid
numbers. The effect of changes in searching efficiency on the stability region is
illustrated for two levels of parasitoid aggregation in figure 14. As with the
more simple models, the equilibrium host density increased, though only slightly,
with a decline in searching efficiency. More importantly, the stability region

became much smaller.

52

 

 

 

 

 

 

 

 

 

 

 

9 9
k-.75 a-2.5 1122.0 a-2.5
9 ° '
.. .. .-°’
e. i 9’
n (L °I
e r.
.l z I
9 e
e. . 9
'2 t O c . . g 9 ..
I O

”0.0 110 210 :10 E110 “0.0 1.0 210 3:0 410

H H
e- e-

101-96.0 o=2.5 RB” a-2.5
3" I.- ‘e 3"
“- \ n. . . ...
I! D
64 3 a" \
a : 1 I
e I o . 9, 9
0.4 I V T I 24 I I U *1
0.0 1.0 2.0 3.0 4.0 0-0 1.0 2.0 3.0 4.0
H H
Figure 13. Influence of parasitoid aggregation with respect to host

density on the
host model:

H1+1

stability region of the following parasitoid-

Htaexp(—7Pth/(62+H§))(1+aPt/k)'k
Ht(1—(l+aPt/k)‘k)

t+1
The stability region is indicated by the shaded areas. k
is a measure of parasitoid aggregation with low k reflecting
strong aggregation and (a) is a measure of parasitoid searching

efficiency. H

is the host density, P is the parasitoid density,

Pb is the density of background predators, 615 the rate of

increase of H,1'is the maximum number of H consumed per P
and a is the density of H for which predator consumption

Es 7/2.

Here, 7Pb = 3.75, a = 1.0 and 6 = 10.0.

53

 

 

 

 

 

 

 

 

 

 

 

 

"2-
k-2.0 o-2.5 k=2.0 6:1.5
.4' °-
. U‘
0
O. 0..
<90
0
f .- i ’1
. O I
. .. 9 0..
IL— I I I o 1 I —1 I
no 8m :41 no (L0 no as 341 no
11 11
ID 10
5- :5
k-6.0 o-2.5 k=6.0 0-1.5
3- ' -. 31
.. X ..
0.9
:33 3 2+
g .8 .0...
O. 9‘ O O.
“0.0 110 2:0 3:0 410 °b.0 1:0 210 3:0 :10
H H
Figure 14. Influence of parasitoid host searching efficiency on the

stability region of the following parasitoid-host model:
Ht+l = thexp(-7Pth/(a2+HE))(1+aPt/k)'k
Pt+1 = Ht(l-(1+aPt/k)’k)
The stability region is indicated by the shaded areas. (a)
is a measure of parasitoid searching efficiency with lower
(a) reflecting poorer efficiency. k is a measure of para-
sitoid aggregation with respect to host density with low k
reflecting strong aggregation. H is the host density, P is
the parasitoid density, Pb is the density of background
predators, 5 is the rate of increase of H, 7 is the maximum
number of H consumed per Pb and a is the density of H for
which predator consumption is 7/2. Here, TPb = 3.75, a== 1.0
and 5 = 10.0.

54

The implications of the empirical observation are far different when
viewed in the context of this model as opposed to the simpler one parasitoid—one
host models. In this case, in addition to parasitoid aggregation, the attack
efficiency of the parasitoid is of paramount importance in establishing a stable
and resilient system. This is not a new revelation, since biological control
scientists have long emphasized the importance of host searching (Huffaker e_t
21: 1976). Factors which influence the searching efficiency of a parasitoid or
group of parasitoids now do not simply determine an equilibrium level but also
help determine system stability. As a result, determination of controllable and
uncontrollable factors which influence parasitoid-host searching are important
aspects of parasitoid management. Aggregation is still a valuable property of a
parasitoid from the biological control point of view. However, parasitoids that
do not aggregate can still be important natural enemies, and improved pest
control can be obtained from management actions taken to improve their
searching efficiency.

This is important because empirical data suggests that more times than
not, parasitoids fail to significantly aggregate in areas of high host density
(Morrison and Strong 1980). These observations may be explained three ways.
First, as indicated by our study of Q. fumiferanae and studies of other
parasitoids, the spatial distribution of these insects is influenced by factors other
than host numbers. Second, as discussed by Royama (1970), parasitoids may
respond to areas of higher host densities but only in a limited capacity due to a
less advanced nervous system. When aggregation is measured in terms of
parasitism, slight aggregation will result in constant or declining parasitism when

expressed as a function of host density. Finally, these observations may reflect

5.5

an inappropriate scale for measuring aggregation since it is well known that the
distribution of a population of samples is a function of the size of the sample

unit. For instance, Q. fumiferanae does not aggregate with respect to the host

 

within a tree but may do so between trees. In passing, we note that this was
investigated in our study; however, no relationship was found between host
numbers and trap catch in different trees. Further studies of parasitoid
behavior, of spatial variation in the distribution of adult parasitoids, and of the
spatial variation in parasitism intensity are needed to fully answer the important
questions of parasitoid aggregation and thereby determine if aggregation can be
manipulated through habitat management.

The results obtained with (5) are not restricted to the particular case
examined, since the results will hold for any set of mortality factors which
produce a net recruitment curve similar to that portrayed in figure 12.
Furthermore, these mortality factors may in themselves produce a stable
equilibrium, in which case the parasitoid serves to enlarge the stability region
about an equilibrium. The inclusion of a limited capacity for parasitism by each
parasitoid so that the number of hosts parasitized does not increase indefinitely
as the number of hosts increases will not alter the general results obtained. The
affect of inclusion of this limitation will be a contraction of the stability region,

the size of which will be dependent on the density at which limitation occurs.

Conclusiom

In this paper, we have presented data which indicate that: (1) the
searching efficiency of Q. fumiferanae is reduced in wet and cool weather, (2)
habitat does not influence the parasitoids' ability to obtain nutrients and

moisture, and (3) the spatial distribution of the adult female parasitoid and of

56

the ovipositions made by these insects within a tree crown is influenced by
temperature and light. These results and those obtained by a number of other
authors point to the fact that abiotic factors and biotic factors other than the
host play an important role in determining the number and distribution of hosts
attacked by a parasitoid. This, in turn, may have a pronounced affect on the
ability of a parasitoid to act as a biological control agent. In some cases, the
factors which influence the intensity and distribution of the parasitoids' search—
ing activity will be amenable to manipulation and should then serve as an object
of control for parasitoid management. However, identification of these factors
requires detailed studies of the temporal and spatial dynamics of the adult

parasi toids.

57

Forest Harvesting and the Spruce Budworm

58

Introduction

(The eastern spruce budworm is native to North America and is distributed
throughout the northern boreal forest from Alberta to Maine and the Maritimes.
The preferred hosts are balsam fir (Abies balsamea (L.) Mill.), white spruce
(Picea muca (Muench) Voss), red spruce (P. m Sarg.), and to a lesser extent,
black spruce (P. mariana (Mill.) B.S.P.) (Greenbank 1963). Defoliation of balsam
fir and spruce by spruce budworm occurs at periodic intervals. Depending upon
defoliation intensity, the death of individual trees or whole stands can occur.
Spruce and fir are valued for paper production and lumber. Budworm outbreaks
often kill more trees than can be used rapidly. In addition, a future shortage of
fiber can result from extensive budworm-induced tree mortality.

Outbreaks of the budworm occur at 20 to 40 year intervals. The outbreaks
themselves may extend only 8-10 years, but the effects are longer lasting. In the
past, especially in the East, large—scale spraying programs minimized the
budworm damage. However, concerns have been voiced about the effectiveness
and environmental impact of the spray programs. In the Lake States, recent
supplies of spruce and fir have exceeded demand. As a result, few aerial
sprayings of forests were conducted. Instead, greater emphasis was placed on
cutting to salvage damaged material or to presalvage stands.

Management techniques are needed that take demand for fiber into
account, take commercial management objectives into account, and provide
resistance to spruce budworm. Without such management techniques, the future
will hold the same scenario that has developed during recent budworm outbreaks;

a large acreage of killed timber with no hope of marketing all of the product.

59

There are several techniques that can be used. These techniques can be
grouped into three general approaches: (1) those which are directed at the
forest, (2) those which are directed at the insect, and (3) those which combine (1)
and (2).

GROUP 1.

The first group of approaches, those directed at the forest, largely involve
the way the forest is harvested or the timing of harvest. The following illustrate
what is meant:

I) M M — This is the deliberate avoidance of any action by man. This
approach is appropriate where the cost of utilizing a particular stand is greater
than the value of the product it will yield. Stands categorized as beyond salvage
fall into this category.

2) M33 - This is the marking, selling, and harvesting of stands which
are in the process of dying but have not deteriorated too far to be uneconomical
to cut. The prime limitations of this tactic are lack of manpower to carry out
the action and lack of spruce-fir markets where loggers can sell the pulpwood.
During a spruce budworm outbreak, an oversupply of material results in both of
the above.

3) Presalvag -- This is the marking, selling, and harvesting of stands which
are healthy but vulnerable to spruce budworm (i.e., these stands, because of age
and composition, would suffer damage if subjected to budworm outbreak).
Presalvage is difficult to carry out efficiently and effectively during an outbreak
because both manpower availability and market availability are limiting.

4) Changing Stand Composition — This involves the outright removal of
some spruce and fir from stands to encourage a species mix. Although an

elegant concept, realization of such conditions over a large area is unrealistic.

610

5) 40-year Rotation - This is the deliberate utilization and marketing of
stands such that no individual stand ever exceeds 40 years of age. This is based
on the supposition that spruce budworm creates the greatest damage in older
stands (usually older than 50 years of age). In concept, this approach is perhaps
the most appealing of all techniques available today. However, it is too
idealistic. Many spruce-fir stands already exceed 40 years of age. In the next
rotation, this is a target that forest managers may be able to aim toward.
GROUP II.

The second group of techniques are activities directed at the spruce
budworm itself and, for the most part, involve chemical and biological pesti-
cides. These techniques are often inappropriate. The prime reason is that
techniques directed at the insect are often uneconomical for stands being
managed for timber production.

GROUP III.

The third group of techniques are those which are combinations of methods
directed at the forest and at the insect. By this we mean that through forest
directed activities we affect factors which influence spruce budworm numbers.
This group of techniques relies on small block cutting which adds a "checker-
board" pattern to existing healthy stands (those which we expect to hold for 5 to
20 years and then market). These techniques are explicitly designed to add
resistance to residual stands through cutting by enhancing predator and parasite
populations and increasing mortality that occurs during the larval dispersal
period.

A project was begun in 1979 to examine how the problem of budworm,

mature forests, and the demand for wood fiber could be addressed by partial

61

harvesting of existing, living stands. The following is a report of work done
during this project. It is comprised of three parts: (1) a theoretical basis for
partial cutting, (2) the economic aspects of the strategy, and (3) a measurement

of the response of the biological system to partial cuts.

A Theoretical Basis for a Strategy of Partial Cuts

Fluctuations in spruce budworm numbers have been the focus of scientific
study for several decades. It has been suggested that population changes can be
described by a model whose general form has been used for many different
biological populations ranging from bacteria to big game (e.g.; Noy-Meir 1975,
Gulland 1975, Clark and Mangell 1979, Petermen _e_t g. 1979, Weckham and
Botsford 1980, Fleming 1980, Campbell and Sloan 1977, Clark _e_t_ _al. 1979,
McLeod 1979, Southwood and Cummins 1976, Ludwig e_t _a_l_. 1978). The
components of such a model include an intrinsic logistic growth rate coupled
with mortality factors that increase in intensity as the population density
increases (density-dependent). The growth rate and density-dependent mortality
factors are also often coupled to habitat conditions.

With such models, it is possible to analyze population changes over a range
of densities from very low (endemic) to very high (epidemic). When this is done,
analysis often reveals conditions where the rate of increase is balanced by an
equal mortality rate. Such conditions are termed equilibrium states. If a
p0pulation tends to remain at an equilibrium, it is considered stable. In the case
of the spruce budworm, two stable equilibrium states may be evident: one at

very low densities and one at very high densities.

62

The rate of change of the budworm population as a function of budworm
density is portrayed in figure 15. In this figure, the solid line depicts the
intrinsic biological growth rate of the budworm population. The dashed lines are
losses due to predation and parasitism (M). Where the dashed line lies above the
solid line, the net growth rate of the budworm population is negative, and where
the dashed line lies below the solid line the net growth rate is positive. Points of
intersection of the dashed and solid lines indicate possible equilibrium points.
For an intermediate value of M, there are stable low and high density equilibrium
points (A and C) and an unstable intermediate equilibrium point (D). Budworm .
numbers will remain low provided their density remains below T. If they exceed
T, the population density will move to C.

The forest plays an important role in determining fluctuations in budworm
numbers. This role is manifested through the influence of forest composition and
forest structure on the intrinsic growth rate of the budworm population and on
the level of budworm predation and parasitism.

Forest composition and structure influence the intrinsic growth rate of the
budworm population through egg mortality from parasitism and through the
dispersal loss of early instars. Typically, the intrinsic growth rate of an insect
p0pulation is determined by the number of eggs laid by females. However, with
budworm, most significant density-dependent mortality occurs after the bud-
worm are established in feeding sites in the spring. Hence, the number of
surviving third instars represents the intrinsic growth rate for a particular year.

Parasitism of budworm eggs has been found to increase with an increasing

proportion of non-host trees in a stand (Kemp and Simmons 1979a). Unfortunate-

63

 

 

 

 

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Figure 15. The relationship between the rate of increase of spruce budworm
populations (solid line) and different levels of predation

and parasitism (dashed lines)

64

1y, little is known of egg parasitism at low budworm densities. At high densities,
it is an insignificant mortality factor.

Dispersal loss of budworm larvae occurs in the fall and spring and results in
a 6096 to 85% reduction in the population (Miller 1958, 1975). Mortality factors
during the dispersal period are: (1) air dispersal to non-host material, (2)
predation, (3) failure to spin hibernaculae, and (4) diapause—free development
(Miller 1958). Of these, the most important is air dispersal to non-host material.
Kemp and Simmons (1979b) found that a higher proportion of non-host trees in
the understory, reduced crown closure, and the presence of aspen in the
overstory resulted in higher mortality during the dispersal period. Similar results
were obtained in a simulation study of spruce budworm dispersal (Kemp gt 31.

1980). A recent report on the closely related jack pine budworm (Choristoneura

 

ping) (Freeman) indicated that dispersal losses increased with decreased stand
stocking (Batzer and Jennings 1980).

