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Aggressive mimicry in the Pirate Spider, Mimetus notius (Aranae; Mimetidae)

By

Carl T. Kloock

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Zoology and Division of Ecology, Evolution and Behavioral
Biology

2000

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ABSTRACT
Aggressive mimicry in the pirate spider Mimetus notius (Aranae; Mimetidae)
By

Carl T. Kloock

Aggressive mimicry has long been an ignored aspect of the phenomenon
of mimicry. A literature review is carried out which determines that current theory
developed to help understand protective mimicry does not apply to aggressive
mimcry. A new modeling paradigm, based on a combination of an optimal
foraging model (the flu criterion) and signal detection models is developed to try
to aid our understanding of aggressive mimicry systems. A representative
aggressive mimic, the pirate spider Mimetus notius, was chosen for developing
and testing this paradigm. The natural history of this spider was virtually
unknown, so basic natural history data was collected and is presented. This data
leads to the identification of Then'dion sp. as the most common prey and victim of
aggressive mimicry. Measurements of the response of Then'dion sp. to a variety
of organisms in the web were conducted, and the signals emitted by each of
these organisms were also measured. These measurements lead to the
conclusion that M. notius does not mimic prey, but mimics small invading spiders.
This information is used to develop a species-specific model based on the
modeling paradigm developed previously, and this model is tested using a

combination field/laboratory experiment. The model accurately predicts the level

of cautiousness displayed by Then'dion in a variety of sites varying in the
abundance of Then'dion and Mimetus. These predictions serve to validate, in
part, the new modeling paradigm, and give confidence that the predictions of
simpler, more general models developed within this paradigm can be used to
increase our understanding of aggressive mimicry and the perceptual

interactions between predators and prey in these systems.

Copyright by

Carl T. Kloock
2000

 

nl

This dissertation is dedicated to my wife, Jennifer White-Kloock and my parents,
Marilyn and Peter Kloock. Without their unswerving support and confidence in
my abilities, this dissertation would never have been completed.

ACKNOWLEDGMENTS

I would like to express my appreciation to the following people and
organizations for their aid throughout my research.
Committee members:
Tom Getty, Cathy Bristow, Fred Dyer and Alan Tessier
Administrative Guidance:
Char Adams, Alice Gilespie and Sally Shaw
Undergraduate assistants:
Renata Zappala, Rose Bryan
Expert spider assistance:
Mark Stowe, Robert Jackson, Daniel Mott, Stim Wilcox, Gary Polis, Richard
Snider
Mathematical advice:
Tom Getty, Andy Sih
Providing access to Field sites: Kellogg Bird Sanctuary, KBS LTER Site,Lux
Arbor reserve, Kellogg Forest, Kalamazoo Nature Center, Michigan DNR,
Barry State Game Area, Mr. and Mrs. J. Pruess, and Mr. and Mrs. H.
Vander Horst
Aid in too many ways to detail:
Nina Consolatti, Tom Getty, John Gorentz, Kay Gross, Carolyn
Hammarskjold, Mike Klug, Greg Kowaleski, Steve Norris, Mary Stage, Phil

Brownell

vi

KBS Grad Students, for uncountable discussions, and patience in listening to me
rant and rave about spiders and other aggressive mimics.

Puja Batra, Jeff Birdsley, Brian Black, Laura Broughton, Andrea Corbett,
Natalie DuBois, Jeff Dudycha, Bryan Foster, Becky Fuller, Kevin Geedey,
Casey Huckins, Melissa McCormick, Rob Olendorf, Jessica Rettig,
Elizabeth Smiley, Stephanie Whitmire

Babysitting
Rob, Laura, Coben, Noelle and Amanda Ashley
Funding:

American Arachnological Society Fund for Arachnological Research,
November 1996 and July 1997.

Sigma Xi Grant-in-aid of research, July 1997.

G.H. Lauff Research Award, July 1994 and July 1995.

Michigan State University Zoology Department Research Fellowship, April
1995.

National Science Foundation Research Training Group Graduate Fellowship,
May 1993-August 1997 at the WK. Kellogg Biological Station, Michigan

State University.

vii

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TABLE OF CONTENTS

List of Tables

List of Figures

List of Abbreviations

Introduction

Chapter 1: An overview of aggressive mimicry systems
Introduction
Methods
Results
Discussion
Literature cited
Tables
Figures

Chapter 2: Aggressive mimicry: a new theoretical approach to
a long-ignored phenomenon.

Introduction

The modeling scenario

Combining signal detection theory with the flu criterion.
Simulations

A correlative analysis

Discussion

Literature cited

Tables

Figures

Chapter 3: Natural history of Mimetus notius and signal
sources in prey webs.

Introduction
Study species
General field methods

viii

xi
xii
xix

28

28
30
33
36
40
43
47
51
53

65

65
67
67

Se
Ve
Mir
Pre

 

 

Seasonality and life cycle 71

Vegetation preferences 73
Mimetus notius diet 73
Predatory efficiency 75
Signal sources in Then'dion webs 79
General discussion 82
Literature cited 83
Tables 85
Figures 87
Chapter 4: Determining the model(s) in the Mimetus notius 99
aggressive mimicry system.
Introduction 99
Methods 1 01
Results 1 05
Discussion 109
Literature cited 1 13
Tables 1 15
Figures 117
Chapter 5: Foraging under threat from the aggressive mimic 125
Mimetus notius.
Introduction 125
The Species-specific model 126
Parameter Estimates 127
Simulations 128
Simulation Results 129
Experimental test 130
Methods 1 30
Results 1 35
Discussion 1 37
Literature cited 141
Tables 142

Figures

Appendices
Appendix 2.1 -- Solving the general model
Appendix 2.2 -- MATLAB program: prey-based model
Appendix 2.3 - The criteria for switching curve shapes

Appendix 5.1: - Development of the species specific model for
Mimetus notius

Appendix 5.2.: A representative Matlab© program simulating
variation in the parameter W, the probability of winning
against an invader

144

174
174
176
177
179

183

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LIST OF TABLES

Table 1.1 Proposed Aggressive Mimicry Systems.

Table 2.1. Proposed aggressive mimicry systems involving food or mates.
Table 3.1. Mimetid encounters.

Table 3.2. Theridion prey collected from webs in 7 sites in September of 1997.
Table 4.1. Theridion response data.

Table 4.2 Signal data in Theridion webs

Table 5.1. ANOVA results for test of local adaptation

Table 5.2. Test of Model: predicted cautiousness predicts observed risk index Vs
Mimetus.

xi

(U

 

LIST OF FIGURES

Figure 1.1. Selection on models and mimics in Batesian and MUllarian mimicry
systems. In Batesian systems, a dupe attacks and kills models and
mimics based upon their appearance. The dupe must discriminate
palatable mimics from unpalatable models, which it avoids. The more
similar a mimic is to a model, the more likely it is to be mis-identified as a
model and avoided, so it receives more protection from its appearance,
and mimics are selected to look more like models. On the other hand, the
more a model resembles a mimic, the more likely it will mis-identified as a
mimic and consumed. This selects for models whose appearance
diverges from that of mimics. In Mullerian systems, a dupe also attacks
and kills models and mimics based upon their appearance. In this case,
however, both models and mimics (aka co-mimics) are unpalatable.
Predators tend to avoid the common mean, so that individual prey at the
extremes of the combined distribution are more likely to be killed, selecting
for models and mimics that more closely resemble one another..

Figure 1.2. Selection in aggressive mimicry systems based on analogy with
Batesian and Mullerian mimicry systems. In systems in which the model
is banned, dynamics similar to that seen in Batesian mimicry are
expected. In these cases, for example when mimics mimic mates, a dupe
is attempting to discriminate from a model which benefits when it is found
and a mimic which will harm the dupe. Models similar in appearance to
the mimic will be avoided by cautious dupes, driving selection of models
away from similarity with mimics. In systems where the model benefits,
such as when prey are mimicked, the situation is analogous to that seen in
MiJIlerian systems. In this instance the dupe must discriminate between a
mimic and a model which is harmed by the dupe. In this case, models
whose appearance is similar to the mimics will be more likely to be
avoided, thus increasing their fitness.

xii

Figure 2.1. Relationship of an ROC curve to the underlying distributions. Panel
A illustrates hypothetical overlapping distributions of cues from safe and
dangerous resource populations. A threshold criterion (c) divides the safe
distribution into misses below c and hits above c. The probability of a hit
given a response to cues 2 c is H, given by the area under the curve to the
right of c (shaded with horizontal lines). The same criterion divides the
dangerous distribution into correct rejections and false alarms with
corresponding probability F (vertical lines). The resulting values of H and
F are plotted as the point c on the corresponding receiver operating
characteristic (ROC) curve in panel B. Two alternative criterion points, d
and e, are also shown with corresponding points in ROC space. The ROC
curve traces out, from upper right to bottom left, the possible combinations
of H and F that would result from moving the criterion from the minimum
(left) to the maximum (right) in pane A. The ratio H/F decreases from the
lower left to the upper right along the ROC curve. Lower values of H/F, at
the upper right of the ROC curve, correspond to a low criterion and
indicate a bold forager (point (I). Higher values of H/F, at the lower left of
the ROC curve, correspond to a high criterion and indicate a cautious
forager (point e).

Figure 2.2. Hit (dashed) and False alarm (solid)probabilities with respect to the
difference between distribution means, in units of standard deviation when
DOPOA

<1, based on simulations for prey mimicry.
SOVom

Figure 2.3. Hit (dashed) and False alarm (solid) probabilities with respect to the
difference between distribution means, in units of standard deviation when
DOPOA

<1, based on simulations for prey mimicry.
SUV-m

xiii

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Fig lie

 

Figure 2.4. Trajectory of dupe response to increasing model/mimic similarity.
When no mimicry is present, dupes can (and should) operate at the point
(0,1) in ROC space. When mimic resemblance to models is perfect (Solid
ROC along the line H=F), a opposite strategies are optimal depending
upon whether D-P-A/S-V-m >1, where the operating point (0,0) is optimal,
or D-P-AIS-V-m <1, where the operating point (1,1) is optimal. The three
intermediate ROC curves {dashed curves traversing the distance from
(0,0) to (1,1)} show the optimal operating points at intermediate values of
signal overlap, and demonstrate how dupes should change their
responses for different levels of similarity between models and mimics
depending upon the value of D-P-A/S-V-m. The upper trajectory is favored
when D'P-A/S-V-m <1, and the left-hand trajectory is favored when
D-P-A/S-V-m >1. This results in two adaptive regions in the ROC curve
and explains the difference between figures 2.2 and 2.3. The shape of
these trajectories is what drives the hump that is seen in F in figure 2.3
and the dip that is seen in H in figure 2.2.

Figure 2.5. The potential tradeoff between individual and group fitness. Each
solid line represents a separate population of mimics, the dashed line
goes through the mean similarity of each population. In this situation, the
fitness of mimics within a population is a function of both the individual's
similarity to the models and the population average similarity to models.
Individual fitness always increases with increasing similarity within a
population, but the same level of similarity in two different populations may
yield very different fitness in absolute terms. In this way, an individual with
low similarity can have a higher fitness than a nearly perfect mimic, if it is
in a population of low average similarity. This is the situation mimics find
themselves in with faced with the dupe response curve depicted in figure
2.3.

Figure 2.6. Hit (dashed) and False alarm (solid) probabilities with respect to the
difference between distribution means, in units of standard deviation.
From simulations based on mate mimicry.

Figure 3.1. Mimetus notius seasonal abundance across four sites in A) 1995 and
B) 1996.

Figure 3.2. Seasonal abundance of all spiders across four sites in A) 1995 and
B) 1996.

Figure 3.3. Seasonal abundance of Theridion across four sites in 1995 and
1996.

xiv

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Figure 3.4. Seasonal representations of adult and juvenile mimetids, summed
across all sites for 1995. The total number (n) for each sample is given
above the bar.

Figure 3.5. Potential signal sources in Then'dion webs, 1996, seasonal.
Absolute number and percentage of all signal sources (n=194). Data
pooled from 4 sites censused monthly, April-October, 1996. Prey were
included only when found actually being fed upon by Theridion.
Percentages given are of all potential signal sources in 1996.

Figure 3.6. Potential signal sources in Theridion webs 1997, aseasonal.
Absolute number and percentage of all signal sources (n=297). Data
pooled from 7 sites censused once each, September, 1997. All prey in
Theridion webs were collected during census. Potential mates are not
included because these censuses took place outside of the mating
season. Percentages given are of all potential signal sources in 1997.

Figure 4.1. A representative signal series from a M. notius in a Theridion web.
The recording was made on the audio track of a videotape and decoded
using CANARY© (Cornell Bioacoustics Research Program 1994). The
upper panel shows a frequency spectrum derived from the signal trace in
the lower panel. Important measurements are also shown. A=Frequency
of peak power (a.k.a peak Hz); B=interbout (>1 sec between initiation of
one pulse and the next); C=interpulse (<1 sec between initiation of one
pulse within a bout and the next); D= Bout length (time from the initiation
of the first pulse in a bout to the initiation of the last pulse in the bout. In
this example the interpulse duration and the bout duration are identical
since there are only two pulses in the bout shown.

Figure 4.2. Biplot of ratios of qualitative variables involving Theridion response.
The x-axis displays the type of first response, either signal or locomotion,
in % of Theridion whose first response was to locomote. The y-axis
displays the first locomotion, either approach or retreat, in % of theridion
whose first locomotion was an approach. Since these are percentages
with small sample sizes, nor error bars are shown.

Figure 4.3. Biplot of the qualitative variables of Theridion response, average
approach speed per movement and distance at first approach. Neither of
these variables were normally distributed. Therefore the plot displays
median values with error bars as 25% and 75% quartiles.

XV

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Figure 4.4. Biplot of signal variables with significant differences between M.
notius signals and other web "visitor's signals - residual peak Hz and bout
length. Data are normally distributed. Points represent averages and error
bars give standard errors.

Figure 5.1. Distributions of bout length measurements for Theridion (solid line)
and Mimetus (dashed line). The mean Then'dion value was 3.6 seconds,
the mean Mimetus value was 2.1 seconds. The pooled standard deviation
was 1.7

Figure 5.2. The Receiver Operating Characteristic (ROC) curve corresponding to
the distributions presented in figure 5.1

Figure 5.3. Response of (HIF). to variation in Fw, the feeding rate while on the
web. The value at standard conditions (open triangle) and the observed
range of the indicated parameter (dashed vertical lines) is provided. The
value of H/F at standard conditions was 6.73. The lower limit of H/F is 1,

and the curves are indicated from 1 (if reached) until just before (H/F)'=oo
(F=0).

Figure 5.4. Response of (HIF). to variation in Em, the encounter rate with
Mimetus. The value at standard conditions (open triangle) and the
observed range of the indicated parameter (dashed vertical lines) is
provided. The value of H/F at standard conditions was 6.73. The lower
limit of H/F is 1, and the curves are indicated from 1 (if reached) until just
before (HIF)'=oo (F=0).

Figure 5.5. Response of (HIF). to variation in K, the probability of dying given an
attempt to defend against Mimetus. The value at standard conditions
(open triangle) and the observed range of the indicated parameter
(dashed vertical lines) is provided. The value of H/F at standard
conditions was 6.73. The lower limit of HIF is 1, and the curves are
indicated from 1 (if reached) until just before (HIF)'=oo (F=0).

Figure 5.6. Response of (HIF). to variation in W, the probability of retaining a
web given defense against a Theridion invader. The value at standard
conditions (open triangle) and the observed range of the indicated
parameter (dashed vertical lines) is provided. The value of HIF at
standard conditions was 6.73. The lower limit of HIF is 1, and the curves
are indicated from 1 (if reached) until just before (H/F)'=oo (F=0).

xvi

Figure 5.7. Response of (HF) to variation in m, the background mortality rate.
The value at standard conditions (open triangle) and the observed range
of the indicated parameter (dashed vertical lines) is provided. The value
of H/F at standard conditions was 6.73. The lower limit of HIF is 1, and
the curves are indicated from 1 (if reached) until just before (HIF)'=oo
(F=0).

Figure 5.8. Response of (H/F)‘ to variation in E, the encounter rate with
Then'dion invaders The value at standard conditions (open triangle) and
the observed range of the indicated parameter (dashed vertical lines) is
provided. The value of H/F at standard conditions was 6.73. The lower
limit of HIF is 1, and the curves are indicated from 1 (if reached) until just
before (HIF).=oo (F=0).

Figure 5.9. Response of (H/F)’ to variation in Tn, the time to inhabit a new web.
The value at standard conditions (open triangle) is provided. No range is
provided since systematic observations of this variabler were not made.
The value of HIF at standard conditions was 6.73. The lower limit of H/F
is 1, and the curves are indicated from 1 (if reached) until just before
(H/F)'=oo (F=0).

Figure 5.10. The response of the model detailed in equation 5.1 to variation in
the difference between cue distributions. Since each new difference
requires a new ROC, (H/F) is not a reliable indicator of relative
cautiousness, so H (solid line) and F (dashed line) at the maximum f/p are
plotted separately. Due to scale differences, H is plotted on the left hand
Y-axis and F on the right hand Y-axis.

Figure 5.11. Residual condition index of Theridion (1 Standard Error) by block
and predicted cautiousness of home site. Spiders from incautious sites
are expected to have higher condition indices. An ANOVA shows a
significant interaction between interaction date and predicted
cautiousness. Examination of this figure shows that the significant
differences are due entirely to the effect of the middle pair of sites.

Figure 5.12. The risk index of Theridion (a: Standard Error) killed vs. surviving
against Mimetus in the unpaired site. A separate variances t-test of risk
index vs. survival shows that the risk index accurately reflects the mortality
risk of Theridion (p=0.03; mean risk index of eaten Theridion=0.864,
SD=0.560, n=6; mean risk index of Theridion surviving=0.188 SD=0.344,
n=26)

 

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Figure 5.13. Test for local adaptation between Theridion and Mimetus. Sites are
broken up into seasonal blocks by relative interaction dates: early, middle
and late. Within each block are four conditions, representing the four
pairings of Mimetus and Theridion by sites within the pair. The four
groups within each block are: both Theridion and Mimetus from the site
where Then'dion was predicted to be cautious; Then'dion from the site
where they are expected to be cautious paired with Mimetus from the site
within the block where Theridion were predicted to be incautious;
Theridion from the site where they are expected to be incautious and
Mimetus from the site where Theridion were expected to be cautious; Both
Theridion and Mimetus from the site where Theridion were expected to be
incautious. The only significant effect in the complete ANOVA was the
seasonal block (p=0.025; see table 5.2 for complete ANOVA table). As
can be seen from the figure, Then'dion in the early season block were
generally less cautious than Theridion later in the season.

Figure 5.14. Risk index of Theridion versus Mimetus (:I: Standard error) from
each site, grouped by interaction date and predicted cautiousness. An
ANOVA demonstrates a significant difference in the risk index of Theridion
from Cautious Vs. incautious sites (p=.021, one-sided). The sample size
(n) is given under each bar.

Figure 5.15. Risk index of Then'dion versus invading Theridion (1: Standard error)
from each site, grouped by interaction date and predicted cautiousness.
An ANOVA demonstrates no significant difference between the risk index
of Theridion from cautious Vs. incautious sites (all p's >0.5). The sample
size (n) is given under each bar.

xviii

LIST OF ABBREVIATIONS

Chapter 2.

A = the background rate of harvesting alternative resources.
C = the probability of successfully harvesting resource from the risky opportunity.
D = (1 - S) = the probability that the risky resource is dangerous.

F = the probability of accepting the opportunity, given that it is dangerous (a false
alarm).

H = the probability of accepting the opportunity, given that it is safe (a hit).

K = the probability of being killed given an encounter with a risky resource.

m = the background rate of mortality.

P = the probability of being killed, given acceptance of a dangerous resource.
R = the rate of encountering the risky opportunity.

S = the a priori probability that the risky resource is safe.

V = the value of a successfully harvested resource.

Chapter 5.

E5=Encounter rate with invading Then'dion.
Em=Encounter rate with Mimetus.

F=Probability of a false alarm.

ftotaFOverall feeding rate.

fw=Foraging rate while on web.

H=Probability of a Hit.

HIF, (HIF)'=Cautiousness and optimal cautiousness (').
K=Probability of being killed given defense against M. notius.
m=Background mortality rate.

Po,.=Probability of leaving web due to an invader.
Po,m=Probability of leaving web due to M. notius.
Tn=Time to locate a new web.

Toj=Time off of web due to invaders.

To,m=Time off of web due to M. notius.

xix

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Tw=Time spent on web.

W=Probability of successful web defense given defense against Theridion
invaden

p=Mortality rate.

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INTRODUCTION

The phenomenon of aggressive mimicry has a long history of study, but
most of that study has been anecdotal in nature. There has been no
comprehensive study of aggressive mimicry. This dissertation aims to develop
some general theory about the patterns and processes that occur within and
across aggressive mimicry systems. The approach used is threefold. First, in
chapter one, the many anecdotal accounts of aggressive mimics are collected,
and general patterns among these diverse organisms are described. Second, in
chapter two, a new modeling system is developed that combines life history
theory, in the form of the u/g and flu criteria, and signal detection theory. This
results in an optimal foraging model that combines the risk of death and
perceptual uncertainty, the two most important aspects of foraging under threat
of an aggressive mimic. Finally, the last three chapters of the dissertation focus
on developing the data needed to use this new theory, including basic natural
history (chapter three) and measurement of signal properties and responses
(chapter four) of a forager to an aggressive mimic, Mimetus notius (Aranae,
Mimetidae). All of the information is brought to bear in a comprehensive
experiment presented in chapter five, where the new modeling system is used to
develop a species-specific model of foraging under threat of predation via
aggressive mimicry by Mimetus notius. This final chapter draws together
information from each of the previous chapters to show that the new modeling
system can be used to predict the cautiousness of foragers in a variety of

community settings. More importantly, this limited validation allows us to use the

model to explore the implications of aggressive mimicry on the behavior of their
prey, and look at some potential long-term ramifications of this mode of

predation, increasing our understanding of the dynamics of these systems

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Chapter 1

AN OVERVIEW OF AGGRESSIVE MIMICRY SYSTEMS

Introduction

"To many workers, especially theoretical modelists, 'mimicry' means only one
phenomenon: Batesian mimicry, the very name of which has obscured the fact that Bates

([1861]) described different kinds of mimicry" — Georges Pasteur (1982: 169).

