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thesis entitled

THE EFFECTS OF PREDATOR MEDIATED HABITAT
USE ON CONSUMER-RESOURCE INTERACTIONS

presented by

Andrew Mark Turner

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THE EFFECTS OF PREDATOR MEDIATED HABITAT USE ON
CONSUMER-RESOURCE INTERACTIONS

By

Andrew Mark Turner

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

WK. Kellogg Biological Station
and
Department of Zoology

1994

ABSTRACT

THE EFFECTS OF PREDATOR MEDIATED HABITAT USE ON
CONSUMER-RESOURCE INTERACTIONS

By

Andrew Mark Turner

In addition to killing and consuming prey, predators alter the behavior of prey, and
the indirect effects of predator-mediated behaviors may be strong and far-reaching. In this
thesis I show that the freshwater snail 311%]?! gm alters its behavior when in risk of
being preyed upon, and that this change in behavior can affect the abundance of the
periphyton that snails feed on. EhyglLa use covered substrates more in lakes containing
the molluscivorous pumpkinseed sunﬁsh Lem m than in adjacent lakes lacking
pumpkinseeds. I found that the survivorship of Mse—lla in experimental pools was much
higher when covered habitats were available. Ma do not change their habitat use
when exposed to the water that has been in contact with pumpkinseeds. However, when
exposed to water that had been in contact with crushed conspecifics, M increased its
refuge use two-fold over controls, demonstrating that P_hy&lla can perceive mortality risk
and facultatively alter it's behavior in an adaptive manner. Habitat structure also affects
the behavior of P_hysell_a. In experimental pools containing a covered habitat m
respond to risk by moving under cover, while in pools lacking cover Mil; respond to

risk by moving to the water's surface.

In a second set of experiments I tested the hypothesis that the behavioral response of
liaise—Ila to predation risk would inﬂuence periphyton standing crop. m responded
to risk by abandoning open habitats, and periphyton standing crop in the open habitat was
positively related to the level of predation risk on snails. However, the strength of the
responses were time dependent. Early in the experiment predation risk had a strong effect
on Ma habitat use, but a weak effect on periphyton standing crop. Late in the
experiment predation risk had a weak effect on M habitat use, and a strong effect on
periphyton standing crop. Finally, I present a theoretical framework that synthesizes these

results and makes predictions amenable to experimental testing.

This work is dedicated to the two people who taught me where to find the fish: my

Grandparents, Woody and Rosemary Patton.

ACKNOWLEDGEMENTS

First and foremost, I acknowledge the large role that the academic community at the
Kellogg Biological Station has played in my graduate training. We learn best from the
examples of our peers, and a Ph.D. thesis mirrors the institution from which it was created
as much as the person who created it. The members of my committee were Gary
Mittelbach, Tom Getty, Alan Tessier, Kay Gross, and Steve Tonsor; other KBS/MSU
faculty who have inﬂuenced me include Lars Hedin, Susan Kalisz, Phil Robertson, Mike
King, George Lauff, Don Hall, and Don Straney, and Bill Cooper.

There is one person whose contributions to this work demand special
acknowledgement. The demons that haunt every Ph.D. candidate fought me to a
standstill, leaving me exhausted and confused, and the battle appeared lost. However,
when the skies of my academic future were at their darkest, Wendy Reed had to courage
to enter the battle and fight alongside me. Wendy reminded me by the force of her own
example that strength of character can overcome all because, in the end, character is all
that matters. Thank-you Wendy.

The Lux Arbor lakes were made available for study through the generosity of Dr.
Richard U. and Irrngard Light. The Lights also gave me the opportunity to live at Lux

Arbor for the past seven years; much of the biology I have absorbed during my time here

I learned through my experiences at Lux Arbor (literally a " garden of knowledge"). The
lessons learned at Lux Arbor have deepened my world perspective, and I will always be
grateful to Doe and Irmgard for allowing me to learn those lessons.

Perhaps the most important acknowledgement is that of the friendships I have shared
in here at KBS. My memories weave a rich and colorful tapestry that I will always carry
with me. Much of the past several years has been lived out on the edge, but someone was
always willing to explore with me and pull me back in when I ventured a bit too far. My
thanks go out to those friends, namely: Mike Brown, Brian Kennedy, Kellie Ellis, Chuck
Bellanger, Maile Keagle, Michelle Keagle, Jen Klug, Lars Hedin, John Ferguson, Sandy
Halstead, Carolyn Miller, Joe vonFisher, Doug Jakubiak, Jackie Smith, Denise Thiede,
Mark McPeek, Jackie Brown, Kathy Weist, Mathew Leibold, Kevin Geedey, Art Weist,
Mark Olson, Pete Smith, Judy Teeter, Casey Huckins, Jill Fisher, Donna Fitzstephens, Lisa
Huberty, Dan Detweiller, Dawn Jenkins-Klus, Paco Moore, Bryan Foster, Jean Tsao, Jeff
Birdsley, Chris Rodgers, Michelle Potkin, Pete Stahl, Michel Cavigelli, Martha Tomecek,
Jessica Rettig, Jenny Molloy, Tim Laatsch, Liz Smiley, Pam Woodruff, Brian Black, Rob
Lu-Olendorf, Lisa Horth, Joe Picciano, Alice Gillespie, Olivia Damon, Kevin Kosola, to all
of these and to many others, my gratitude for the affection and the good times and the
adventures in the world we shared, that I will never forget, and that can never be lost.

This work was funded by NSF Dissertation Improvement Grant BSR-9101389 to A.
M. Turner, NSF Grant BSR-9207892 to G.G. Mittelbach, and the KBS Research Training

Group funded by NSF grant DIR-9113598.

TABLE OF CONTENTS

LIST OF TABLES ............................. ix
LIST OF FIGURES ............................. x

CHAPTER 1 FRESHWATER SNAILS ALTER HABITAT USE IN
RESPONSE TO PREDATORS ............. 1
INTRODUCTION .......................... 2
METHODS AND RESULTS ..................... 3
Lake Patterns ......................... 3
Are Covered Habitats Safer? .................. 9
Howls Refuge Use Induced? ................. 13

Does Habitat Structure Affect the Behavioral Responses To

Predation Risk? ........................ 23
DISCUSSION ............................. 29

CHAPTER 2 SHORT-TERM AND LONG-TERM RESPONSES OF
CONSUMERS AND RESOURCES TO PREDATION

RISK .......................... 34
INTRODUCTION .......................... 35
METHODS ............................. 38
RESULTS ............................. 41

Snail Survivorship and Growth ................ 41
Snail Habitat Use and Periphyton Standing Crop ........ 44
DISCUSSION ............................. 49

CHAPTER 3 THE EFFECTS OF PREDATION RISK ON CONSUMER

HABITAT USE AND FEEDING RATES ........ 68
INTRODUCTION ......................... 69
EFFECTS OF PREDATION RISK ON RESOURCE LEVELS . . . . 70
THE DISTRIBUTION OF CONSUMERS AMONG HABITATS
OF EQUAL VALUE ......................... 75
EFFECTS OF PREDATION RISK ON CONSUMER
FEEDING RATES .......................... 86
SUMMARY .............................. 94

APPENDICES

APPENDIX A: SNAIL FAUNA OF EIGHT LAKES WITHIN THE
LUX ARBOR RESERVE, MICHIGAN STATE UNIVERSITY . . . 97

APPENDIX B: GROWTH AND STABILITY OF RESOURCE
POPULATION S .......................... 98

LIST OF REFERENCES ......................... 100

LIST OF TABLES

Table Page

1 Two-way AN OVA of chemical cue effects on snail refuge use over the
seven-day experiment. P-values for Time and Time x Treatment effects
are adjusted (Geisser-Greenhouse correction) for a heterogenous
correlation structure among dates. Error1 represents the variance due to
pools within treatments, and is used to test treatment effects. Error2 is the
residual error, and is used to test the effects of time (Gill 1986) ......... 24

LIST OF FIGURES

Figure Page

1

An illustration of the two-level ceramic substrate used to assess
the tendency of snails to use open and covered habitats in natural
lakes. ................................... 5

The proportion of snails occupying the covered half of artiﬁcial substrates

placed into lakes lacking and lakes containing pumpkinseed sunfish.