The picture painted is that, in stands with non-host trees and Open areas,
the intrinsic rate of increase of the budworm is reduced. As a forest stand
matures and crown closure increases, the growth rate of the budworm p0pulation
increases. Depending on the magnitude of the increase in the growth rate of the
budworm population, the change in early larval survival may be sufficient to
catalyze a budworm outbreak. However, forest dynamics also have a significant
effect on natural control agents. The most important of these natural enemies
are those which attack the large larvae and pupae.

Stand composition and structure can influence the mortality of large larvae
and pupae through bird predation. Views on the importance of bird predation in

maintaining budworm populations at low numbers are varied. We feel that it is

65

unlikely that bird predation alone is responsible for maintaining budworm at low
densities. However, when complemented with other mortality factors, bird
predation is important.

The bird predator guild can be classified into two groups: ground feeders
and crown feeders. Gage gt_ 91. (1970) have shown that ground feeders feed less
frequently on budworm than crown feeders, while their mean consumption per
individual is much higher. If we assume that differences in feeding frequency
and comsumption rates tend to cancel each other, then the important aspect of
the bird predator guild is not the species mix, but rather the density of all bird
predators. Data presented by Titterington gt_ Q. (1979) and Gage and Miller
(1978) suggest that the densities of the predator guild reach a maximum in stands
characterized by a mix of hardwoods, softwoods, and stand openings. As a stand
matures, crown closure increases, tree species diversity declines, and the
number of avian predators decreases.

In addition to changes in bird predator numbers, forest dynamics may also
influence the searching efficiency of bird predators. Birds search foliage in
order to find budworm. As the forest matures, the foliage area to be searched
increases and the efficiency of birds in locating and capturing budworm likely
declines.

A large numbers of parasitoids attack the late instars and pupae of spruce
budworm. The role of these parasitoids as mortality agents has been largely
discounted since they depend on alternate hosts and their parasitism rates are
generally low. However, no study has attempted to determine their influence on
budworm dynamics at low densities. Stand characteristics influence the para-

sitism of budworm by these parasitoids. Simmons e_t g1. (1975) found that pupal

66

parasitism of budworm increased as stand diversity increased and crown closure
decreased. The reasons for this are twofold: (1) increased stand diversity
provides more habitat for alternate hosts required by the pupal parasitoids, and
(2) stand openings provide sources of food and water for the adult parasitoids.

The net effect of forest-induced changes on avian predators and insect
parasitoids is a reduction in their ability to limit budworm numbers as the forest
becomes more uniform in composition and as open area declines.

The contentions raised here are supported elsewhere. In particular, it has
been found that budworm-induced tree mortality is related to stand composition
and often declines with increases in the density of non-host trees and along
borders of stand openings (MacLean 1980).

It is clear that the dynamics of the spruce-fir forest and the budworm are
closely related. In general, as a forest matures, the food resources of the
budworm increase and the impact of various mortality factors acting on the
budworm are diminished. Forest management might therefore make an effort to
reduce the impact of budworm by either maintaining or transforming the forest
to a successional state where these mortality factors can better limit budworm

numbers. Such a state may be achieved through the use of partial cuts.

Mathematical Analysis

A theoretical basis for partial cutting to reduce budworm impact has been
presented. In essence, a system (the forest, the budworm, and a harvesting
strategy) has been envisioned through which a set of objectives (minimizing fiber
loss, maintaining a steady supply of fiber, or maximizing economic returns)

might be met. The next step is to analyze this system through the use of a

67

mathematical model. In so doing, we hope to increase understanding of real
world phenomena and better develop management or design policies.

If, instead of seeking better ways to manage spruce fir stands, we were
asked to design a controller for an industrial chemical process, the task would be
relatively straightforward. Mathematical models could be employed to design
the controller and analyze its operation. However, mathematical models of
biological processes are usually too abstract to capture the real world. For this
reason, they normally cannot be used alone as a design tool. Instead, they should
be used to explore a range of possible outcomes, and then one or some of the
logical management approaches can be field tested. This is the philosophy
adopted here.

As stated earlier, the swift change that can occur in budworm numbers
depends in part on slow changes in forest composition and forest structure. In
order to capture the complete dynamics of the spruce budworm and spruce fir
forest, these fast and slow changes must be coupled. However, we are not
interested in the dynamics of the budworm from the beginning of one outbreak to
the next one, but rather in the transition from the endemic to the epidemic
states. This is because our objective is to prevent, delay, or lessen the severity
of a budworm outbreak in the residual forest stand following a partial cut.

The rate of change in budworm numbers for a particular forest condition is
given by the intrinsic rate of increase of the budworm population (feeding third
instars) minus the rate at which budworm are lost to mortality factors. This rate
can be described in terms of a mathematical model:

dB/dt = r83 - (Hz/(«2 + 32))6 (1)

68

In (1), B is the budworm density per m2 foliage, r is the rate of increase of the

budworm, S is the number of m2

units of foliage per hectare, c is the density per
1112 foliage of budworm at which one half the maximum efficiency of budworm
natural enemies is reached, and 6 is the maximum number of budworm per
hectare lost to natural enemies. A differential equation is an approximation of
what is actually a discrete time process. However, adoption of a continous
representation facilitates analysis and will not invalidate any general conclusions
reached.

Ludwig, Jones, and Holling (1978) used a form of (1) and concluded that 6
is principally attributable to bird predation. To begin, we will ad0pt their
conclusions and use their estimates of parameters of (l) which place the
budworm population in a transition between the endemic and outbreak states.
Equation (1) can then be written as:

dB/dt = 1.52(B)37050 - (1320.12 + 32))106210
The relationship between the rate of increase of the budworm population and the
budworm density for these values is presented as curve 0 in figure 16. It can be
seen that the rate of change of the budworm is greater than zero for all
budworm densities, and budworm numbers will therefore quickly increase. The
effect of reducing the rate of increase by 1096, 2096, and 3096 is portrayed in
figure 16. With a 2096 and 3096 reduction of the intrinsic rate of increase, an
outbreak would not develop unless budworm numbers exceeded 1.5 and 2 larvae
2

per 111 , respectively. The reduction in this rate may be brought about as a result

of increased dispersal loss in areas subjected to a partial harvesting strategy.

Figure 16.

69

The influence of different levels of dispersal loss and
predation on the rate of change of spruce budworm numbers.
This rate is described by;

dB/dt = r38 - (B2/(¢2+B2))8

B is the number of budworm per 1112 foliage, r (1.52) is the
growth rate of B, S (37050) is the number of m2 units of
foliage per hectare, a (1.1) is the density of budworm at
which predation is 1/2 the maximum and 6 (106210) is the
maximum predation of budworm per hectare. The topmost curve
in A,B and C correspond to these values. In A, dispersal loss
is increased 10, 20 and 30%; in B predation is increased

10, 19 and 26%; and in C both dispersal loss and predation

are increased 10 and 10% and 20 and 19% respectively.

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In addition to a reduction in the intrinsic rate of increase, a partial cutting
strategy will also result in an increase in losses to natural enemies. If these
losses are wholly attributable to bird predation, this comes about as a result of
an increase in bird densities and a decrease in foliage area.

The effect of increasing losses to natural enemies by 1096, 1996, and 2696 is
illustrated in figure 16 . Once again, an outbreak will not develop unless the
critical thresholds of budworm densities are exceeded.

By combining the influence of partial harvesting on the intrinsic rate of
increase and on the loss to natural enemies, dramatic changes in the rate of
increase of the budworm population can be achieved. This is illustrated in figure
16 for a 1096 reduction in the rate of increase and 1096 increase in losses to
natural enemies, and a 2096 reduction in the rate of increase and a 1996 increase
in losses to natural enemies, respectively. In the latter case, the threshold
density for an outbreak is approximately 2.5 budworm per m2.

Unfortunately, the analysis presented cannot be considered conclusive.
While the general forms of the relationships presented are likely correct,
questions exist with respect to model components and the actual parameters
used. First, it is unlikely that avian predators are the only density-dependent
mortality factors. The influence of parasitic insects and infectious diseases has
been ignored. Second, the maximum consumption rate of the avian predators is a
gross estimate and may deviate by 1 3096. Finally, it is not possible to predict
the actual effect of a partial cut on the intrinsic rate of increase or on losses to
natural enemies. The important point, though, is that modest changes in the

intrinsic rate of increase of the budworm and in the number of budworm lost to

 

72

natural enemies can have significant effects on the rate of increase of the
budworm population.

An obvious confounding factor is the immigration of budworm into stands
which have been partially cut. This immigration need not be extraordinary to
push budworm densities beyond the threshold of 2 to 5 larvae per 1112 foliage for
which budworm numbers cannot be regulated by natural enemies. Miller e_t g1_.
(1978) estimated that moths immigrating into a test plot from surrounding areas
with moderate to high budworm densities deposited g. 10 egg masses per m2
foliage. Assuming 20 eggs per mass and 8096 cumulative mortality of eggs and
small larvae, the density of large larvae will exceed the mortality caused by
(functional response) natural enemies. For this reason, a partial harvest may not
be able to prevent high budworm densities in treated stands.

Within the context of the model, once the rate of increase of the budworm
population exceeds natural enemy induced mortality, the population quickly
increases to the carrying capacity of the habitat and remains there until the food
supply is exhausted. However, there are instances in which the budworm
p0pulation has increased well beyond an endemic density but did not destroy the
habitat. This model, therefore, cannot be considered representative of all real
world situations. It is conceivable that, by decreasing the intrinsic rate of
increase of the budworm and increasing losses to natural enemies, an outbreak
may not be prevented but may be diminished in intensity. As a result it is
important to examine the dynamic interaction between the budworm and forest
when budworm numbers are greater than endemic levels.

Ludwig _e_t g1. (1978) suggested using two variables to describe the forest:

the number of units of an area of foliage (S), and an artificial variable to

73

describe the physiological state of the trees (E). In this case, S is the number of
m2 units of foliage per hectare. The rate of change of these variables is
described by the following model:

dS/dt = rSS(l - (SKSXKE/E» <2)
dE/dt = 1,3120 - (E/KE» - was (a)

In (2), the increase in S is limited by a maximum (KS) which we have set equal to
49,400 per hectare. A similar situation exists for E; however, the peak
physiological condition (KE) is equal to 1. Where the physiological condition of
the tree is poor, the value of S/KS is multiplied by KE/E so that S does not
increase. In (3), B/S is budworm larvae per m2 foliage and P is the rate of
consumption of foliage per larvae. It is assumed that a decline in the
physiological condition of the tree is directly pr0portional to the loss in foliage.
S does not decline directly as a result of budworm feeding, but rather through a
decline in the physiological well-being of the tree. Ludwig, _e_t g. estimated P as

1.5 x10-3

, rS as .10 and r e as 1.0. We will use these values initially.

For a given budworm density, (2) and (3) constitute a dynamic system which
has no analytical solution. In order to gain insight into the properties of this
system, graphical methods are used. In figure 17, the values of S and E for which
the rates of change of each is zero are plotted.

The points where these lines intersect are equilibrium points. For any
initial value of S and E and a given value of B, the rate of change ofthe complete
system (dS/dE) can be evaluated. By so doing, the dynamics of S and E can be
determined. Approximate system trajectories for various values of S and E are

given in figure 17. If the equilibrium points exist, then the forest will remain

alive, providing the physiological condition of the trees is good.

Figure 17.

74

The influence of spruce budworm defoliation on the survival
of host trees. The dynamics of the host trees is described
by two equations ; ‘

dS/dt - rsS(l-(S/KS)(KE/E))
dE/dt = rEE(1-(E/KE))- P(B/S)

Where S is the number of m2 units of foliage per hectare, rS(.l)
is the growth rate of S, K (49,400) is the maximum 8 per
hectare, E is the physiological condition of the tree, (1.0)
is the maximum E, r (l. ) is the growth rate of E, P (. 017)

is the proportion of a m unit of foliage consumed by 1 budworm
and B is the number of budworm per hectare. In (1) B = 1x105.
The arrows indicate general system dynamicg for various initial
conditions. In (ii) 3 = 1x105 for A, 8x10 for B, and 2x106 for
C. In (iii) B = 5x10 and extensive tree mortality occurs.

1Ludwig, D., D.D. Jones, and C.S. Holling. 1978. Qualitative
analysis of insect outbreak systems: The spruce budworm and
forest. J. Anim. Ecol. 47:315-332.

75

 

 

 

 

 

 

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The forest (S) will succumb to budworm under two conditions. First, the
equilibrium points may vanish. This will occur if budworm densities exceed some
critical level. Second, the physiological state of the trees may decline below a
critical value as a result of budworm feeding.

The second condition can also be evaluated graphically. In figure 18,
equation (3) is portrayed for different values of B/S and rE. As shown, the tree
remains vigorous even for relatively high densities of budworm and values of PE
less than that given by Ludwig e_t _a_l. In the real world, it is likely that sustained
moderate defoliation will result in a decline in rE, and the physiological
condition of the tree may then decline. In addition, parameter values used are
gross estimates and will vary from site to site. Accurate predictions of the
budworm density required to cause extensive tree mortality cannot be made.
However, this is not the purpose of the analysis. The important point is that
extensive tree mortality will not occur with moderate budworm densities for a
number of years. Hence, if a policy of partial harvesting can lessen the intensity
of an outbreak in the residual stand, mortality of the remaining trees can at
least be delayed and may be reduced.

To conclude this section we have shown that a reduction in the rate of
increase of budworm populations coupled with an increased loss of budworm to
natural enemies dramatically alters the dynamics of the insect. Immigration of
moths from surrounding stands may, however, cancel these effects. The forest
can tolerate moderate defoliation by the budworm for many years. It is
conceivable that, as a result of a partial cut, the intensity of an outbreak is
diminished. Without more information, though, a mathematical analysis can go

no further. A real world evaluation of a partial harvest policy is desirable and

77

 

 

 

 

 

Figure 18. Influence of spruce budworm on the physiological condition of:
host trees. The physiological condition is described by1

dE/dt = rE(l-(E/K)) - PB

where E is the physiological condition, r is the rate of increase
of E, K.(1.0) is the maximum E, P (.0017) is the rate of
consumption of a 1112 unit of foliage per larvae and B is the
budworm density per 1112 foliage. The dashed lines are PB and

the solid lines are rE(1-(E/K)).

1Ludwig, D., D.D. Jones, and C.S. Holling. 1978. Qualitative analysis

of insect outbreak systems: The spruce budworm and forest. J. Anim. Ecol.
47:315—332.