Eighteen years ago, Georges Pasteur bemoaned the lack of theoretical work on
mimicry systems other than Batesian mimicry. Since that time, very little has been done
to change the situation. Theoretical work has included Miillerian mimicry, but the many
other types of mimicry categorized by Pasteur (1982) have remained unexplored by
theoretical biologists, largely due to the paucity of empirical work. Although several
good reviews of general mimicry phenomena exist (Wickler 1968, Vane-Wright 1976,
Pasteur 1982, Starrett 1993), these have focused on classification rather than the
development of theory. Classification is an important first step in understanding any
system, but so far no progression beyond this stage has occurred for non-protective
mimicry. Here I will refine the current categorizations to better address the important
phenomenon of aggressive mimicry. In addition, I will determine whether predictions
based on theory derived from study of Batesian and Miillerian mimicry can be used to aid
our understanding of aggressive mimicry systems.

To begin, it is necessary to present an operational definition of aggressive

mimicry. For the rest of this work the following definition will be used:

Aggressive mimicry occurs when one organism (the mimic), via a
resemblance to a model, directly reduces the fitness of another

organism (the dupe) that actively responds to the model.

This definition roughly combines Vane-Wright's (1976) " Class II, synergic
aggressive mimicry" and "Class VII, antergic aggressive mimicry", with the minor
difference that Vane-Wright did not explicitly include direct fitness effects (though they
are implied). The basic difference between antergic and synergic is in the benefit to the
model, which I will explore in more detail below. This definition excludes several cases
which others may consider to be aggressive mimicry. Cases where dupe fitness is
indirectly affected, such as the lacewing larvae system (Eisner et al. 1978), are not
considered to be aggressive mimics. In this system the larvae use their mimicry to hide
from ants. These ants protect the lacewing’s prey, aphids. Although this potentially
affects the ants fitness, that effect is indirect - mediated through the aphids. Cases not
involving an active response (that is, a change in behavior) by the dupe are not
considered aggressive mimicry primarily because of the practical difficulty in
discriminating between passive response and no response. For example, if ground
squirrels fail to change what they are doing when a zone-tailed hawk approaches (Willis
1963), is it due to a failure to detect them because they are hidden among the turkey
vultures they resemble (camouflage), or due to mis-identification as turkey vultures afier

detection (mimicry)? According to the definition above, such examples are not

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considered aggressive mimicry since the "response" is passive (i.e. they don't do
anything) rather than active.

The active response clause in the definition also excludes the many internal
parasites that avoid host defenses through resemblance to the host's self-recognition
compounds (Goodenough 1990). While this is certainly aggressive, whether it is mimicry
or camouflage remains an open question. An analogous situation exists in eusocial insect
colonies; some parasites and predators prevent attack from the colony by adopting the
colony's cuticular "signature" (Howard, McDaniel and Blomquist 1980; Vander Meer and
Wojcik 1982; Bagneres et al. 1996). This exclusion prevents us from getting bogged
down in the long-standing debate over where the dividing line between mimicry and
camouflage should be (Pasteur 1982; Getty 1987; Starret 1993) and allows us to focus on
cases that are unambiguously mimetic.

Pasteur (1982), in his broad treatment of all mimicry systems, used the nature of
the model (agreeable vs. forbidding) and the taxonomic relationships between model,
mimic and dupe as the backbone for his classificatory scheme. While this was a logical
system, it led to a large array of different types of mimicry: eighteen total types of
mimicry, five of which can be considered aggressive mimicry. Vane-Wright (1976) also
developed a complicated scheme. This scheme was based on taxonomic relationships
and fitness effects on the model and dupe. This system produced 5 taxonomic classes
and 8 classes based on effects to models and mimics. Combining these two systems
produces 40 different classes of mimicry, and 10 different types of aggressive mimicry.
These cumbersome classification schemes may serve to obscure rather than clarify broad-

scale patterns.

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antergic/synergic dichotomy proposed by Vane-Wright (1976), but removing the
taxonomic details. Note that the operational definition of aggressive mimicry above
requires that the mimic's fitness is, on average, increased by the mimetic resemblance,
and the dupe's fitness is reduced. This is true regardless of taxonomic affiliations. The
model, however, can be affected in three different ways. An aggressive mimic might
affect the model's fitness positively, neutrally, or negatively. This suggests a simple
classification scheme: positive aggressive mimicry occurs when a mimic enhances the
fitness of the model, neutral aggressive mimicry occurs when the model's fitness is
unnaffected, and negative aggressive mimicry occurs when the mimic reduces the
model's fitness. (see table 1.1 for examples of each). This scheme holds regardless of the
taxonomic affiliations of model, mimic and dupe. The model need not be a living
organism, though all such cases must, by default, be classified as neutral since an abiotic
model has no fitness. In neutral aggressive mimicry the model does not actively take part
in the evolution of the model and mimic, regardless of whether the model is biotic or
abiotic. In cases with neutral biotic models, their appearance could change in response to
outside factors. While these factors can certainly influence the appearance of the mimics,
it would not change the basic concept that the model is not actively involved in the
evolution of these systems. This classification also incorporates one of the basic
distinctions between Batesian mimicry (model fitness decreased by mimic presence) and
"classic" Miillerian mimicry between two equally noxious model/mimics (model fitness
enhanced by mimic presence). This classification has two advantages over Pasteur's

mimicry classes for aggressive mimicry. First of all, it provides a more manageable

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number of categories and second, as will be seen below, it reveals an interesting and
unexpected pattern across aggressive mimicry systems.

When mimics negatively affect their models, as in Batesian mimicry, the models
are expected to "run away" from the resemblance, starting the classical evolutionary
chase seen in most Mathematical models of Batesian mimicry (figure 1.1). Recent theory
suggests that Batesian systems should evolve to a monomorphic model and polymorphic
mimic in most cases. On the other hand, when mimics positively affect their models, as
in "classic" Miillerian mimicry, the model and mimic should both become monomorphic
(Gavrilets and Hastings 1989). Thus, we would expect closer mimicry in systems where
the model and mimic have a mutual interest in similarity than in systems where their
interests diverge, an intuitively appealing expectation (see Figure 1.1 for a graphical
version of this argument). If there is no effect on the model, then the mimic should
eventually converge on the model, but the model should not change its appearance in
response to the mimic; resemblance in these cases could vary widely, and would be
dependent primarily on the time since mimicry began, selection strength, and the
presence or absence of outside selective factors on model appearance. Do these simple
and intuitive predictions, based on theory developed for protective mimicry, hold true for

aggressive mimicry?

Methods

I have searched the literature on aggressive mimics extensively. Much of this

literature is anecdotal in nature, and some is purely speculative. I have followed Pasteur

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(1982) in accepting published reports with a fairly uncritical eye on the theory that what
is not reported will not be studied in further detail — and nearly all proposed cases of
aggressive mimicry need more study. In order to present the reader with some idea of
how well established each example of aggressive mimicry is, I have included a rating
with each example, describing the level of work that has been reported supporting it. The
ratings I have assigned are based solely on the quality of information for identifying
potential aggressive mimics, and do not reflect the overall quality of the papers listed.
For example, while many of the cases listed from Wickler (1968) are speculative, I
consider this excellent treatment to be required reading for anyone interested in mimicry
(aggressive or otherwise). The rating system is given in the legend to table I.

In order to reduce taxonomic redundancy, taxa where the same type of aggressive
mimicry occurs frequently are treated as a single occurence, on the conservative
assumption that only one evolutionary origin occurred in these groups. Thus not all
species of aggressive mimics receive equal weight: the hundreds of species of
Lophiiforrnes (anglerfish) are treated as a single instance, as is the single species of
alligator snapping turtle, which uses a similar tactic but almost certainly acquired it
independently.

In most of the cases reviewed, the effect of the mimic on the model has not been
demonstrated rigorously. I have inferred an effect for these cases, but these must be
considered as potential effects, based on logic, rather than as demonstrated effects based
on empirical study. I will detail a few of the more common situations here as examples.
Many aggressive mimics mimic prey. In general, prey can potentially benefit from the

presence of an aggressive mimic through both reduced numbers (via losses to mimics)

and/or increased cautiousness of their predators. Flowers are a food item, but generally
benefit (via pollination) from visits by dupes — thus flowers are postulated to be
detrimentally affected by mimics through reduced numbers (via losses to mimics) and/or
increased cautiousness of pollinators. Similarly, when females are the models of
predatory mimics, females are considered as detrimentally affected by mimics through
reduced numbers and/or increased cautiousness of males (though indirect fitness may
benefit from mating with higher quality males). When the model is inanimate, there are
no fitness effects. These cases are therefore considered neutral. Similar deductions,
based on the natural history of each individual case, were made for each postulated case
of aggressive mimicry.

Cases that can be considered as aggressive mimicry, but where fitness effects on
dupes are likely to be negligible have also been excluded so that cases where selection is
weak will not obscure any larger patterns. For example, nectar-less flowers (Wiens
1978) can be considered "aggressive" since they rob dupes of time that could be spent in
other activities and thus at least potentially reduce dupe fitness; compared to the fitness
cost of approaching a predator disguised as a flower this is likely to be negligible,
provided abundances are similar. Similarly, mimicry of female bees by some orchids
(Wiens 1978) most likely has negligible fitness effects on the dupes unless they are
severely sperm-limited. Another borderline case involves the mimicry of females by
males, allowing them to approach females defended by a territorial male (e. g. "Sneaker"
males). In these cases fitness effects on the female are frequency dependent. Because of
this frequency dependence average fitness effects on the model (female) vary over time

(when mimics are rare, mating with them is advantageous since mimetic offspring in the

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next generation will likely have high relative fitness; when they are common, however,
mimetic offspring will have low relative fitness), This situation is most closely
approximated as neutral mimicry. By restricting the cases examined to those in which
the dupe is directly and physically harmed (killed, attacked or infected) I keep only those
cases where selection strengths on dupes are relatively strong at a given frequency and
therefore more likely to have strong effects throughout the aggressive mimicry system.

The main prediction of the arguments presented centers on how similar mimics
and models are in appearance. Unfortunately, most of the cases in the literature do not
provide measurements of model and mimic signals as presented to dupes. In the absence
of this information, the concepts of abstract and concrete mimicry (Pasteur 1982) can be
used as a rough, qualitiative guide to similarity. Simply stated, concrete mimicry
involves detailed mimicry of a single species (e. g. Apis mellifera), while abstract mimicry
involves less detailed mimicry of a general group of models (e.g. bees). A concrete
mimic, such as the cleaner wrasse mimic, Aspidontus taem'atus, mimics the cleaner
wrasse Labroides dimidiatus in size, appearance and behavior (Wickler 1968).
Conversely, an abstract mimic such as the alligator snapping turtle, Macroclemmys
tenmickii, possesses a worrnlike appendage on its tongue —- this appendage is easily
confused with a worm or insect larvae, but is not identifiable as any particular species of
worm. Table 1 identifies each case of aggressive mimicry as either abstract or concrete,
based on this dichotomy. This use rests upon the assumption that concrete mimics are, in
general, "closer" mimics than abstract mimics.

There are difficulties involved with the abstract/concrete dichotomy. Whether a

mimic is considered abstract or concrete will depend to some extent on the level of study

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it has received. For example, poor concrete mimics may be improperly identified as
abstract mimics if the system is not sufficiently well known. Similarly, it is likely that
concrete mimics begin as abstract mimics, and there is no way to identify these
"incipient" concrete mimics — that is, mimics that function primarily as concrete mimics
but are still abstract enough to fool some organisms (including scientists) that aren't a
major target of their mimicry. Another important problem is that of bias — in some
systems, for example mimicry of mates, a mimic that is not terribly close in appearance is
likely to be defined as abstract if it only captures a single species, while prey mimicry is
likely to be defined as abstract, even with a similar level of objective similarity. While
these are serious problems with the use of this dichotomy, it is still true that in most
examples of concrete mimicry the models are fairly easy to identify to species, while in
cases of abstract mimicry models cannot be easily identified. Until measurements are
made on models and mimics to quantitatively deal with the question of mimetic

"distance", the abstract/concrete dichotomy is the best tool available.

Results

The results of the literature review are presented in table 1, organized by fitness
effects on the model (positive, neutral or negative). In one case it is not clear from the
papers available whether the mimicry was abstract or concrete — this has been omitted
from the following analysis. Only three of the mimics in table 1 were considered to be

neutral, and one of these was the case mentioned above, where it was not possible to

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determine whether it was abstract or concrete. Although this leaves all of the neutral
cases as abstract, it is obviously too small a sample from which to draw conclusions.

The remainder of Table 1 demonstrates a striking pattern: 14 of 19 cases of
abstract mimicry involve situations where the model is affected positively, while 13 of 13
cases of concrete mimicry involve cases where the model is affected negatively. A
deeper inspection of table 1 reveals that 12 of 13 cases of concrete mimicry involve
systems where the dupe and the model are the same species (one variant of conjunct
mimicry according to Vane-Wright 1976) and 18 of 19 examples of abstract mimicry
involve disjunct (Vane-wright 1976) systems, where model, mimic and dupe belong to
three separate species.

These two ways of looking at mimicry systems confound one another. 13 of 18
systems where models are negatively affected involve conjunct systems while 14 of 14
cases where models are positively affected involve disj unct systems. This confounds the
affect of "junctivity" of a system with fitness effects. However, even with this confound
in place it can easily be seen that the predictions derived from analogy with protective

mimicry fail.

Discussion

That predictions from protective mimicry theory should fail for aggressive

mimicry is not surprising: after all they are qualitatively different systems. However, this

finding also refutes the intuitively reasonable prediction that systems where model and

mimic both benefit from the resemblance should tend to resemble each other more than in

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instances where they do not share a common interest in convergent appearance. The
failure of both protective mimicry theory and intuition to accurately predict this strong
qualitative pattern highlights the need for separate theory to explain the operation of
aggressive mimicry.

The data used here are somewhat flawed: the accounts are usually anecdotal, and
as can be seen from table 1 much of the "data" is weak or even speculative. The
existence of an apparent link between the effect on the model and species composition
makes all analysis difficult, since the relative importance of conspecifics vs
heterospecifics could have large effects on the magnitude of selective forces. In addition
several exclusions have been made in the name of clarity that may influence the results.
As far as the data quality, this is the best data available on aggressive mimicry. The
overall poor data quality shows more strongly than anything the need for detailed study
of this phenomenon.

The link between species composition and effect on the model is a logical
consequence of the relationships between model, mimic and dupe in these systems. This
makes new studies of those few cases where the link doesn't hold, for example the
Cleaner fish system (Wickler 1968), particularly important — these exceptions to the
apparent rule may hold the key to developing a firmer understanding of aggressive
mimicry. For the moment this problem will be untackled, since the predictions from
protective mimicry are silent in regard to this problem — protective mimicry systems with
model/dupe conj uctivity appear to be rare (Vane-Wright 1976).

The exclusions present a potentially more serious problem. These were made

with the objective of removing difficult to interpret instances so that patterns would not

13

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be obscured by mis-interpretations, but it is also possible that these omissions introduced
bias. Now that a pattern has been detected we must examine these omissions in an
attempt to uncover any potential bias.

First, consider the exclusion of internal parasites and the predators and parasites
of social insects. These organisms avoid attack by resembling their hosts, which they
damage. Thus, they negatively impact their models. If we consider this as mimicry
rather than as camouflage then we must conclude that they are concrete mimics since
they appear to mimic species-specific recognition factors (Howard, McDaniel and
Blomquist 1980; Vander Meer and Wojcik 1982; Bagneres et al. 1996). As negative,
concrete mimics, these examples reinforce the pattern detected if included, so their
elimination was conservative with respect to detecting the pattern.

Now consider the exclusion of examples where fitness effects on dupes are
expected to be weak. Flowers that rely on pseudocopulation for pollination reduce the
availability of mates for their models and appear to be species—specific mimic (Weins
1978). Again, as concrete, negative mimics they reinforce the detected pattern. In other
nectar-less flowers, there are two categories: in one category individuals within a species
fail to produce nectar, while others produce nectar; in the other category are entire
species that have given up nectar production. In the first category, we cannot tell whether
the resemblance functions as mimicry, is merely the result of the close phylogenetic link
between model and mimic or both. Thus these cases are not appropriate for analysis
here. In the second category, mimicry could affect the model species negatively if they
compete for pollinators, but could also affect their models positively if they increase the

effective size of the flower patch, which can increase visitation rates to the model. Given

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the contradictory possibilities we cannot predict, in a general sense, whether these cases
are more likely to demonstrate positive or negative fitness effects. This situation can add
no information to the pattern detected here, since it predicts variation based on the
individual details of each example. Wiens (1978) reports cases of both abstract and
concrete mimicry among floral mimics. Given the available data, exclusion of cases
where selection on the dupe was weak appears not to have introduced bias in detecting
patterns in abstract versus concrete mimicry.

The available data are anecdotal and problematical due to large differences in
methodologies and interpretation. A strong pattern emerges from them nonetheless. In
systems where models suffer from the presence of an aggressive mimic, close
resemblance (as measured by concrete mimicry) is common; in systems where models
benefit from the presence of an aggressive mimic poor resemblance (as measured by
abstract mimicry) predominates. Current mimicry theory is inadequate to deal with this
observation; in fact it predicts exactly the opposite pattern.

This situation calls for a two-pronged approach. First, a new theoretical approach
to aggressive mimicry that is capable of explaining this pattern must emerge. Then this
theory must be tested against new data using a well-documented aggressive mimicry
system. This dissertation sets out to accomplish both of these goals. Chapter two
develops a new general modeling paradigm based on a combination of two well-
developed branches of mathematical ecology: life history theory and signal detection
theory. Chapter three presents the natural history of a previously little-known aggressive
mimic, Mimetus notius (Aranae; Mimetidae) and its most common prey, T heridion sp

(Aranae; Theridiidae). Chapter four takes an in-depth look at the signal properties in this

15

system, including the signals received by Theridion from six different organisms and
Theridion's responses to these organisms. Finally, chapter five builds upon all of the
previous chapters to develop and test a model specific to the M. notius system, extending
and testing the general paradigm developed in chapter two. This work thus develops and

tests a new theoretical approach to the study of aggressive mimicry.

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20

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23

Figure 1.1. Selection on models and mimics in Batesian and Mullarian mimicry
systems. In Batesian systems, a dupe attacks and kills models and mimics based
upon their appearance. The dupe must discriminate palatable mimics from
unpalatable models, which it avoids. The more similar a mimic is to a model, the
more likely it is to be mis-identified as a model and avoided, so it receives more
protection from its appearance, and mimics are selected to look more like models.
On the other hand, the more a model resembles a mimic, the more likely it will
mis-identified as a mimic and consumed. This selects for models whose
appearance diverges from that of mimics. In Mfillerian systems, a dupe also
attacks and kills models and mimics based upon their appearance. In this case,
however, both models and mimics (aka co-mimics) are unpalatable. Predators
tend to avoid the common mean, so that individual prey at the extremes of the
combined distribution are more likely to be killed, selecting for models and

mimics that more closely resemble one another.

24

 

 

Frequency in population

Frequency in population

Figure 1.1

Batesian Mimicry

 

Direction of selection
4— 4—

Models Mimics

 

 

 

Trait value

Miillerian Mimicry

 

Direction of selection
—> ‘—

Models Mimics

 

 

 

 

 

 

Trait value

25

 

Figure 1.2. Selection in aggressive mimicry systems based on analogy with Batesian
and Miillerian mimicry systems. In systems in which the model is harmed,
dynamics similar to that seen in Batesian mimicry are expected. In these cases,
for example when mimics mimic mates, a dupe is attempting to discriminate from
a model which benefits when it is found and a mimic which will harm the dupe.
Models similar in appearance to the mimic will be avoided by cautious dupes,
driving selection of models away from similarity with mimics. In systems where
the model benefits, such as when prey are mimicked, the situation is analogous to
that seen in Mullerian systems. In this instance the dupe must discriminate
between a mimic and a model which is harmed by the dupe. In this case, models
whose appearance is similar to the mimics will be more likely to be avoided, thus

increasing their fitness.

26

 

Frequency in population

Figure 1.2

Aggressive Mimicry:

Model harmed

 

Direction of selection
4— 4—

Models Mimics

 

 

 

Trait value

Model benefited

 

Direction of selection
———> 4———

odels Mimics

 

Frequency in population

 

 

Trait value

27

 

 

 

 

Chapter 2: Aggressive mimicry: a new theoretical approach to a

long-ignored phenomenon.

INTRODUCTION

All predators must find prey in order to survive. One way for a predator to find
its prey is to mimic prey's food and wait for the prey to come to it. This is one type of
aggressive mimicry. Familiar examples include the lures of anglerfish and alligator
snapping turtles; many other examples exist (see table 1). Other aggressive mimics copy
the signals of mates; predatory fireflies (Lloyd 1984) and bolas spiders (Stowe et al.
1987, Yeargan 1994) are stunning examples. As has been shown in chapter one, existing
theory dealing with protective mimicry is inadequate for explaining a strong pattern
among aggressive mimics. Aggressive mimics that benefit their models tend to display
mimicry that is poor relative to mimics that harm their models, counter to expectations
based on theory derived for protective mimicry. This paper will use life-history theory
and signal detection theory to create a theoretical tool capable of explaining this pattern.