"Combined Snails" are all taxa summed together. Vertical bars represent 1

SE, N=4 lakes ................................... 8

Survivorship of Physella in experimental pools with covered habitats absent or
present, and pumpkinseeds absent or present. Vertical bars represent 1
SE, N=4 pools .................................. 12

Mean proportion of the Physella population utilizing the refuge in each of
four predator cue treatments. Habitat use was censused each day 1/2 hour
prior to addition of cue. Vertical bars represent 1 SE, N=4 pools ........ 17

The short-term effects of daily cue addition on refuge use. Single hatched

bars represent mean habitat use 1/2 hour prior to cue addition on days four,

ﬁve, and six, and double hatch represents mean habitat use 1/2 hour after

cue addition on days four, ﬁve, and six. Vertical bars represent 1 SE,

N=4 pools .................................. 20

The pattern of habitat use over the one-week long one experiment. The

ﬁlled circles represent the mean refuge use of snails in the Control and Fish
treatments, while the open circles represent the mean refuge use of snails in

the Crushed Snail and Crushed Snail + Fish treatments. Vertical bars

represent 1 SE, N=8 pools ........................... 22

10

11

12

Crawlout frequency in experimental pools into which Physella were

exposed to two levels of simulated mortality (crushed snails added, crushed

snails not added) and two sorts of habitat structure (covered habitat

available, covered habitat not available). Vertical bars represent 1 SE,

N =16 pools .................................. 27

Change in snail dry mass over the course of the l4—day experiment at each of
the four mortality levels. Each point represents the mean of four
pools i 1 SE .................................. 43

The overall pattern of snail habitat use and periphyton standing crop in

relation to simulated mortality. Each point represents the mean of four

pools i 1 SE. Top: Open habitat use over the entire 14-day experiment.

Bottom: Periphyton standing crop on tiles in the open habitat (closed

circles) and on tiles in the refuge (open triangles) at the conclusion of the
experiment .................................. 46

Snapshots of snail habitat use (top) and periphyton standing crop (bottom)

in relation to risk of mortality early and late in the experiment. Top row: A
two-day wide window of habitat use immediately prior to the ﬁrst and last
periphyton sampling dates (days 3 and 14), e.g., "Early" is the mean

proportion of snails using the open habitat during days two and three.

Refuge use is equal to l-(open habitat use). Bottom row: The ash-free dry

weight of periphyton on day 3 (Early), and on day 14 (Late). Filled circles

are the standing crop of periphyton in the open habitat; open triangles are

the standing crop of periphyton in the refuge .................. 48

The F-ratio of linear regressions (Ho: slope=0) performed on the

relationship between mortality level and habitat use (solid circles) and

periphyton standing crop (open triangles) over the course of the

experiment. Habitat use data are two day means. Dashed line represents
F0.05,1,14=4.60. Solid line is a cubic spline interpolation .............. 51

Use of the open habitat in the 1/4, 1, and 4 snails/day mortality treatments
expressed as a percentage of the open habitat use in the 0 snails/day

treatment. Data are two day means over the ﬁrst eight days of the

experiment .................................. 55

13

14

15

The effects of food and predation risk on the habitat use of Physella. Top:
Food added to both open and covered habitats. Use of open habitat is
shown under two levels of predation risk (absent, present) and two levels of
food (periphyton covered tiles added to both habitats). Bottom: Food
added to open habitat only. Use of open habitat is shown under two levels
of predation risk (absent, present) and two levels of food in the open
habitat (no spinach added, spinach added). The perception of risk was
manipulated by pairing each pool with an aquaria housed in an adjacent
laboratory. The predation cue was then generated by feeding five

Physella daily to pumpkinseed sunﬁsh housed in aquaria, and

adding one liter of water from these aquaria, along with untreated water
from control aquaria, daily to predator and no-predator pools. For both
experiments "Use of Open Habitat" is the mean proportion of the
population in the open habitat (j; 1 SE) over the course of the

experiment, N =4 ................................ 59

Hypothetical switching curves at ﬁve levels of relative risk as suggested by

Gilliam and Fraser (top) and Abrahams and Dill (bottom). Curves

represent the combination of resource levels in habitats one and two which

are predicted to yield equal value to foragers under 5 levels of relative

predation risk in the two habitats. Curve 1 represents equal risk in each

habitat; curves 2 through 5 represents the effect of increasing risk in habitat

two relative to habitat one ............................ 63

Hypothetical switching curves of consumers under two levels of relative
risk, and the resource depletion trajectories produced by these behaviors.
Switching curves are those combinations of resource levels in habitats 1 and
2 which yield habitats of equal value to consumers under a given level of
relative risk. Dashed line represents equal risk in habitats 1 and 2, solid line
represents habitat 2 more dangerous than habitat 1. Consumers are
predicted to deplete resources from the point shown by the open circle to
the point shown by the filled circle when habitat 2 becomes more dangerous
than habitat 1. Top: the pattern of habitat selection behavior and resource
depletion when consumers are using the ratio rule developed by Gilliam and
Fraser (1988). Bottom: the pattern of habitat selection behavior and
resource depletion when consumers are using the difference rule developed
by Abrahams and Dill (1989) .......................... 74

16

17

18

19

Resource production and harvest functions as a function of resource

standing crop. Humped curve represents the population birth rate of

resources, and the function is assumed to be equal in the two habitats. The

two linear functions are the rate at which consumers in each of the two

habitats harvest resources, and their slope is dependent on the distribution

of consumers among habitats. The intersection of the production and

harvest curves gives the equilibrium resource standing crop in each habitat

(Rf, Rz‘). The model (equation 6) solves for the proportion of the

consumer population needed in each habitat to maintain R1' and R; at the

level of difference speciﬁed by the individual decision rule. ........... 77

The proportion of a consumer population feeding in habitat 1 as a function

of the level of risk in habitat 1 relative to habitat 2. Relative risk is the ratio

of mortality risk in habitat one to the mortality risk in habitat two (0 =

til/#2), and is assumed here to be equal to the ratio of resources in

habitats 1 and 2 (R1=QR2). Equal risk corresponds to a relative risk value

of 1. In this hypothetical example a = 2 and r = 3. I show the model

predictions for two densities of consumers: N = 10 consumers for the

"low consumption" curve, and N = 30 consumers for the "high

consumption" curve ............................... 82

The proportion of a consumer population residing in habitat 1 as a function

of the level of risk in habitat 1 relative to habitat 2. Relative risk is assumed

here to be equal to the difference between resources in habitats 1 and 2

(R1=Q+R2). Equal risk corresponds to a relative risk value of O. In this
hypothetical example a = 2 and r = 3. I show the model predictions for two

levels of grazing pressure: N = 10 consumers for the "low consumption"

curve, and N = 30 consumers for the "high consumption" curve ......... 85

The predicted growth dynamics of consumers as a function of the level of

risk in habitat 1 relative to habitat 2. Relative risk is defined by the ratio

rule (equal risk = 1). Overall growth represents the average growth of a

population, or the growth of individuals when all members of a

population behave alike. Also shown are habitat-speciﬁc growth rates,

which are appropriate predictors of growth if individuals specialize.