78

necessary but also difficult to conduct. Nevertheless, an effort has been made

to perform such an analysis.

Implementation and Assessment of a Partial Cut Strategy

A policy of partial harvesting was evaluated on three sites in the Hiawatha
National Forest in Delta County in Michigan's Upper Peninsula. The specific
sites are all within 30 miles of the city of Escanaba. The spruce-fir type is
scattered throughout the region, with individual stands ranging from about 30
acres up to about 100 acres in size.

Three forest stands (fig. 1) were selected for implementing the partial
harvest strategy based on the following criteria: (1) species composition: spruce
fir type with some hardwood component, either aspen or northern hardwoods; (2)
area size: a minimum of 40 acres with a control plot of no less than 10 acres,
preferably adjacent to the treatment plot; (3) budworm density: low budworm
numbers at the time of harvesting; and (4) harvestability: sufficient volume of
timber so that partial cutting may be commercially feasible, if road-building
costs and distance to mills is not prohibitive. In fall 1979, stands 1 and 3 (fig. 1)
were identified. In fall 1980, stand 2 (fig. 1) was added, although budworm
densities were already at moderate population levels.

In stand 1, cuts laid out as patches were used to partially harvest the stand.
The layout of the cuts and the control plot is shown in figure 19. Harvesting was
conducted in the winter of 1979/1980. In stand 2, cuts were laid out in strips and
were made during the winter of 1981. Harvested strips are 40 m wide and the
uncut strips are 60 m wide. The layout of the strips and the control plot is shown

in figure 19. In stand 3, cuts were laid out in strips 20 m wide with an uncut

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80

strip 40 m wide separating each cut (fig. 19). Harvesting of this area took place
in the winter of 1979/1980.

The structure and composition of each cut and control area was described
by measuring stand parameters in five fixed-radius plots in the residual stand of
the treatment areas and in the control areas. In the strip cuts, plots were
established in the center of each residual strip. In the patch cut, plots were
located 20 m from the edge of the cut. In all control areas, plots were located
60 m or more away from a cut area.

Plot measurements were made according to procedures developed by Mog
and Witter (1979). This data is presented in tables 6 through 8. The live tree
species composition and tree condition parameters for budworm hosts in the cut
and control areas for stands 1 and 2 are very similar. In stand 3, the total
percentage of budworm hosts is approximately the same; however, the control
area has a larger percentage of white spruce.

Evaluation of a policy for managing or designing a system must address two
things: (1) Is the policy feasible and (2) are the objectives as originally set forth
met by applying the policy? The feasibility of partial harvesting is determined
by profitability and compatibility with other forest management objectives.
Whether partial cutting can help meet these objectives is determined by how this

policy affects the budworm population.

Feasibility of a Policy of Partial Harvests
Any feasibility analysis of a partial cut strategy is based on determining
when and how much of a forest stand to harvest. The timing of timber harvest

involves two considerations: (1) stand growth, and (2) financial maturity of a

81

Table 6. Comparison of Species composition of live trees and tree
condition parameters for spruce budworm host trees by treatment
in stand 1. Species composition is based on data collected from
5 .04 hectare plots and tree parameters are based on data from
5 .02 hectare plots.

Cut Control
Trees Basal Trees Basal
hectare 2 area m 2 hectare 2 area m2 1
hectare 6:36;;3
Balsam fir 554 58 12.6 40 563 53 13.7 39
White spruce 20 2 1.2 4 25 2 1.7 5
Trembling aspen 198 21 12.1 39 237 22 12.3 35
Paper birch 44 4 1.0 3 124 12 2.9 8
N. white cedar 114 12 3.1 10 89 8 3.7 10
Sugar, red maple S l 0.2 1 20 2 0.4 1
Other hardwoods 15 2 0.8 3 10 1 0.2 1
Hemlock 0 0 0 0 5 0 0.4 1
All species 950 100 31.0 100 1073 100 35.3 100
Parameter x a; n x s;' n
Balsam fir
DBH (cm) 17.5 0.69 53 15.9 0.42 62
Tree height (m 14.8 0.41 53 14.5 0.34 62
Crown position 2.7 0.15 53 2.8 0 10 62
Live crown length (m) 7.2 0.37 53 8.0 0.36 62
Dead crown length (a) 1.0 0.15 53 1.7 0.15 62
Proportion3crees dead 0.11 0.04 53 0.17 0.05 62
site 1ndex 60.0 ‘ 29 60.0 27
White spruce
DBH (cm) 32.6 3.46 3 26.4 4.25 4
Tree height (m) 18.0 1.56 3 17.8 1.85 4
Crown 6661:1662 1.0 0.0 3 2.2 0.5 4
Live crown length (a) 10.5 1.79 3 8.8 0.95 4
Dead crown3lengch (n) 3.7 0.0 3 4.0 0.0 [I
site index 52.0 12 55.0 13

1Includes balsam paplar

2Crown position ranking: l-dominant, 2-co-dominant, 3-intermediate,
4-suppressed

3Based on USDA Forest Service Lake States Exp. Sta. Tech. Notes 465 and 474
by S. R. Gevorkiantz

82

Table 7. Comparison of species composition of live trees and tree
condition parameters for Spruce budworm host trees by treatment
in stand 2. Species composition is based on data collected from
S .04 hectare plots and tree parameters are based on data from
5 .02 hectare plots.

 

Cut Control
Trees Basal $5555 Basal
Species hectare Z pgggg_g_ 2 hectare 2 area m 2
hectare hectare
Balsam fir 763 71 18.12 66 788 85 16 29 7
white spruce 0 O 0 0 6 1 0:07 1
Aspen 313 29 9.18 34 131 14 4.36 20
Total 1076 100 27.30 100 925 100 20.72 100
Parameter x s; n I; a; n
Balsam fir
DBH (cm) 16 85 0 51 54 15 70
. . . 0.41 53
Tree height (m1 14.66 0.30 54 14.09 0.37 53
Crown position 2.40 0.12 54 2.72 0.16 53
Live crown length (a) 7.78 0.33 54 6.03 0.28 53
Dead crown length (m) .50 0.16 54 0.35 0.14 53
Proportion trees dead 0.16 0 05 54
2 . 0.19 0.05 53
site index 62 12 65 12

}Crown position rankings: l-dominant, 2-co-dominant, 3-intermediate,
4-suppressed

2Based on USDA Forest Service Lake States Exp. Sta. Tech. Notes 465 and 474
by S. R. Gevorkiantz

83

Table 8. Comparison of species composition of live trees and tree
condition parameters for spruce budworm host trees by treatment
in stand 3. Species composition is based on data collected from
5 .04 hectare plots and tree parameters are based on data from
5 .02 hectare plots.

Cut Control
Trees Basal Trees Basal
hectare 2 area m 2 hectare 2 area m 1
hectare hectare
Balsam fir 469 55 12.3 39 183 29 5.4 16
white spruce 35 4 1.3 4 247 27 7.4 21
Trembling aspen 193 23 13.5 43 114 12 11.0 31
Paper birch 84 10 2.3 7 247 27 6.3 18
N. white cedar 64 7 2.0 6 124 13 4.1 12
Sugar, red maple 5 1 0.3, 1 10 1 0.7 2
Other hardwoods 0 0 0 0 0 0 0 0
Hemlock 0 0 0 0 0 0 0 0
All species 850 100 31.7 100 925 100 34.9 100
Parameter E s- n 3? s- n
x x
Balsam fir
DBH (cm) 17.6 0.50 62 20.6 1.31 17
Tree height (m 13.5 0.42 62 16.2 0.92 17
Crown position 2.9 0 13 62 2.5 0.27 17
Live crown length (m) 8.1 0.36 62 7.6 0.78 17
Dead crown length (m) 0.5 0.06 62 1.0 0.15 17
Proportion3trees dead 0.04 0.02 62 0.14 0.08 17
site index 64.0 27 59.0 18
White spruce
DBH (cm) 20.5 2.25 4 19.3 1.0 27
Tree height (m) 10.7 1.45 4 15.2 0.64 27
Crown position 3.0 0.60 4 2.5 0.23 27
Live crown length (m) 6.0 3.70 4 6.2 0.44 27
Dead crown31ength (m) 0.0 0.0 4 0.6 0.06 27
site index 52.0 11 50.0 33

llncludes balsam pOplar

2Crown position ranking: l-dominant, 2-co-dominant, 3-intermediate
4-suppressed

3Based on USDA Forest Service Lake States Exp. Sta. Tech. Notes 465 and 474
by S. R. Gevorkiantz

84

 

Mean Annual Increment

Volume

Current Increment

 

 

Age

 

 

 

Relationship between the mean annual increment and the current
increment in timber volume growth. The maximum mean annual
increment occurs when this variable equals the current increment.
This can also be shown with a first order condition since

volume = F(age) and the mean annual increment . F(age)/age so
d(F(age)/age)/dt = (ageF'(age)-F(age))/age2 = 0 =====$>

F'(age) = F(age)/age which is equivalent to the current increment
equal to the mean annual increment.

Figure 20.

85

stand. When determining a time to harvest, most foresters Opt for maximizing
the mean annual growth increment (fig. 20) (Clawson 1977). However, growth
rates change slowly over a span of years. Any harvest timing which seeks to
take advantage of a growth relationship can be varied without significant
consequences. Further, this policy ignores forest management costs, markets for
fiber, and prices for stumpage. If the objective of forest management is to
maximize the volume of wood produced by a parcel of land, then this is a proper
strategy. Most often, economic considerations should also be included in a
harvesting decision.

The financial maturity of a stand involves costs and returns of growing
timber. Three separate costs can be identified: (1) inputs of capital, labor and
materials throughout the rotation of a stand; (2) interest on the returns that
might be realized from the immediate harvest of a stand; and (3) rent on the
bare land. Given these costs and knowledge of tree growth and future returns
from this growth, the age of financial maturity can be computed. This is the
point in time when net returns are maximized. The age of financial maturity
will almost always be sooner than when the maximum mean annual growth
increment is reached.

In practice, things are not as simple. A number of factors confound
computation of financial maturity. First, the markets for the wood and the
effect of the harvest volume on the market price have not been considered.
Changes in either of these factors may dramatically influence the point in time
when financial maturity is reached. In an extreme case, markets could cease to
exist and render the concept of financial maturity meaningless. Second, the

timing and intensity of harvest will partially determine the stand type and

86

number of trees available for the next harvest. This consideration must also be
part of the harvest decision. Third, age/growth relationships are not precise.
Thus, financial maturity is not a point, but an interval in time. Finally, a harvest
decision may be motivated by factors other than an optimal economic return.
For instance, a steady flow of fiber, minimizing loss of trees to damaging
organisms, or conversion of a site to different tree species are other considera-
tions which may dictate harvest of a forest stand.

In addition to the general considerations discussed, harvest decisions are
strongly dependent upon timber ownership. There are three broad categories of
timber owners: (1) small, private landowners; (2) timber firms which grow trees
and use this fiber and fiber from other sources to produce a product (a vertically
integrated forest firm); and (3) state or federal agencies.

Small, private forest owners are well advised to use financial maturity in
deciding when to harvest. In addition, though, the owner must accept the market
as given and adjust operations to it. If prices for fiber fluctuate, a strictly
economic analysis of an optimal date for a timber sale is useless. Faced with the
prospects of such variability, a small forest owner may seek to minimize risk by
cutting prior to financial maturity.

For a vertically integrated forest firm, the cost of wood taken from the
forest is a small, though not insignificant, part of total costs for processing and
marketing the finished wood products. Clawson (1977) has estimated that these
costs are on the order of 1596 to 2096 of total expenditures. As a result of
operating costs, it is important that the firm continue operating at or near full

capacity. This is especially true of pulp and paper plants.

87

Under these circumstances, low wood costs are desirable but not as
important as a constant supply of wood. The vertically integrated forest firm
usually chooses harvest dates within very wide limits for processing and
marketing efficiency. The date of financial maturity is an important considera-
tion, but it is not dominant in decisions about the date of harvest. These firms
will cut more or less of their own timber or buy more or less from other sources
for market and processing reasons and not for efficiency of growth in the forest
stand.

When the Forest Service or other public agencies offer wood for sale, the
market for fiber can be influenced because of the large land holdings of these
agencies. In addition, the Forest Service, and perhaps other public agencies,
have traditionally paid great attention to local economic stability. Judgements
of timber harvest to meet these conditions may override economic and biological
analysis. Finally, the Forest Service is directed through the National Forest
Management Act of 1976 to grow and market timber within specific guidelines.
All of these factors influence the decision as to when and how much timber to
harvest.

In summary, a number of factors, other than the characteristics of stand
growth and financial maturity, influence decisions to harvest timber. These
considerations vary depending upon forest ownership.

For each category of timber owner, the feasibility of a partial cut strategy
is strongly influenced by forest management objectives. For the small, private
landowner, the principle management objective will likely be to secure the
maximum economic return with the least risk. For this objective, a partial cut

strategy is likely not feasible because the residual stand will probably not

88

increase in value faster than returns are accrued from the immediate full
harvest of the stand. This is more fully explained in appendix 5. Hence, the best
policy for a small, private landowner is, if possible, to completely presalvage a
stand. If maximization of economic returns with least risk is not a management
objective then a policy analysis for the small, private landowner is similar to
that for the vertically integrated forest firm or the public agency.

For a vertically integrated forest firm or a public agency, we will assume
that it is: (l) desirable to spread the harvest, marketing or processing of spruce-
fir fiber over a longer time interval than would result from complete presalvage;
or (2) harvest the stand to promote regeneration of multi-aged spruce-fir which
is less vulnerable to budworm. Feasibility is then a question of whether a partial
cut can be profitably implemented.