When the risks associated with a particular type of resource are variable and there
are correlated cues, there should be selection on prey to discriminate between instances
with higher and lower risk. A discriminating fish that selectively avoids some worm-like
objects might have higher fitness than one that never eats worms in order to avoid
predation by worm-mimicking alligator snapping turtles. Signal detection theory is a
powerful mathematical tool that has proven useful in behavioral settings where partial

discrimination is important (Getty and Krebs 1985; Getty 1995), including Batesian

28

 

III

(I

w

in:

HE

mimicry (Oaten et al. 1975; Getty 1985) and aggressive mimicry (Davies et al. 1996).
Thus, signal detection theory is a good place to start. However, due to the risk of death
involved, we need to go beyond simple behavioral decisions and approach the problem
with a life-history perspective.

Most animals face mortality risks when they seek resource rewards. Ultimately,
the risks and rewards combine in the common currency of fitness. In the realm of
foraging, it is often useful to analyze these risks and rewards in units of resource returns
per unit of investment, for instance, calories/time (Stephens and Krebs 1986). This works
when the risks of bad choices or bad luck are lost energy, time or opportunity. However,
when the risk is death, the search for a common currency takes us into the realm of life-
history theory, with fitness as the currency (Schaffer 1983, Stearns 1992). Gilliam used
optimal control theory to show that given certain assumptions, most importantly that
reproduction comes later, fitness would be maximized by the criteria: "minimize u/g"
(Gilliam 1982, 1990; Werner and Gilliam 1984; Gilliam and Fraser 1987; Werner 1992),
where u, and g are mortality rate and growth rate. Here I will substitute a more
behaviorally oriented criterion using the feeding rate, f, as a stand-in for g. This
"maximize f /u" (Gilliam 1990) criterion has been shown to be an effective predictive
instrument (Gilliam and Fraser 1987). This criterion provides the life-history perspective
necessary for tackling the problem of aggressive mimicry.

We will tackle the problem of foraging in an aggressive mimicry system by
adopting the "maximize-f /u" criterion and utilizing signal detection theory (Egan 1975;
Macmillan and Creelman 1991). The f /u criterion provides an elegant general

framework for understanding the tradeoff between feeding rate and predation risk, while

29

 

 

pi

\\

OI

signal detection theory provides a way of integrating variable cues with variable risks.
The combination of these frameworks reveals general patterns showing how foragers
might adaptively vary their probability of making different kinds of errors, depending on

their perceptual abilities and the community context in which they are embedded.

THE MODELING SCENARIO

We will develop this model from the point of view of a forager faced with a
predator that mimics a food resource. Whenever the forager encounters cues associated
with the resource (and mimicked by the predator) it must decide whether to pursue the
opportunity, and risk encountering a predator, or ignore it, and risk missing a profitable
reward. (An imperfectly camouflaged predator hiding in or near a resource - for
example, a crab spider camouflaged inside a flower — presents its prey with a
qualitatively similar dilemma). The decision whether or not to pursue a particular
opportunity should depend on the forager's assessment of the likelihood that the cues are
from the aggressive mimic. In order to make this assessment, the forager has two
potential sources of information. First, it can utilize its individual or phylogenetic
experience to estimate the average, prior probability that a predator is present (e. g.
alligator snapping turtles are rare here, so it is probably safe). Second, it can use sensory
cues to refine this average and estimate the posterior probability for this particular
instance (e.g. alligator snapping turtles are rare here but that worm looks wrong in some

way; in this particular instance it is probably not safe).

30

 

(‘1.

ref

mi

\‘a:

 

OI“

lei,

 

We will assume that the variable cue used by the forager can be represented along
a univariate axis, for example light wavelength or a discriminant function score that
incorporates multiple cues. We can then describe the probability density functions for the
cue along this axis: one distribution for safe opportunities (i.e. resources) and another for
dangerous opportunities (i.e. aggressive mimics). If the predator is not mimetic, there is
no overlap in the probability density distributions and resources and predators are
perfectly discriminable. The forager can set a threshold criterion cue value (c) that
completely separates the two distributions, and consequently reject all dangerous
resources and accept all safe resources. If perfect mimicry exists, the probability density
distributions are identical. No criterion improves on the prior odds, and the forager must
either accept the average risk of the mimic or drop the resource from its diet. Most
models of foraging under predation risk assume this situation, which corresponds to a
perfectly camouflaged predator (see reviews by Lima and Dill 1990, Brown 1992, and
references therein). These models have not yet addressed the situation of an imperfectly
mimetic or camouflaged predator. If mimicry is good but imperfect, the probability
density distributions overlap partially (fig. 2.1A). In this situation, a forager can use the
cue value to update its assessment of the risk of predation at each particular opportunity
and selectively pursue only those instances where the cue is below some adaptively
variable threshold criterion, ci. Breipohl (1970) has shown that a threshold criterion is
optimal. This results in variable partial preferences for the resource type (Getty 1985;
Getty and Krebs 1985).

This scenario can be represented graphically with a useful device known as a

receiver operating characteristic (ROC) curve (Egan 1975; Getty 1985, 1995; Macmillan

3]

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and Creelman 1991; Wiley 1994). This curve is drawn in probability space (fig. 2.1B).
The X—axis of the ROC curve is the probability of a false alarm (F). A false alarm occurs
when the forager misidentifies a predator as the resource being mimicked. (The term
"false alarm" is taken from signal detection theory; although its use here may cause some
confusion since the forager is seen as "alarming" at food and "false alarming" towards
predators, we will keep the terminology so as not to obscure the direct connections with
signal detection theory. Think of a false alarm as an error; trying to eat a predator is very
intuitively an error in judgment.) The probability of a false alarm equals the cumulative
probability of getting a cue greater than the selected criterion c, given that the cue came
from a predator. The Y-axis is the probability of a hit (H). A hit occurs when the forager
attempts to use the resource when it is in fact a resource. The probability of a hit equals
the cumulative probability of getting a cue greater than the selected criterion c, given that '
the cue came from a resource. For each possible criterion (c) there is a corresponding
point (F, H) on the ROC curve.

The ROC curve traces out the tradeoff between hits and false alarms, constrained
by the relationship between cue distributions (fig. 2.] A & B). Although the ROC curve
defines an outer edge of possible values of H and F, the particular point on the curve
where the forager should operate depends on the probabilities and values of the payoffs
for each of the various outcomes. The forager can decide where to operate along the
curve by varying the selection criterion 0. The ratio H/F decreases along the ROC curve,
from the lower left to the upper right, and can be interpreted as the relative cautiousness
of the forager. A cautious forager accepts a low level of hits (H) to get a low level of

false alarms (F) and consequently operates toward the lower left of the ROC curve, where

32

the ratio H/F is high. A less cautious forager accepts a high level of false alarms (F) to
get a high level of hits (H) and consequently operates near the upper right of the ROC
curve, where H/F is low (approaching one). ROC curves are constant for a particular
relationship between probability density functions -- if that relationship changes, a new
ROC curve results. Note that H/F values cannot be used to compare relative cautiousness

across different ROC curves.

COMBINING SIGNAL DETECTION THEORY WITH THE f/p CRITERION

We start with the maximize-f /u model. The feeding rate, f, depends on the
combined encounter rate (R) — which is the encounter rate with both resources and
mimics — the probability that any given encounter is with a resource (S), the probability
of successfully harvesting an encountered resource (C), the value of the resource if it is
successfiJlly harvested (V), and the background rate of harvesting alternative resources
(A) (eq. 1). The mortality rate, p, depends on the combined encounter rate (R), the
probability that any given encounter is with a mimic (D=1-S), the probability of being
killed as a result of the encounter (K), and the background mortality rate (m) (eq. 2). We
make the simplifying assumptions that variation in the probability of accepting or
rejecting the resource has a negligible impact on the ambient background mortality rate
(m) and resource reward from other sources (A).

f=R-S-C-V+A (1)

p=R°D°K+m (2)

33

Next, we use signal detection theory to incorporate the prey’s ability to
discriminate variable risks. The probability of successfully harvesting an encountered
resource (C) depends on the probability that the forager makes a hit by accepting it (H): C
= H. The probability of being killed by a mimetic predator (K) depends on the
probability that the forager accepts a mimic (F), and the probability that the mimic
successfully kills the forager given acceptance (P): K = F °P. Substituting these values in
equations 1 and 2 yields equations 3 and 4:

f=R-S-H-V+A (3).
u=R°D°F-P+m (4).

H and F are constrained by a tradeoff given by the ROC curve, so we can

represent H as a function of F: H(F). Making this substitution and dividing equation 3 by

equation 4 results in equation 5:

f ROS-H(F)-V+A

_: 5
,u ROD-F0P+m ()

 

The forager is selected to maximize f /u subject to the tradeoff constraint between H(F)
and F, and the parameters R, S, V, A, D, P, and m. If the ROC constraint H(F) is known,
we can solve equation 5 for the value of F (and hence H(F)) that maximizes f / u. If it is
not known, we can still solve for the level of relative cautiousness (H(F)/F). that
maximizes the criterion along any single ROC, even if we do not know what that ROC

looks like (appendix 2.1). At the maximum f /u:

 

 

 

 

H+_:°:_
dF F+ m
ROD-P

34

Recall that high values of the ratio H(F)/F (which is just the slope at any point
along the ROC) occur at the lower left of the ROC curve, corresponding to high values of
the critical threshold c, and vice versa. The optimal operating point, (H(F)/F): is just the
point on the ROC of interest with slope defined by equation 6. From eq. 6 we can see
that this optimal slope (and the optimal threshold c. ) should increase with the prior odds
that an encounter is with a mimic (D), the probability that a false alarm results in death
(P), and with increasing alternative resources (A). Optimal slope (and the optimal
threshold c. ) should decrease with increases in the probability that a risky resource is
safe (S), the resource value of a safe resource (V), and with increasing background
mortality (m). Hidden in the final form of the equation is the effect of the overlap
between signal distributions. The solution uses implicit differentiation, which assumes a
simple function describes the relationship between H and F. This is fine for getting a
general solution, but does not allow for comparison between specific solutions. When we
vary the underlying signal distributions, this effects the relationship between H and F as
described earlier, and the general solution cannot analyze these specific differences.
Although the general predictions for the "unhidden" variables are straightforward,
analysis of the effects of changes in the relationship between the underlying distributions
reveals unexpected dynamics in the relationship between optimal error rates (F‘) and
discriminability.

In order to vary the overlap between signal distributions, we will retreat from the
final form of the model and return to equation 5. This makes it easier to see that varying

the overlap between the signal distributions will cause the relation H=H(F) to change, in

35

I1

(34

It

.Cl.

Ii.

 

turn affecting the optimal behavior. Numerical simulations based on equation 5 show
that, under certain conditions, foragers should actually increase their mortality risk in the

face of increasing ability to discriminate.

SIMULATIONS

Setting H=H(F) allows for an analytical solution to the model, but obscures
important information about how foragers should respond to changes in the overlap
between distributions. Remember that H=H(F) depends on the amount of overlap
between model and mimic distributions (see figure 2.1). In order to look at the response
to variation in the amount of overlap, simple computer simulations have been conducted
using Matlab© (see appendix 2 for program). In these simulations the ability of the
forager to discriminate between models and mimics was altered by changing the
difference between the means of the distributions (for simplicity, both distributions are
asSumed normal, with identical standard deviations). This simple manipulation changes
the amount of overlap between the model and mimic distributions, thus changing the
relationship H=H(F) — i.e. changing the ROC curves. All other parameters were held
constant and given standard values. A second simulation, where the overlap of the
distributions was varied by changing the standard deviation of the distributions with the
means held constant (with SD(mimic)=SD(model) in all cases) was also conducted. The
qualitative results of these two simulations were identical, so here we will simply report
the results of the simulation involving the difference between means.

When the difference between means is varied, we move from one ROC curve to

the next; H/F (or H(F)/F) is not a valid indicator of relative cautiousness on different

36

O

V.

 

(A

 

Cr

03

ROC curves. For this reason, we will look at changes in Optimal H and optimal F (H. and
F' respectively) separately as the difference between distribution means changes. 'F‘ is a
better indicator of cautiousness in these simulations since it can be solved for directly, as
opposed to the situation in the general solution. Ft and H‘ were found by selecting the
values of H and F resulting in maximal f/u for each ROC curve generated. ROC curves
were generated from underlying distributions with identical standard deviation (=02), but
with their means differing by a variable amount, d (varying between 0 and 1.5 in 0.01
increments). As (1 increases, discrimination between the distributions becomes easier.

The results of these simulations show two qualitatively different patterns. These

patterns show a switch point when —D—.P.—A = l.(See appendix 3 for the derivation of
SOVom
. . . . DOPOA .
this cutoff pomt). The results of the Simulation when S7— < 1, are shown in figure
0 o m

2.2. The difference between distributions (a measure of discriminability) is displayed in
increments of standard deviation. Here we see an intuitive pattern; as discriminability
increases, the error rate decreases. Since H is tied to F, H shows some initial decrease
with F until discrimination becomes easy enough that they are functionally dissociated.

. . . . . A
Figure 2.3 displays the results of this Simulation when $1:— > 1. The
S-Vom

simulation shows, unsurprisingly, that as the difference between distributions increases,
Hi, the optimal probability of correctly selecting a model (i.e. resource) increases.
However, F., the probability of incorrectly selecting a mimic (i.e. a predator), shows
counter-intuitive behavior. As discriminabilty increases, F. first increases, then levels
off, and finally decreases, creating two regions with low error rates on either end of the

discriminability axis and a region of increased risk at relatively moderate

discriminability values (figure 2.3). Thus, when distributions have more than a critical
amount of overlap it is actually optimal to increase the error rate (and thus mortality risk)
in response to greater ease in discrimination. The energetic gains from increasing H.
outweigh the increased mortality risk associated with increasing F‘ when differences
between distributions are small and the parameters satisfy the criterion that

DOPOA
SOVOm

> 1. The marginal benefit of increasing H. decreases as the difference
between distributions increases. Eventually, the marginal increase in fitness associated
with increasing H. no longer offsets the marginal decrease in fitness associated with
increasing Fi. At this point, F. begins to decline. This produces the hump-shaped curve

in figure 2.3. The exact position of the hump varies with variation in the parameters, but

. DOPOA . . H
as long as the ratio —— > I, the hump eXists. Thus, under certain conditions, as the

0 V o m
ability to discriminate increases, individual prey can increase their fitness by increasing
their susceptibility to predation via aggressive mimicry. Figure 2.4 redisplays this data in

ROC space. The two adaptive basins (the upper curve and lefi-hand curve) show the

same dividing line (at M = 1) as in the above figures, with a better demonstration

SOVom
of why the points (1,1) and (0,0) act as attractors — these can be mapped directly onto
figures 2.2 and 2.3 respectively. From this figure it can be seen how the dupes response
is constrained by the similarity between model and mimic.
A logical result of this outcome is that aggressive mimics in these circumstances
will tend to be more efficient predators when their population consists of imperfect
mimics. Feeding rates of the mimic are directly tied to error rates of the prey, so we can

also interpret F. in figure 2.3 as a graph of the relative feeding rates of aggressive mimics

38

in these systems. As a population of mimics approaches perfect mimicry, their average
success will actually drop as prey become more cautious. Depending upon the relative
frequency of models and mimics, the mimics could eventually cause their prey to stop
responding to either model or mimic, reducing mimic success to zero.

This sets up a group/individual conflict that similar to that developed by Steams
(1992). (see figure 2.5 for a graphical representation). The basic conflict is that,
regardless of the response rate of dupes, individual mimics that are closer to perfect
mimicry should be favored. This will tend to drive the population closer to the left of the
graph. However, as the population of mimics moves in this direction, their average
success will drop. Thus, although the relative fitness of "better" mimics will select for
closer mimicry, the population as a whole will do worse from generation to generation,
possibly mimicking itself to extinction, depending on other factors such as alternative
prey. This conflict should make aggressive mimicry systems that rely on prey mimicry
unstable unless either group selection is an important factor, or some other factor (ability

to mimic other prey?) acts to counteract individual selection for enhanced mimicry.

39

A CORRELATIVE ANALYSIS

In response to changes in the relationship between distributions, the model makes
the counter-intuitive prediction that, under certain conditions and when discriminability is
below a certain threshold, as the distributions become easier to discriminate dupes should
actually increase their probability of making a discrimination error (a false alarm) -- in
this case a potentially lethal one.

Lethal mimic populations that are too similar on average to their models should
cause their prey to become unresponsive, and we would expect to find food-based
aggressive mimicry systems where models and mimics match closely to be relatively rare
(Except in cases where alternative foods for dupes are unavailable). Since selection on
individual mimics will always favor better mimics when prey are responding (as long as
prey respond to the resource, they will respond more to better mimics regardless of the
optimal response threshold), we expect that prey-based aggressive mimicry systems
where D°P°A/S-V-m >1 should be unstable in the absence of a mechanism preventing
model and mimic convergence. If prey response to the model drops to zero, aggressive
mimicry becomes useless, regardless of an individual mimic's resemblance; selection for
further increases in similarity ends as mimics either starve or switch to an alternative
prey. Realistically, this should happen at some point before response drops to zero, when
prey response is low enough that mimics relying on this food source can no longer
survive. One important caveat is that this model is based upon systems where a food

resource is mimicked -- no predictions about the level of matching between model and

40

mimic in other systems (for example, where mates are mimicked) can be supported at this
point.

Given this caveat, we can look at the existing literature on aggressive mimics to
determine if aggressive mimics tend to be "close" to a particular model — at this point no
data exists on the stability of aggressive mimicry systems. Unfortunately, measurements
of signal distributions have not been made in aggressive mimicry systems, making
quantitative comparisons impossible. In order to provide a qualitative measure of
closeness we will use the concept of abstract mimicry as outlined by Pasteur (1982) and
Pough (1988). Abstract mimicry involves the mimicry of a class of organisms rather than
a specific organism. Thus, the alligator snapping turtle, Macroclemmys temminckii,
possesses a worm-like organ on its tongue that does not resemble a particular species of
worm. Compare this to the concrete mimicry of the cleaner wrasse mimic, Aspidontus
taeniatus (Wickler 1968), which mimics almost exactly the cleaner wrasse, Labroides
dimidiatus both physically and behaviorally. Whether a system is considered abstract or
concrete will depend to some extent on the level of study it has received, but in most
cases concrete mimics very obviously mimic a particular model, while models in abstract
mimicry systems are less easily categorized. Thus we can use this dichotomy as a rough
index since abstract mimics are generally expected to mimic any specific biological
model less "closely" than does a concrete mimic. The model presented here predicts that
a general pattern should exist. Mimics that use food as a model should more often
display weak mimicry than close mimicry. The abstract/concrete dichotomy can help us

to confirm such a pattern.

41

Table 1 presents twenty-five proposed aggressive mimicry systems (see chapter
one for methods of creating this table) involving mimicry of food or mates. Of these
twenty-five, eighteen cases involve mimicry of food; in each of these eighteen cases the
mimicry is considered abstract. Thus, weak mimicry is more common among lethal
aggressive mimics of food (provided alternative foods are available to the dupe) just as
we would expect based on arguments resulting from the model.

Table 1 also includes seven cases involving mimicry of mates. Given two major,
but realistic, assumptions, the current model can be simply modified to represent the
situation of predators mimicking mates. These assumptions are: 1) birth rate/death rate is
a valid criterion for maximizing fitness just as feeding rate/death rate has been shown to
be and 2) there are no alternatives to mates that result in a fitness benefit in this currency
(i.e. A=O). These two assumptions allow a model (equation 7) that is identical to that in
equation 5 except that the units of V change to represent offspring/encounter rather than
calories/encounter and the variable A drops out.

i_ ROS-H(F)0V

_ 7
p R0D0F0P+m ()

 

The loss of A yields an equation similar to the previous equations, and once again
simulations can be conducted. Figure 2.4 shows the results of this simulation (varying
the difference between distribution means). In this case we see that as the difference
between means decreases, F* approaches one while H* displays more complex behavior
— in this case showing a decrease in hits (i.e. attempting to mate with a potential mate) as
discriminability increases, when the means are “close”. The shape of this curve allows

selection to continue to refine the similarity between model and mimic; dupe response to

42

mimics increases as similarity increases. This leads to the expectation that concrete
mimicry should be common among mate mimics. All seven cases of mate mimicry
appearing in table 1 are concrete. The data available from the literature thus support the

expectations inferred from the models.

DISCUSSION

The models developed here describe a mechanism for adaptive variation in
selective risk taking, where one of the risks is death. They are simple and precise, but
probably more general than realistic. They make quantitative predictions fi'om
measurable variables, and are amenable to experimental and observational tests. Most
simply, we expect that in habitats where aggressive mimics are abundant, foragers should
be cautious, raising their threshold for accepting a risky opportunity and accepting lower
hit rates (many missed opportunities) to lower the false alarm rate. Where aggressive
mimics are rare, we expect less cautious foragers with a low threshold for accepting a
risky opportunity and accepting high false alarm rates (risking predation) to lower lost
opportunity costs (misses). This is analogous to Wiley’s (1994) concept of “adaptive
gullibility” in mate choice, with the additional oddity that we see in this case dupes being
more gullible when the deception is worse (i.e. as discriminability increases).

The models developed here predict logical and intuitive changes in cautiousness
in response to changes in other parameter values as well. As parameters positively
correlated with mimic associated mortality (D, P) increase, prey should behave more

cautiously. Similarly, as alternative resources (A) become more valuable (and/or

43

available), cautiousness increases. Conversely, as the parameters associated with
resource quality (S, V) increase, cautiousness should decrease, and cautiousness also
decreases when background mortality rates (m) increase. None of these results are
particularly surprising, and they give confidence that the model captures important
aspects of the forager's behavior.