Parameter values are as in Figure 3, except that N=20. Values on Y-axis

are consumer feeding rates (prey eaten / time) .................. 89

20

21

The predicted growth dynamics of consumers as a function of the level of

risk in habitat 1 relative to habitat 2. Relative risk is deﬁned by the

difference rule (equal risk = 0). Overall growth represents the average

growth of a population, or the growth of individuals when if all members of

a population behave alike. Also shown are habitat-specific growth rates,

which are appropriate predictors of growth if individuals specialize.

Parameter values are as in Figure 4, except that N = 10. Values on Y-axis

are the number of resource individuals consumed per unit time ......... 91

The predicted pattern of consumer growth as a function of relative risk

when resources are near their carrying capacity (Low Consumption, N=1O
consumers) and when resources are held by consumers further below their

carrying capacity (High Consumption, N=30 consumers). Top: Growth of
consumers using the ratio rule, parameter values as in Figure 3. Bottom:

Growth of consumers using the difference rule, parameter values as in

Figure 4. Y-axis is the number of resource individuals captured per unit

time .................................. 93

xiv

CHAPTER 1

FRESHWATER SNAILS ALTER HABITAT USE IN RESPONSE TO PREDATORS

2

INTRODUCTION

Freshwater gastropods are poorly defended against shell-crushing predators relative
to their marine counterparts (V ermeij and Covich 1978). While a few freshwater species
possess morphological defenses such as thick shells or large body size, most taxa are small
and have surprisingly thin shells (V enneij and Covich 1978). Despite such poorly
developed morphological defenses, snails are among the most ubiquitous of freshwater
animals, and most snails coexist successfully with abundant predators (Lodge et a1. 1987,
Osenberg 1989, Brown 1991). Verrneij and Covich (1978), Bronmark (1989), and
Alexander and Covich (1991) have suggested that snails have the ability to evaluate local
predation risk and select safe micro—habitats. For example, it is thought that snails may
use protective microhabitats such as shallow water or the underside of logs and cobbles to
a greater degree in lakes with fish predators than they do in lakes without ﬁsh predators.
However, while marine gastropods are known to exhibit predator avoidance behaviors
(F eder 1963, 1972, Hughes 1986) there are few studies of predator avoidance by
freshwater snails. Specifically, it is not known if variation in snail habitat use among lakes
is related to predator abundance, or if variation in habitat use acts to minimize mortality
from predators. Further, it is not known how habitat structure might affect the avoidance

tactics employed by snails.

3

In this study I present data on the habitat use of snails in natural lakes and in
experimental pools aimed at answering the following four questions:
1) Is there a relationship between snail habitat use in lakes and the presence/absence of fish
predators?
2) Do the behavioral patterns shown by snails function to lower their mortality rates?
3) Are the behavioral patterns ﬂexible, and if so, how is variation induced?

4) How does habitat structure affect the avoidance tactics used by snails?

METHODS AND RESULTS

Lake Patterns

I compared snail habitat use in four lakes containing an important snail predator, the
pumpkinseed sunfish (gaping gym), to snail habitat use in four lakes lacking
pumpkinseeds. Pumpkinseed sunﬁsh are morphologically specialized molluscivores
(Lauder 1983), as adults feed predominately on snails (Sadzikowski and Wallace 1976,
Mittelbach 1984), and can have strong impacts on snail abundance and species
composition (Osenberg 1988, Osenberg et al. 1992, Bronmark et al. 1992). The tendency
of snails to use open versus covered habitats was estimated by periodically censusing their
position on standardized artificial substrates. Substrates were built from two pieces of
unglazed ceramic tile: a square tile (15 cm on a side) was supported by four acrylic legs 2
cm tall on one half of a second rectangular tile (30 x 15 cm). Thus, the substrates were

comprised of two open surfaces (the exposed tops) and two covered surfaces (the covered

Figure 1. An illustration of the two-level ceramic substrate used to assess the tendency of

snails to use open and covered habitats in natural lakes.

 

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6

half of the rectangular tile and the underside of the square tile) equal in area (Figure 1).
The eight study lakes lie within the Lux Arbor Reserve of Michigan State University
(Barry County, Michigan). They range in surface area from 0.2 to 127 ha and in
maximum depth from 1.5 to 4 m. They are permanent, hardwater lakes with rich snail
assemblages similar to those found in other local lakes (Appendix A). The presence or
absence of pumpkinseeds and other ﬁsh species was determined by repeated seine hauls.
When present in these lakes, pumpkinseeds are quite abundant, sharing dominance with
bluegills (13m macrochirus) and largemouth bass (Mm §a_lrm_idr§). Three of
the lakes lacking pumpkinseeds are completely ﬁshless, and the fourth contains fathead
minnows (Pimephales promelas). I placed the four substrates 1-2 m apart on each lake
bottom in water 30 to 50 cm deep on May 8, 1994, and checked them every 2 days
thereafter for four weeks (N=14 sample dates). I recorded the number and identity of
snails occupying the Open and covered portions of each substrate, removed the snails, and
returned the substrate to the lake bottom. Data from the four substrates per lake were
pooled for each sample date, and the use of cover was calculated by dividing the number
of snails found under cover by the total number of snails found on the substrates. The
overall mean use of covered habitats in each lake was then calculated by averaging across
dates. A total of 10 taxa were found on the substrates Ma gm, Amnicola m

Gﬂaulus parvus, Laevapex fuscus, Promenetus exacuous Gyraulus deﬂectus Aplexa

 

 

elongata, Planorbella trivolvis Physella integra, and Pseudosuccinea columella in order of

 

 

frequency of occurrence), and overall snail density averaged 0.82/substrate/date (0.09 m2

Figure 2. The proportion of snails occupying the covered half of artificial substrates placed
into lakes lacking and lakes containing pumpkinseed sunfish. "Combined Snails" are all

taxa summed together. Vertical bars represent 1 SE, N=4 pools.

Refuge Use (%)

100

01
O

 

Lokes Locking Pumpkinseeds
E§§g Lokes Contownng Punuﬁonseeds

 

Conﬂﬂned SnoHs

PhyseHo

surface area/substrate).