To determine profitability, questionnaires (appendix 6) were sent to the
loggers responsible for harvesting each stand. Only one questionnaire was
returned. The information from this questionnaire is given in table 9. It can be
seen that the strip cut operation in stand 3 was profitable. In all likelihood, the
operations in stands 1 and 2 were also profitable, since it was quite easy to
secure a contractor for these harvests. Hence, a forest owner could implement a
partial cut in a profitable manner. For the same reasons that a small, private
landowner would likely not maximize returns from a partial harvest, neither will
a vertically integrated firm or a public agency. However, as explained earlier,
these forest owners do not make harvest decisions based solely on maximizing
economic returns (is; harvest at financial maturity). Forest management

objectives and fiber processing and marketing considerations are also heavily

89

 

Table 9. Costs and revenues incurred by logger in harvesting stand 3.
59515
Labor
wages for harvesting 412 cords 3,708.00
($.ZOIstick s 45 sticks/cord - 59.00lcord)
Employee insurance 300.00
Labor cost subtotal 4,008.00 4,008.00
mite-ice;
Original cossl,:
1-4500 Ford iron mule 38,700.00
3 Husqvarna chain saws 900.00
Operating costs: I 39,600.00
Capital equip-ent cost; 661.15
PUCI 295.80
Haintenance 91.50
Insurance 471.00
Equip-ent cost subtotal 1,519.05 1,519.05
Transportation
Road-building costs - 0 -
Trucking wood to mills (hired out at 59.00/cord) 3,708.00
Transportation of crew to and from job site (80 si.lday) 218.40
Transportation cost subtotal 3,926.40 3,926.40
Stun a as,
1,392.08 1,392.08
TOTAL COSTS 10,845.53
REVENUES
Delivered stggpage
Product: Hill: Volume in cords: Value/ed:
Pulpwood Head Paper Co. 276 33.58 9,268.00
Sawtimber Escanaba Lumber Co. 32 35.00 1,120.00
Products-Cedar habitant Pence Co. 104 35.00 3,640.00
TOTAL REVENUE 14,028.00 14,028.00
KIT REVENUE 3,180.67
l/lron mule and chain saws purchased 1979.
.3/0eternination of capital cost of equipment: n
annual cost - (purchase price - salvage value) 11 1 :){)- 1 where: i - interest rate (122)

n - life of eqiupnent in yrs.
(10 yrs. for iron sole,

5 yrs. for chain saws)
salvage value - 10! purchase price
cost for job - (annual cost /

working days per yr.) (8 days worked on job) 8 days worked on job - 28

(236 working days per year assumed)

where:

 

3, . Quantity Price Species
Species Product (cunits) (S/cunit)__ Total (5)
Balsam fir pulpwood 35 8.90 311.50
white spruce pulpwood 19 16.14 306.66
Cedar products 80. 5.03 402.40
Paper birch pulpwood 58 3.94 228.52
Aspen pulpwood 120 1.15 138.00
Mixed hardwoods pulpwood 5 1.00 5.00
Sale total 317 cunits $1,392.08

90

weighed. Whether or not these objectives can be reached with this policy depend

upon the dynamics of the budworm and the forest in the residual stands.

Biological Response of the System

The objective here was to assess the biological response of the system to a
partial cut. To do this, budworm survival and balsam fir defoliation was
evaluated in cut and control areas of each stand. Budworm survival was selected
as an indicator of all the processes operating on the budworm population.

In late summer 1980, egg mass densities were estimated in the cut and
control areas of stands 1 and 3. Egg mass densities were not estimated in stand
2 because the harvest of this stand had not been completed. Three branches
were clipped with a pole pruner from the mid to uppercrown of 16 host trees in
the cut and control areas of each stand. The number of white spruce or balsam
fir sampled was based on percentage composition. From each branch, the
current year's viable egg masses and parasitized egg masses were removed and
recorded. If an egg mass was incompletely parasitized, those with less than half
of the eggs attacked were classified as viable. Each branch was checked a
second time by a different worker for overlooked egg masses. The foliage
surface area of each branch was measured with a grid. Egg mass densities were
converted to egg densities by assuming there were 20 eggs per viable egg mass.

In spring and summer 1981 the densities of small and large larvae, pupae,
and adults were estimated in the cut and control areas in each stand. The dates
for each sample and the budworm life stages sampled are given in table 10. Four
branches were clipped with a pole pruner from either 5 or 10 randomly selected

balsam fir trees. The foliage area was estimated similarly to the egg mass

91

0
Table 11L Dates and degree days (base 5.56 C) for five sampling periods

during which spruce budworm densities were determined in three
Peak 3rd instar occurs at c. 167 DD, peak 6th instar at

stands.

c. 416 DD and initial emergence of male moths at c. 472 DD.

Sample

3rd Instar

4th Instar

5th Instar

Pupae S

Pupae S

111111213 c. 1., D. c. Eidt, and c. A. McDougall. 1971. Predicting

Stand

Date
Degree Days
Base 5.56 C

Date
Degree Days
Base 5.56 C

Date
Degree Days
Base 5.56 C

Date
Degree Days
Base 5.56 C

Date
Degree Days
Base 5.56 C

1
Cut
6-09

218

6-12
250

6-23
364

7-03
478

7-08
560

Control

6-08
208

6-12
250

6-23
364

7-03
478

7-08
560

2

Cut
6-04
168

6-17
309

6-19
329

7-02
464

7-07
543

Control

6-03
160

6-17
309

6-19
329

7-02
464

7-08
560

3
Cut
6-05

183

6-11
239

6-18
321

7-01
451

7-07
543

Control

6-06
192

6-11
239

6-18
321

7-01
451

7-07
543

spruce budworm development. Dept. Environ. Can. For. Serv.,

Bi-mon.

Res. Notes.

27:33-34.

92

sample. Samples of 3rd, 4th, and 5th instars were examined in the field and
densities expressed as larvae per m2 foliage. Larvae and pupae found during the
first and second pupal samples (Pupae Sl’ Pupae 81) were collected and reared.
From these rearings, the mortality from parasitism and unknown causes was
determined. Adult densities were determined from rearings and from pupal
cases from which adults had emerged in the field. Defoliation of old and new
foliage was estimated during the two pupal samples by classifying the percentage
of foliage missing per branch into 5 groups: 0-2096, 21-4096, 41-6096, 61-8096,
and 81-10096. Differences in budworm densities in the cut and uncut areas in
each stand were statistically tested after necessary transformations with
ANOVA. Differences in percentage mortality were tested by comparing the
parameter p of a binomial distribution from the cut and control areas through a
normal approximation. Defoliation estimates were tested for differences
between the cut and control areas with a Mann-Whitney U test.

Dispersal loss—Estimates of budworm population densities for the different

 

life stages sampled in the cut and control areas of stands 1, 2, and 3 are given in
tables 11, 12, and 13. No significant differences in egg mass densities occurred
in the cut and control areas from stands 1 and 3. Based on the close proximity
and similar stand composition of the cut and control areas in stand 2, we can
infer that equality of egg mass numbers likely occurred here also.

The density of feeding 3rd instars was significantly less in the control areas
as compared to the cut areas in all three stands. In stands 1 and 3, this
apparently indicated a greater mortality of early instars in the control areas. If
egg mass densities were equivalent in the cut and control areas of stand 2, the

same can be said for this plot. Since dispersal loss is apparently the major

Table 11.

93

Density per m2 balsam fir foliage of various life stages of

the spruce budworm in 1981 and percentage mortality due to
ANOVA (F0) or a
normal approximation of a binomial distribution (Z) were used

parasitism and unknown causes in stand 1.

to test for treatment differences.
was not computed due to a small sample size.

Treatment

Sample Stage

Eta
hatched
parasitized

Larvae
3rd instar
4th instar
5th instar
4th + 5th instar

Pupae S1
total
larvae

2 parasitized
2 unknown
mortality
pupae
1 parasitized
2 unknown
mortality
adults

Pupae 82
total
larvae

2 parasitized
1 unknown
mortality
pupae
Z parasitized
2 unknown
mortality
adults

 

”I

63.01
17.13

124.31

142.37
95.72
119.05

51.71
14.75
.536

.338
36.96
.167

.106
31.68

45.37
1.84
1.0

0.0
43.53
.112

.157
32.45

Control

5.
X

6.20
2.98

7.80
16.64
10.13

6.53

7.04
2.77
.059

.056
5.17
.025

.021
4.40

5.09
0.0
0.0
5.44
.033

.039
4.49

20

62.09
21.94

218.20

191.26
111.62
151.44

66.52
14.96
C 512

.233
51.56
.225

.056
40.68

54.35
7.52
.450

.500
46.82
.185

.059
36.23

Cut

.054

.046
5.21
.025

.001
4.68

6.58
2.05
.111

.112
5.65
.033

.020
4.80

48
48

40
20

20
40

40
86
86
284

284
40

20
20
20
135

135
20

F or 2*

0

.01
1.19

23.56

2.60
.10
1.41

2.47
.003
0.207*

.24 *
.96
.45 *

hfihah‘

.00 *
.96

MN

.17
.36

OUII-l

.176
1.35 *

2.28 *
.332

C indicates the statistic

”Pal-‘0) or
F(zsz or zzZ)*

.915
.278

.001
.115
.754
.239

.120
.955
.417*

.108*
.050
.075*

.023*
.166

.287
.026
C

C
.677
.09 *

.01 *
.5681

Table 12.

Density per 1112 balsam fir foliage of various life stages of

the Spruce budworm in 1981 and percentage mortality due to
ANOVA (F ) or a

normal approximation of a binomial distribution (2)0were used
C indicates the statistic

was not computed due to a small sample size.

parasitism and unknown causes in stand 2.

to test for treatment differences.

Treatment
Sample Stage

£11
hatched
parasitized
Larvae
3rd instar
4th instar
5th instar
4th + 5th instar
Pupae 51
total
larvae
2 parasitized
2 unknown
mortality
pupae
2 parasitized
1 unknown
mortality
adults
Pupae 82
total
larvae
2 parasitized
2 unknown
mortality
pupae
Z parasitized
2 unknown
mortality

174.19
132.09
135.05
133.57

74.50
12.34

.449

.174
62.17
.137

.197
44.81

85.28
1.83
.50

.50
83.44
.201

.072

Control

5.
X

N O T C O L L E C T E D

18.48
13.09
18.37

7.04

7.31
1.58
.060

.046
7.18
.020

.023
4.67

12.14
.89
.25

.25
6.43
.028

.018

209

xl

276.32
201.86
137.52
169.69

66.31
10.98

.576
I 197

55.33

.146

.208

37.04

62.12
1.34
.50

.50
60.78
.164

.079

Cut

x?

22.09
19.12
11.79

7.73

6.07

1.96
.061
.049

5.15
.020

.023
3.86

6.27
.25
.25

6.43
.029

.021

40
20
20
40

4O
40
66
66
40
308

308

165
165

12.57

9.96
3.60
5.76

.74
.22
1.4609

.2888
.60
.2906

1.64

1.49
.18
C

C
1.28
1.489*

.241*

F0 or 2* F(FzF) or

F(rsz or zzZ)*

.001
.003
.552
.019

.392
.592
.072*

.384*
.442
.386*

.385*
.204

.230
.675

.266
.068*

.405*

95

Table 13. Density per 1112 balsam fir foliage of various life stages of
the spruce budworm in 1981 and percentage mortality due to
parasitism and unknown causes in stand 3. ANOVA (F0) or a
normal approximation of a binomial distribution (2) were used
to test for treatment differences. C indicates the statistic
was not computed due to a small sample size.

Treatment Control Cut
Sample Stage 1': S- n i S- n F0 or 2* P(FZF ) or
x x P(st or 222)*
£66
hatched 43.80 4.43 48 36.80 3.96 48 1.39 .241
parasitized 12.22 2.36 48 11.84 1.67 48 .228 .635
Larvae
3rd instar 95.86 7.82 40 198.83 15.83 40 38.90 .001
4th instar 96.67 7.98 20 127.85 15.56 20 1.67 .204
5th instar 77.53 9.88 20 142.43 18.48 20 10.59 .002
4th + 5th instar 87.11 6.46 40 135.14 11.98 40 10.88 .002
Pupae S
total 1 40.89 4.76 40 79-87 6-83 40 20.59 .001
larvae 14.24 1.95 40 32.81 3.92 40 9.07 .004
z parasitized .467 .052 92 -635 .035 189 2.69 9 .0049
2 unknown
mortality .152 .037 92 .212 .030 189 1.2049 .1159
pupae 26.65 5.88 40 47.06 5.38 40 10.55 .002
Z parasitized .114 .025 158 9142 9022 253 .829* .203*
2 unknown
mortality .165 .030 158 ~198 -025 253 .8509 .1989
adults 23.80 2.93 40 35.23 3.78 40 4.98 .028
Pupae 5
total 2 22.96 4.57 20 37-76 6.15 20 3.34 .075
larvae .50 .34 20 8.18 1.93 20 15.35 .001
Z parasitized 1.0 0 2 .905 .064 21 c C
2 unknown
mortality 0.0 0 2 .095 .064 21 c C
pupae 22.46 4.57 20 29.57 5.89 20 .76 .390
z parasitized .162 .036 105 -158 -042 76 .0739 .4729
2 unknown
mortality .086 .027 105 .092 .033 76 .0939 .4649
adults 16.98 3.42 20 21.19 4.52 20 .165 .687

96

mortality factor during this period of the budworm's life cycle, the results
suggest that dispersal loss was greater in the control areas. This contradicts the
theoretical basis we developed for the partial cut strategy. As indicated in that
section, dispersal loss of budworm has been found to increase with increases in
the number of non-host trees and increases in stand openings. It is possible that
stand factors which influence dispersal loss function on a finer spatial pattern
than that provided by the strip and patch cuts. However, a comparison of stand
parameters in the cut and control areas of each stand (tables 6, 7, and 8)
provides no indications of contrasts between these areas which might explain the
large differences in dispersal loss. The sampling methodology has also been
reviewed in an effort to uncover a systematic bias which may have led to an
underestimation of egg mass numbers in the cut areas or an overestimation in
the control areas. We have found none.

The empirical evidence, therefore, seems to refute the theory which
suggests that partial cuts will lower the intrinsic rate of increase of the
budworm. In fact, it appears as though this rate is higher in the cut areas.
However, it must be remembered that only a snapshot of a long-term process has
been taken. If differences in dispersal loss are a random phenomena there is a l-
in-8 chance that observed differences occurred by chance alone. Taking into
account the data presented here and that discussed previously, little is actually
known of budworm dispersal. Before abandoning the idea that partial cuts can
increase dispersal loss, it would be wise to collect long-term data on actual
dispersal losses.

Predation and parasitism—The survival of budworm from the 3rd instar to

 

the adult stage was less in all three cut areas than in the check areas. In fact, in

97

stand 2, the combined density of large larvae and pupae (Pupae $1) is less in the
cut area than in the control plot. Survival curves constructed from data in
tables 11, 12, and 13 are presented in figures 21, 22, and 23. In these figures, the
survival rate between successive sampling points is represented by the slope of
the line joining the density estimates at these points. Survival curves in the cut
areas in each stand are similar and those for the control areas in each stand are
also similar. This suggests that the higher mortality rate in the cut areas may be
attributable to increases in natural enemies following harvest. However, no
systematic and statistically significant difference in parasitism of large larvae
or pupae was found in the cut and control areas. On the other hand, it has been
demonstrated that bird densities increase following a partial harvest (Tittering-
ton gt _a_l_. 1979). A breeding bird census (appendix 7) in the three stands
substantiates this.