Results from simulations varying the level of overlap between the distributions
yield counter-intuitive predictions that are supported by the anecdotal data available on
aggressive mimicry systems -- aggressive mimicry systems where food is mimicked are
abstract in nature while systems where mates are mimicked are concrete. The dichotomy
between food and mate mimics also falls closely into the categorization developed in
chapter one based on fitness effects of the mimic on the biological model in an aggressive
mimicry system. Living food can often (with the exception of flowers) be expected to
benefit, at least potentially, from the presence of an aggressive mimic in the community
because their own predators will respond to the mimics either by increasing their
cautiousness, suffering losses to predation, or both. The fitness of mates will generally
suffer from the presence of a mimic because access to their mates (the mimics' prey) will
be reduced -— either through a reduction in numbers, increased catiousness or both. Thus
not only do these models predict the counter-intuitive pattern seen in the above data, but
they help to explain at least part of the pattern detected in chapter one — that mimicry
systems where the organism being mimicked benefits from the presence of the mimicry
tend to be abstract systems whereas concrete mimicry is common in systems where

models suffer from the presence of the mimic.

44

Models and mimics both benefit from similarity in traits in prey-mimicking
systems. This would seem to lead to convergence in appearance over time. However, we
have seen that these systems are abstract in nature. Some mechanism must prevent
convergence of models and mimics for the observed pattern to hold. We will not address
here all of the potential mechanisms by which convergence of models and mimics might
be prevented. This will require further theoretical development, incorporating
evolutionary dynamics between the three actors in the system and, more importantly,
empirical observations of additional aggressive mimicry systems. Some potential
mechanisms include zero selection for similarity beyond a certain level, prey switching
by mimics, or frequency dependent selection. Even group selection, as detailed above,
may play a role in resisting the evolutionary forces expected to result in close mimicry.

Similarly, we will not discuss in detail mechanisms preventing mimicked mates
from escaping their mimics. The most likely explanation is that large changes in
appearance will be prevented by associated difficulties in mate recognition. Other
mechanisms are of course also possible in both of these types of systems; detailed
experimentation will be necessary to understand which mechanism functions in any given
system, and many systems must be studied experimentally to determine if general
patterns exist.

The data from the literature search are admittedly flawed — see chapter 1 for a full
discussion of the problems with the data set. Another difficulty associated with the way
they are used here is that the model was developed in the hopes of finding an analytical
means of explaining a pattern seen in the data. The current models do this, but the

inherent circularity involved in using old data to check "predictions" makes all of the

45

conclusions of this chapter tentative in nature. What is really needed to test this
modelling paradigm is to test it against new data. While it is unlikely that enough new
data will arise to allow a test of the general predictions outlined in this chapter,
investigation of particular systems can yield valuable insights. For example, selection
experiments can be conducted to test for the hump shape in figure 2.3. Selection
experiments can also be used to test for the existence of the criterion outlined in appendix
3. On a more short-term basis, the cautiousness of dupes from a variety of sites varying
in relative abundances of models and mimics can be measured to see that predictions
from these models make realistic ecological predictions.

The models developed here provide insight into the way aggressive mimicry
works in a very general way. Further elaboration of this modeling paradigm,
development and testing of hypotheses about the dynamics of aggressive mimicry are
likely to prove fruitful. The plethora of studies on protective mimicry has made an
enormous contribution to the development of ecology and evolution. Mimetic predators,
however, have long been ignored; detailed, systematic study of these systems is long
overdue and can potentially make a similar contribution to our understanding of predator-
prey dynamics, the evolution of discrimination, and the co-evolution of perception and

appearance.

46

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Oecologia 106:266-271.

50

 

Table 2.1. Proposed aggressive mimicry systems involving food or mates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mates

 

 

lWinnie Scientific name of Proposed model Concrete or References
mimic - model type Abstract?
Siphonophores Agalma okem‘ Copepods - Food Abstract Purcell 1980
Scorpionfish Iracundus signifer Fish — Food Abstract Fchallenberger and Madden
1973.
Siphonophore Athorybia rosacea Fish larvae — Food Abstract Purcell I980.
Flounder Aslerorhombus Fish or crustacean Abstract Amaoka et al. 1994.
fijiensis - Food
Shellfish (Parasitic) Lampsilis sp. Fish or Fish tails — Abstract Wickler 1968; Haag et al.
Food 1995,1999.
Argiope Spiders Argiope sp. Flowers — Food Abstract Horton 1979; Craig and
Bernard 1990; T50 1998.
Pitcher Plants Wapenlhes sp. . Flowers - Food Abstract Wickler 1968, Wiens 1978;
Cephalotus sp. Moran 1996; Newell and
Sarracenia sp. Nastase 1998.
Darlingmnia sp
Praying mantis Idolum sp. Flowers — Food Abstract Wickler 1968.
Humping Spider Portia fimbriata Insects — Food Abstract ackson and Blest 1982;
Jackson and Hallas 1990
Pirate Spiders Mimetus maculosus Insects — Food Abstract Jackson and Whitehouse 1986.
Snowy Egret Leucophoyx thula Insects — Food Abstract Kushlan 1973.
Anglerfish Lophiformes (many worm-like or fish- Abstract Pietsch and Grobecker 1978.
species) like — Food
Colubrid snake [sop/11's portoricensis Worms -— Food Abstract Leal and Thomas 1994.
Green Pit Viper fiathrops bilineatus Worms — Food Abstract Greene and Campbell 1972.
Horned Frog C eralophrys sp. Worms - Food Abstract Wickler 1968; Murphy 1976.
Burtons Pygopodid Lia/is burtonis Worms —Food Abstract urray et al. 1991.
Trematode Leucochloridium Worms —Food Abstract ickler 1968.
(parasitic) macrostomum
Alligator Snapping Macroclemmys Worms—Food Abstract Wickler 1968; Drummond and
Turtle Iemmincki Gordon 1979; Pritchard 1989.
Characoid fish Probolodus Female Astyanax Concrete Sazima 1977
heterostomus fasciatus — Mates
Bolas Spiders Mastophora sp. Female Concrete Huthison I903; Gertsch 1947;
Pheremones -— Wickler 1968; Eberhard 1977;
Mates Stowe et. al. 1987; Yeargan
1988, I994; Yeargan and
Quate I996.
Spiders Kaira sp. Female Concrete Stowe 1988; Stowe et al.
Pheremones — 1995.
Mates
Spiders Phoroncidx‘a sp. Female Concrete Stowe 1988; Stowe et al.
Pheremones — 1995.
Mates
Fireflies Photuris sp. Female Photinus - Concrete Lloyd 1975, 1984; Copeland

1983; but see Vencl et al.

 

1994 and references therein.

 

51

 

 

Table 2.1. Proposed aggressive mimicry systems involving food or mates

 

 

 

 

 

 

 

IMimic Scientific name of Proposed model Concrete or References
mimic — model type Abstract?
Fish Erythrinus ereythrinus Female Rivuls Concrete Brosset 1997.
agilae — Mates
Pirate Spiders Erofurcata ale Meta Concrete Czajka 1963.
Egmentata -
ates

 

 

52

 

Figure 2.1. Relationship of an ROC curve to the underlying distributions. Panel A
illustrates hypothetical overlapping distributions of cues from safe and dangerous
resource populations. A threshold criterion (c) divides the safe distribution into misses
below c and hits above c. The probability of a hit given a response to cues 2 c is H, given
by the area under the curve to the right of c (shaded with horizontal lines). The same
criterion divides the dangerous distribution into correct rejections and false alarms with
corresponding probability F (vertical lines). The resulting values of H and F are plotted
as the point e on the corresponding receiver operating characteristic (ROC) curve in panel
B. Two alternative criterion points, (I and e. are also shown with corresponding points in
ROC space. The ROC curve traces out, from upper right to bottom left, the possible
combinations of H and F that would result from moving the criterion from the minimum
(left) to the maximum (right) in pane A. The ratio H/F decreases from the lower left to
the upper right along the ROC curve. Lower values of H/F, at the upper right of the ROC
curve, correspond to a low criterion and indicate a bold forager (point d). Higher values
of H/F, at the lower left of the ROC curve, correspond to a high criterion and indicate a

cautious forager (point e).

53

 

Probability

Figure 2.1

 

Mimic cue distribution Model cue distribution

 

 

 

 

 

 

C
Cue Value
d
C
a
:34
e
P(False Alarm)

54

Figure 2.2. Hit (dashed) and False alarm (solid)probabilities with respect to the

. . . . . . . . D 0 P 0
difference between distribution means, in units of standard devration when —————A < 1

SUV-m ’

based on simulations for prey mimicry.

55

 

 

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56

Figure 2.3. Hit (dashed) and False alarm (solid) probabilities with respect to the

. . . . . . . . D o
difference between distribution means. in units of standard devration when A <

SOVOm 1’

based on simulations for prey mimicry.

57

 

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n v m N H

 

 

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58

Figure 2.4. Trajectory of dupe response to increasing model/mimic similarity. When no
mimicry is present, dupes can (and should) operate at the point (0,1) in ROC space.
When mimic resemblance to models is perfect (Solid ROC along the line H=F), a
opposite strategies are optimal depending upon whether D-P-A/S-V'm >1, where the
operating point (0,0) is optimal, or D-P-A/S-V-m <1, where the operating point (1,1) is
optimal. The three intermediate ROC curves {dashed curves traversing the distance from
(0,0) to (1,1)} show the optimal operating points at intermediate values of signal overlap,
and demonstrate how dupes should change their responses for different levels of
similarity between models and mimics depending upon the value of D-P-A/S-V-m. The
upper trajectory is favored when D-P-A/S-V-m <1 , and the left-hand trajectory is favored
when D-P-A/S-V-m >1. This results in two adaptive regions in the ROC curve and
explains the difference between figures 2.2 and 2.3. The shape of these trajectories is
what drives the hump that is seen in F in figure 2.3 and the dip that is seen in H in figure

2.2.

59

 

 

Figure 2.4

 

 

 

E. 3.. QESEm

 

1

0.8

0.6
Probability of a false alarm

60

Figure 2.5. The potential tradeoff between individual and group fitness. Each solid line
represents a separate population of mimics, the dashed line goes through the mean
similarity of each population. In this situation, the fitness of mimics within a
population is a function of both the individual's similarity to the models and the
population average similarity to models. Individual fitness always increases with
increasing similarity within a population, but the same level of similarity in two
different populations may yield very different fitness in absolute terms. In this
way, an individual with low similarity can have a higher fitness than a nearly
perfect mimic, if it is in a population of low average similarity. This is the
situation mimics find themselves in with faced with the dupe response curve

depicted in figure 2.3.

61

Figure 2.5

 

 

 

 

 

 

 

32:: 13232:

Similarity

62

Figure 2.6. Hit (dashed) and False alarm (solid) probabilities with respect to the
difference between distribution means, in units of standard deviation. From

simulations based on mate mimicry.

63

 

 

 

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64

Chapter 3
Natural history of Mimetus notius and signal sources in prey

webs.

Introduction

Spiders of the family Mimetidae prey upon web-weaving spiders (Archer 1941;
Czajka 1963; Cutler 1972; Lawler 1972; Lowrie, et al. 1972; Heimer 1986; Jackson &
Whitehouse 1986). Although they utilize a variety of behaviors to obtain prey (Heimer
1986), one of the more intriguing is their use of aggressive mimicry. Several mimetid
species have been observed to enter webs of other spiders and delicately pluck at the silk
threads, luring the resident spider into striking range; approximately one mimetid body
length (3-5 mm). The mimetid leaps at its prey, seizing it in its chelicerae and injecting
an apparently spider-specific venom, quickly immobilizing it. This remarkable behavior
has received little study, and the basic natural history critical to understanding the
behavior has not been studied. This chapter will address the natural history of a
representative Mimetid, Mimetus notius (Chamberlin 1923).

What little detailed information is known of the Mimetidae, aside from taxonomic
description, comes primarily from one major study (Jackson and Whitehouse 1986) and
three smaller studies. Lawler (1972) provided details on the life cycle and activity
patterns of Mimetus eutypus, but all of the diet information came from laboratory
interactions. Lawler also described the predatory behavior of this species, which
apparently does not use aggressive mimicry to capture its prey. Archer (1941) gave brief

details of several mimetid species’ habitats and diets, but was more concerned with

65

taxonomy than ecology. Heimer (1986) also provided some ecological information in a
taxonomic treatment, including a description of the range of behaviors used by different
species of mimetids to capture araneid prey. Two sets of anecdotal accounts of field
observations exist as well (Cutler 1972; Lowrie et al. 1972), but these provide little in the
way of detailed ecological information. In the most comprehensive study, Jackson &
Whitehouse (1986) present a detailed ethogram of the luring behaviors of two species of
Mimetidae from New Zealand and Queensland, document the families of prey taken by
these spiders in the field, and measure success rates in the lab. Although detailed
descriptions of the luring behavior of these spiders are presented, responses of the prey
are not discussed in detail. This provides part of the picture, but in order to understand
how the system as a whole functions, data on both sides of the interaction are crucial.

In order to understand the nature of the mimetid lure, it will be necessary to
measure the signals presented by mimetids and various potential models as well as the
reactions of mimetid prey to mimetids and to each potential model. Before measurements
can proceed it is necessary to identify the major arachnid prey of a mimetid species and to
identify the signal sources that occur in the webs of that prey. These signal sources
represent the most likely biological models of Mimetid mimicry for that particular prey
species. A detailed natural history is needed to provide this information.

While the studies above provide some information on the diet of several mimetid
species, only Jackson and Whitehouse (1986) quantify the relative abundance of different
prey in the diets of mimetids, and they do so only at the family level. The occurrence of

different signal sources in prey webs is completely unknown. Even such basic

66

information as life cycle, fecundity and habitat preference is known for only a few species
(Archer 1941; Lawler 1972).

The first step of an investigation into mimetid predatory behavior is presented
here, using Mimetus notius Chamberlin. The primary goals of this chapter are to present
some general natural history data for M noti us, identify their prey, and to identify the

major signal sources present in their prey's webs.

Study Species

Mimetus notius was first described by Chamberlin (1923). The most recent
taxonomic treatment is in Mott (1989), from which adult size data is taken; for detailed
taxonomic information, please see this excellent treatment. M. notius is a moderate sized
spider, adult females averaging 4.9 mm in length and adult males 3.6 mm. They occur
throughout coniferous forests in the eastern United States (Archer 1941; Mott 1989).
They are nocturnal; during the daytime they adopt a very cryptic posture on the
undersides of tree limbs making them extremely difficult to locate. After sunset they
begin moving among the branches, searching for the webs of their prey. They can be

readily located by searching coniferous forest edges at night with the aid of a flashlight.

General Field Methods

Censuses of nineteen different populations of M. notius were conducted over the

three years of the study, 1995-1997. Censuses differed somewhat both between and

67

within years due to ever-increasing knowledge of the spider and the different goals
associated with different aspects of the study. Below I will describe each of the different
censuses.

From March-November 1995 and April-October 1996 field censuses were
conducted to document seasonal changes in populations of spiders in four coniferous
forest plantations in southwestern Michigan, USA. Preliminary attempts to locate M.
notius (throughout the summer of 1994) showed that they are virtually absent in
deciduous trees, except in locations with conifers in close association, in agreement with
Archer (1941). Each census consisted of five twenty meter transects laid out along the
forest edge, where preliminary observations indicated that mimetids were most abundant.
The transects faced into the forest edge, penetrated one meter into the vegetation, and
were visually searched with the aid of a headlamp from the trees’ lowest branches to
approximately two meters above the ground. Censuses were conducted from 10 PM until
completion of all five transects. Total census time varied, with most transects averaging
45 minutes to an hour to sample. Seasonal variation in sampling time existed, with times
being shorter early and late in the seasons when fewer spiders were encountered. Visual
censusing was used because other sampling methods, such as sweep netting, destroy data
on interactions within webs. While visual sampling may miss smaller, non-web weaving
spiders, these are not of interest in the current context since they rarely interact with M
notius. Because spider community data is not analyzed here this does not present a
problem for the conclusions in this study.

All spiders located were identified, counted and assigned a web status (i.e.,

whether or not they were on a web). All M. notius encountered had their size, sex (if

68

adult), behavior (immediately upon detection), and prey recorded. For M. notius found on
webs, the status of the web (with or without a resident spider) and identity of web
residents (if any) were recorded. Mimetid egg sacs found were noted, with some
collected and reared in the lab.

In 1996 data collection on M. notius’ most common prey (Theridion sp., see table
3.1) occurred, including interactions between web-resident Theridion and their mates,
invaders and prey. Several spider species invade T heridion webs, including other
T heridion. Theridion invaders capable of mating with web residents (i.e. adults of the
opposite sex of an adult resident) were identified as mates, while large juveniles
(obviously past the first. molt) or same-sex spiders in a web were considered to be
conspecific invaders. Juveniles before first molt were considered to be recently emerged
and not included as invaders. This interpretation stems from the observation that nearly
all juveniles in this size range were encountered in large groups near an egg sac. All
heterospecific spiders in Theridion webs were identified as invaders. In these censuses,
only prey actually held in the chelicerae of Theridion were identified as T heridion prey.

Identification of most spiders occurred in the field. Spiders not immediately
recognizable were collected live and brought to the lab for identification and use in
various laboratory observations. The Araneidae, Dictynidae, Linyphiidae, Tetragnathidae,
Theridiidae and Uloboridae were identified only to genus due to the large number of
immature spiders encountered. Agelenidae, Clubionidae, Micryphantidae, Salticidae, and
Thomisidae were identified only to family since they were considered unlikely to be prey
for M notius, due to their size and/or lack of web-use. These spiders were also relatively

rare in the censuses. Identifications were made using Kaston (1948).

69

In 1995 transects were positioned randomly along the forest edge at each census
and censuses occurred at 2-4 week intervals. In 1996 five permanent transects were
established at each of the four sites and censused in regular 4 week intervals. Small
numbers of mimetids (no more than 1/transect) and potential prey (SS/transect) were
collected occasionally to provide laboratory specimens, except for the final census in
1996, when all mimetids encountered and large numbers of prey were collected for a
laboratory experiment to determine predatory efficiency (see below).

In addition to these seasonal censuses, five one-sample censuses were conducted
in 1996 during the peak of mimetid abundance. These censuses differed from the
previous censuses; they were single samples rather than being broken up into five
transects, and the amount of time was recorded for each census. During these censuses
collection of Mimetus and Theridion sp. ocuurred — the spiders collected were included in
the 1996 experiment on predatory efficiency. Data collection was the same as for other
1996 censuses.

A final series of censuses was conducted in 1997, consisting of two samples,
separated by 4 weeks, for each of nine sites. These censuses were standardized as 5 hour
censuses. All spiders located at the forest edge during the period from 10:00 PM —3:00
AM were counted. Data collection was as in other censuses except that no specimens
were collected in the first census, while in the second census at each site all Mimetus and
a large number of Theridion were collected for an experiment not discussed here (see
Chapter 5). Also in the second census, all prey in the webs of Theridion were collected

from the web and brought into the lab for identification.

70

Each section below presents a different aspect of the natural history of M notius.
In the portions describing methods the particular set of censuses used will be given, as

well as any methods beyond these general methods that are necessary for that portion of

the study.

Seasonality and life cycle

Methods.-- The seasonal data comes from the censuses of four sites in 1995 and
1996 that spanned the entire active season of Mimetus. The sites described here include
one dominated by white pine (Pinus strobus), one dominated by white spruce (Picea
glauca), one dominated by Norway spruce (Picea abies) and one site of mixed white
spruce and red pine (Pinus resinosa). Fourteen egg sacs were collected or produced in
the lab by Mimetids from these four sites in 1995. These were kept in the lab until
emergence of spiderlings. Each spiderling was measured within 24 hours of emergence.
Most were released into the site of origin within 48 hours of emergence, but several from
each egg sac were kept longer for observations of spiderling behavior.

Results and discussion.-- Figure 3.1 shows the seasonal abundance of M notius
on each of the sites in each year. The pattern of seasonal abundance was similar to that of
all spiders (figure 3.2) and to that of M notius' most abundant prey, T heridion sp. (figure
3.3). M notius emerged from their over-winter retreats as late-instar juveniles or adults
as early as March (Earliest observation, March 20), but no mating activity was observed
until May. Six matings were observed in the field between the dates of may 9 and June 6.

Sixteen egg sacs were found between May 30 and July 25 — fourteen egg sacs were

71

 

 

 

Sue

Nb

of f.

USU

SI

'xl- J

successfully collected. Adult spiders appear to die shortly after laying eggs, as adults
were rarely found after early July and before September (see figure 3.4). Egg sacs were
placed, unguarded, in the distal forks of spruce or pine twigs. Juveniles appeared in large
numbers in the field in July, and increased in size until late September. By September
roughly one-third of the mimetids found were adults (see figure 3.4). Overall numbers
began to decrease in October, and by mid-November no individuals could be located (see
figure 3.1). Overwintering appears to occur as adults or late instar juveniles.

Ten of the fourteen egg sacs produced spiderlings (emergence success=7l %).
Successful egg sacs averaged 16.9 (s.d. 9.7) spiderlings. These spiderlings were
relatively large (average 1.4 mm total length, s.d. 0.1) equaling ~28% of the total length
of females (4.9 mm; Mott 1989). Spiderlings emerged one at a time for 24-48 hours,
usually at a rate of ~ l/hour. The long time between mimetid spiderling emergence may
be a mechanism to avoid cannabilism, but no cannibalism was observed among mimetus
spiderlings left in vials for up to two days post emergence. After 2 days cannibalism was
observed, but no data were taken — spiderlings were generally separated earlier than this.
The large size of the offspring allowed the spiderlings to immediately begin to hunt the
spiderlings of other spiders, which emerge at a similar time of year (see figures 3.2 and
3.3). Several spider species that appeared inVulnerable to M notius as adults due to their
large size were readily taken in the lab as spiderlings by M notius spiderlings, when the
size advantage lies with M notius. M notius spiderlings successfully lured and captured

other spiderlings within 24 hours of emergence.