The pattern of snail habitat use differed markedly between lakes without
pumpkinseeds and lakes with pumpkinseeds (Figure 2). Considering all snail taxa
summed, use of the covered portion of substrates was 18 _+_- 9% (mean i: 1 SE, N=4) in
lakes lacking pumpkinseeds, but use of the covered portion increased to 77 i 9% (mean i:
1 SE, N=4) in lakes containing pumpkinseeds (Figure 2 left, F1,6=22.1, £<.01). Because
individual snail taxa did not occur on the substrates at the same frecuency in lakes with
and without pumpkinseeds, the observed differences in overall snail habitat use between
lake types may be due to different species-specific behaviors. However, the pulmonate
snail Elyse—Ila ﬁll—TIE was found on substrates in 6 of the 8 lakes (it was rare or absent in
two of the lakes lacking pumpkinseeds), and it too used the covered portion of the
substrates much more often in the presence of pumpkinseeds (Figure 2 right, F1,4=18.3,
13:.01). Although M m was the most abundant snail on the substrates (it
comprised on average 24% of the snails censused), removing them from the analysis does
not change the overall pattern: the remaining snail species also used covered habitats more
often in the presence of pumpkinseeds (76i9% versus 22: 13%, F 15:98, £=0.03).

Are Covered Habitats Safer?

The differential use of covered habitats by snails in lakes with and without
molluscivorous fish is consistent with the notion that covered habitats serve as a refuge
from ﬁsh predation. I experimentally tested this hypothesis by manipulating the presence

of ﬁsh and the presence of cover in experimental pools, and monitoring the survivorship of

10

EELSQLIQ gym. I performed this experiment in 16 polyethylene wading pools, each
containing 270 liters of water (200m deep x 1.3m dia.). The pools were placed in a
greenhouse at the Kellogg Biological Station, filled with well water, and allowed to aerate
48 hours. A size distribution of 335111;; representative of the overall population were
collected from shallow littoral areas (< 10cm deep) of Middle Crooked Lake (one of the
pumpkinseed lakes used in the habitat use measurements), and 10 snails were randomly
selected and stocked into each pool. Eight of the 16 pools contained a square unglazed
ceramic tile 31 cm on a side supported by four acrylic legs 2.5 cm tall. These tiles were
designed to mimic natural refuges from fish predators such as the underside of logs or
cobbles, and were placed into the middle of the pools, where they covered 4% of the 2.15
m2 substrate available to the snails. Pumpkinseed sunfish (105 to 120 mm Standard
Length) were seined from Middle Crooked Lake and a single fish was added to each of
eight pools, cross-factored with the refuge treatment. I ran the experiment for three days,
checking the number of survivors and censusing their habitat use every 12 hours.
Pumpkinseeds readily consumed M and had a strong effect on the number of
snails surviving after three days (Figure 3; ﬁsh effect: F3,12=70.7, P < 0.01). However, the
effect of pumpkinseeds on P_hyse_lla survivorship depended on whether cover was present
or not; P_hy_s_e;l_l_a survivorship was higher in those fish pools with cover available (Figure 3;
fish x cover interaction: F3,12=10.1, _P_ < 0.01). Thus, snails in the covered habitat are safer
from pumpkinseed predation than are snails in open habitats, and cover served as a partial

refuge even at the high densities of pumpkinseeds used here.

11

Figure 3. Survivorship of Physella in experimental pools with covered habitats absent or

present, and pumpkinseeds absent or present. Vertical bars represent 1 SE, N=4 pools.

Surﬁvorshk>(%ﬂ

100

50

Pumpkinseeds
Present

12

 

Punuﬂdnseeds
Absent

13

Pumpkinseeds also had a strong effect on the tendency of snails to use the covered
habitat. Among the eight pools containing a covered habitat, the mean proportion of
surviving snails found in the covered habitat averaged only 8 i 1% (i 1 SE) in the absence
of ﬁsh, but averaged 37 j; 6% (j; 1 SE) in the presence of ﬁsh (fish effect: F1'6=19.2,
130.01). The habitat use pattern could not have been produced by simple depletion of
snails in the open habitat by pumpkinseeds without any behavioral response by snails: the
mean number of snails using the refuge over the course of the experiment was higher in
the ﬁsh than in the fishless treatments (1.85 _-i_-_ 0.46 versus 0.75 i 0.17 snails (mean i 1 SE,
N=4), F1.6=8.14, E = .03), despite lower overall numbers. Thus, the shift into the safer
habitat in the presence of predatory ﬁsh appears to be an adaptive and ﬂexible behavior.
How is Refuge Use Induced?

If M do facultativly alter their behaviors in response to the presence of
predators, they must first acquire information regarding the local risk of predation. The
mechanism, however, by which they might gather such information is unknown. Snails
locate food patches by chemoreception (Townsend 1973, Croll 1983, Sterry et al. 1983,
Bronmark 1985), and chemical cues released when predators feed on conspecifics induce
changes in the life-history characteristics of m mgata (Crowl and Covich 1990). It
is not known, however, if m gyrjna use chemoreception to assess predation risk.
Accordingly, I conducted a second experiment designed to answer two questions: 1) Does
Ma respond behaviorally to chemical cues associated with the predation process? and

2) What is the source of a cue (or cues) which may induce refuge use by Physella?

14

I tested the hypothesis that 3.115% can evaluate local predation risk and select safe
habitats when exposed to chemical cues associated with the predation process by
presenting various chemical stimuli to snails in wading pools and monitoring their habitat
use. In mid-July, 16 pools (described above) were placed outdoors at the pond lab facility
of the Kellogg Biological Station in a 4x4 grid, filled with well water, and allowed to
aerate for 24 hours before snails were stocked. Each pool contained a covered habitat
(hereafter the "refuge") as described above. Physelg were collected from Middle Crooked
Lake, and 10 individuals were added to each pool. The following day I conducted a
census of habitat use, and then imposed the experimental treatments by adding water from
cue-generating aquaria assigned to one of four treatments.

I imposed treatments by matching each pool with one of 16 cue-generating aquaria
housed inside an adjacent laboratory. Each 36 liter aquarium was first washed with a
dilute phosphoric acid solution, rinsed, ﬁlled with well water, and gently aerated with an
airstone. One of four treatments was then imposed on each aquarium. "Control" aquaria
received no additional treatment. "Crushed Snail" aquaria received five crushed snails
daily from the same source population and of the same size as the experimental snails
(snails crushed manually). The "Fish" aquaria each housed one pumpkinseed sunﬁsh
between 112 and 117 mm standard length, which were fed a single earthworm
(Lumbriscus sg) daily, and the "F ish + Crushed Snail" aquaria contained a pumpkinseed
sunﬁsh which was fed ﬁve snails daily in addition to an earthworm. Each day I transferred

one liter of water from each aquarium to its paired wading pool and replaced it with

15

aerated tap water. I crushed snails and fed fish one hour before the water was removed
from the aquaria and added to the pools. To control for any spatial effects and insure
adequate randomization, I assigned pools to treatments in a Latin-square manner, with
each treatment represented just once in any row or column of pools.

The experiment ran for 7 days after the treatments were first imposed on 17 July.
Snail habitat use was censused in the mid-afternoon of each day prior to the addition of the
aquarium water. I recorded the number of snails under the refuge, the number in the open,
and the number within 1 cm of the water's surface. For each pool I estimated the
probability that an individual snail would use the refuge by dividing the number of snails
observed under the tile by the total number censused. In addition, on days four, five, and
six I censused snail habitat use one hour following the addition of water from the cue-
generating aquaria. The pattern of habitat use in the four treatments was compared to the
pre-cue addition pattern with Multivariate Analysis of Variance to see if the response was
time dependent.