Another explanation is that budworm survival is a function of density. In
the cut areas, the density of 3rd instars is much greater than in the control plots.
The survival of budworm between the 3rd and 4th instars is much less in the cut
areas than in the controls. This suggests that survival during this period is a
function of density. If true, then, at least at moderate densities, mortality
during the 3rd and 4th instars compensates for mortality during the dispersal
period.

Defoliation—Defoliation of old and new balsam fir foliage in the cut and
control areas of each stand is given in table 14. Defoliation of the new foliage
was significantly less in the cut areas of stand 2 and 3, and no difference was
found in stand 1. Defoliation of old foliage was significantly less in stands 1 and

2, while no difference was found in stand 3. This data seems contraditory to the

Figure 21.

Density Per 14' Foliage

98

 

1600

 

250

r * El Cut

1400

   

Control

1200

1000

800
J

 

600
1

 

 

 

400
L,

200
1

 

 

 

Sample Stage

The density per 102 foliage of various life stages of the
spruce budworm in the cut and control areas of stand 3.

The life stages are; l-egg, 2-3rd instar, 3-4th and 5th

instar, 4-6th instar and pups, and S-adult.

Figure 22.

99

 

350

300
1

250
L

   

 

9 Cut

0 Control

200
1

Density Per M2 Foliage
ISO

 

 

 

r I I l
‘3 2 8 .4 5

Sample Stage

The density per 102 foliage of various life stages of the
spruce budworm in the cut and control areas of stand 2.
The life stages are; 2-3rd instar, 3-4th and 5th instar,
4-6th instar and pupae, and S-adult.

Density Per M’ Foliage

Figure 23.

100

 

1600

 

n
250
a

1400

i c! Cut

D
g 4 0 Control

1200

 

800 1000
L

600
1

 

 

 

400
1

200
1

 

 

 

 

Sample Stage

The density per 1112 foliage of various life Stages of the
spruce budworm in the cut and control areas of Stand 1.

The life stages are; l-egg, 2-3rd instar, 3-4th and 5th

instar, 4-6th instar and pupae, and S-adult.

101

Table 14. Defoliation of balsam fir by spruce budworm in three stands in
which part of the stand was partially harvested and the other

part served as a control.

lowing scale; 0 : O-ZOZ foliage missing, 1 :
missing, 2 : 41-602 foliage missing, 3 : 61-80% foliage missing,

4 : 81-1002 foliage missing.

Stand Treatment
1 cut
control
2 cut
control
3 cut
control

1Defoliation occurred in 1981

Defoliation was ranked on the fol-

21-402 foliage

Treatment effects were tested with
the Mann-Whitney U test. The sample size in each case is 60.

Defoliation f new

X

foliage.
Probibility of a
Type I error
.6753

.0074

.0001

2Defoliation occurred in or prior to 1981

Defoliation f old

E
1.45
1.98

1.12
1.82

1.37
1.53

foliage.
Probibility of a
Type I error
.0018

.0001

.5277

102

population estimates in tables 11, 12, and 13 since most defoliation by budworm
result from feeding by 5th and 6th instars. This discrepancy may result from two
things. First, there may have been a systematic bias in the estimation of
defoliation. Second, the cut may have influenced the trees in the residual stand
in some manner to produce the observed result.

In summary, no substantiating proof of the hypothesized system response
can be offered. The effect of partial cuts on the dispersal loss of budworm
seems to be completely opposite from what we hypothesized. In the three stands
in which a partial harvest was tested, the survival of budworm from the 3rd
instar to the adult life stage was less in the cut areas. It is, however, unclear as
to what caused this reduction in survival. Defoliation of old and new balsam fir
foliage was generally less in the cut areas than in the control plots; however, the

cause of this difference is unknown.

Conclusion

The partial harvest of spruce/fir stands has been proposed as a strategy to
help reduce the impact of spruce budworm. A theoretical basis for this strategy
has been developed, the feasibility of the strategy has been assessed, and a
superficial check on the response of the system to the strategy has been made.
At this point, sufficient information is not available to prescribe the strategy.
However, when the study was initiated, there was no pretense of accomplishing
such an objective.

For many years, information has been collected on the dynamics of the
forest and budworm and, more recently, conceptual models have been advanced

to explain these dynamics. We felt it was important to take these empirical

103

observations and theory and begin to mold them into a holistic strategy for
dealing with the budworm problem. This report has demonstrated one way this
might be done. It also serves as a basis for future work.

The major shortcoming of the proposed strategy is the unanswered question
of what affect a partial harvest has on budworm and forest dynamics in the
residual stands. In order for the strategy to be successful, the vulnerability of
the residual stand to the budworm must be reduced. The data we collected to
address this question offers no clear-cut answer. In order to adequately answer
this question it will be necessary to collect information over a number of years.
This is because the response of the system to a partial harvest will not be
immediate and a long term series of data is indispensible for analyzing complex
biological systems. Although we tried to implement the partial harvests in
stands with low budworm numbers, budworm papulations were well beyond the
endemic level once the harvests were completed. In future work, it will be
important to ensure that the strategy is implemented at low budworm densities.

Even with these shortcomings, we feel a strategy has been identified which
might help forest managers deal with the spruce budworm. It certainly merits
further investigation. Furthermore, the philosphy presented, that of manipulat-
ing the structure of a cropping system, should have broad applicability to other

pest management problems.

104

Conclusions:

The results of two studies which were motivated by the concept of designing
crop production systems in order to reduce the impact of crop-damaging pests have
been presented. The first study explored the dynamics of an adult parasitoid and
used these findings to catalyze extensions to parasitoid host theory. Three
important results were generated: (1) A methodology for assessing the dynamics of
adult parasitoids was developed; (2) It was demonstrated that parasitoids respond to
factors in addition to the host when searching for these organisms; and (3) the
attributes of a successful biological control agent were revised, the most important
attribute being host searching. The theoretical results provide a foundation for
further work directed toward parasitoid management. The sampling method
provides a tool for acquiring information necessary for managing these biocontrol
agents. In addition, this methodology might also prove useful in on-line pest
management (Tummala and Haynes 1977) if it evolves to explicitly include
biological control agents.

On-line pest management seeks to use models driven by monitored
environmental variables to improve knowledge of the state of crop-pest systems.
Biological control agents are important components of these states. Berryman
(1982) has synthesized the concept of intolerant biological control agents. An
intolerant biological control agent is one which is made ineffective as a result of
changes in the biotic or abiotic environment. Intolerant biological control agents
may give rise to thresholds which separate endemic and epidemic pest p0pulations.
Factors which contribute to intolerance are often part of the monitored
environment or part of the system structure. The sampling method presented here
may be used to develop models of natural enemies driven by monitored variables

and can be incorporated in on-line pest management systems.

105

Use of the sampling method in other systems may require further
development of the model used to describe parasitoid activity. In particular, daily
activity patterns should be included. This is discussed with reference to another
data set in appendix 7.

The second study sought to change system structure through the use of forest
harvesting in order to reduce spruce budworm damage. The feasibility of this
system design rested on increasing the mortality of spruce budworm in residual
forest stands. Previous studies suggested that this was a likely outcome; this
study, however, did not substantiate these findings.

Both studies point to a considerable gap in empirical data and theory. This
gap must be bridged if design-mediated pest management is to be successful.
Undoubtedly, theory cannot do for pest management what it has done for physics,
chemistry, and the engineering sciences. It can, however, serve as a template upon
which empirical studies can be shaped. Studies which seek to develop crop system
designs will require a long-term time commitment. This is perhaps the most
serious shortcoming of the spruce budworm/forest harvesting study. Currently,
there is considerable difficulty in securing funding for such long-term work.
Finally, many design studies will necessarily have to be conducted an endemic
populations. Before this can be done, sampling and analysis methods for such

studies will have to be developed.

APPENDICES

106

Appendix 1.

 

In this appendix we briefly show that if the transition of an insect from one
stage to another occurs via a random time delay with no mortality within and
between stages, then an aggregate approximation of a population of these
transitions can be made using the probability density function of the delay.
Further details can be found in Pugh (1963) and Manetsch and Park (1977).

Let Kij(t) be an indicator variable which is equal to one if insect i enters
stage j at time t and is zero otherwise. Define u(t) as a unit step function such
that:

l for t > 0
u(t) =
0 for t :0
Also , let Ti be the delay in physiological time between stages j and j + l for
insect i. We note that this variable is a random variable with probability density
function f (t).

For a population of n insects:

j - '-1
Kin-Kl, (t-Tl)u(t-Tl) (1)

i - i-1
K n(t) - K n (t-tn)u(t-'rn)
Taking the Laplace transform of both sides of (1) produces:
Kits) = xrksws <2)
1 1

By summing both sides of (2) over i, assuming KiJ'l and Ti are independent and

taking expectations we have:

 

107
Ele(s)] = Eth‘kun 31675 (3)
. n
where NJ(s)= 2 813(5)
i=1

Because ‘1' is a random variable EIe-Ts] can be expressed as:
- °° its
Ele t0 = Io f(t)e dt = F(s)

where F(s) is the one-sided Laplace transform.

Substituting this result in (3) yields:

Ele(S)] = widens) (4)

Multiplication in the 5 domain is equivalent to convolution in the time domain.

Hence, assuming F(s) is time invariant (4) becomes:
E[nj(t)] - I: E(nj- l(z))f(t-z)dz.

In other words, the expected aggregate rate of insects entering stage j is a
convolution of the rate they enter stage j-l and the probability density function
of the time interval between these stages.

If mortality does occur within or between stages this can be easily

incorporated (see Manetsch and Park 1977).

Appendix 2

108

 

 

Temperature Controller For Environmental Chamber

all resistors Mn unless speciiled in“,

 

 

 

HEATING
ELEMENT

4025-2qu 1
in parallel ‘i

vv

712v

 

    

'06 '08.

-———-————-———fi—-

 

discharge

T’

31681. 5 5 s

  
 

 

threshold
2 trigger

 

 
      

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rnd 5
I
ac J :
* F
.. ..., 4 in "12 out .104 i *4
17m ; EEizvac 61' are ”35' l
- 1.2am commsarj '
I 43750:!" 1.5,. f i
" 35v I
I 888! alum I
I
I

Figure 24.

Circuit diagram for temperature controller of an environmental
chamber. The portion to the right of the dashed line is
replicated for each group of heating elements. The controller
was designed by James Pieronek, Michigan State University.

109

Appendix 3.

 

In this appendix the method employed in the analysis of the parasitoid-host
model is outlined. A coupled, discrete generation parasitoid-host model was given in
the main text as:

H

(1) t
Pt +1 = Ht(1-f(Pt,Ht))

At equilibrium (11,13) the following conditions hold:

{(13, Ii) = F'1
13' = 11(1-F-l)

The local stability of (1) can be determined by examining the dynamics of a

pertebation model defined as

_ * * * s s s a a
xt+l - PM + xtXH + xt)f(P + yt, H + xt)- F(H)Hf(p, H)

(2) s s a a a s
yt+l = (H + xtXl - f(P + yt, H + xtii- H(1- f(P, H1)
and linearized about 11 and F.

For stability, x(t) and y(t) —-+ 0 as t —-+ 0°.

The linearized model obtained through a Taylor expansion and after

substitution of equilibrium conditions is given as _

 

 

 

 

 

 

F1 ass--1 9:an 9:88qu-
xt+l = 1+F(H)HF(H) +F(H)H3H, HF(Hra—P, xt
__ 9-1 9.3.1: 133.2
yt+1 ' I‘m“ “H 3H* ' aP“ J yt
L .l . b m

(A)

A necessary and sufficient condition for stability of the linearized model is that the

dominant eigenvalue of matrix A has modulus less than 1.

110

For model (5) in the text an equilibrium value for 11 can be found by solving
the function
aH(‘l’-l -k. =
where ‘1’ = Aexpl—yH/(oz2 + H2)]. This was done using Newton's method for
*
determining the roots of an equation. An equilibrium value for P can then be easily

found using the equilibrium conditions. Matrix A for model (5) is given as

 

 

i (oz-HZfiH _1
- 2 2 2 22)
(0: +H ) H(l + k a
A:
-k a -(k+l) *
14132) Hi1 +15) 8 H
m R J I:

The stability region can be found by solving (2) through simulation for various values

of xt and yt.

111

Appendix 4.

 

Computer program listings.

112

*UOBCARD‘.UC2000.RGZ.
ATTACH,B,BNPGCOMPLEX.

000000000000000000000000000OOOOOOOOOOOOOOOO00000000000000

THIS PROGRAM USES AN OPTIMAZATION ALGORITHM TO ASSIGN VALUES

TO PARAMETERS OF A MODEL DESCRIBED IN SUBROUTINE FUNC.

THE

OPTIMIZATION ALGORITHM IS BOX’S COMPLEX ALGORITHM DESCRIBED IN;

KEUSTER. d.L..
TECHNIQUES WITH FORTRAN.

OPTIMIZATION
NEW YORK.

AND J.H. MIZE. 1973.

MCGRAU-HILL. SOOPP.

REQUIRED DATA IS CONTAINED IN THE SUBROUTINES AND AT THE END OF

THE PROGRAM AS FOLLOWS

CARD COLUMNS CONTENTS

1 1 - 5 N (NUMBER OF VARIABLES)

1 6 - 10 M (NUMBER OF CONSTRAINTS)

1 11 - 15 K (NUMBER OF POINTS IN COMPLEX)
1 16 - 20 ITMAx (MAXIMUM ITERATIONS)

1 21 - 25 10 (NUMBER OF IMPLICIT VARIABLES)
1 26 - so IPRINT (PRINT CONTROL)

2 1 ~ 10 ALPHA (REFLECTION FACTOR)

2 11 - 20 BETA (CONVERGENCE PARAMETER)
2 21 - 25 GAMMA (CONVERGENCE PARAMETER)
3 1 - a INITIAL X(1)

3 9 - 16 INITIAL x(2)

3 17 - 24 INITIAL x(s)

3 25 - 32 INITIAL X(4)

4 1 - 8 6(1) (LOVER CONSTRAINT)

4 . .

5 1 - a H(1) (UPPER CONSTRAINT)

5 . .