72

Vegetation Preferences:

Methods.—- Results from the 1995 and 1996 field censuses suggested that M
notius might be more abundant on spruce sites than on pine sites (see figure 3.1). The
data from the first set of 1997 census can be used to test this hypothesis. The second set
of 1997 censuses is not included in the test because the collection of specimens reduced
the number of spiders encountered sufficiently that averages of the two censuses
overestimate the variance. Of the ten sites sampled in the first set of censuses, three were
pine dominated and seven were dominated by spruce

Results and discussion.-- The absolute number of mimetids did not statistically
differ between spruce dominated and pine dominated sites (spruce: mean=9.0 SD=4.3,
n=7; pine: mean=5.3, SD=2.9, n=3, separate variances t-test, t=1.565, p=0.l69).
Relative abundance of mimetids, expressed in mimetids per web, also did not differ
(spruce: mean=0.036, SD=0.020; pine: mean=0.046, SD=0.044, t=0.368, p=0.743).
Thus, mimetids maintained themselves in approximately the same numbers and relative
abundance in spruce and in pine. The differences in the initial four sites may be caused

by other factors, but vegetational differences appear to be minimal.

Mimetus notius diet

Methods.- In all censuses, prey of M notius were collected and brought into the
lab, where they were identified, if possible, from their remains. All occupied webs

invaded by M notius had their residents identified, either in the field or by bringing them

73

into the laboratory. Residents were identified as being eaten or as “in web” depending on
whether the mimetid had begun devouring it. Interactions with mimetids can sometimes
last for several hours before either successful capture or abandomrient of the web by
either the resident or the mimetid, so these data are snapshots in time. Spiders “in web”
may or may not have been eaten later in the night, and were considered potential prey for
Mimetus. Because of the small numbers of prey captured at each site and census, no
attempt will be made to identify site or seasonal variations. Instead, all data will be
pooled.

Results and discussion.-— The composition of prey encounters from all censuses
is summarized in table 3.1. Although Mimetids are frequently referred to as being
exclusively araneophagic (Foelix 1982; Wise 1993), I found that insects comprise 32.5 %
of the diet of M notius. Jackson and Whitehouse (1986) studied two mimetid species
from New Zealand that exhibited kleptoparasitic insectivory in the lab. They did not
observe insectivory in the field, however. Heimer (1986) described several species of
mimetids that actively capture insects in the field. In the present study both active capture
and kleptoparasitism have been observed rarely in the field. Unfortunately, most
observations of insects as prey occurred after the mimetid obtained the prey. Thus it is
unknown in most cases whether a particular insect was actively captured or
kleptoparasitized by the mimetid. Regardless of capture method, insects unexpectedly
constitute a major portion of M notius’ diet.

Crab spiders (Thomisidae) formed an unexpectedly large fraction of M notius’
diet, given that these spiders do not normally inhabit webs (Table 3.1). All observed

instances of predation on crab spiders occurred in webs of Theridion or Dyctina,

74

suggesting that these crab spiders attempted web invasion themselves before falling prey
to M notius. The low number of encounters with uneaten crab spiders indicates that they
are either encountered infrequently or that interactions with these spiders occur rapidly, in
contrast with encounters with web-weaving spiders.

M notius attack and capture spiders primarily in the Theridiidae, Araneadae, and
Dictynidae. One genus, Theridion, accounts for 22.1 % of all prey captured, 32.7 % of
spider prey captured, and 40.4 % of all encounters with spiders (n=201 encounters; see
table 3.1). In addition, observations of interactions between Theridion and Mimetus in
both the lab and field show that luring is effective against Theridion. This leads to the
conclusion that T heridion is the major target of M notius mimicry in this system.
Although M notius utilizes mimicry against other spiders, we will limit further
consideration to Theridion. As the major prey it is the most important interactor in the
system, and trying to follow the entire food web for M notius and its prey would

introduce unnecessary complications into the remainder of this analysis.

Predatory efficiency

Methods.-- M notius and Theridion were collected from all of the sites censused
in 1996 for this portion of the study. In order to estimate the predatory efficiency of M
notius and to determine if coevolution was occurring across sites a two-part experiment
was conducted. These experiments involved staging interactions in the lab between M
notius and T heridion. All interactions occurred in small rectangular behavioral arenas.

These arenas were 15.2 x 10.2 x 3.3 cm in size, and constructed from pine with plexiglas

75

sides. Each arena had two access ports (2.1 cm diameter) in the top to allow for
introduction of organisms. These holes were plugged by #5 rubber stoppers when not in
use. Theridion and Mimetus carapace width was measured by taking ~5 seconds of video
tape of each spider in a dorsal view, then digitizing a single frame and measuring
carapace width using Image Pro Plus© software. Theridion were placed in behavioral
arenas with a single Drosophila and allowed 2 days to acclimate to the arena, build a
web, and eat the Drosophila. Theridion generally built webs in one of the upper corners
of the arena. After acclimation a Mimetid was introduced to the arena via the access port
opposite the web. The arena was then left for 12 hours (from 10 PM until 10 AM). The
success or failure of the mimetid was recorded at the end of this period.

Experiment 1. Effect of mimetid site. In order to determine whether local
adaptation by mimetus affected their predatory efficiency, M notius from 8 sites in 1996
(mimetids from the ninth site were used in experiment 2, below) were used to determine
predatory efficiency againt a common prey. Each M notius was paired with a single
Theridion; all T heridion were collected from a single site. Order of presentation was
randomized with respect to Mimetus site, and trials were conducted from 9/26/96-
11/12/96. A total of 78 M notius were presented with Theridion inexperienced with
laboratory conditions. In addition , due to difficulty in collecting large numbers of
T heridion from a single site, another 48 M notius were presented with experienced
T heridion, who had survived a previous laboratory interaction with M notius.

Experiment 2. Effect of Theridion site. In the second experiment, Theridion from

each of the nine sites were paired with M notius from a single site. Because of the small

number of M notius available from any one site, a repeated measures design was used.

76

Several of the mimetids died during the course of this experiment (conducted from
9/23/96 to 11/6/96), reducing an initial sample size of 30 to a final sample size of only 18.
Between experiments mimetids were housed in small Drosophila vials, and fed one
Drosophila two days before each interaction to maintain constant hunger levels.
Individual Mimetus were presented with Theridion of approximately the same size (1 0.5
mm) in each repetition to minimize variation due to size assymmetry. Order of
presentation was randomized with respect to Theridion site, and each T heridion was used
only once.

If Mimetus have locally adapted to Theridion, we would expect to see an effect of
Mimetid site in experiment 1. If T heridion have locally adapted to Mimetus, an effect of
Theridion site was expected in experiment 2. Coevolution would be implied if significant
effects were found in both experiments. If variation is detected in both experiments, then
we should be able to relate this variation to the abundance of Mimetus in the sites and/or
the cautiousness of T heridion in the sites. Mimetus emerge at a large size (see seasonality
and life cycle, above), and I have not observed them ballooning, nor are they commonly
found in samples of aerial disperising spiders (Salmon and Homing 1977). T heridion
also appear to balloon infrequently according to Salmon and Homing (1977), and I have
not observed them to do so in this study site. This reduces their ability to migrate
between populations, increasing the possibility of local adaptation.

Results and discussion.-- Experiment 1. No effect of Theridion experience on
Mimetus predatory efficiency was detected. Experienced Theridion survived 72.9 %
(n=48) of the time, while na'i've Theridion survived 73.1% (n=78) of the time (Pearson’s x

2<0.001, DF=1, p=0.98, N=126). Results from trials with experienced and naive

77

Theridion will be pooled even though power was weak (~0.2). The extremely small
effect size naturally leads to a test with low power. Mimetus success ranged from 8% to
36% across 8 sites, but no effect was detected(Pearson’s x2=, DF=7, p=0.77, N=126,
power E 0.5). Overall predatory efficiency in these trials was 27%.

Experiment 2. There was also no effect of Theridion site (Cochran’s Q test,
Q=8.5, d.f.=8, p=0.39). Overall predatory efficiency in these trials was 57%. The large
difference in predatory efficiency between experiment 1 and experiment 2 suggested that
Mimetus learned the “game” within the arena after repeated trials. A posterior test of this
possibility, using mimetid trial number as a factor, showed no effect of mimetid
experience on predatory efficiency in this experiment (Cochran’s Q test, Q=9.5, d.f.=8,
p=0.30).

Neither of these experiments revealed an effect of local adaptation on mimetid
predatory efficiency. Keep in mind, however, that there is, at this point, no underlying
mechanism postulated for such effects. A more powerful test would be to look for trends
in a dimension relevant to a particular mechanism that predicts the direction of evolution
in each species. The model in chapter 2, with appropriate modifications (see Chapter 5)
provides a mechanism for predicting the relative cautiousness of prey confronted with

differing environments.

78

Signal sources in Theridion webs

Methods.» In censuses conducted in 1996 and 1997, all potential signal sources
in Theridion webs were identified, either in the field of the lab. The second set of
censuses in 1997 were designed primarily for collection of Mimetus and Theridion for
laboratory experiments, and collection of prey from Theridion webs. The 1997 samples
were limited to 7 sites because two of the sites sampled yielded no Theridion prey in the
second census. This is most likely a sampling error due to very low numbers of
Theridion at these sites. The data for 1997 include only prey collected in the second set
of censuses.

Results and discussion.- Figures 3.5 and 3.6 present the data on occurrence of
various signal sources in the webs of Theridion sp, the most common prey of M notius.
Prey, mates, and invading spiders (Theridion, A rgyrodes or Grammonota) were the most
consistently abundant signal sources in Theridion webs; all other potential signal
generators were rare in these samples. These signal sources must thus be considered as
the most likely models of M notius aggressive mimicry.

In both years, small Diptera made up a major portion of Theridion’s diet, and
were an abundant signal source. Diptera were found in the diet at all sites in both years
and at all times of the year. In 1997 small Homoptera were also very abundant, but they
were absent from the 1996 samples. The difference between years may result from the
different prey sampling methods used in the two years (in 1996 only prey currently being
fed upon were collected, while in 1997 all prey in the web were collected). Available

data suggest, however, that Homoptera are not a consistently important part of

79

Theridion’s diet. Homoptera, even in 1997, did not occur in all of the sites; their high
overall abundance was the result of their being extremely abundant in only two sites. One
hundred Homoptera were collected in 1997; eighty-seven were found in just two sites,
with the remaining thirteen being distributed across four other sites (table 3.2). Because
of their more consistent availability dipteran prey are a more likely model for M notius
aggressive mimicry than homopteran prey.

The 1996 sample included four sites censused throughout the season, including
Theridion’s breeding season. Mates appeared as a fairly small percentage of the overall
signal sources (table 3.2), but are actually the predominant signal source during the short
breeding season. Mates do not show up in the 1997 sample because this was a single

sample taken outside of the mating season. Thus, like Homoptera, males are an
inconsistent presence in T heridion webs and appear to be an unreliable model for
Mimetus to mimic.

Web invaders, both conspecific and heterospecific, form a large percentage of the
potential signal sources in both years. Web invaders occurred at all sites censused. In the
seasonal samples taken in 1996, web invaders were found throughout the year, unlike
mates or homopteran prey. Web invasion appears to be an important and consistent
aSpect of Theridion’s ecology, and web invaders could potentially serve as a model for M
notius mimicry if they elicit approach from Theridion as part of their web-defense
behavior.

Three different hypotheses exist concerning the identity of the model in this
aggressive mimicry system. Two of these are derived from the literature, by analogy with

previously studied mimetids. First, Jackson and Whitehouse (1986) suggested that the

80

lure used by mimetids from New Zealand and Queensland (Mimetus maculosus and an
undetermined species of Mimetus) mimicked the signals sent by prey trapped in the web,
a conclusion shared by Bristowe (1941) and Gerhardt (1924). secondly, Czajka (1963)
described a single incident in which an Erofurcata displaced a courting male Meta
segmentata, then proceeded to lure, kill and eat the female. This suggested to Czajka the
hypothesis that Erofurcata mimicks the courtship signals of its prey. The third
hypothesis postulated here is based upon my observations of Theridion webs and
interactions between Mimetus and Theridion. The abundance of invaders of T heridion
webs, both conspecific and heterospecefic, forces consideration of the possibility that M
notius mimics these invaders. Invading spiders may either take over the web
(conspecifics, Riechert 1982; Wise 1993: heterospecifics, Toft 1988) or act as
kleptoparasites (conspecifics, Jakob 1991: heterospecifics, Cangialosi 1991): in either
case, defense will often be advantageous to the resident. Thus, invading spiders can
present cues that elicit approach of the resident in the form of active defense. These cues
could be mimicked by M notius to lure T heridion within range.

Dipteran prey, mates, invading Theridion, Argyrodes and Grammonota represent
the most consistently abundant signal sources in prey webs. Determination of which of
these five sources actually functions as the biological model in this system will require
measurements of the signals each emits and the responses of Theridion to each.
Comparison of these data with the signals of M notius and the responses of Theridion to

M notius should then reveal the identity of the biological model (see chapter 4 for these

data) of M notius aggressive mimicry.

81

General Discussion

This documentation of Mimetus notius natural history had three major goals.
First, to document some basic natural history of this species. Second, to identify the
major prey of M. notius for which aggressive mimicry might be useful. Third, to identify
the important signal producers in that prey's web. This chapter presented the data
necessary to achieve each of these goals.

The single most abundant prey susceptible to M notius aggressive mimicry has
been identified as Theridion sp. In the process of discovering this it was also found that
insects form an unexpectedly large part of the diet of M notius. Insects formed a larger
portion of the diet than any single spider species (remember though that spiders as a
group formed 67.5 % of M notius diet). Since it is unlikely that insects respond to the
vibratory lure used by M notius, Theridion (32.7 % of spiders eaten) is still considered to
be the primary dupe of M notius.

Five major signal sources in Theridion webs have been identified. Each of these
signal sources is a potential biological model of M notius aggressive mimicry. In
addition to the previously suggested possibilities -- mates (Czajka 1968) and prey
(Jackson and Whitehouse 1986) -- web invaders have been identified as a major aspect of

Theridion ecology. In this study there were three important web invaders: Argyrodes,
Grammonota, and non-mate Theridion. These results narrow the field of potential
candidates for the biological model in this system. The signal properties and response of
Theridion to each potential model need to be studied in greater detail before a more

definitive determination of the biological model can be made.

82

Literature cited

Archer, AF. 1941. Alabama spiders of the family Mimetidae. Papers of the Michigan
Academy of Arts, Science and Letters 27:183-193.

Cangialosi, KR. 1991. Attack strategies of a spider kleptoparasite: effects of prey
availability and host colony size. Animal Behaviour 41:639-648.

Cutler, B. 1972. Notes on the biology of Mimetus puritanus Chamberlin (Araneae:
Mimetidae). American Midland Naturalist 87:554-555.

Czajka, M. 1963. Unknown facts of the biology of the spider Erofurcata. Polskie
Pismo Entomologiczne 33 2229-23 1.

Foelix, RF. 1982. Biology of Spiders. Harvard University Press. Cambridge, MA.

Heimer, S. 1986. Notes on the spider family Mimetidae with a description of a new genus
from Australia (Arachnida, Araneae). Entomologische Abhandlungen 49(7):]13-
137.

Jackson, R.R. and M.E.A. Whitehouse 1986. The biology of New Zealand and
Queensland pirate spiders (Araneae, Mimetidae): aggressive mimicry,
araneophagy and prey specialization. Journal of Zoology, London 210:279-303.

Jakob, EM. 1991. Costs and benefits of group living for pholcid spiderlings: losing food,
saving silk. Animal Behavior 41:711-722.

Kaston, B.J. 1948. Spiders of Connecticut. State Geological and Natural History Survey
Bulletin # 70. State of Connecticut.

Lawler, N. 1972. Notes on the biology and behavior of Mimetus eutypus Chamberlin and
Ivie (Araneae: Mimetidae). Notes Arachnol. Southwest 3:7-10.

Lowrie, D.C., W.R. Icenogle and ME. Thompson 1972. Notes on the biology of the
genus Mimetus. Notes Arachnol. Southwest. 3:19.

Mott, DJ. 1989. A revision of the genus Mimetus in North America (Araneae,
Mimetidae). Unpublished PhD. Dissertation, Department of Zoology, Southern
Illinois University at Carbondale.

Riechert, SE. 1982. Spider interaction strategies: communication vs. coercion. pp. 281-
315 IN: Spider Communication: Mechanisms and Ecological Significance. Witt,
RN. and J .S. Rovner, eds. Princeton University press, Princeton, NJ.

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Salmon, J .T. and Homer, NV. (1977). Aerial Dispersion of Spiders in North Central
Texas. Journal of Arachnology 5:153-157.

Toft, S. 1988. Interference by web take-over in sheet-web spiders. XI. Europaisches
Arachnologisches Colloquim, Technische Universitéit Berlin, Dokumentation
Kongresse und Tagungen 38:48-59.

Wise, DH. 1993. Spiders in Ecological Webs. Cambridge Studies in Ecology.
Cambridge University Press, Cambridge.

84

Table 3.1. Mimetid encounters — Data summed over all censuses (n=23l encounters)

 

Prey type # eaten # In web % of all encounters % of eaten
Araneidae
Araniella l 0 0.4 1.3
C yclosa l l 0.9 l .3
Epeira 2 3 2.2 2.6
Eustala 2 4 2.6 2.6
Mangora 0 2 0.9 0.0
Neoscona 2 4 2.6 2.6
N uctenea 0 3 l .3 0.0
Wixia O l 0.4 0.0
Unknown 4 2 2.6 5.2
Araneidae
Dictynidae
Argenna l O 0.4 1.3
Dictyna 7 l 1 7.8 1 1.
0
Liniphiidae
Frontinella 0 3 l .3 0.0
Pityohjphantes l l 3 6. l l .3
Salticidae 0 2 0.9 0.0
Tetragnathidae
Tetragnatha 3 8 4.8 3.9
Theridiidae
Argyrodes 4 19 10.0 5 .2
Grammonota 0 4 1 .7 0.0
Mysmena 0 l 0.4 0.0
Steatoda 0 l 0.4 0.0
Theridion 17 65 35.5 22.
l
Thomisidae 6 l 3.0 7.8
Uloboridae 0 2 0.9 0.0
Uloborus 0 2 0.9 0.0
Insects 25 3 12.1 32.
5
Unidentifiable 1 1 0.9 1.3
spiders
Total 77 154

85

Table 3.2. Theridion prey collected from webs in 7 sites in September of 1997.

 

 

Prey Order # found in Average % # of sites found
webs of prey/site in as prey

Unidentifiable Insects 107 49.7 7

Homoptera 100 20.2 6

Diptera 54 19.3 7

Hymenoptera 1 l 5 .6 7

Other insects (4 Orders) 6 2.0 3

Aranaea 9 3.2 5

Total prey 287

86

 

Figure 3.1. Mimetus notius seasonal abundance across four sites in A) 1995 and

B) 1996

87

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89

 

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92

 

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93

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Figure 3.5. Potential signal sources in Theridion webs. 1996. seasonal.

Absolute number and percentage of all signal sources (n=194). Data
pooled from 4 sites censused monthly, April-October, 1996. Prey were
included only when found actually being fed upon by Theridion.

Percentages given are of all potential signal sources in 1996.

95

 

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98

Chapter 4.

Determining the model(s) in the Mimetus notius aggressive mimicry system.

Introduction

Spiders of the family Mimetidae have been hypothesized to mimic the vibrational
"signatures" of two different stimuli in order to entice their prey within striking range.
An early study suggested that mates may be the model of mimicry by the mimetid Era
furcata (Czajka 1968), while Jackson and Whitehouse (1986) suggested that prey were
the model for Australomimetus maculosus and an undetermined species of Mimetus from
New Zealand. Determination of the model must be made explicitly by comparing the
responses of spiders to mimetids and potential models and by studying the nature of the
vibrations each of these organisms cause in the web. Neither Czajka (1968) nor Jackson
and Whitehouse (1986) explicitly compared the responses or signals of their mimetids to
potential models, but based their conclusions on limited, qualitative observations and
inference. Other papers on Mimetids have failed to address this question entirely (Archer
1941; Lawler 1972; Lowrie et al. 1972; Heimer 1986). This chapter focuses on empirical
measurement and comparison of signals within the web of a common dupe of Mimetus
notius, Theridion sp., and the responses of T heridion to those signals.

Natural history data (chapter three) point to five stimuli that are present in high
enough abundance to be considered as potential models for M. notius mimicry:

chironomid prey, conspecifrc web invaders, mates, and two species of heterospecific web

99

invaders, Argyrodes sp. and Grammonota sp. Although the idea of potential competitors
acting as a lure has not been raised before in aggressive mimicry, web-invading spiders
normally elicit approach for the purpose of active defense; web-invading spiders could
thus be a reasonable model for an aggressive mimic attempting to lure Theridion within
its grasp. Military tacticians use a similar tactic when they send what appears to be a
weak force after a stronger force in an attempt to lure them out of a defensive position.
The presence of multiple potential models also suggests the possibility that M. notius is
an abstract mimic, using signals that are general enough to be mistaken for any one of
several potential models.

This chapter will present data collected during laboratory-induced interactions
between T heridion and each of the potential models of M. notius. The data from these
interactions will be compared to data from interactions between Theridion and M notius.
These data comprise 2 sets: The responses of Theridion to each of the intruders and the
properties of vibrations created in the webs of Theridion by each intruder. The first data
set will be used to determine which potential model causes a response in Theridion
similar to the response caused by M. notius. The second data set will be explored to
discover what properties of these signals are most similar to those used by M. notius. The
results of these analyses will determine the most likely model(s) in this aggressive

mimicry system.

100

Methods

All interactions occurred in small rectangular behavioral arenas. These arenas
were 15.2 x 10.2 x 3.3 cm in size, and constructed from unfinished pine with Plexiglas
sides. Each arena had two access ports (2.1 m diameter) in the top to allow for
introduction of organisms. #5 rubber stoppers plugged these holes when not in use.