Refuge use data were analyzed using two-way repeated-measurements analysis of
variance (RM-AN OVA) with crushed snail presence/absence as one factor and ﬁsh
presence/absence as the other. Time (N =7 observations) was a repeated factor. Note that
for the main effects and their interaction (Crushed Snails and Fish) RM-AN OVA is
equivalent to taking a mean of all 7 dates for each pool, with each pool thus generating

one observation, and then using two-way ANOVA to test for treatment effects. All

16

Figure 4. Mean proportion of the Physella population utilizing the refuge in each of four
predator cue treatments. Habitat use was censused each day 1/2 hour prior to addition of

cue. Vertical bars represent 1 SE, N=4 pools.

17

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Crushed Snails: Absent Present

Fish: Absent Present Absent Present

18

analyses were done using the Statistical Analysis System (SAS Institute Inc. 1991).

m responded strongly to crushed conspeciﬁcs, doubling their refuge use in the
crushed snail and fish + crushed snail treatments over the control and fish only treatments.
Mega showed no response to the presence of ﬁsh alone (Figure 4, Table 1). These data
conﬁrm that P_hy&ll_a habitat use is a ﬂexible behavior: the degree to which an individual
uses the refuge depends on the level of predation risk perceived by that individual. The
habitat use of P_hys_ella was completely contingent on the presence of crushed snails, and
they were oblivious to the presence of fish (Figure 4, Table 1). This suggests that Physella
respond behaviorally to a chemical cue released by injury to conspecifics, and that this one
does not require modification by pumpkinseeds in order to invoke a behavioral response.

Each habitat use census was conducted 23 hours after cues were last added, yet the
effects were still strong. Were the short-term effects any stronger? Evening censuses
conducted one hour following cue addition on days 4, 5, and 6 also found strong effects of
crushed snails, but no fish effects (two-way ANOVA, Fish effect 2:027, Crushed Snail
effect P=0.01, Fish x Crushed Snail effect P=0.48). However, this response was not
different from the pre-cue addition response; the overall pattern of habitat use across
treatments was indistinguishable one hour and 23 hours after cue addition (Figure 5,
MANOVA, B > 0.10).

An examination of the patterns of habitat use over time showed that refuge use was
initially high, peaked on day two, and decreased significantly during the experiment (E <

0.01 for the Time effect; Fig. 6 and Table 1). However, the ﬁsh and the crushed snail

17,,

19

Figure 5. The short-term effects of daily cue addition on refuge use. Single hatched bars
represent mean habitat use 1/2 hour prior to cue addition on days four, ﬁve, and six, and
double hatch represents mean habitat use 1/2 hour after one addition on days four, ﬁve,

and six. Vertical bars represent 1SE, N=4 pools.

20

 

 

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0.4

cm: mmchm

Present

Crushed SnoHs:Absent

Present Absent Present

Absent

ﬁsh:

21

Figure 6. The pattern of habitat use over the one-week long cue experiment. The ﬁlled
circles represent the mean refuge use of snails in the Control and Fish treatments, while the
open circles represent the mean refuge use of snails in the Crushed Snail and Crushed Snail

+ Fish treatments. Vertical bars represent 1 SE, N=8 pools.

 

Refuge Use

0.6

0.4

0.2

0.0

22

 

 

l l

O Crushed Snoil Trt.

\ O No Crushed Snoil Trt.

i\§

l l

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3 6

After Experiment Initiotion

_ _.. -m LLB“!

23

treatments declined in parallel, demonstrating no treatment effects on the rate of change in
refuge use (2 > 0.10 for Time*Fish and Time*Crushed Snails effects). The three way
interaction of Time, Fish, and Crushed Snails was signiﬁcant (P < 0.05), but is difficult to
interpret.

ﬂygna may sometimes respond to predation risk by moving to the water's surface
(Alexander and Covich 1991, AM. Turner primary; observation). However, I found that
the number of snails utilizing the near-surface substrate (the area higher than 1 cm below
the water's surface), and the proportion of snails in the open habitat using the near-surface
area, did not differ among treatments (two-way ANOVA, 12 > 0.10). It is possible that
movement to the surface is more likely to occur when no other refugia are available. In the
next experiment I test the hypothesis that habitat structure affects the predator avoidance

tactics employed by Physella.

Does Habitat Structure Affect the Behavioral Response to Mortality?

 

I tested the hypothesis that the frequency with which Ma uses the near-surface
habitat depends on both habitat structure and predation risk by manipulating the presence
of a covered habitat and the perception of mortality risk. This experiment was conducted
in 16 wading pools (270 liters each) in the KBS greenhouse. Pools were ﬁlled with well
water, allowed to aerate 24 hours, and then 10 EELS/91141 gym; collected from Lower
Crooked Lake (adjacent to Middle Crooked Lake, where snails for the previous
experiments were collected), were stocked into each pool. Half the pools received a

covered habitat (a square tile 31 cm on a side, supported by four legs 2.5 cm tall).

24

Table 1. Two-way ANOVA of chemical cue effects on snail refuge use over the seven-day
experiment. P-values for Time and Time x Treatment effects are adjusted (Geisser-
Greenhouse correction) for a heterogenous correlation structure among dates. Error,
represents the variance due to pools within treatments, and is used to test treatment

effects. Error2 is the residual error, and is used to test the effects of time (Gill 1986).

Source of Variation ss df ms F P
Fish 0.0002 1 0.0002 0.02 0.90
Crushed Snails 0.1687 1 0.1687 17.54 <0.01
Fish x Crushed Snails 0.0002 1 0.0002 0.02 0.89
Block 1 (Rows) 0.0266 3 0.0088 0.92 0.48
Block 2 (Columns) 0.0137 3 0.0046 0.48 0.71
Error, 0.4039 6 0.0673

Time 1.1144 6 0.1857 12.21 <0.01
Time x Fish 0.1383 6 0.0230 1.52 0.24
Time * Crushed Snails 0.1794 6 0.0299 1.97 0.15
Time * Fish * Crushed Snails 0.4027 6 0.0671 4.41 0.02
Time "‘ Block 1 0.4505 18 0.0250 1.65 0.17
Time * Block 2 0.4346 18 0.0241 1.59 0.19
Error2 0.5477 36 0.0152

25

Cross-factored with the refuge treatment was a second treatment in which perceived
mortality was manipulated.

I simulated mortality on snails in the high mortality treatment by adding two crushed
conspecifics each day. The snails were placed into the appropriate pools, and immediately
crushed by hand. The preceding experiment demonstrates 11131me behavioral
response to manually crushed snails is identical to the response to snails consumed by fish.
The crushed snails were of the same size, and from the same source population, as the
experimental snails. This approach is advantageous to placing a natural predator into the
experimental pools because any behavioral shifts observed are not confounded with
changes in snail density. Also, by crushing newly introduced snails, I avoid changing the
level of past experience of the experimental snails, as would be the case if I crushed
experimental snails and replaced them with conspecifics. Snail habitat use was censused in
the mid-afternoon of each day, immediately before the daily mortality treatments were
imposed. I recorded the number of snails under the ceramic tile, the number in the open,
and the number that were at or above the waters surface. The experiment ran for five
days. In addition to the daily mid-afternoon censuses, on days 3, 4, and 5, I censused snail
habitat use two hours after sunset.