SUBROUTINE FUNC

PURPOSE

DESC

DESC

MODEL OF MALAISE TRAP CATCH OF GLYPTA FUMIFERANAE WHICH
IS BASED ON THE TEMPORAL CHANGES IN THE NUMBER OF ADULTS
AND WEATHER FACTORS HHICH INFLUENCE ADULT ACTIVITY. THE
SUBROUTINE IS USED BY THE OPTIMIZATION ALGORITHM TO FIT
PARAMETERS TO THE MODEL:

CATCH=(PROPOR+AW)‘FLYAD
WHERE:

PROPOR IS A PROPORTIONALAITY CONSTANT

A 15 A VECTOR OF PARAMETERS TO BE DETERMINED

w IS A VECTOR OF HEATHER FACTORS

FLYAD IS THE DENSITY OF ADULT G. FUMIFERANAE
THE INITIAL INPUT (PUPIN) IS ARBITRARY AS THE VARIABLES IN THE
MODEL ARE SCALED ACCORDING TO THIS VALUE

RIPTION OF SUBROUTINE PARAMETERS

N - NUMBER OF EXPLICIT INDEPENDENT VARIABLES

M - NUMBER OF CONSTRAINTS

K - NUMBER OF POINTS IN COMPLEX

X - INDEPENDENT VARIABLES (PARAMETERS TO BE FITTED TO MODEL)
F - OBJECTIVE FUNCTION

I - POINT INDEX

RIPTION OF VARIABLES USED IN SUBROUTINE

RP, RAl r INTERMEDIATED RATES IN DISTRIBUTED DELAYS
NDD4B - DEGREE DAYS BASE 48F PER DAY
PRECIP - PRECIPTATION IN INCHES BETWEEN 800 AND 2200 HRS

113

RH - AVERAGE RELATIVE HUMIDITY BETWEEN 800 AND 2200 HRS
TEMP - AVERAGE TEMPERATURE (F) BETWEEN 800 AND 2200 HRS
TRUCAT - ACTUAL CATCH OF G. FUMIFERANAE IN MALAZSE TRAPS

REMARKS
THE OPTIMIZATION ALGORITHM ASSIGNS VALUES TO X TO MINIMIZE THE
SUM OF THE SOUARED DIFFERENCES BETWEEN THE TRUE AND PREDICTED
TRAP CATCH. IT USES SUBROUTINE DELAY2 WHICH IS A DISTRIBUTED
DELAY AND IS DESCRIBED IN

MANETSCH.T.J.. AND G.L. PARK. 1974. SYSTEM ANALYSIS AND
SIMULATION WITH APPLICATION TO ECONOMIC AND SOCIAL SYSTEMS
PART II. MICH. STATE UNIV.. E.LANSING. 239PP.

OOOOOOOOOOOOOOO

SUBROUTINE FUNC(N.M.K.X.F.I)

DIMENSION x(2O.2O).F(2O).RP(1O).RA1(1O).NDD4B(27)
+.PRECIP(27).TRUCAT(27),TEMP(27).RH(27)

C ASSIGN VALUES TO VARIABLES

DATA RP /O..O..O..O..O..O..O..O..O..o./

DATA RA1 /O .O..O..O..O..O..O..O..O..O./

DATA NOD48 /24.22.23.22.14.15.16.13.14.20.12.5.11.
+14.19.12.8.11,11.15.19.24.22.21.2O.17.19/

DATA PRECIP /O..O..O..O..O..O...O1..26.0..O...4..3.0..
+0..O...35.O...32..11.0..0..O..2.34.O...36..O1.O./

DATA RH /34.B.59.8.74..46.6.60.5.52.6.73.4.69.7.BO..65.5.
+93.1.66.6.49.5.56.6.64.5.79.1.59.2.44.5.49.2.53.1.57.1.
+61.6.65.6,76.B.B4.5.BO.2.54.9/

DATA TEMP /.809..765..757..755..663..698..661..698..656.
+.735..623..552..646..690..712..612..606..646..629..711.
+.726..773..708..718..709..675..737/

DATA TRUCAT /O .O..1..16..29..25..21..16..25..33..7..
+7..16..30..28..5..6..4..1..B..4..5..4..1..1..O..o./

C DELAY OF PUPAL STAGE
DELPUP-1OO
C K'S OF ERLANG DENSITY FUNCTIONS USED IN DISTRIBUTED DELAYS
KPUP=4
KAD=8
C INITIALIZE STATE VARIABLES
ADULT=RMORT=TADULTsTMORT=O.
DTx.125
C INITIALIZE INPUT INTO SYSTEM
PUPIN=50/DT
C ASSIGN VARIABLES IN MODEL TO DECISION VARIABLES OF OPTIMIZATION
C ALGORITHM

DELAD=x(I.1)

PROPOR=x(I.2)

ALPHA=x(I.3)

BETA=x(I.4)

C SET OBJECTIVE FUNCTION TO ZERO
U=O.
C DETERMINE SIMULATION ITERATIONS
C SIMULATION IS RUN FOR N DAYS AND x 0048 FOR EACH DAY

T=0.0

DO 10 11:1.27

IENDsNDO4B(I1)/DT+.OOOO1

NN1-IENO/2

C NN1 Is THE DEGREE DAYS MIDWAY THROUGH A DAY. ADULT DENSITY AT
C THIS TIME IS USED TO RELATE TRAP CATCH TO OTHER VARIABLES

DO 20 I2-1.IEND

T-T+DT

730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890

910
920
930
940
950
960
970
980
990

1010
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1030
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
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1200
1210
1220
1230
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330

114

C CALL DELAYS WHICH MODEL THE PUPAL AND ADULT LIFE STAGE
CALL DELAY2(ADULT.RMORT.RA1.DELAD.DT.KAD)
CALL DELAY2(PUPIN.ADULT.RP.DELPUP.DT.KPUP)
C COMPUTE STORAGE IN DELAYS WHICH IS THE NUMBER OF PUPAE OR
C ADULTS AT ANY POINT IN TIME (PUP.FLYAD)
VAR1=VAR2-O.
DO 15 3:1.KPUP
15 VAR1-VAR1+RP(U)
DO 16 O-1.KAD
16 VAR2=VAR2+RA1(U)
PUPsDELPUP/KPUPvVAR1
FLYAD=DELAD/KAD*VAR2
IF (I2.Eo NN1) FLYAD2=FLYAD
PUPIN=O.
2O CONTINUE
C COMPUTE MULTIPLIER TO RELATE TRAP CATCH. ADULT DENSITY AND
C EXTRINSIC FACTORS
RMULT=PROPOR+(ALPHA‘PRECIP1I1))+(BETA'TEMP(I1))
IF (RMULT.LT.O) RMULT=O.
CATCH=RMULT¢FLYAO2
C COMPUTE OBUECTIVE FUNCTION
U=U+(CATCH-TRUCAT(I1))*‘2
F(I)--U
1O CONTINUE
END

000

SUBROUTINE OELAY2 (RINR.ROUTR.CROUTR.DEL.DT.K)

DIMENSION CROUTR(1)

OEL1=DEL/(FLOAT(K)-DT)

RINsRINR

DO 1 1-1.K

ABCsCROUTR(I)

CROUTR(I)-ABC+(RIN-ABc)/DEL1
1 RIN=ABC

ROUTR=CROUTR(K)

RETURN

END

SUBROUTINE CONST

PURPOSE
SPECIFIES EXPLICIT AND IMPLICIT CONSTRAINT LIMITS. IT

PARAMETERS ARE DEFINED ABOVE.

0000000000

SUBROUTINE CONST(N.M.K.x.G.H.I)
DIMENSION x(2o.2o).G(20).H(20)
RETURN
END

REDS

180.0
110.0
250.0
'EOP

!°.°°'
O<D~I
m
1 O
MO
0»
PPPwo
(DCDO

MUST BE INCLUDED EVEN IF NO IMPLICIT CONSTRAINTS ARE USED.

1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
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1550
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1570
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1930

115

PROGRAM Box(INPUT.OUTPUT) 1
DIMENSION x(20.20).R(20.20).F(20).G(20).H(20).XC(20) 2
INTEGER GAMMA 3
KOUNT-O 4
READ 1.N.M.K.ITMAx.IC.IPRINT 5
1 FORMAT (BIS) 6
READ 2. ALPHA.BETA.GAMMA 7
2 FORMAT(2E10.4.Is) a
DELTA=0.0001 9
READ 4. (x(1.d).d=1.N) 10
READ 4. (G(I).I=1.M) 11
READ 4. (H(I).I=1.M) 12
4 FORMAT(9F6.4) 13
DO 100 II=2.K 14
DO 3 dd=1.N 15
3 R(II.OU)=RANF(1.O) 16
100 CONTINUE . 17
PRINT 10 18
10 FORMAT(1H1.//.18X.24HCOMPLEX PROCEDURE OF Box) 19
PRINT 1B 20
18 FORMAT(//.2x.10HPARAMETERS ) 21
PRINT 11.N.M.K.ITMAX.IC.ALPHA.BETA.GAMMA,DELTA 22
011 FORMAT (//.2x.4HN . .I2.3x.4HM . .I2.3X.4HK . .I2.2x.BHI23
+TMAx . . 23,
1I4.2x.5HIC - .I2.//.2x.BHALPHA . .F5.2.5x.7HBETA - .F10.24
+5.3x. 24.
28HGAMMA - .I2.3X.8HDELTA . .F6.5) 25
PRINT 900 26
900 FORMAT(//.2x.16HINITIAL x VALUES) 27
DO 200 U - 1.N 28
PRINT 16. a. X(1.d) 29
200 CONTINUE 30
50 CALL CONsx (N.M.K.ITMAX.ALPHA.BETA.GAMMA.DELTA.X.R.F.IT.31
1IEV2.NO.G.H.XC.IPRINT) 32
IF (IT-ITMAx) 20.20.30 33
20 PRINT 14. F(IEV2) 34
014 FORMAT (///.2x.30HFINAL VALUE OF THE FUNCTION - .E20.8) 35
PRINT 15 36
015 FORMAT (//.2x.14HFINAL x VALUES) 37
DO 300 d-1.N 38
PRINT 16. U. x(IEV2.d) 39
016 FORMAT (/.2x.2Hx(.I2.4H) . .E20.8) 40
300 CONTINUE 41
PRINT 9. IT 42
9 FORMAT (//- THE NUMBER OF ITERATIONS IS 1. 15) 43
GO TO 999 44
30 PRINT 17. ITMAx 45

017 FORMAT (///.2X.38HTHE NUMBER OF ITERATIONS HAS EXCEEDED 46
+.I4.1OX.

999

10
20

11BHPROGRAM TERMINATED)

STOP
END

SUBROUTINE CONSX (N.M.K.ITMAX.ALPHA.BETA.GAMMA.DELTA.X.R50

+0F.
1IT.IEV2.NO.G.H.XC.IPRINT)

DIMENSION x(20.20).R(20.20).F(20).G(20).H(20).xc(20)
INTEGER GAMMA

IT - 1

KODE - 0

IF (M-N) 20.20.10

KODE - 1

CONTINUE

DO 40 II-2.K

30
40

50

70

72
21

22
80

90
100

110
120

130

140

150

160

170

180

190

200

116

DO 30 d=1.N
x(II.d) - 0.0
CONTINUE
DO 65 II=2.K
DO 50 d=1.N
I . II
CALL CONST (N.M.K.x.G.H.I)
x(II.d) = 6(0) + R(II.U)'(H(d)-G(U))
CONTINUE
K1 = II
CALL CHECK (N.M.K,X,G.H.I.KODE.XC.DELTA,K1)
IF (II-2) 51. 51. 55
IF (IPRINT) 52.65.52
PRINT 18
FORMAT (//.2x.30HCOORDINATES OF INITIAL COMPLEX)
IO = 1
PRINT 19. (IO. u. X(IO.d). d=1.N)
FORMAT (/.3(2x.2Hx(.I2.1H..I2.4H) = .1PE13 6))
IF (IPRINT) 56.65.56
PRINT 19. (II. a. X(II.d). d=1.N)
CONTINUE
K1 2 K
00 70 I-1.K
CALL FUNC(N.M.K.X.F.I)
CONTINUE
KOUNT=1
IA=0
IF(IPRINT) 72.80.72
PRINT 21
FORMAT(/.2x.22HVALUES OF THE FUNCTION )
PRINT 22 . (d.F(d). d=1.K)
FORMAT(/.3(2x.2HF(.I2.4H) = ,1PE13.6))
IEv1=1
DO 100 ICM=2.K
IF(F(IEv1)-F(ICM)) 100.100.90
IEv1=ICM
CONTINUE
IEV2=1
DO 120 ICM=2.K
IF(F(IEV2)-F(ICM)) 110.110.120
IEV2=ICM
CONTINUE
IF(F(IEV2)-(F(IEV1)+BETA)) 140,130,130
KOUNT=1
GO TO 150
KOUNT=KOUNT+1
IF(KOUNT-GAMMA)150.240.240
CALL CENTR(N.M.K.IEV1.I.XC.X.K1)
DO 160 dd=1.N
X(IEV1.UU)=(1.0+ALPHA)-(xc(dd))-ALPHAc(X(IEV1.UU))
I-IEV1
CALL CHECK(N.M.K.X.G.H.I.KODE.XC.DELTA.K1)
CALL FUNC(N.M.K.X.F.I)
IEv2-1
DO 190 ICM=2.K
IF(F(IEV2)-F(ICM)) 190.190.180
IEV2=ICM
CONTINUE
IF(IEv2-IEV1) 220.200.220
DO 210 dd=1.N
x(lEV1.dd)=(X(IEV1.dd)+XC(dd))/2.0