All spiders were weighed to the nearest 0.05 mg on a Mettler B6 analytic balance.
Carapace width was measured by videotaping them from below along with a metric ruler
for scale. These video images were then digitized and measurements made using Image
Pro-Plus© software. Carapace width measurements were made to the nearest 0.1 mm.
After measurement, Theridion were placed into behavioral arenas with a single
Drosophila. Theridion were allowed 2 days to acclimate to the arena, build a web, and
eat the Drosophila. Theridion generally built webs in one of the upper corners of the
arena.

After acclimation, the webs were attached to a vibrometer and illuminated by red
light. Red light >650 nm was used to illuminate the arenas to avoid disturbing the spiders
(Yamashita 1985). Red light production involved filtering white light with a combination
of red and blue filters (Leec High temperature Bright Red #27 and Congo Blue # 181)
that effectively eliminated all light <650 nm. A preliminary experiment demonstrated
that red light produced in this way had no effect on M. notius' predatory success against
Theridion (50% success in red light vs. 54% in dark conditions, Fisher exact test, p=1.00,
n=2 1 , 6 hr trials). A paper grid was placed along the rear of the arena to provide scale for

measurements. Two different grids were used: initially a .25 cm grid was used, but later

101

experiments used a 1 cm grid. No differences resulted in the data from this as the grids
were used merely as a way of converting distances measured on the screen to actual
distances.

The vibrometer used in these experiments was originally developed by Wilcox
and Kashinsky (1980) for measuring the water surface vibrations of water striders, but
has since been modified for use in spider webs. (Wilcox et al. 1996; Wilcox pers. com.)
The vibrometer consisted of a galvanometer with a stylus attached to it. The stylus was
then attached to the web — the web adhesive provided firm attachment. When the web
vibrated, the stylus also vibrated, causing an induction of current within the
galvanometer. This signal was amplified by a World Precision Instruments DAM-50
amplifier O (Settings: Low filter 0.] Hz, High filter lOOHz, AC Mode, Gain 1000).
Following amplification, the signal was frequency modulated by a Vetter Model lOOOt
recording adaptor so that the signals could be recorded on the audio track of a videotape.

Theridion were allowed to acclimate to the illumination and the presence of a
stylus in its web for 30 min. If during that time the Theridion abandoned the web or
attacked the stylus the interaction was terminated. After the acclimation period an
intruder (either a M. notius, chironomid, Theridion mate, Theridion invader,
Grammonota or Argyrodes) was introduced into the arena via the access port opposite the
comer of the arena where Theridion had built its web. This allowed the intruder to enter
the web under its own power. Interactions were video taped with a Canon L2 Hi-8
camcorder set on slow shutter (1/30 second) to accommodate the low light levels. The

signal from the vibrometer was simultaneously recorded on the audio track of this tape,

102

providing concurrent records of the spiders’ movements and the vibrations of the web
caused by those movements.

The main question being addressed was whether there were similar patterns in
signal and response. To address this question, signals and responses were analyzed
separately for patterns; the subsequent patterns were then compared for similarity. Due to
equipment failures and uncooperative subjects there are several cases where responses
were recorded but no signals were measured or signals were measured but no response
occurred. For this reason the sample sizes of the data sets are not equal.

Response of Theridion to each of the stimuli was measured from video taped
records of the interaction trials. In each trial, each of the following was measured: type of
first response (signaling vs. locomotion), direction of first locomotion (approach intruder
vs. retreat from intruder), distance between subjects at first Theridion response (cm) and
average speed and direction of each locomotion. The qualitative variables were simply
coded from the videotapes. Distances were calculated by measuring the distances on the
video screen and calibrating to an actual distance using the grid lying along the rear wall
of the arena.

Times for movements were measured from the counter on the videotape (to the
nearest 1/30 second). Speed was measured for each movement by dividing the distance
moved by the time taken to move that distance. Approaches (movement towards the
visitor, within a tolerance of 60 degrees to either side of the line connecting the two
creatures) were coded as positive values, retreats (the opposite of approaches) as negative
values, and movements that were considered neither approaches nor retreats (i.e.

movement perpindicular to the line connecting the 2 animals, defined as outside the

103

tolerances for approach or retreat) were not included in the analysis. The average speed
per movement was used as a summary variable and was calculated as:

I approach speeds + Qetreat speeds

total number of approaches and retreats
This formulation allowed this variable to contain information about both the direction and
magnitude of movement; Theridion that retreat faster or more often than they approach
receive a negative value, those that approach more often or more rapidly than they retreat
receive a positive value. This also has the advantage that fast movements get weighted
heavily compared to slow movements. This is advantageous because these rapid events
are generally the most important in terms of capture or escape. It was also thought, a
priori, that the first response of Theridion would be particularly important, so the speed
and direction of the first response were collected as a separate variable.

Signals were analyzed by downloading the signal data stored on the videotape
into CANARY, a Fourier analysis program (Cornell Bioacoustics Research Program
1994). From this program the frequency of peak power (hereafter referred to simply as
peak Hz) of each signal was determined. Signal pulses closer together than 1 sec
(measured from the start of one pulse to the start of the next pulse) were considered as
part of the same bout and analyzed together. Any break between pulses of greater than
one second was considered as part of another bout, and a separate Fourier analysis was
run for each bout (see figure 4.1 for a representative signal with definitions). The
breakpoint of one second was decided upon by analysis of the interpulse intervals for a
subset of the trials. These intervals had a mean of ~0.5 sec and a long tail starting at

approximately 1 second, thus 1 second was determined to be a “natural” as well as

104

convenient breakpoint. In addition a “baseline peak Hz” was measured before
introduction of the intruder. This baseline measurement gave an indication of the noise-
level in the system for each trial and provided a means for standardizing measurements
with respect to that noise.

As well as Peak Hz and base line Hz, the frequency range of the signals was
measured, as were the time of the bout (bouts as defined above) and the interpulse
interval. The interpulse interval was measured simply as the average time between the
initiation of one pulse in the bout and the initiation of the next pulse in the bout. The time
of the bout was measured from the initiation of the bout until the beginning of the last
pulse in the bout — bouts consisting of a single pulse were excluded from this analysis due
to the difficulty of judging precisely when a pulse "ended" from the spider's point of
view. Other studies have used similar variables to study the timing and frequency
characteristics of vibrations emitted by prey (Suter 1978), mates (Bleckmann and Bender
1987; Schmitt, Friedel and Barth 1993; Femandez-Montraveta and Schmitt 1994),
conspecific aggressors (Femandez—Montraveta and Schmitt 1994) and web residents
(Vollrath 1979). All variables were averaged over an entire trial, and each trial average

used as a single data point in all analyses.

Results:

Response data: All response data are summarized in table 4.1. The two

qualitative variables, first response and direction of first locomotion, reveal similar

patterns. For each of these variables, M. notius provoked responses from resident

105

Theridion that were very similar to the responses provoked by invading Theridion. Also
showing close similarity were responses to potential mates and to Argyrodes. Signaling
rates in response to Grammonota differed marginally from response to M. notius (p<0.1,
Fisher exact test). Direction of first locomotion differed significantly for Grammonota
(p<0.001, Fisher exact test), which Theridion never approached first, and marginally for
chironomid prey (p<0.1, Fisher exact test), which Theridion usually approached on their
first locomotion. Figure 4.2, a biplot of these variables, shows that considering these
variables together reveals that resident Theridion's response to M. notius is more similar
to their response to invading Theridion than to any other stimulus.

The data on distance at first response was non-normal, and transformations failed
to normalize it, so a Kruskal-Wallace (K-W) nonparametric analysis of variance was
conducted, showing a significant difference existed between Theridion responses to
intruder types (K-W test statistic: 29.24, p<0.001). Responses to each type of invader
were compared individually to the responses to M. notius using Mann-Whitney U-tests.
This analysis revealed significant differences between Theridion’s distance at first
response when confronted with M notius and T heridion '3 distance at first response in
interactions with Grammonota (U=10, p=0.00008) and in the distance at first response
when confronted with Mimetus vs. when confronted with prey (U=3 l , p=0.006).
Theridion did not respond to Grammonota until they were less than 0.5 cm away, and
then always retreated. Conversely, they responded to prey at extremely long distances,
generally by approaching them. Responses to the other stimuli occurred at intermediate
distances. Distance at first response to M. notius did not differ (p>0. 1) from distance at

first response to conspecific invaders (U=93), mates (U=48.5), or Argyrodes (U=66.5).

106

Average response speed per movement was also non-normal, so the analysis for
this data follows that for distance at first response. Again, the over-all Kruskal-Wallace
Analysis of variance yields a significant result (K-W Test statistic=19.616, p=0.001).
Analysis of Mann-Whitney U statistics reveals that T heridion move much more quickly
toward prey than toward M. notius (U=14, p=0.001). This procedure also reveals a
potential difference between responses to Mimetus compared to mates — T heridion
approach mates slightly more quickly than they approach Mimetus (U=63, p=0.083). No
significant differences were found in approach speed per movement between T heridion
confronted with M. notius and any of the other spiders (p>0. l; Conspecific invaders,
U=64;Argyrodes, U= 70; Grammonota, U=72).

Speed at first response was highly correlated with average response speed per
movement (Pearson correlation coefficient=0.66, p<0.001); it is presented primarily to
highlight the rapid first approach of Theridion towards prey when compared to first
response speeds towards other invaders. This variable was normally distributed, so t-tests
were used to compare the difference between T heridion responses to Mimetus to
Theridion responses to the other invaders. This analysis shows a significantly faster
approach towards prey than toward Mimetus (t=3.4, p=0.003), but no other differences
(Argyrodes, t=0.16; Grammonota t=1.3; mates t=0.4; invaders t=0.08; All p-values
>0. 1 0).

Viewing the variables distance at first response and average speed per movement
in a biplot (figure 4.3) highlights the difference in Theridion responses to the various
stimuli. Because of the correlation mentioned above, the third variable is not presented

as part of this graphic since it would add little, if any, information. Again, a large

107

difference between response to prey compared to spiders are visible, with all of the
spiders clustering around M. notius’ position on the graph.

Signal Data. Signal data are summarized in table 4.2. The main variable from
Fourier analysis, peak Hz, was significantly correlated with the size of the resident spider,
and despite an attempt at constrained randomization of sizes there were significant
differences in resident size between groups (ANOVA, F =7.12, p=0.00002). This was due
in large part to the constraint of having to use adult females as residents in mating trials.
Juveniles were available for other trials. In addition, peak Hz were also correlated with
the base-line Hz, which was also correlated with size. A multiple regression was
performed on log(peak Hz) (a log transform was necessary to normalize the data), using
size and base line Hz as predictors. This regression was highly significant (p<0.00001)
and each factor contributed to it (Log(resident weight), p=0.0006; Log(Base peak Hz),
p=0.005). The residuals of this regression were used for further analysis to eliminate the
effects of these confounds. The residuals were approximately normally distributed, so an
analysis of variance was performed using the residuals as the dependent variable and
intruder type as a categorical variable. This overall test was not significant (F=1.88,
p=0.l 1). In order to keep the analyses for signal and response data similar, separate t-
tests were carried out as in the response data, revealing a significant difference between
Mimetus signals and prey signals (t=3. l , p=0.007), keeping in mind of course the non-
significance of the overall test. None of the other individual t-tests revealed significant
differences in this residual value (Argyrodes, t=0.008; Grammonota, t=0.7; mates, t=O.2;

invaders, t=0.6; all p-values >>O. l).

108

The other signal variables presented fewer difficulties. The frequency range of
the signals showed no significant differences between Mimetus and any of the other
invaders in an overall ANOVA or in individual t-tests. Similarly, the inter-pulse interval
revealed no significant differences. Bout length, however, revealed several interesting
differences. An overall ANOVA showed a significant effect of invader type (after log
transformation; F =49, p=0.001). Further investigation of this using individual t-tests
(log-transformed) comparing Mimetus signals to each of the other signal types revealed
significant differences between Mimetus signals and signals from prey (t=2.5, p=0.02),
and mates (tr-2.9, p=0.01). Neither Argyrodes (t=2.5, p=0.1), Grammonota (t=0.6,
p=0.5), nor conspecific invaders (t=1.4, p=0.2), displayed a tendency to differ from
mimetids in bout length.

Displaying the two variables that reveal significant diffemces together in a biplot
(figure 4.4) highlights once again that prey are extremely different from the other stimuli.
As in the response data we see a tendency for M. notius to positioned in the center of a

cluster formed by the other spiders.

Discussion:

T heridion responses to chironomid prey differ from their responses to Mimetus.
Prey, which have been considered the most likely model in the past (Jackson and
Whitehouse 1986), were also the only potential model to display a significant difference
from M. notius signals in both residual peak Hz and bout length. Based on both response

and signal data, Chironomid prey can be ruled out as potential models in this system. It

109

is still possible that other prey-types are models in this system, but given the importance
of chironomids in T heridion's diet (see chapter 3) this is unlikely.

Grammonota can be ruled out as a model, since Theridion never approach
Grammonota and respond to them at much shorter distances than they respond to
Mimetus. Observation of Grammonota behavior while in Theridion webs reinforces this
conclusion. Grammonota, unlike Mimetus, conspecifics and Argyrodes, tend to spend a
relatively short amount of time in their interactions with Theridion. They enter the web
quickly, usually near the hub, and rarely signal — they charge toward the resident, through
the web and then exit, sometimes displacing the resident entirely, but often just causing it
to shift to the side as the Grammonota goes past. Grammonota do not appear to be
invaders that take over the web for long periods, and would not make a good model for
an aggressive mimic, as evidenced by Theridion's first responses to it — they never
approach, and retreat from Grammonota faster than from any other stimulus in the web
(see table 4.1).

Mates provoke only a slightly different response than mimetids in average
approach speed. This marginal result is not enough, by itself, to rule out mates as a
potential model in the system. Small differences were also seen in bout length between
mates and M. notius, but again, are not enough in and of themselves to rule out mates as a
potential model. The natural history data presented in chapter three show us that mates
are only available for a brief part of the year, while invaders (Theridion, Argyrodes, and
Grammonota) are abundant throughout the active season. M. notius lures Theridion

throughout the active season, not solely during the breeding season. This information,

110

combined with the small differences in approach speed and bout length, argues strongly
against mates being an important model, at least outside of the mating season.

Neither A rgyrodes nor conspecific invaders can be ruled out as potential models
for M. notius mimicry by the responses of Theridion to them. Responses toward
Mimetids, conspecific invaders and Argyrodes were very similar, and based on the
responses of Theridion, neither conspecifics nor Argyrodes can be ruled out as potential
models. Based on the evidence available it is impossible to determine a single model, but
the possibilities have been reduced to two from the original five: the potential models left
are invading conspecifics and Argyrodes: these potential models fit into the general
category of web usurpers. Looking again at the biplots presented in figures 4.], 4.2 and
4.3, you can see that M. notius appears roughly in the center of a cluster of
responses/signals caused by other spiders, with prey being away from this cluster. This is
especially evident in figure 4.3. This suggests that M. notius may be an abstract mimic of
a general class of web visitors, namely potential invaders. M. notius is a much larger
spider than any of the others, and should cause a much different response on the part of
residents than these other spiders if they can be detected. By emitting signals in the
middle of this "cloud" of invading small spiders it could be hiding its' identify well
enough that T heridion needs to closely inspect the intruder in order to determine its
identity. The possibility of mimicking competitors has not been studied before, so this
system offers a unique opportunity.

In the mathematical models and data presented in chapter two, mimicry of mates
was predicted to produce concrete mimicry systems, while mimicry of prey was predicted

to produce abstract mimicry systems. Mimicry of web usurpers (or, more generally,

111

competitors, be they conspecific or heterospecific) was not addressed at that point. Given
that the data here suggest that the most likely model for M. notius mimicry may be
competitors, and a variety of them at that, a new mathematical model must be devised to
represent this situation. If abstract mimicry is favored under these conditions it is not
surprising that this portion of the study was unable to clearly identify a single model:

multiple models may exist, and may even be expected.

112

Literature cited

Archer, AF. 1941. Alabama spiders of the family Mimetidae. Papers of the Michigan

Academy of Arts, Science and Letters 27:183-193.Czajka, M. 1963. Unknown
facts of the biology of the spider Ero furcata. Polskie Pismo Entomologiczne
33:229-231.

Bleckmann, H. and M. Bender, (1987). Water surface waves generated by the male
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Heimer, S. 1986. Notes on the spider family Mimetidae with a description of a new genus
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Jackson, RR. and M.E.A. Whitehouse 1986. The biology of New Zealand and
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Lawler, N. 1972. Notes on the biology and behavior of Mimetus eutypus Chamberlin and
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Schmitt, A., T. Friedel, and F .G. Barth (1993). Importance of pause between spider
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NJ.

114

 

Table 4.1 Theridion response data.
For non-percentage data, Lower quartile, median, and upper quartile are shown.

 

Responses of Theridion to:

 

 

 

 

 

 

 

Variable M. notius Theridion Mates Grammonota Argyrodes Prey
invaders

First response 40 45 33 8 ** 61 22

(% signaling)

First movement 50 43 67 0 ** 56 89 *

(% approaching)

Distance at first 0.7 0.8 0.9 0.1 0.8 5.0

response (cm) 1.2 2.1 1.8 0.3“ 4.3 9.4 **
4.0 6.8 7.1 0.4 11.4 13.9

Average approach -0.33 -0.31 0.02 -0.31 -0.01 0.46

speed per -0.07 -0.20 0.14 * -0.14 0.06 0.78 **

movement (cm/sec 0.14 0.01 0.20 -0.09 0.17 1.33

towards “invader”/

movement)

Speed of first -0.33 -0.16 -0.10 -0.55 -0.24 0.13

response (cm/sec 0.05 -0.02 0.02 -0.27 0.03 0.86 **

towards invader) 0.14 O. 14 0.20 -0.09 0.24 1.54

N 14 14 6 12 7 11

 

 

 

 

 

 

 

 

*=p<0.l, **=p<0.05

 

115

 

 

Table 4.2 Signal data in T heridion webs.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

JS.D.]

Value of signals by:

Variable M. notius Theridion Mates Grammonota Argyrodes Prey
invaders

Residual Peak -O.10 -0.38 -0.15 0.08 -0.10 0.26 **
Hz [0.2] [0.3] [0.5] [0.5] [0.5] [0.3]
Range (Hz) 6.1 6.2 7.4 6.3 5.4 5.7

[1.6] [2.9] 2.5] [3.0] [1.3] [1.7]
Bout length 2.1 3.5 3.7 ** 1.5 0.9 1.0 **
(seconds) [1.1] [2.4] [1.1] [0.3] [0.3] [0.5]
Interpulse 0.5 0.4 0.5 0.5 0.4 0.5
interval [0.2] [0.2] [0.2] [0.2] [0.1] [0.3]
(seconds)
N 14 12 7 5 3 11
**=p<0.05

 

116

 

 

Figure 4.1. A representative signal series from a M. notius in a Theridion web. The
recording was made on the audio track of a videotape and decoded using
CANARYO (Cornell Bioacoustics Research Program 1994). The upper panel
shows a frequency spectrum derived from the signal trace in the lower panel.
Important measurements are also shown. A=Frequency of peak power (a.k.a peak
Hz); B=interbout (>1 sec between initiation of one pulse and the next);
C=interpulse (<1 sec between initiation of one pulse within a bout and the next);
D= Bout length (time from the initiation of the first pulse in a bout to the
initiation of the last pulse in the bout. In this example the interpulse duration and

the bout duration are identical since there are only two pulses in the bout shown.

117

9.7 "

4.8 "i

0.0 -‘

 

 

uW/Hz
Hz

1000 "

500 '4

~500 "

 

4000.1

 

 

80

 

V
m 30.0

2.0

118

3.0

 

Figure 4.2. Biplot of ratios of qualitative variables involving Theridion response. The
x-axis displays the type of first response, either signal or locomotion, in % of
Theridion whose first response was to locomote. The y-axis displays the first
locomotion, either approach or retreat, in % of theridion whose first locomotion
was an approach. Since these are percentages with small sample sizes, nor error

bars are shown.

119

 

Figure 4.2

 

 

 

 

 

100%

90% ‘ .
.5 80% .
E
8 70% ~
3 A
3; 60% ~
.2 I
LL.
3 50% ~ X
on
-_§ 40% - 0
ii
a 30% -
é”
°\o 20% ‘

10% -

0% r I r— $
0% 20% 40% 60% 80% 100%
% Signaling as First Response
XM. notius D Theridion invaders A Theridion Mates
0 Grammonota I Argyrodes o Prey

 

120

 

Figure 4.3. Biplot of the qualitative variables of Theridion response, average approach
speed per movement and distance at first approach. Neither of these variables
were normally distributed. Therefore the plot displays median values with error

bars as 25% and 75% quartiles.

121

 

Figure 4.3

 

 

 

(cm toward/sec/movement)

 

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Average Approach speed per movement

 

 

.5
m

 

 

j
0 5 10
Distance at first response (cm)
LEGEND
X M notius u T heridion Invaders A T heridion Mates

9 Grammonota I Argyrodes o Prey

 

122

 

 

 

Figure 4.4. Biplot of signal variables with significant differences between M. notius
signals and other web "visitor's signals -— residual peak Hz and bout length. Data
are normally distributed. Points represent averages and error bars give standard

errors.

123

 

Figure 4.4

 

 

 

 

 

 

 

 

0.6

 

6
5 -t
33 4 *
{a Hr“
E 3 1
OD
E
a “r
m 2 “
1—0—1
1 ~ +
J.
0 I I I I r
-0.6 -0 4 —0.2 0 0.2 0.4
Residual peak frequency (Hz)
XM. notius D Theridion invaders A Theridion Mates

0 Grammonota

I Argyrodes O Prey

124

 

Chapter 5:
Foraging under threat from the aggressive mimic Mimetus notius.