Snails in the eight pools containing a refuge showed the same response to mortality
as found in the previous experiments: 111% refuge use was higher in the presence of
mortality risk than in its absence (68i5%- vs. 18i7%, F ,’6=25.4, £<0.01). The experiment

as a whole revealed that use of the near-surface habitat was higher when snails were

26

Figure 7. Crawlout frequency in experimental pools into which Physella were exposed to
two levels of simulated mortality (crushed snails added, crushed snails not added) and two
sorts of habitat structure (covered habitat available, covered habitat not available).

Vertical bars represent 1 SE, N=16 pools.

Use of Near Surface Habitat (%)

27

 
  
   

    

60
gag; Refuge Absent
EEEE Refuge Present
30
0

Crushed SnaHs Crushed SnaHs
Absent Present

+__ -.__ ,1

    
  
  
  

Figure 7. Crawlout frequ
two levels of simulated
sorts of habitat structi

Vertical bars represrr

28

exposed to mortality risk (mortality effect F,,,2=20.5, £50.01; Figure 7). Most
importantly, the response to risk clearly depended on whether a covered habitat was
available or not: the risk of mortality increased near-surface habitat use much more in the
absence of a covered habitat than in the presence of a covered habitat (habitat structure x
mortality interaction, F = 350.01; Figure 7).

The habitat use of mm; at night contrasts sharply with its daytime habitat use.
Elyse—Ila abandoned both the covered and near surface habitats at night, and were found
almost exclusively on the open substrates of the wading pools, even when exposed to
simulated mortality. Averaging across the three nights of observations, there were no
signiﬁcant differences among treatments in use of covered habitats or use of near surface
habitats (£90.10 for all treatment effects). Averaging across treatments, use of the covered
habitats at night was only 3%, and no snails were found using the near-surface habitat.
Note that this pattern can not be caused by a decay of the cue over time; the diurnal
habitat use data were collected each day before the cue was added. The data show that
snails moved back into covered or near-surface habitats after occupying open substrates at

night.

29

DISCUSSION

Behavioral ﬂexibility may allow prey to coexist with predators while minimizing the
costs of predator avoidance. In this study I have linked ﬂexible behaviors with their
survivorship functions, and shown that inter-population variation in behavior is related to
the presence of predators. Payse_lla are able to evaluate local predation risk via chemical
cues and facultatively adjust their habitat use by moving under covered habitats when they
perceive greater risk of predation. This habitat shift appears to decrease their vulnerability
to predators: covered habitats are a refuge from pumpkinseed predation. Finally,
variation among lakes in snail habitat use is related to the presence of ﬁsh predators:
Physella, as well as the snail community as a whole, select covered habitats more often in
lakes containing pumpkinseeds than in lakes without molluscivorous ﬁsh.

Like most animals, snails face a wide array of potential predators (e. g. fishes,
leeches, crayﬁsh, insects; Brown 1991), and in selecting habitats they must evaluate the
level of risk posed by each predator. Predator avoidance behaviors often have significant
costs associated with them (Werner et al. 1983, Skelly 1992), and obviously being preyed
upon is costly. Foragers can minimize these costs by avoiding false alarms and changing
their behavior only when predators pose a substantial threat (Phillips 1978). One way to
accurately assess predation risk is to respond behaviorally only when predators are actively
feeding on conspeciﬁcs, but this requires specific information about the diet of predators.
Chemoreception potentially offers a low risk means by which prey can monitor a

predator's diet. While evaluation of predation risk by chemoreception may be widespread

30

in aquatic systems (e.g. ﬁshes, Weldon 1990, Keefe 1993, Mathis and Smith 1993;
amphibians, Petranka et al. 1987, Wilson and Lefcort 1993; insects, Peckarsky 1980,
Soluk and Collins 1988, Kohler and McPeek 1989, Tjossem 1990; cladocerans, Dodson
1988, Leibold 1990), few studies are adequately designed to identify the source of the
chemical cue to which the prey are responding. As a result, the degree of specificity
regarding the cues which induce behavioral changes is poorly understood (Wilson and
Lefcort 1993). The experiments described above demonstrate that Mach—a alter their
habitat use in response to a chemical cue emanating from injured conspeciﬁcs, but not in
response to the mere presence of a predator.

The predators of freshwater gastropods can be divided into two general classes:
large predators that usually crush snails (e. g. fish, ducks, crayfish, turtles) and smaller
predators that invade the shell (e.g. leeches, hemipterans, coleopterans). The behavioral
responses that snails showed in the present study (moving under a refuge) are most
effective against large-bodied predators that cannot follow them into confined areas.
Because large predators usually crush snails, moving into a confined space is an
appropriate response to cues released by a crushing action. In contrast, snails show no
pre-contact response to leeches, a small predator that invades the shell (Townsend and
McCarthy 1980, Bronmark and Malmqvist 1986). Instead, snails showed an escape
response (shell twisting and detachment from the substrate) only after being attacked by
leeches. Therefore, it appears that the behavioral response used to avoid or escape

predators is linked to the type of cue used to detect each sort of predator.

31

The use of open habitats by walla in lakes lacking pumpkinseeds and at night
support the notion that their behavior is adapted to minimize mortality from
pumpkinseeds. Pumpkinseeds are visual predators and are not active foragers at night.
Alexander and Covich (1991), however, found that in a lake dominated by crayfish
predators, a nocturnal predator that relies on tactile and chemical cues to locate prey,
snails showed strongest the strongest avoidance behaviors (movement to the water's
surface) at night. Crayﬁsh are very rare, or possibly absent, from my study lakes (A. M.

Turner, personal observation E. Smiley, personal observation).

 

Predator mediated behaviors have the potential to signiﬁcantly alter species
interactions in communities containing mobile animals (Werner 1992). Predator avoidance
may levy non-lethal costs on prey; however, few studies have been able to quantify these
non-lethal consequences. This stems, in part, from the difﬁculty of manipulating prey
behavior and the methodological problem of disentangling the numerical and behavioral
effects of predators on prey. However, ﬂexible behaviors such as the habitat shifts
documented in this study present valuable opportunities to measure the consequences of
predator avoidance. Because Lhyarila respond to chemical cues, I can experimentally
present Ease—11a, with the perception of risk and measure the various extended effects of
any behavioral responses without any confounding effects of the direct mortality imposed
by predators. Taxa such as M that respond to mortality on conspecifics, regardless
of the source, are excellent model systems because the investigator can experimentally

impose mortality risk in a highly controlled manner.

32

Although Physalla lowers its rate of mortality from fish predators by moving into
safer habitats when confronted by risk, this response does not necessarily diminish the
strength of food-web interactions involving predators. Because M can control
resource levels within habitats (Lowe and Hunter 1988), and fish predators cause P_hy£lla
to move among habitats, it seems likely that predator-induced habitat shifts by snails can
have important consequences for the snail's periphyton resources. Predation risk may
increase periphyton abundance in risky habitats by causing vulnerable species to move into
safer habitats.