210

220

230
23

24

25

26
228

240

10

20
30
50

60

70
80

90
100

110

10

20

117

CONTINUE
I=IEV1
CALL CHECK(N.M.K.X,G.H.I.KODE.XC.DELTA.K1)
CALL FUNC(N.M.K.X.F.I)
GO TO 170
CONTINUE
IF (IPRINT) 230.228.230
PRINT 23.IT
FORMAT(//.2x.17HITERATION NUMBER .15)
PRINT 24
FORMAT(/.2x.30HCOORDINATES OF CORRECTED POINT)
PRINT 19. (IEV1.dC.X(IEV1.dC). UC=1.N)
PRINT 21
PRINT 22. (I.F(I).I=1.K)
PRINT 25
FORMAT(/.2x.27HCOORDINATES OF THE CENTROID)
PRINT 26. (dC.XC(dC).dC=1.N)
FORMAT(/.3(2X.2HX(.I2.6H.C) . .1PE14.6.4x))
IT=IT+1
IF(IT—ITMAx) 80.80.240
RETURN
END
SUBROUTINE CHECK(N.M.K.X.G.H.I.KODE.XC.DELTA.K1)
DIMENSION x(20.20).G(20).H(20). xC(20)
KTso
CALL CONST(N.M.K.X.G.H.I)
DO 50 Us1.N
IF(X(I.d)-G(d)) 20.20.30
X(I.d)- G1d)+DELTA
GO TO 50
IF(H(d)-x(l.d)) 40.40.50
x(I.U)=H(d)-DELTA
CONTINUE
IF(KODE)110.110.60
NN=N+1
DO 100 UsNN.M
CALL CONST(N.M.K.X.G.H.I)
IF(X(I.d)-G(d)) 80.70.70
IF(H(d)-X(I.J))80.100.100
IEV1=I
KT=1
CALL CENTR (N.M.K.IEVI.I.XC.X.K1)
DO 90 dd=1.N
x(I.UU) = (x(I.Jd) +xc (dd))/2.0
CONTINUE
CONTINUE
IF (KT) 110. 110. 10
RETURN
END
SUBROUTINE CENTR (N.M.K.IEV1.I.XC.X.K1)
DIMENSION x(20.20).xc(20)
DO 20 U=1.N
XC(J) = 0.0
00 1O IL=1.K1
xc(U) = xc(d) + x(IL.U)
RK-K1
xc(u) - (XC(d)-X(IEV1.d))/(RK-I.O)
RETURN .
END

121
122

124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179

118

PROGRAM STABLE (INPUT.OUTPUT) 100

C THIS PROGRAM COMPUTES THE REGION OF STABILITY FOR STABLE 110
C EOUILIBRIA OF THE FOLLowING MODEL: 120
c H(T+1)=H(T)EXP(-BH(T)/C--2+H(T)c~2)(1+AP/K)~--K 130
C P(T+1)=H(T)(1-(1+AP/K)fi--K) 140
C DATA REQUIREMENTS ARE EOUILIBRIA VALUES AND VALUES FOR 150
C PARAMETERS AND ARE INPUT IN DATA STATEMENTS. 160
c THE STABILITY REGION IS DETERMINED ITTERATIVELY BY 170
C PERTERBING HE BY SOME VALUE DELTA AND CHECKING THROUGH 180
C SIMULATION CONVERGENCE OF THE MODEL BACK TO HE AND PE. 190
C PRECISION IS DETERMINED BY THE TEST VALUE OF 00 LOOP 1. 200
C K=O FLAGS K=INFINITY 210
DIMENSION DRK(4).DA(4).DHE(4.4).DPE(4.4) 220

DATA DRK/.75.2.0.6.0.0./ 230

DATA DA/1.5.2.O.2.5.3.0/ 240

DATA (DHE(1.M).M=1.4)/1.12039..85213..73440..66097/. 250
+(DHE(2.M).M=1.4)/.91BO2..73042..62695..557BO/. 260
+(DHE(3.M).M=1.4)/.85923..68300..58156..5127O/ 270
+.(OHE(4,M).M=1.4)/.B3137..65886..55793..48903/ 280

DATA (DPE(1.M).M=1.4)/.39855..30951..29494..28999/. 290
+(DPE(2.M).M=1.4)/.3234B..29462..2B796..282BO/. 300
+(DPE(3.M).M=1.4)/.31079..29133..2B4B4..27710/ 310
+.(DPE(4.M).M=1.4)/.30607..28987..28261..27422/ 320
Y-10.0 330
B=3.75 340

C=1.0 350

OD 300 L=1.4 350

OD 301 M=1.4 370
RK=DRK(L) 380
A=DA(M) 390
HsaoHE(L.M) 400
PS=DPE(L.M) 410

PRINT 100. B.C.Y.A.RK.HS.PS 420

100 FORMAT ("OB=".F4.2.1x.'C=~.F3.1.1x.'Y=~.F4.1.1x.'A='.F3.430
+1.1x. 435
+“RK='.F3.1.1X.'HE=“.F7.5.1X.'PE='.F7.5) 440
PRINT 101 450

101 FORMAT (“OMAX HOST AND PARASITE DENSITIES FOR wHICH MODE460
+L IS STABL 465

+E') 470
SIGMA-.05 480

00 1 I=1.2O 490

DO 2 1221.2 500
SIGN-1. 510
IF(12.EO.2)SIGN=-1. 520
P1=PS+(SIGMAvI-SIGN) 530
IF(P1.LT.0.) GO TO 21 540

P-P1 550
CHECK=S¢HS 560

DO 3 d-1.2 570
SIGN=1. 580
IF(J.EO.2)SIGN=-1. 59o
DELTA=.05 600

H1-HS 610

4 CONTINUE 620
DELTAsDELTAt2 630
H3=HS+(DELTA'SIGN) 64o
IF(H3.LT.0.) H3*.OO1 650

H=H3 660

CALL DYNAM (P,H.INOEx.Y.B.C.RK.A.CHECK) 670

P=P1 680
IF(INDEx.E0.1) GO TO 4 690

5 CONTINUE 700

119

IF(H3 LT H1) VAR1=H1-H3 71o

IF(H1 LT.H3) VAR1=H3-H1 720
IF(VAR1.LT..005) GO TO 6 730
H2=(H1+H3)/2 740

H=H2 750

CALL DYNAM (P.H.INDEx.Y.B.C.RK.A.CHECK) 760

p=p1 770
IF(INDEx.EO.1) H1=H2 780
IF(INDEX.E0.0) H3=H2 790

60 T0 5 800

6 CONTINUE 810
PRINT 102.P1.H1 820

102 FORMAT (~ PARASITE DENSITY= “.F7.5.“HOST DENSITY= '.F7.5830
4) 835

3 CONTINUE 840
GO T0 25 850

21 CONTINUE 860
PRINT 22 B70

22 FORMAT (" PARASITE DENSITY LESS THAN ZERO“) 880
25 CONTINUE 890
2 CONTINUE 900
1 CONTINUE 910
301 CONTINUE 920
300 CONTINUE 930
END 940

C 950
C 960
C 970
SUBROUTINE DYNAM (P.H.INDEx,Y.B.c.RK.A.CHECK) 980
INDEXII 990
00 1 181.100 1000
IF(RK.E0.0 ) GO TO 10 1010
V=(1/(1+A0P/RK))-9RK 1020
GO TO 11 1030
10 CONTINUE 1040
VSEXP(-A*P) 1050
11 CONTINUE 1060
P=Ho(1-v) 1°70
H=H°Y0EXP(-8'H/((0'02)+(H"2)))RV 1080
IF(H.GT.CHECK) INDEX=0 1090
1 CONTINUE 1100
RETURN 1110

END 1120

0000000000

10

C

C

C

11

12
C

120

PROGRAM EIGENV (INPUT.OUTPUT) 100
THIS PROGRAM COMPUTES THE EIGENVALUES OF THE FOLLOWING PARAs110
ITE 115
HOST MODEL LINEARIZED ABOUT THE EQUILIBRIUM POINT 120

H(T+1)zH(T)YEXP(-BH(T)/C~o2+H(T)-t2)((1+AP/K)-.-K) 130

P(T+1)-H(T)(1-(1+AP/K)¢o—K) 14o
DATA REQUIREMENTS ARE VALUES FOR ALL PARAMETERS AND EQUILIBR150
IUM 155
DENSITY OF THE HOST POPULATION (K=0 FLAGS INFINITY. Hso FLAG160
S NO 165
EQUILIBRIUM) 170

DIMENSION DC(3).DRK(4).DA(5).DH(3.4.5) 180

DATA (DH(1.1.I).I=1.5)/.66097..7344..85213.1.12039.0.l. 190

+(DH(1.2.I).I=1.5)/.557B..62695..73042..91902.1.53906/. 200
+(DH(1.3.I).I-1.5)/.5127..58156..683..85923.1.32473/. 210
+(DH(1.4.1).I=1.5)/.46903..55793..65866..63137.1.25647/ 220
+.(DH(2.1.1).Is1.5)/.76831..66262.1.02186.1.47663.0./. 230
+(DH(2.2.I).I=1.S)/.61619..69588..81580.1.03479.1.74045/.231
+(DH(2.3.I).I=1.5)/.554B9..63154..74510..94161.1.44326/. 232
+(DH(2.4.I).I-1.5)/.52304..59908..71039..89939.1.34973/. 233
+(DH(3.1.1).I=1.5)/.55807..61367..69655..66409.0./. 234
+(DH(3.2.I).I-1.5)/.49852..55404..64030..79407.1.29533/. 235
+(DH(3.3.I).I=1.5)/.46634..52631..61441..76741.1.16364/, 236
+(DH(3.4.I).I-1.5)/.45033..51133..60064..75400.1.14571/ 237

DATA DA/3..2.5.2..1.5.1./ 270

DATA 06/1 .1 1..9/ 280

DATA DRK/.75.2..6..0./ 290

Y=10. 300

B=3.75 310

DO 1 L-1.3 320

DO 2 M=1.4 330

OO 3 N=1.5 340

FLAGsO. 350

C=DC(L) 360

RK-DRK1M) 370

A=DA(N) 380

H=DH(L.M.N) 390

PRINT 10.C.RK.A.H 400

FORMAT (“0C8 '.F3.1.1X.'K= -.F4.2.1x.-A= '.F3.1.1X.'HOST410

+ EQUILs '.F7.3) 420

IF(H.E0.0.) GO TO 100 430
COMPUTE PARASITE EOUIL. DENSITY 440

FsYtEXP(-B—H/((c--2)+(H-t2))) 450

P=((F-1)/F)'H 460
COMPUTE FOUR TERMS OF MATRIX FOR LINEARIZ MODEL 470

SIGN=-1 480

x=Co-2 490

V=Hoc2 500

T11'(1-(((X-V)’B‘H)/((X+V)*'2)))‘SIGN 510
IF K=INFINITY USE POISSON ZERO TERM 520

IF(RK E0.0 ) GO TO 110 530

w-(AcP/RK)+1 540

T12=HoA/w 550

T21-(1-((1/W)0-RK))'SIGN 560

T22'(((1/W)*t(RK+1))0HtA)°SIGN 570

GO TO 120 571
0 CONTINUE 580

w=-AoP 590

T12-onoSIGN 600

T21-(1-Exp(w))cSIGN 610

T22-H-ExP(w)vAoSIGN 620
0 CONTINUE 621

TERMS OF QUADRATIC EQUATION 630

121

0T1=((T11+T22)/2.)°SIGN 64o
0I1=T11oT22 650
012=T12oT21 660
013=011-012 670
OI4=((0T1¢2)"2)-(49013) 680
IF(QI4 LT 0.) FLAG=1 690
IF(QI4.LT.0.) OI4=014*SIGN 700
0T2-(SORT(QI4))/2 710

PRINT 20.0T1.QT2 720

20 FORMAT('0EIGENVALUES= ”.F7.5.1X.”PLUS AND MINUS”.1X.F7.5730
+) 735
IF(FLAG.EQ.O.) GO TO 3 740

PRINT 30 750

30 FORMAT (“ PLUS AND MINUS TERM IS COMPLEX“) 760
GO TO 3 770

100 CONTINUE 780
PRINT 40 790

40 FORMAT (' NO EOUIL. FOUND. NO EIGENVALUES COMPUTED”) 800
3 CONTINUE B10
2 CONTINUE 820
1 CONTINUE B30

END 840

122

Appendix 5.

 

In this appendix we show why a partial cutting strategy is probably not
compatible with maximizing economic returns with least risk. The return (Rt)
from the sale of a tract of timber at time t is determined by price (Pt) and
volume (Vt):

Rt = P1; ' Vt (1)
We will assume that the only costs associated with growing timber are foregone
returns from immediate harvest of the trees. (The conclusions reached will be
the same even if this is not true). The value (Valt) of a stand at some future

point in time (t) is then given by:
Valt = R1; - R10 el(t-t°) (2)

In (2), Rto are the current returns and i is the interest rate obtained on
investments. The exponential function is used to approximate the future value
of the current stand.

Suppose some proportion (6) of the stand is harvested prior to a budworm

outbreak where 0 _<_ 6 g 1. Then (2) can be written as:

Valt =11 - 5m. +12: -1)Rtoe‘“"°’ <3)
The rate at which the value of the stand increases is given by:

dVal - -

# =11 - 1S) th/dt + (26 -1)iRtoe‘(t t0) (4)

This is a complicated function; however, its general nature can be determined
by evaluating three harvesting policies.
If the complete stand is harvested at time to, then 6 = l, and (4) becomes:
dValt/dt = iRtoei“’t°) (5)
The rate of increase of the stand is equal to the rate of return on an

investment. If it is possible to harvest the stand, this policy entails no risk.

123

If none of the stand is harvested prior to the outbreak, (4) becomes:
dValt/dt = dedt - iRtoeiu—to) (6)
In order that the rate of increase in value be positive, price and volume must
increase in combination at a rate faster than returns are accrued from an
immediate harvest. This is an unlikely situation since the volume of Spruce fir
stands greater than 50 years in age generally increases at a rate less than or
equal to 596 of the present volume (Bowman 1944). This increase may decline
or even be less than zero during a budworm outbreak. It is even more
improbable that this policy will be superior to the first one or:
th/dt > 211:, Oei“‘t°) (7)
If half of the stand is harvested prior to an outbreak, (4) becomes:
dValt/dt = .5th/dt ' (8)
For this policy to be superior to the first one, equation (7) must be satisfied.
Once again, this is unlikely. Therefore, complete presalvage is the best

strategy for maximizing returns and minimizing risks.

124

Appendix 6.

 

FOrm sent to loggers to determine costs and returns of harvests.

Location:
Sale number:

Logger:

 

Please fill in the blanks as accurately as possible. write an (X) by
those estimates you consider to be very rough estimates.