INTRODUCTION

Chapter two presented a very simple, very general model based on the idea of
integrating the perceptual relationships between model, mimic and dupe into the trade-off
developed in the formulation of the flu criterion (Gilliam 1982, 1990). In the formulation
of that model, several assumptions were made in the interest of maintaining generality.
Application of the model requires detailed knowledge of a specific system, including
important aspects of the natural history and perceptual relationships between the
members of the system. In chapter three the necessary natural history for the aggressive
mimicry system involving Mimetus notius was presented. In chapter four this
information was used to discover the identity of the models in this system and show the
relationship between the vibratory cues presented by the model and cues provided by the
mimic. This chapter will develop a more specific model using the f/u criterion and signal
detection theory in order to more closely approximate this particular aggressive mimicry
system.

The model presented in chapter two was based on the idea that most aggressive
mimicry systems involve mimicry of the dupe's resources; a common resource mimicked
is the dupe’s food. A simple extension of this model showed that concrete mimicry is
predicted when mates are mimicked and weak mimicry is predicted when prey are

mimicked. These predictions were supported by a review of the literature on aggressive

125

mimicry. These two scenarios (mates vs. food as model) provided simple models, but M.
notius aggressive mimicry violates both of them. From chapter four we have seen that M.
notius mimics neither prey nor mates; instead M notius appears to mimic invading
spiders on the web. The response data presented there were insufiicient to resolve
whether conspecific web invaders or heterospecific web invaders (Argyrodes sp.) were
"the" model in the system, but the signal data points to conspecifics as being more likely
to serve that function. For simplicity, we will assume that conspecifics are the major
force driving T heridion behavior and derive a model based on this assumption.

The life history trade-off between feeding and mortality rates still applies, but
exactly how web invasions affect feeding rate must be specified for the earlier modeling
paradigm to be applied. This chapter returns to the mathematical realm to specify the
relationship between feeding rate and web invasions, explore the properties of the new
model, and arrive at some general predictions. It will then report the results of an

experiment testing some of the simpler predictions of the model.

THE SPECIES-SPECIFIC MODEL

Web invasions negatively affect feeding rate. While a spider is on its web it has
some feeding rate, fw, based on the rate of prey arrival. When a potential usurper invades
a web the resident must deal with the challenger. If unsuccessful it is ejected from the
web and its feeding rate drops to some low, off-web level, f0, until it can either build a
new web or successfully invade another web. If defense is successful, the resident then

maintains its feeding rate at fw. When a predator (for example M. notius) attempts to

126

invade a web, the resident may either defend, with some probability of dying, or abandon
its web, resulting in a feeding rate of f0.

Using this information, a new model can be built to calculate the overall feeding
rate of Theridion given encounter rates with the various invaders, probabilities of
winning and losing the various encounters, and time to inhabit a new web. This model is
developed in detail in appendix 5.1. The final form of the model is presented below as

Equation 5.1.

f
a“ f“ Equation 5. l

# =[1+Ei-Tn-(l—H-W)+Em~Tn-(1—F-K)]-[Em-F~K+m]

 

 

An analytical solution to equation 5.1 has not been discovered. Numerical
simulations will be utilized to determine what effect each variable has on the optimal
feeding rate and to determine the optimal cautiousness (H/F)t given the constraint in the
relationship between H and F defined by the overlap in signal distributions of Mimetus
and invaders. These numerical simulations can help us to increase our understanding of

predator-prey dynamics involving perception in this aggressive mimicry system.

PARAMETER ESTIMATES

In order to perform useful simulations, realistic estimates of the model's
parameters must be available. Data on signal similarity (presented in chapter four)
provide a means of estimating the relationship between H and F for this mimicry system.
The distributions of the bout length of signals emitted by M notius and Theridion

invaders provide the probability density functions (PDF’s) that will be used throughout

127

the simulations presented here (figure 5.1). These PDF’s in turn determine the shape of
the ROC curve (figure 5.2; see chapter 2 for a detailed explanation of PDF’s, ROC curves
and signal detection).

The data presented in chapter three will be used to estimate most of the remaining
parameters in this model. The 1997 data will be used to test the model (below), so these
data will not be used to estimate parameters here. In 1995, not all parameters were
measured, so to maintain consistency all parameters will be estimated using 1996 data
(pooled across all sites). Experience in the lab has shown that it generally takes Theridion
1-2 nights to build a functional web. We will adopt the value of 1 night as a standard
value for T.,.

Parameter estimates are presented in table 5.1. The estimate for feeding rate is
extremely low. This is due to the conservative rule used for identifying prey in 1996. In
1996 only items actually being fed upon were included as prey (see chapter three). The
estimates in table 5.1 are intended to provide a reasonable range for simulations. While
deviations from these values have quantitative effects, they do not affect the more general

qualitative results.

SIMULATIONS

All simulations were accomplished using Matlab°. See appendix 5.2 for a
representative Matlab simulation program. Simulations investigating the effects of model
parameters were conducted using the relationship between H and F described by the ROC

curve in figure 5.2. The optimal cautiousness, (H/F)‘, was determined by finding the

128

maximum of fave/p. for each value of the parameter of interest and then dividing the H
value corresponding to the maximal flow/p by its paired F value. Each parameter was
systematically varied with all other parameters held constant, and (H/F)‘ calculated for
each value.

Two additional simulations study the effect of variation in the relationship
between F and H. (H/F)’ is not a valid indicator of relative cautiousness when the
relationship between H and F (the ROC curve) is allowed to vary — accordingly we will
look directly at H and F in these simulations. 1n the first simulation the distance between
the means of the distributions was varied. In the second simulation the standard

deviation of the distributions was varied.

SIMULATION RESULTS

The results of the first set of simulations were straightforward. Feeding rate in the
web , fw, had no effect on (H/F)* (figure 5.3), which makes the assumption of web
homogeneity (#4 above) and the problem of underestimation of fW inconsequential. As
the encounter rate with mimics (Em, figure 5.4) or the probability of dying (K, figure 5.5)
increase, cautiousness increases until F=0 (i.e. where H/F=OO). The remaining
parameters [probability of successfully defending the web (W, figure 5.6), background
mortality rate (m, figure 5.7), encounter rate with conspecific invaders (Ei, figure 5.8)
and time to find a new web (Tn, figure 5.9)] all have negative relationships with H/F.

The simulation in which the difference between the distributions was varied

(figure 5.10) shows behavior similar to that exhibited by the simple model of prey-

129

mimics presented in chapter two, as does the simulation involving changes in standard
deviation (not shown). From this it is not surprising that the identification of a biological
model in the system (chapter four) was difficult, since the shape of this curve indicates

that abstract mimicry is likely in this system (see chapter two).

EXPERIMENTAL TEST

Methods

Parameters used. In developing the model above, seven parameters were
identified as being potentially important to Theridion's decision making process. One of
these parameters, the feeding rate on the web, was determined to have no impact on
T heridion's optimal behavior. Four more parameters are difficult to measure on a site-by-
site basis and are, in any case, unlikely to vary from site to site. The time to acquire a
new web (Tn) is unlikely to vary consistently across sites. Tn will be estimated by the
time it takes a spider to build a new web in the lab — approximately one night. The size
difference between Theridion and Mimetus is such that Theridion have no reasonable
defense against a mimetid that has attacked. Thus, the probability of being killed once
responding to a mimetid (D) should not vary significantly between sites. The probability
of maintaining web ownership given an invasion (S) relies primarily on relative size
(Reichert 1982). In any given habitat the average spider's a priori probability of being
bigger than an opponent is ~ 0.5, assuming that no size bias in invasion behavior exists.

Variance across sites should be negligible, even though average size may vary across

130

sites. Background mortality (m) in these sites appears to be driven primarily by abiotic
factors and chance encounters with wide-ranging predators (birds, parisitoid wasps etc.).
As long as all the sites are in a similar geographic area, it is reasonable to assume that
these effects will be similar from site to site. Each of these assumptions is reasonable,
and making them significantly increases the ease with which the model may be tested.
These five parameters will be treated as constant across sites from this point on.

Encounter rates depend upon the abundance of the two types of spiders in the
field. Earlier observations indicated that abundance of both Mimetus and Theridion
varied across sites (chapter 3), though encounter rates were too low to allow specific
comparison. Measurement of encounter rates across a number of sites will provide the
variance in these parameters necessary to test this model.

Field Measurements. A series of two censuses in each of seven sites was
conducted in 1997 (see chapter three for extensive details of censusing procedures).
These censuses were conducted during August and September, the period previously
identified as the peak abundance for M notius (chapter three). The timing was chosen in
an effort to maximize the number of M notius available for study. Each census was
conducted as a five-hour (10PM-3AM) visual census. The first census in each site was
conducted with no collection of individuals. In the second census, all individuals of M
notius, Theridion and all prey in T heridion webs were collected (see chapter three for
data from these collections). During censuses the identity of all spiders encountered (to
genus), status (on or off of web) and presence and identity of all invaders on Theridion

webs was recorded.

13]

The second censuses were conducted as paired trials to aid in correcting for
seasonal fluctuations. Data from the first set of censuses were used to pair sites; the three
sites with the highest modelzmimic ratio (Theridion abundancezMimetus abundance) were
paired sequentially with the three sites with lowest modelzmimic ratio (i.e. the highest site
was paired with the 4th highest, 2'nd with 5'“, 3rd with 6th). The seventh site was paired
with Mimetus from a population where Theridion were observed to become locally
extinct. The presence of an unpaired site allowed for independent tests of measures of
risk of Theridion behavior.

Laboratory.-- Theridion and M notius from each site were brought into the lab to
test the response of Theridion to conspecific invaders and to M notius. Interactions were
carried out in small behavioral arenas (as in chapter four). The arenas were
15.2x10.2x3.3 cm in size, constructed of pine with plexiglas sides. Each arena had two
access ports in the top for introduction of invaders; #5 rubber stoppers plugged these
ports except during introductions of animals into the arenas.

All measurements on spiders were carried out within twenty-four hours of
capture. All spiders were weighed to the nearest 0.05 mg with a Mettler B6 analytical
balance. Carapace width was measured by video-taping the spiders fi'om below with a
metric ruler at the same distance from the lens for scale. Video-taped images were later
digitized and magnified using Image Pro Plus0 software, which was also used to calibrate
each image and measure carapace width. After measurement, resident T heridion were
each introduced to a separate arena and given a single Drosophila. Non-resident

Theridion and Mimetids were maintained in Drosophila vials and were unfed. Resident

132

T heridion were allowed two nights to acclimate to the arena and build webs before
interactions began.

Interactions were conducted between spiders from the paired sites, as outlined in
the field section above. The site where Theridion were predicted to have higher (H/F)t
was termed the "cautious" site and the site with lower predicted (H/F)t termed the
"incautious" site. Censuses for a pair of sites were conducted on subsequent nights, so
that a total of twenty-nine hours elapsed between the start of the first census and the end
of the second census. Spiders collected in each census were measured within twenty-four
hours of the census, but resident spiders from both sites were introduced to arenas
simultaneously, and from the point of introduction on all spiders were treated identically.
Collection order (expected cautious vs. expected incautious) alternated between seasonal
blocks. This paired design was adopted so that experiment date ("season") could be
treated as a blocking factor in subsequent analyses.

Resident Theridion were subjected to one of three web invaders: Mimetus from
the same site, Mimetus from the paired site, and conspecifics from the same site: sizes
were assigned randomly. All trials from the paired sites were conducted in a single night.
Introductions were started under white light at 10:00 PM. Lights were turned off as soon
as all arenas held invaders, and all observations were conducted under red light, which
spiders cannot detect (Yamashita 1985). Each arena had a numbered lcm x 1 cm paper
grid attached to the back (outside the plexiglas). At 20 minute intervals each arena was
observed and the grid number of each spider recorded — this allowed for calculations of
distances to within ~ 1 cm and provided a means of measuring the movement of spiders

from one interval to the next. All instances of predation were recorded during the first

133

interval in which Mimetus was observed feeding on Theridion (no instances of
cannibalism occurred).

Observations of T heridion behavior during earlier experiments (see chapter 4) led
to the construction of the following "Risk Index": the distance of T heridion approach
(retreats scored as negative values) divided by the separation between the spiders +1 (to
avoid dividing by zero). This index was adopted because neither measure alone was an
accurate indicator of risk. The distance of Theridion approach is only important in light
of the separation distance — an approach of 5 cm does not increase the risk of a Theridion
20 cm from the mimetid, but the same approach distance by a T heridion 6 cm away puts
it within Mimetus striking distance. Similarly, even a separation of less than 1 cm
appears to be safe as long as T heridion do not approach the mimetid. Mimetus have
never been observed to successfully attack stationary or retreating T heridion. The
combination of proximity and approach are necessary for successful mimetid predation.
The risk index was calculated over every interval in which T heridion remained alive, and
averaged over the entire experiment to yield an average “risk”. The risk index and the
actual predation on Theridion from the unpaired site can be compared to test whether or
not this index provides a reasonable analog of risk.

The model predictions that risk indices should be higher in incautious sites than in
cautious sites for interactions between T heridion and Mimetus as well as interactions

between Theridion and Theridion invaders (i.e. non-mates).

134

Results

Field data: If cautiousness has an effect on the feeding rate of Theridion, we
would expect T heridion from incautious sites to have higher feeding rates, since they are
less likely to abandon their webs, and thus be in better condition than Theridion from
cautious sites. To test this possibility a residual condition index (Jakob et a1. 1996) was
calculated for each spider collected. This index is derived by regressing spider weight on
carapace width, then using the value of the residuals as the condition index. A positive
value indicates better than average condition, while a negative value indicates worse than
average condition. The regression of log(weight) on carapace width is significant
(1.52*Carapace width-1.30, p<.001), but with a large amount of scatter (r2=0.16). An
ANOVA of the resultant condition index by interaction date and predicted cautiousness
of the spider's home site (Cautious Vs Incautious) shows a significant interaction between
interaction date and predicted cautiousness (p=0.031; figure 5.11). The presence of this
interaction makes interpretation of the other factors problematical, so within-block tests
were conducted to further explore the relationship between cautiousness and condition.
These tests reveal that the middle block accounted for the significance of the overall
ANOVA. Theridion from the incautious site in this block were in significantly better
condition than Theridion from the cautious site ((Incautious site mean index =0.094,
cautious site mean index= -0.303; pooled variance t-test, one-tailed p=0.0005, other
blocks p>0.5, figure 5.11). This block possessed the largest difference between predicted
cautiousness (differences in predicted cautiousness (Cautious-incautious): Early

block=40.1-35.7=4.4; Middle block=infinity-17.7; Late block=27.7-20.8=6.9), and

135

differed in the fashion predicted: the cautious site possessed a significantly lower
condition index. It is encouraging that the only pair exhibiting a significant difference
was also the pair with the largest expected difference.

Similar arguments lead to the prediction that Mimetus from cautious T heridion
sites would possess a lower condition index as a result of reduced feeding rate. An
ANOVA of Mimetus condition by interaction date and predicted cautiousness revealed no
significant differences.

Laboratory data: The mean "risk index" is an accurate indicator of the degree of
risk Theridion places itself in by its behavior. A log transform (log(Index+1))is
necessary to normalize the index. Using only the data from the unpaired site to avoid
conflicts with later analyses, 3 separate variance t-test on the transformed data shows that
risk index accurately reflects the risk of mortality (figure 5.12).

No evidence of co-evolution was present in the paired sites. A full factor
ANOVA on the transformed risk index using Theridion site, Mimetus site and season as
factors revealed only a significant effect of season (figure 5.13; table 5.1). Removal of
season as a factor does not produce any p-value <0.05, but a marginal effect of Theridion
site (p=0.058) becomes apparent. Because no effect of Mimetus site exists and there are
no significant interaction effects, all remaining analyses will ignore Mimetus site and
focus on Theridion site as the primary factor of interest. This has the effect of pooling
the cross-site interactions into the T heridion site in all remaining analyses.

The model accurately predicted the relative risk index in Mimetus trials for each
season in the paired laboratory interaction experiments. Within each block, the site

predicted to be cautious showed a lower risk index than the site predicted to be

136

 

 

 

incautious (figure 5.14). An ANOVA of the log-transformed risk index (table 5.2)
demonstrates that Theridion from populations expected to have high cautiousness exhibit
significantly lower risk indices than do Theridion from populations predicted to be less
cautious.

The model did not perform as well with respect to T heridion trials. In Theridion
trials risk indices were still higher in incautious sites than in cautious sites, but not
significantly so (Figure 5.15; tested using ANOVA similar to above; no significant
differences existed). The lack of significance in these tests may be attributable to the low

power of these tests caused by the small sample sizes.

DISCUSSION

The model developed here predicts logical and intuitive changes in cautiousness
in response to changes in environmental conditions. As parameters positively correlated
with mimetid-associated mortality (Em, K) increase, Theridion should behave more
cautiously. Conversely, as the value of possessing the web increases, cautiousness
should decrease, resulting in increased web defense and thus more time on the web.
When it takes a long time to build a new web (Tn is high) the current value of the web is
high because of the long expected time without feeding following web loss. When
background mortality (m) is high, web ownership becomes relatively more valuable
because rapid resource acquisition (i.e. before death from some other source) is critical
for maximizing fitness. When the probability of maintaining a web is high, defense is

more beneficial. The probability of maintaining a web is a function of the encounter rate

137

with conspecifics (Bi) and the probability of winning given defense (W), so it makes
sense for cautiousness to decrease with increases in these parameters. None of these
results are particularly surprising, and they give confidence that the model captures
important aspects of the Theridion behavior.

The model's ability to accurately predict qualitative differences between sites (i.e.
accurately predicted high vs. low sites) demonstrates that it captures important aspects of
the behavior of foragers targeted by aggressive mimics. Further refinement of the model
could lead to accurate quantitative predictions as well, but more important than
qualitative prediction is the increase in our understanding of the selective pressures in
these systems. Further elaboration of the model to non-mimetic systems (for example,
cryptic predators) could potentially lead to new insights about how perception and
appearance evolve in many predator-prey interactions.

The model developed here predicts the same counter-intuitive increase in risk
with increasing discrimination, at least over a small region of similarity, that the simple
prey-based mimicry system in chapter two predicted (figure 5.10), indicating that abstract
mimicry is a likely possibility in this system. Observations on Theridion responses to
invaders (Mimetus, Argyrodes and conspecifics; chapter four) are consistent with the
hypothesis of reduced selection for mimicry of a single concrete model. The existence of
this risk increase is a potentially important discovery made by this approach. Further
testing will be necessary to validate the model in this respect, but the presence of the
"hump" in the curve and its absence in some modeled situations (i.e. mate-based
mimicry), combined with the correlated natural patterns detected (see chapter two)

provides a new means of attacking the general problem of aggressive mimicry.

138

 

 

The prediction that under some circumstances foragers should increase their
mortality risk resembles Wiley's (1994) concept of adaptive gullibility — that is, selection
favoring a failure to penetrate a deception. Wiley showed that susceptibility to deception
can actually be an optimal strategy if: encounter rates with deceivers are low; the costs of
being deceived are low; or deception is nearly undetectable. In the current situation we
see some similar results. As encounter rates with mimics decrease, cautiousness
decreases, and as the probability of dying decreases (i.e. potential cost decreases),
cautiousness decreases. When the deception is nearly undetectable (i.e. discriminability
approaches zero), this system tends away from adaptive gullibility — that is, susceptibility
to deception decreases. This difference between Wiley's formulation and this one is most
by the ability of the spiders in this model to maintain a reasonable feeding rate even when
they abandon their web at every encounter (i.e. H=F=0). In the mate-mimicking situation
presented in chapter 2, there were no available alternatives, and the situation more closely
resembled Wiley's — as discriminability approaches zero, response to mimics approaches
one.

The current experiment tested some of the simpler predictions of the model. The
more complex predictions, such as the hump-shaped relationship between errors and
discriminability seen in figure 5.10, must await experiments where the level of overlap
between distributions can be more tightly controlled and varied over a wider range than
these populations made available. For example, selection experiments where the
experimenter controls the distributions of signals and selects “prey” based on responses
to these signals could be used to test for the presence of such a response in evolutionary

time. Such a test, while outside the scope of the present work, will provide a stronger test

139

of this modeling paradigm. The ability of the model to make reasonably accurate
predictions under field conditions strongly argues that such an experiment should be a
priority of future research attempting to develop our understanding of this under-studied

phenomenon.

140

LITERATURE CITED

Egan, J .P. 1975. Signal Detection Theory and ROC Analysis. Academic Press series in
Cognition and Perception. Academic Press New York, New York.

Gilliam, J .F. 1982. Habitat use and competitive bottlenecks in size-structured
populations. Ph.D. Dissertation, Michigan State University.

Gilliam, J .F. 1990. Hunting by the hunted: optimal prey selection by foragers under
predation hazard. pp 797-818 In: Behavioural Mechanisms of Food Selection.
R.N. Hughes (ed). Springer-Verlag, Berlin.

Jakob, E.M., S.D. Marshall and G.W. Uetz 1996. Estimating fitness: a comparison of
body condition indices. Oikos 77:61-67.

Pough 1988, EH. 1988. Mimicry of vertebrates: are the rules different? American
Naturalist 131(Supplement):S67-S102.

Riechert, SE. 1982. Spider interaction strategies: communication vs. coercion. pp. 281-
315 IN: Spider Communication: Mechanisms and Ecological Significance. Witt,
RN. and J .S. Rovner, eds. Princeton University press, Princeton, NJ.

Wiley, RH. 1994. Errors, exaggeration and deception in animal communication.
Chapter 7 In: Behavioral Mechanisms in Evolutionary Ecology. L.A. Real, ed.
University of Chicago Press, Chicago IL.

Yamashita, S. 1985.Photoreceptor cells in the spider eye: spectral sensitivity and efferent
control. pp 102-117 In: Neurobiology of Arachnids (F.G. Barth, Ed.) Springer-
Verlag, Berlin.

Zar, J .H. 1998. Biostatistical Analysis. Third edition. Prentice Hall, Upper Saddle River,
NJ.