A number of studies have documented that the effects of adding or removing a top
predator in a food chain can be transmitted to lower trophic levels (e.g. Paine 1966), but
the relative importance of numerical and behavioral effects is usually not known. For
example, Bronmark et a1. (1992) showed that pumpkinseed sunfish have a positive effect
on snail resources (periphyton). These effects were assumed to be numerical in nature:
pumpkinseed sunﬁsh reduced snail population sizes, thereby reducing snail grazing
pressure and allowing periphyton to increase in abundance. However, the behavioral
responses of snails to pumpkinseeds documented here suggests an alternative
interpretation of these observations. If fish predators cause snails to move to the safety of
covered habitats, then periphyton resources in more open and dangerous habitats would be
expected to increase in abundance without any change in overall snail density, i.e. the
indirect effects of snail predators on snail resources may be mediated though changes in

snail habitat use.

33

I tested this prediction by presenting snails with the perception of mortality by
adding crushed snails to experimental pools and monitoring periphyton resources grown
on ceramic tiles in open habitats. I found that even though snail density was held constant,
the periphyton resources increased in the open areas (a positive indirect effect) when
perceived snail mortality is increased (Chapter 2). Thus, it is likely that the positive effect
of snail predators on snail resources is due at least in part to the adaptive behaviors of the

snails themselves.

CHAPTER 2

SHORT-TERM AND LONG-TERM RESPONSES OF CONSUMERS AND

RESOURCES TO PREDATION RISK

34

35

INTRODUCTION

Animals often respond to increases in predation risk by moving from dangerous
habitats into safer habitats (reviews in Kerfoot and Sih 1987, Dill 1987, Lima and Dill
1990). Ecological theory suggests that if animals regulate resource levels within habitats,
then predator-induced habitat shifts will result in higher resource levels in more dangerous
habitats relative to safer ones (Covich 1976, Abrams 1984, Kotler 1984, Gilliam and
Fraser 1988, Werner 1992). Such behaviorally mediated effects of predators on resource
levels may be widespread and common (e.g. Power 1984a, Power 1987, Power et al.
1985, Turner and Mittelbach 1990), yet there are still few empirical studies which allow us
to gauge the necessity of incorporating habitat selection behavior 'into models of trophic
interactions.

Predictions regarding the short-term effects of predation risk on the habitat use of
foragers are clear: if habitats are otherwise of equal value, foragers should respond to
increased risk by moving into safer habitats. Resources in safe habitats will then
experience higher mortality rates than resources in dangerous habitats, and resources will
be depleted more rapidly in safe habitats than in dangerous ones. Over time, however,
resource levels among habitats may diverge such that foragers expect equal ﬁtness returns
in high food/high risk habitats and low food/low risk habitats. Several studies have
"titrated" food and predation risk, and they show that foragers will often accept a higher
level of risk in return for a higher foraging rate (Gilliam and Fraser 1987, Abrahams and

Dill 1989, Nonacs and Dill 1990, Todd and Cowie 1990, Kotler et al. 1991). What then,

36

will be the long-term equilibrium distribution of foragers among habitats that offer similar
fitnesses, but positively covary in food and risk? Clearly, the prediction that foragers
should respond to increased levels of predation risk by moving into safer habitats only
works in the short-term. At present it is difﬁcult to predict how foragers will distribute
themselves among habitats that differ in both foraging rate and predation risk, but are of
equal value. Experimental studies provide little insight here: there are no experiments
which manipulate predation risk on foragers dynamically interacting with their own
resources in two or more habitats, and record forager habitat use over time. A primary
goal of this study is to follow the response of both forager habitat use and resource
dynamics over time, contrasting the short-term and long-term responses of foragers and
resources to manipulations of habitat-speciﬁc predation risk.

Many species can detect the presence of predators and facultatively adjust their
behaviors, but few studies have determined if animals can quantitatively adjust their
behavior in relation to the level of risk. That is, do animals employ a fixed response to a
threshold level of risk, or is their behavior modulated in relation to the increase in risk? A
continuous response to increasing risk would suggest that animals are balancing the
increase in risk against other, conﬂicting opportunities. There are potentially far-reaching
implications of such a balancing act. For example, these incremental effects could
potentially be transmitted to the resources, structuring them such that resource standing

crop is proportional to predation risk.

37

Empirical demonstrations of behavioral indirect effects may be rare because
manipulations of predator density usually result in numerical as well as behavioral effects
on prey. The behavioral response is thus confounded with a numerical response, making it
difﬁcult to tease apart the relative roles of the two in affecting resources. A possible
solution to this problem is to simulate mortality, thereby altering perceived mortality
without actually changing prey density. Models of predators may offer a viable approach
(e. g. Milinski and Heller 1978). However, the level of risk perceived by prey is not
known, and prey may habituate to the model if it is not associated with mortality. A
second approach is to impose known levels of mortality on experimental animals, replacing
the animals killed with conspecifics so as to hold density constant (e.g. Werner et al.
1983). I use a variant on the second approach here to explore the consequences of
predator avoidance by the common freshwater snail ﬂagella m.

I have shown in Chapter 1 that M gym is usually found under cover in
lakes containing the molluscivorous pumpkinseed sunﬁsh (Lappm_is_ gibbosus ), whereas in
lakes lacking pumpkinseeds, P_hysalla is usually found on exposed substrates. Experiments
showed that Ma offered covered substrates had lower mortality from pumpkinseeds
than M offered only exposed substrates, and that the presence of pumpkinseeds
cause M to move into safer (covered) habitats. I experimentally investigated the
source of the cue which triggers the habitat shift, and I found that M responds to
crushed conspeciﬁcs in the environment, regardless of whether the snails were crushed by

a natural predator (a pumpkinseed sunfish) or by the experimenter (Chapter 1).

38

Here I present the results of an experiment in which I stocked Ma into pools
with two habitats: a large open area and a smaller, covered area. A ceramic tile supporting
a crop of periphyton was placed in each habitat. I then imposed four levels of simulated
mortality and monitored both the habitat use of the snails and the response of their
periphyton resources over time. Because PM are known to alter their habitat use in
response to risk of mortality (Chapter 1), and they are known to depress resource levels in
habitats in which they graze (Lowe and Hunter 1988), I hypothesized that increasing the
level of mortality perceived by the snails would initially cause them to leave the open
(dangerous) habitat, allowing periphyton to increase in abundance. Further, if the
magnitude of the snail habitat shift depends on the level of risk, then the periphyton
abundances should reﬂect the level of risk. Finally, I predicted that both snail habitat use
and periphyton standing crop would change through time, and therefore I measured snail
distributions and periphyton standing crop repeatedly over the course of the experiment.
By these methods I was able to examine the behavioral indirect effects of snail predators

on the snail resources without the confounding inﬂuence of numerical changes.

METHODS
I performed this experiment in 16 circular polyethylene wading pools, each
containing 270 liters of water (20cm deep x 1.3m dia.). The pools were placed outdoors
at the Kellogg Biological Station in a 4x4 grid and ﬁlled with unchlorinated well water

(alkalinity equivalent to CaCO3 concentration > 100 mg/l). Each pool contained a 31 x

39

31cm unglazed ceramic tile raised off the bottom by four legs 5.5 cm tall. These tiles were
designed to mimic natural refuges from predators, and were placed in the middle of the
pools, where they covered 4% of the 2.15 m2 of substrate available to the snails. Thus,
each pool was comprised of two habitats: a small refuge and a large open area. Twelve
adult M gm were stocked into each pool on 27 July (mean shell length = 9.9 mm,
mean dry mass (excluding shell material) = 10.06 mg). The snails were collected from
dense aggregations (>100/m2) in shallow littoral areas (<10 cm deep) of nearby Middle
Crooked Lake, and were selected to be similar in size (coefﬁcient of variation in length =
5%).