A. wages
1. Number of people employed in the harvest of this sale area
2. Number of days spent working in this area

3. Hourly wage rate and total 'man-hours' worked at each rate

 

waze rate total hours wage rate t0tal hours
1) 4)
2) S)

3) 6)

A. Insurance cos: (Workman's Comp.)

5. Other wages:

3. Equipment

1. What equipment was used to harvest this sale area?
a)
b)
c)
d)
e)

 

 

 

 

 

Please itemize costs 2-6 for each equipment item above:

2. Investment in equipment (original cost)
a) d)
b) e)
c)

 

 

 

125

3. Fuel cost

 

 

 

 

 

 

 

 

 

a) d)
b) - e)
c)

4. Maintenance cost
a) d)
b) e)
c)

 

5. Insurance cost (for equipment)

 

 

 

 

 

 

 

 

 

a) d)
b) e)
C)
6. Depreciation charged to equipment per year
a) g ' d)
b) e)
c)

 

7. Scheduledoperating hours:

 

8. Approximate down-time in Z

 

Transportation
1. Road-building cost (if any)

 

2. Other costs in this category:

Revenues

1. Name and location of mill(s) that sawlogs, pulpwood. or chips were sold to:

 

 

 

2. Total volume removed (mill scale)

 

:roduct volume value
pulpwood

sawlogs

other,

3. Other revenues:

Appendix 7.

 

126

Bird census data for stands 1, 2 and 3.

LE: 10 use 6.....0055 -----
AF - Alder Flycatcher OB - Ovenbird
nrw - Block and white warbler PF - Purple Finch
88 - Blackburnian warbler (or 8H) PS - Pine Siskin
BC - Brown Creeper PH - Palm warbler
BCC - Biack Capped Chicadee (or CD) PwP - Pileated Hbodpecker
BHC - Brown Headed Cowbird R - Robin
RT - Bittern R86 - Rose Breasted Grosbeak
ETC - Black Throated Green Nlrbler RBN - Red Breasted Nuthatch (or NH)
83 - Blackburnian warber (or 83) REV - Red Eyed Vireo
CHw - Cape May warbler RG - Ruffed Grouse
CS - Chipping Sparrow RS - Red Start
SCH - Chestnut sided warbler SS - Song Sparrow
CYT - Common Yellow Throat (or YT) ST - Scarlet Tanager
Dw - Downy whodpecker SV - Solitary Vireo
EP - Eastern Pheobe TH - Tennessee Warbler
EWP - Eastern Hbod Peewee V - Veery
F - Flicker RC - Hbodcock
GCK - Golden Crowned Kinqlet HT - “bod Thrush
HT - Hermit Thrush HTS - white Throated Sparrow
HwP - Hairy Hbodpecker ww - winter wren
la - Indigo Bunting YBC - Yellow Billed Cuckoo
MGR - Haqnolia warbler YBSS - Yellow Bellied Sapsucker
MW - Hourning Warbler YRH - Yellow Rumped warbler
NH - Nuthatch (or RBN) YT - Common Yellow Throat (or CYT)
NH - Nashville warbler
Legend for 81rd Slghtlng Maps

aa - One sighting

aas - Two sightings

aase- Territory confirmed

Methods: The bird census was conducted by mapping singing males.

This was done by transacting each plot on 6-1, 6—3 and
6-4, 1981.

Stand 1.

127

 

 

 

 

 

 

 

 

Cut
83
NW
NW. BTGeaeTw
0 MW,“ BWee
NWee 3” REVee
ww '/ "3‘3 08st
BTWee F-
as
Vee oaee
0300 80000 gtwe RE awee 7w.
BWee
OB 0*
WWee fl» [WW
.... ..m asi/Eh)
‘I’ag Alder Swamp
--severai White Throated Sparrows
Dist. in chains in cut area
I l l l 1
fi I T I 1
O 1 2 3 4
Control
GCK
RBGeO

   
 
 

99>
18106 e

113......

Dist. in chains

1 l l
I I l

i
0 1 2 3

 

 

 

 

Stand 2.

128

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HIV
0.
“a
mgi/1 ”"'
1 ......
Hie 'F9.
IWee'.
ES
lIee
9 0.00
V I0
810D.
III ee
0600'
0.0. ’ lflee
IEVee
IDWOe
OW WWee
”use eeeeeaet While Tamales teens-e
Io eat areas and several acre linen”
Diet. In chains
6 1 I s 4
Control
RBO “7 '
88
NWO e
03“ aw-
NWe s
08‘ Va
800
08“
EWP
ROAD
Radio a
1 WW
BTGOe
$333 w ....
Dist, in chains
l 1 l 1 I
f r I I 1
0 1 2 3 4

 

 

Cut

Stand 3.

129

 

 

 

 

 

 

 

 

 

 

 

CLEAR CUT
R60 ‘
S ‘—*\_m
Nw Ref 3°C“ "w
CMW
ww
oats
CUT CUT 03 ‘ ’
Recs
”“5. WWO. SV‘.
REV. 1:180"l
BHCa
YRWOO NW.a
08cc
88w R
860
08 BHCee
WW ”3 NW 1
a-q ROAD

 

--iarge numbers 01 Evening Grosbeeha
and White Throated Sparrows

Diet. in chains
l l l l J
l l I l I

O 1 2 3 4

 

 

 

Control

816 WW

OBss 88..
08"
GCKes

BTGO RBGs

NW“ YRW

NHs s p3 ww
88st MWss V

NWO
ww 08. t __1
MW

 

 

 

 

Dist. in chains
I 1 l
l l I

: r
O I 2 3 4

 

 

 

Cut

 

130

W-

The malaise traps and method presented for analyzing data collected by
these traps can be used with other parasitoids. It may be necessary, though, to
base the model on the daily activity of these animals. This was unnecessary with
Q. fumiferanae attacking spruce budworm because most adult activity occurred
during an identifiable part of the day. As a result, average temperature and
total rainfall during this time period were good measures of adult activity.

Data on _G_. fumiferanae attacking jack pine budworm (Elliot, unpubl.)

indicate that, in this habitat, Q. fumiferanae is active throughout the day (fig.

 

25). When this data and appropriate weather information (table 15) were
inserted in the model, a poor fit was obtained. One reason model parameters
could not be fit to this data was that rain often fell for only part of the day
while the rest of the day was conducive to parasitoid activity (i.e., 1068 DD and
1091 DD, table 15). This did not happen in the spruce fir habitat. In order for
the model to work, weather (or other influencing variables) and trap catch must
be assessed at regular intervals throughout each day. The part of the model
which predicts adult parasitoid density will still be appropriate, but activity must
be modeled as a convolution of density, intrinsic activity patterns (if any), and
factors (i.e., weather) which influence activity.

The inability of the model to describe the data collected on Q. fumiferanae
in jack pine does not contradict the idea that parasitoid activity patterns are
strongly influenced by weather. This data was collected from two locations and
is plotted as a function of degree days (base 83°C) in figure 26. The pattern of

trap catch is similar in both plots. This similarity can be evaluated statistically.

 

131

Let xl(i) equal 1 if the trap catch on day i is greater than the catch on day
i-1, and 0 if it is less in one of the two locations. The variable x2“) is defined
similarly for the other location. No pattern is expected between x1 and x2 when
adult parasitoid density is relatively constant if weather does not influence trap
catch. If xl(i) and x2(i) are equal then let x126) be 1, and 0 otherwise. The
variable xt, defined as the summation of x120) over i, is a binomial random
variable. A test of a relationship between x1 and x2 is whether p of this
distribution equals 0.5. Ignoring trap catch prior to c. 7096 emergence of the
adult female parasitoids (< 1037 DD) and the tail end of trap catch (> 1477 DD)
x t = 17 and the sample size (N) = 23. Using a one-sided test (we expect p > 0.5)
the probability of this occurring is .017 (p(x t Z. 17); x t " (B, N = 23, p = .5)). The
null hypothesis (p = 0.5) is rejected. Hence, the pattern of trap catch in the two
locations is similar, which suggests that weather influenced Q. fumiferanae's
adult activity. This is reinforced by the observation that the dramatic decline in

parasitoid activity at 1263 DD was accompanied by prolonged cool, wet weather.

 

 

Proporfion

132

Upper Crown

Lower Crown

 

800 1200 1600 2000 800

Hours

Figure 25. Proportion of total malaise trap catch of female Glypta
fumiferanae for 7 time intervals within a day. The sample
period was 6 days (7-19 to 7-24). One trap was located in 48

jack pine trees. Twenty four traps were in the upper crown
and 24 in the lower crown. Data collected by N. Elliott in

Grand Traverse C0., MI.

 

133

Table 15. Malaise trap catch of female Glypta fumiferanae from two plots
and weather data in 1982. One trap was located in 24 jack pine
in each plot. Twelve traps were in the Upper crown and 12 in
the lower crown. Data collected by N. Elliott in Grand Traverse

 

 

Co., MI.
Julian Degree Days Malaise Trap Catch Temperature1 Precipitation2
Date Base 8.90 C. 1 2
191 924 0 1 25.78 .97
192 938 0 0 16.85 .58
193 955 2 4 20.78 0
194 972 4 12 25.63 0
195 991 10 11 23.74 .03
196 1012 22 28 27.21 0
197 1037 35 15 29.67 0
198 1068 14 30 27.15 7.85
199 1091 45 28 23.71 .76
200 1106 28 19 20.44 0
201 1122 33 25 21.71 0
202 1137 54 38 24.56 0
203 1160 40 31 22.89 0
204 1181 64 30 24.37 0
205 1200 92 54 26.74 0
206 1225 41 43 26.11 .03
207 1249 35 24 22.29 .03
208 1263 4 3 18.07 1.04
209 1276 9 9 21.82 0
210 1289 25 4 23.41 0
211 1309 39 25 21.33 0
212 1329 27 17 22.71 0
213 1350 ‘20 20 23.26 0
214 1369 14 8 20.37 0
215 1392 28 22 24.26 0
216 1416 10 14 20.74 0
217 1435 13 11 22.11 0
218 1455 11 6 23.52 0
219 1477 19 9 26.29 0
220 1498 6 2 24.48 0
221 1510 2 15.48 .08
222 1517 5 1 15.93 0
223 1528 0 l 17.89 0
224 1537 l 1 19.48 0
225 1551 0 0 21.67 0

1average oC between 800 and 2200 hours

2
total precipation in cm. between 800 and 2200 hours

134

 

Catch of 9 Glypta. fumiferanae

   

 

' T f l I l
900 1000 1100 1200 1300 1400 1500 1600

 

 

 

Degree Days Bose 8.9' C

 

Figure 26. Malaise trap catch of female Glypta fumiferanae from two plots
in relation to degree days base 8.90C. in 1982. One trap was
located in each of 24 jack pine in each plot. Twelve traps
were in the upper crown and 12 in the lower crown. Data
collected by N. Elliott in Grand Traverse Co., MI.

135

Appendix 9.

Spruce budworm population estimation data from forest harvesting study

9.1

Egg mass densities in stands 1 and 3.

Description by columns; l-stand, 2-treatment; (1) cut, (2) control, 3-blank,
4 and 5-tree, 6-blank, 7-branch, 8-blank, 9-species; (l) balsam fir, (2) white
spruce, lO-blank, 11 through l4-branch surface area (cmz), l5-blank, 16
and l7-hatched egg masses, 18-blank, 19 and 20—parsitized egg masses.
Repeat 3 times.

Early and mid instar densities in stands 1, 2 and 3.

Description by column: l-stand, 2-treatment; (1) cut, (2) control, 3-sample
number, 4-blank, 5 through 7-date, 8-blank, 9 and lO-tree, ll-branch, 12-
blank, 13 and l4-budworm, 15 blank, 16 through l9-branch surface area
(100 cmz). Repeat 2 times.

Late instar, pupal and adult densities in stands 1, 2, 3.

Description by columns: l-stand, 2-treatments; (1) cut, (2) control, 3-
sample number, 4 and 5-tree, 6-blank, 7-branch, 8-blank, 9 and lO-branch
surface are (100 cm2), ll-blank, lZ-defoliation of all foliage; (0) 0-20%, (1)
21-4096, (2)41-6096, (3) 51-8096, (4)81-10096, l3-defoliation of new foliate
(same ranldng), l4-b1ank, 15 and 16-adults, l7-blank, lB-parasitized pupae,
l9-blank, 20-pupal mortality (unknown cause), 21-blank, 22 and 23-
Meteorus trachynotus pupae, 24-blank, 25-9, fumiferanae pupae, 26-blank,

27-Apanteles fumiferanae pupae, 28 and 29-blank, 30 and 3l-total budworm

 

at time of sample, 32-blank, 33 and 34-larvae at time of sample, 35-blank,
36 and 37-parasitized larvae, 38-blank, 39-larval mortality (unknown

cause). Repeat.

 

N U

“““
““““““
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0750
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0800
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M
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”NM”-~‘-fi“‘fi‘d-fid““d~”~NNM-fi‘““dan...“d‘—t““““-fi‘ub-h-O“‘N~N

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1050
2600
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1400
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136

 

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CAI-Ac.d““-ficfi~h““ufid‘dufifl““‘AA‘A‘MMMNMMMNMMNMM
am“...a‘-s.a-a..

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1200
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1700
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1900

taro—1.110.410

0900
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1800
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1500

 

 

9.2

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00000000000000000000060000000000006

 

 

 

9.2

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.0 lo .0 Cm 0 0 0 0 0 O I 0 0 M I 0 0 . 0 0 0 C O I 0 Q 0 0 0 I O I C 0 I I 0 O 0 I C 0 I D
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34.

 

9.2

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139

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021

moomomoooomooooooooooo00000000000000

 

 

903

11101
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140

 

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12102
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9.3

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32101
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143

APPENDIX 10

Record of Deposition of Voucher Specimens*

The specimens listed on the following sheet(s) have been deposited in
the named museum(s) as samples of those species or other taxa which were
used in this research. Voucher recognition labels bearing the Voucher
No. have been attached or included in fluid-preserved specimens.

Voucher No.: 1982—4

 

Title of thesis or dissertation (or other research projects):

Studies Related to the Concept of Pest~- CrOp System Design:
1) Adult Parasitoid Activity and Its Relation to Biocontrol and
2) Forest Harvesting and the Spruce Budworm

Museum(s) where deposited and abbreviations for table on following sheets:

 

Entomology Museum, Michigan State University (MSU)

Other Museums:

 

Investigator's Name (6) (typed)

 

Jan Peter Nyrop

 

 

Date 11-13-82

 

*Reference: Yoshimoto, C. M. 1978. Voucher Specimens for Entomology in
North America. Bull. Entomol. Soc. Amer. 24:141-42.

Deposit as follows:

Original: Include as Appendix 1oin ribbon copy of thesis or
dissertation.

Copies: Included as Appendix lOin copies of thesis or dissertation.
Museum(s) files.
Research.project files.

This form is available from and the Voucher No. is assigned by the Curator,
Michigan State University Entomology MUseum.

144

APPENDIX 10 . 1

Voucher Specimen Data

1 of 1 Pages

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LITERATURE CITED

 

145

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1"!

 

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21.111

 

 

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