141

Table 5.1. ANOVA results for test of local adaptation

 

 

 

 

 

 

 

 

 

 

 

SOURCE (main variable is risk index) SUM-OF- DF MEAN- F-RATIO P
SQUARES SQUARE

Season 0.667 2 0.334 4.006 0.025
Theridion site 0.248 1 0.248 2.973 0.092
Mimetus site 0.021 1 0.021 0.251 0.619
Season*Theridion site 0.009 2 0.004 0.053 0.948
Season*Mimetus site 0.013 2 0.007 0.080 0.923
Theridion site"‘Mimetus site 0.013 1 0.013 0.151 0.700
Season" Theridion site *Mimetus site 0.370 2 0.185 2.219 0.121
ERROR 3.582 43 0.083

 

 

 

 

 

 

142

 

Table 5.2. Test of Model: predicted cautiousness predicts

observed risk index Vs Mimetus.

 

 

 

 

 

 

 

 

 

 

 

SOURCE SUM-OF- DF MEAN- F -RATIO P
SQUARES SQUARE
Season 0.570 2 0.285 3.501 0.038
Predicted cautiousness 0.354 1 0.354 4.356 0.021r
Season*predicted 0.01 1 2 0.005 0.065 0.937
cautiousness
ERROR 3.986 49 0.081

 

 

'1-tailed p-value.

 

143

 

Figure 5.1. Distributions of bout length measurements for Theridion (solid line) and
Mimetus (dashed line). The mean Theridion value was 3.6 seconds, the mean

Mimetus value was 2.1 seconds. The pooled standard deviation was 1.7.

144

 

mi

145

Theridion
interns

 

 

Figure 5.2. The Receiver Operating Characteristic (ROC) curve corresponding to the

distributions presented in figure 5.1

146

 

 

idingtoth:

 

147

 

 

Figures 5.3. Response of (H/F)‘ to variation in Fw, the feeding rate while on the web.
The value at standard conditions (open triangle) and the observed range of the
indicated parameter (dashed vertical lines) is provided. The value of H/F at
standard conditions was 6.73. The lower limit of H/F is 1, and the curves are

indicated from 1 (if reached) until just before (H/F).=oo (F=0).

 

 

148 l

 

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W
n
0
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rd range oft:

ue 0111131

 

 

he caves are

149

 

Figures 5.4. Response of (H/F)‘ to variation in Em, the encounter rate with Mimetus. The
value at standard conditions (open triangle) and the observed range of the
indicated parameter (dashed vertical lines) is provided. The value of H/F at
standard conditions was 6.73. The lower limit of H/F is 1, and the curves are

indicated from 1 (if reached) until just before (H/F)‘=oo (F=0).

150

 

$1..
m
m

.Tat

 

'85313

151

 

Figures 5.5. Response of (H/F). to variation in K, the probability of dying given an
attempt to defend against Mimetus. The value at standard conditions (open
triangle) and the observed range of the indicated parameter (dashed vertical lines)
is provided. The value of H/F at standard conditions was 6.73. The lower limit of

H/F is 1, and the curves are indicated from 1 (if reached) until just before

(H/F)‘=oo (F=0).

152

m
m

; (open

v'fmcal lll'dl

 

153

 

Figures 5.6. Response of (H/F)‘ to variation in W, the probability of retaining a web
given defense against a Theridion invader. The value at standard conditions
(open triangle) and the observed range of the indicated parameter (dashed vertical
lines) is provided. The value of H/F at standard conditions was 6.73. The lower
limit of H/F is 1, and the curves are indicated from 1 (if reached) until just before

(H/F)'=oo (F=0).

154

 

 

ring a web
onditions
lashed ml
3. 11100“

til 1‘er

 

155

 

Figures 5.7. Response of (H/F)‘ to variation in m, the background mortality rate. The
value at standard conditions (open triangle) and the observed range of the
indicated parameter (dashed vertical lines) is provided. The value of H/F at
standard conditions was 6.73. The lower limit of H/F is 1, and the curves are

indicated from 1 (if reached) until just before (H/F).=oo (F=0).

156

m
m.
m

[the

HM

 

T85 31?

157

 

Figures 5.8. Response of (H/F)‘ to variation in E., the encounter rate with Theridion
invaders The value at standard conditions (open triangle) and the observed range
of the indicated parameter (dashed vertical lines) is provided. The value of H/F at
standard conditions was 6.73. The lower limit of H/F is 1, and the curves are

indicated from 1 (if reached) until just before (H/F)'=oo (F=0).

158

 

 

lion

m.

 

311111

159

 

Figures 5.9. Response of (H/F)‘ to variation in Tn, the time to inhabit a new web. The
value at standard conditions (open triangle) is provided. No range is provided
since systematic observations of this variabler were not made. The value of H/F

at standard conditions was 6.73. The lower limit of H/F is 1, and the curves are

indicated from 1 (if reached) until just before (H/F)'=oo (F=0).

160

 

III
H
I.”

 

ES]!

161

 

Figure 5.10. The response of the model detailed in equation 5.1 to variation in the
difference between cue distributions. Since each new difference requires a
new ROC, (H/F)' is not a reliable indicator of relative cautiousness, so H
(solid line) and F (dashed line) at the maximum f/p. are plotted separately.
Due to scale differences, H is plotted on the left hand Y-axis and F on the

right hand Y-axis.

162

 

W.

Lsoll .

 

curl:

163

 

Figure 5.1 1. Residual condition index of Theridion (:t Standard Error) by block and
predicted cautiousness of home site. Spiders from incautious sites are expected to
have higher condition indices. An ANOVA shows a significant interaction
betWeen interaction date and predicted cautiousness. Examination of this figure
shows that the significant differences are due entirely to the effect of the middle

pair of sites.

164

 

block and

are extend.

[anchor
of this in:

of the mill:

Figure 5.11

 

0.3
0.2 -

-0.1 -
-0.2
-0.3
-0.4 -
-0.5 r 1

Early Mid Late

Interaction Date

1

1

Residual Condition Index

 

 

 

 

ANOVA Results
Source
cautiousness

interaction date
Error

165

 

 

El Cautious
Incautious

 

 

 

 

 

Figure 5.12. The risk index of Theridion (i Standard Error) killed vs. surviving against
Mimetus in the unpaired site. A separate variances t-test of risk index vs. survival
shows that the risk index accurately reflects the mortality risk of Theridion
(p=0.03; mean risk index of eaten Theridi0n=0.864, SD=0.560, n=6; mean risk

index of Theridion surviving=0. l 88 SD=0.344, n=26).

166

 

 

Figure 5.12

 

 

 

 

 

 

 

 

 

1.2
A 1 -
>4
'8
c: 0.8 *
p—q
TE» 0.6 -
9?.
w 004 -
.3
0.2 " l+_l
0 * u
m‘ingiéii’f Survived Died
idem Theridion survival

7'1 ,‘1: .-
( llr’l’mtl’l

:6; mean risk

167

 

Figure 5.13. Test for local adaptation between Theridion and Mimetus. Sites are broken
up into seasonal blocks by relative interaction dates: early, middle and late.
Within each block are four conditions, representing the four pairings of Mimetus
and Theridion by sites within the pair. The four groups within each block are:
both Theridion and Mimetus from the site where Theridion was predicted to be
cautious; T heridion from the site where they are expected to be cautious paired
with Mimetus from the site within the block where Theridion were predicted to be
incautious; Theridion from the site where they are expected to be incautious and
Mimetus from the site where Theridion were expected to be cautious; Both
Theridion and Mimetus from the site where Theridion were expected to be
incautious. The only significant effect in the complete ANOVA was the seasonal
block (p=0.025; see table 5.2 for complete ANOVA table). As can be seen from
the figure, Theridion in the early season block were generally less cautious than

Theridion later in the season.

168

 

Figure 5.13

 

 

 

 

 

 

 

 

 

 

 

 

 

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2".
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5mm $3 0.4 4 l i,
a ~ .
remains an 0.2 -
.3
ings oiling} 0 I
1th hlci‘i’ it Early Mlddle Late

 

~rcdictedtr'r

E] Mimetus and Theridion both from cautious site.

morphs: Theridion from cautious site, Mimetus from incautius site.
WW.“ fl Theridion from incautious site, Mimetus from cautious site.
‘ DTheridion and Mimetus both from incautious site.

 

 

 

inCSUIh‘ISiT-

DUS; 8011'!

169

 

Figure 5.14. Risk index of Theridion versus Mimetus (i Standard error) from each site,
grouped by interaction date and predicted cautiousness. An ANOVA
demonstrates a significant difference in the risk index of Theridion from Cautious
Vs. incautious sites (p=.021, one-sided). The sample size (n) is given under each

bar.

170

 

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JVA
rm from (€575

zircn mid”

Figure 5.14

 

0.6
0.5 -
0.4 -
0.3 -
0.2 4
0.1 -

Log (risk Index)

 

 

 

=3

9 9
Early

8 10
Middle

Interaction Date

171

10 9
Late

 

 

E1 Cautious
s Incautious

 

 

 

 

Figure 5.15. Risk index of Theridion versus invading Theridion (3: Standard error) from
each site, grouped by interaction date and predicted cautiousness. An ANOVA
demonstrates no significant difference between the risk index of Theridion from
cautious Vs. incautious sites (all p's >0.5). The sample size (n) is given under

each bar.

172

11rd error! 32::

An .0011

The

given 11an?

[1111017le

Log (Risk index)

Figure 5.15

 

0.35

.9
DJ
1

0.25 d

P
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0.15 -

P
p—l
r

 

 

 

 

 

 

 

[}

 

 

 

I
3 9 8

3
Early Middle

Seasonal Block

173

 

 

 

[

5 5
Late

 

El Cautious
l Incautious

 

 

 

APPENDIX 2.1 — Solving the general model

R = the rate of encountering the risky opportunity.

C = the probability of successfully harvesting resource from the risky opportunity.

S = the a priori probability that the risky resource is safe.

H = the probability of accepting the opportunity, given that it is safe (a hit).

V = the value of a successfully harvested resource.

A = the background rate of harvesting alternative resources.

K = the probability of being killed given an encounter with a risky resource.

D = (1 - S) = the probability that the risky resource is dangerous.

F = the probability of accepting the opportunity, given that it is dangerous (a false alarm).

P = the probability of being killed, given acceptance of a dangerous resource.

m = the background rate of mortality.

H is constrained by a tradeoff (the ROC curve) to be a function of F: H(F).

With the simplifying assumption that variation in the probability of accepting safe (H)

and dangerous (F) resources has a negligible impact on the background rates of

harvesting alternative resources (A), and mortality from other sources (m), the long-term

average rates of harvesting resources (f) and mortality ([1) are:
f=R-C-V+A=R-S-H'V+A (a2.1.l).
u=R°K+m=R-D-F-P+m (a2.1.2).

We want to find the maximum of the ratio:

f =ROSOH(F).V+A ($1.3)

Z RoDoFoP+m

 

174

 

We then take the derivative with respect to F, set it equal to zero and rearrange to find:

 

 

 

H A
dH(F)= +ROSOV (3214)
dF F+__m_____
ROD-P

This is the final form of the model.

175

 

Appendix 2.2: MATLAB program: Prey-based model

% Set initial Parameters

clear; R=1; S=0.5; P=0.01;
D=0.5; V=0.5; m=0.01; [sd=0.2;]
[Modelmean=0.0; A=1 ; [d=0.001];

% Define MODEL distribution {normal(0,sd)}

X=[-5 :d:5];
MODEL=(exp(-0.5*((X-Modelmean)/sd)."2)*(2*((sd)"2)*pi)"-0.5)*d;

% Define vector of H values Given MODEL distribution
H=sum(MODEL)-cumsum(MODEL);
% Cycle over values of mimicmean (0-l.5)

for j=l :15 1;

clear I

Mimicmean(j)=((j-1)/ 100);

% Define MIMIC distribution for each mimicmean {normal(mimicmean,sd)}
MIMIC=(exp(-0.5*((X+Mimicmean(j))/sd)."2)*(2*((sd)"2)*pi)"-0.5)*d;
% Calculate DIFference between modelmean and mimicmean in sd units
[DIF (j )=Mimicmean(i )/sd; ]
% Define vector of F values given MIMIC distribution
F =sum(MIMIC)-cumsum(MIMIC);

% Calculate fovermu vector for each H,F pair and find max fovermu in vector

fovermu=(R.*S*H.*V+A)./(R.*D*F.*P+m);
I=find(fovermu==max(fovermu));

% Calculate H and F corresponding to optimal fovermu for each DIF
OptF (i)=min(F (1));

OptH0)=min(H(I));
end;

176

Appendix 2.3: The criteria for switching curve shapes

The simple prey-based model has two possible states under perfect mimicry. These two
states also act as attractors when mimicry is near-perfect, changing the overall shape of
the curves, yielding 2 basic "families" of curves. One set of curves always has the point
(0,1) — that is, if discriminability =0, then the optimal error rate F =1 -- while the other set
always includes the point (0,0). This is shown below.

Start with the simple equation:

_y:_ R0S0H(F)0V+A
y ROD-F-P+m

 

a 2.3.1 — —Equation 5 from Ch. 2

According to signal detection theory (Egan 1976), the optimal solution under perfect
mimicry is to either always avoid (operating point at F=0, H=0) or always accept
(operating point at F=1, H=1). Since only one of these points is optimal for a given
parameter set, knowing which of these two points yields the higher f/u solves for the
criterion point. This is easily done as follows.

Substituting (0,0) for (F,H) in equation 1 yields:

1’. z 14;, a2.3.2
,u m

Substituting (1 ,1) for (F,H) in the same equation yields:

1— R.S.V+A a2.3.3

,u - RODOP+m°

 

Whichever expression yields a higher f/u under the conditions present will be optimal,
and thus define whether the shape of the curve vs. discriminability will be as in figure 2.2

or 2.3.

177

 

The optimal point defines the F (and H) coordinate when discriminability =0. If

14> ROSOV+A
m RODOP+m

or, simplifying,

a 2.3.4,

 

DOPOA
SUV-m

Then F=0 and H=0 when discriminability =0, and curves of the shape shown in figure 2.3

>1 a235

are favored. When the opposite condition holds, then when discriminability=0 H=F=1,

and curves similar to that in figure 2.2 are favored. In the case where

ELF—'4 = 1, a2.3.6
S-Vom

neither point is favored and the shape of the curve depends on prior conditions.
For mate mimicking systems, the situation is much simpler. The base equation

for these systems is

a237

 

i_ ROS-H(F)0V
,u RODOF0P+m

Substituting (1 ,1) into this equation yields '

= a2.3.8
RODOP+m

 

1 ROSOV
,u

Substituting (0,0) into the equation yields f/u=0. Since

ROS-V
RODOP+m

a.2.3.9

 

cannot be <0, the point F =1 H=l must always exist in these systems.

178

 

Appendix 5.1: - Development of the species specific model for Mimetus notius.

 

Table A.5.l: Definitions and standard values of parameters used in the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

model
Definition parameter “Standard” value
Encounter rate with invading T heridion. E; 0.0025 invasions/web/night.
Encounter rate with Mimetus. E,m 0.00047 Mimetus/web/night.
Probability of a false alarm. F See figure 5.1.
Overall feeding rate. ftotal Equations 5.1, 5.7.
Foraging rate while on web. fw 0.0013 prey/web/night.
Probability of a Hit. H See figure 5.1.
Cautiousness and optimal cautiousness H/F, . Equation 5.9.
0. (WP)
Probability of being killed given defense K 0.31.
against M notius.
Background mortality rate. m 0.011 deaths/Theridion/night.
Probability of leaving web due to an P0,; Equation 5.5.
invader.
Probability of leaving web due to M P0,", Equation 5.6.
notius.
Time to locate a new web. Tn 2 nights.
Time off of web due to invaders. To] Equation 5.3.
Time off of web due to M notius. To)", Equation 5.4.
Time spent on web. Tw Equation 5.2.
Probability of successful web defense W 0.5.
given defense against T heridion invader.
Mortality rate. p Equation 5.8.

 

 

 

The average feeding rate (fave) of a spider during any time period is a function of

its feeding rate on the web (fw) and its feeding rate off of the web (f0) over that time

period. For Theridion, a reasonable and simplifying assumption is that while not on a

web the feeding rate is zero. The average feeding rate (fave) is then simply the feeding

rate while on the web (fw) multiplied by the proportion of the total time spent on the web.

The proportion of time on the web is the time on the web divided by the total time under

consideration (time on the web + time off of the web). Obviously this must be scaled to

179

 

1

some relevant time period. For this system the time per night is the most relevant time
period. If we let tw equal the time on the web per night, to] equal the time off of the web
due to invaders per night, and to,m equal the time off of the web due to mimetids per
night, then the proportion of time on the web is tw/(tw+to,i+to,m). The average feeding rate

is then given by equation a.5.1.

= f w +fo- ° = fw - “’ +0 Equation a.5.1.

 

 

 

The proportion of time on the web per night (tw) is the inverse of the combined
encounter rate (encounters with Mimetus per night plus encounters with invaders per
night). If E: is the encounter rate with invaders and Em is the encounter rate with
mimetids, then the time on the web per night is given by equation a.5.2. The time spent
off of the web due to invaders per night (1m) is the proportion of encounters that are with
invaders [Bi/(Ei+Em)] multiplied by the probability of ejection by an invader given an
encounter with an invader (P03) and the average time it takes to inhabit a new web (Tn;
equation a.5.3). Similarly, the time spent off of the web due to mimetids per night is the
proportion of encounters that are with mimetids [Em/(Ei+Em)] multiplied by the

probability of successful escape from a mimetid given an encounter with a mimetid (Pom)

 

 

 

w = 1 Equation a.5.2
E, + Em
E. ,
or = ' -Po, -Tn Equatrona.5.3
‘ Ei + Em ’
E O
= m P ~ T Equatron a.5.4

0,111 Ei + Em . 0,111 n
and Ta (equation a.5.4).

180

 

We can expand the probabilities in equations a.5.3 and a.5.4 by referring to signal
detection theory (Egan 1975). This allows us to incorporate the distributions of signals
from invaders and mimetids into the model, thus including the ability of the resident to
partially discriminate between them. P0,; is the sum of the probability of failing to defend
against an invader (1-H) and the probability of defending a web but losing [H°(1-W)]
where H is the probability of attempting defense given invasion (a “hit” in signal
detection jargon) and W is the probability of successfully defending the web (equation
a.5.5). Similarly, Po,m is the sum of the probability failing to defend against a mimetid
(l-F) and the probability of surviving given defense against a mimetid [F'(1-K)], where F
is the probability of attempting defense against a mimetid (a “false alarm” in signal

detection jargon) and K is the probability of being killed given defense (equation a.5.6).

P... = (1—H)+H-(1-W)=1-H-w Equationa.5.5
P0_m =(1—F)+F-(1-K)=1-F-K Equationa.5.6

Substituting equations a.5.2-a.5.6 into equation 0.5.] and simplifying yields:

f“ Equation a. 5 .7

f, =
1+Ei-Tn-(1-W-H)+Em-Tn-(1—F-K)

 

The death rate, u, is not changed in basic format from that given in chapter two.
However, the changes above require a minor change in symbols to keep consistent with

the new formulation. The "new" equation for p is presented in equation a.5.8.

181

 

p = Em -F - K + m Equationa.5.8
Em, F and K are as given above; m represents the background rate of mortality.

Combining equations a.5.7 and a.5.8 into the f/u criterion yields:

f“ f“ Equation a.5.9

a =[1+Ei-Tn-(1—H-W)+Em-Tn-(l—F-K)]-[Em-F-K+m]

 

 

Several simplifying assumptions should be pointed out here.

1) The time spent dealing with the threat has negligable impact on the prey capture ratew.

2) Time spent off of the web due to other disturbances (wind, large vertebrates etc.) is
assumed to be beyond T heridion's control and is therefore ignored.

2) Spiders are given only two options — defend or abandon the web.

3) Spiders facing mimetids are assumed to lose their webs if they defend and survive.

4) All webs are assumed to yield similar fw,

An analytical solution to equation 5.9 has not been discovered. Numerical
simulations will be utilized to determine what effect each variable has on the optimal
feeding rate and to determine the optimal cautiousness (H/F)‘ given the constraint in the
relationship between H and F defined by the overlap in signal distributions of Mimetus
and invaders. These numerical simulations can help us to increase our understanding of

predator-prey dynamics involving perception in this aggressive mimicry system.

182

Appendix 5.2.: A representative Matlab© program simulating variation in the
parameter W, The probability of winning against an invader.
SET PARAMETER VALUES TO STANDARD CONDITIONS

1996 Estimates
clear
Ei=0.0025;
Em=0.00047;
% W:0.5;
D=0.31;
Tn=1;
Fw=0.0013;
m=0.011;

sd=(1.7);
Tm=(3.6);
Mm=(2.1);

SET STEP SIZE
d=0.001;
SET SIGNAL DISTRIBUTIONS (Normal-Normal), F AND H VECTORS

X=[0:d:10];
MI=(exp(—O.5*((X-Mm)/sd).‘2)*(2*((sd)“2)*pi)“-0.5)*d;
TH=(exp(-0.5*((X-Tm)/sd).“2)*(2*((sd)“2)*pi)“-0.5)*d;
F=sum(MI)-cumsum(MI);

H=sum(TH)—cumsum(TH);

CYCLE OVER VALUES OF W, CALCULATE F/u, FIND MAX Flu, H AND F
VALUES AT MAX Flu

for j=1:101;

clear I;

W(j)=(j—1)/100;
Z=Fw./((1+Ei.*Tn.*(l-H.*W(j))+Em.*Tn.*(l-F.*D)).*(F.*D.*Em+m));
I=find(Z==max(Z));

OPtthl=min(F(I));
OPtH(j)=min(H(I));
end;

CALCULATE OPTIMAL HIF FOR ALL VALUES OF W

HF=OptH./OptF;

183