I simulated four levels of mortality on snails in the experimental pools by adding
four doses of crushed conspecifics: 0, 0.25, 1, or 4 snails daily. The appropriate number
of snails were placed into each pool and immediately crushed by hand. The crushed snails
were of the same size and from the same population as the resident snails. I employed this
design, rather than imposing mortality on a given number of snails in each pool and then
replacing them with similar-sized conspeciﬁcs, because this design maintained a constant
level of experience amongst the snails in a pool. The 0.25/day mortality treatment was
accomplished by adding a single crushed snail on day one, and every four days thereafter.
The mortality treatments were imposed daily in midafternoon.

I evaluated the effect of variation in snail habitat use on resources by measuring
periphyton standing crop on a pair of ceramic tiles in each pool: one under the refuge and

one in the open. Small tiles (15.2 cm on a side) were ﬁrst incubated for ten days in an

40

outdoor recirculating artiﬁcial stream system. Periphyton quickly grew on tiles in the
stream, reaching a mean standing crop of 3.75:1.55 mg/cm2 (mean ash free dry weight i
1 SE, N=4 samples) after ten days. Two randomly selected tiles were transferred to each
experimental pool (one in each habitat) on 28 July, one day after the introduction of snails.
The periphyton community on the tiles was dominated by highly edible taxa. The
ﬁlamentous overstory was primarily comprised of Oedogonium spp; common prostrate

forms were the chlorophytes Ankistrodesmus Chlamydomonas, Scenedesmus, and

 

Cosmarium and the diatom Navicula. I estimated periphyton standing crop on each tile

 

 

over the course of the experiment by measuring Ash Free Dry Weight (AFDW) two, four,
and fourteen days after the tiles were introduced to the pools. Periphyton was scraped
from a strip 8.75 mm wide and running the width of the tile (13.3 cmz), rinsed onto a
Whatman GF/F glass ﬁber ﬁlter, dried at 60° for 24 hours, weighed, ashed at 500° and
reweighed.

Snail habitat use was censused in the mid-afternoon of each day, immediately before
the daily mortality treatments were imposed. I recorded the number of snails under the
refuge, the number in the open, and the number feeding on periphyton on the small
ceramic tiles in each habitat. For each pool I estimated the probability that an individual
snail would use the open habitat (hereafter "open habitat use") by dividing the number of
snails observed in the open by the total number censused. At the end of 14 days I
collected, counted, and measured the shell length of the surviving snails. Lengths were

converted into dry masses, excluding shell material, using the following length-weight

41

relation: M Dry Mass (mg) = 0.014*(Shell Length (mm))**2.86 (r2=0.86, £50.01,
N =191).

I analyzed the effect of simulated mortality on snail habitat use and periphyton
abundance using linear regression analyses (N =16 points for all analyses). I applied a log
(x+0.1) transformation to the four levels of mortality (0, 0.25, 1, and 4 snails/pool/day) in
order to linearize the relationships and to equalize the inﬂuence of all four levels. Visual
inspection of the residuals conﬁrmed that there was no strong non-linearity. Regression
analysis, as employed here, tests the hypothesis that there is a monotonic relationship
between mortality rate and the dependent variable under consideration (slope equal to zero
was used as the null hypothesis of no treatment effect). For clarity of presentation, figures
show mortality as categorical data.

RESULTS
Snail Survivorship and Growth

Snail survivorship averaged 91%, and was not related to simulated mortality rate (2
> .10). Because there were no treatment effects on snail densities, I was able to examine
the consequences of variation in snail habitat use (i.e. behavioral indirect effects) without
any confounding differences in snail density.

Predation risk had a negative effect on the growth of Mia (Figure 8). Growth of
m declined linearly as a function of mortality rate (_12 < 0.01). There were no effects
of mortality rate on the within-pool variance in snail size at the end of the experiment (l_’ >

0.10).

42

Figure 8. Change in snail dry mass over the course of the 14-day experiment at each of the

four mortality levels. Each point represents the mean of four pools i 1 SE.

Snail Growth (mg)

2.5

2.0

1.0

43

 

 

 

 

 

 

l l l

j

0 0.25 1.0 4.0

Daily Mortality

 

44

Snail Habitat Use and Periphyton Standing Crop

How does predation risk affect m habitat use, and what effect does variation in
M habitat use have on periphyton abundances? When averaged over the entire
experiment, increasing the risk of mortality had a negative effect on use of the open habitat
by Ma and a positive effect on periphyton standing crop in the open habitat (Figure 9,
open habitat use P < 0.05, periphyton standing crop P < 0.01). Periphyton standing crop
in the refuge was much lower than in the open, and there was no effect of mortality on
periphyton in the refuge (Figure 9, B > 0.10) Snail habitat use did not show a threshold
response to increasing predation. Instead, each successively higher level of mortality
resulted in a correspondingly lower use of the open habitat (Figure 9). Periphyton
standing crop, in turn, reﬂected this pattern of behavior by showing a gradual positive
response to increasing mortality (Figure 9).

While the overall effects of increasing mortality was to decrease open habitat use and
increase periphyton standing crop, the strength of these responses changed over the course
of the experiment. PM in high mortality treatments initially avoided open habitats, but
they became indifferent to mortality by the end of the experiment (Figure 10, early
mortality effect _13 < 0.01, late mortality effect P > 0.10). Conversely, periphyton standing
crop in the open habitat initially showed no treatment effects, but showed a positive
relationship with mortality risk at the end of the experiment (Figure 10, early mortality
effect 2 > 0.10, late mortality effect P < 0.01). Periphyton standing crop in the refuge did

not differ among treatments either early or late (Figure 10, B > 0.10 early and late),

‘11

45

Figure 9. The overall pattern of snail habitat use and periphyton standing crop in relation
to simulated mortality. Each point represents the mean of four pools i 1 SE. Top: Open
habitat use over the entire 14-day experiment. Bottom: Periphyton standing crop on tiles
in the open habitat (closed circles) and on tiles in the refuge (open triangles) at the

conclusion of the experiment.

0.7

0.6

Open Habitat Use

0.5

. 2
Periphyton AFDW (mg/cm )

46

 

 

 

 

 

 

_

0.25 1.0 4.0

 

 

§ 9

. =0pen Habitat

V =Covered Habitat

-r-

—

 

 

V @ V V
i l l l
o 0.25 1.0 4.0

Daily Mortality

 

47

Figure 10. Snapshots of snail habitat use (top) and periphyton standing crop (bottom) in
relation to risk of mortality early and late in the experiment. Top row: A two-day wide
window of habitat use immediately prior to the ﬁrst and last periphyton sampling dates
(days 3 and 14), e.g., "Early" is the mean proportion of snails using the open habitat
during days two and three. Refuge use is equal to 1-(open habitat use). Bottom row: The
ash-free dry weight of periphyton on day 3 (Early), and on day 14 (Late). Filled circles are
the standing crop of periphyton in the open habitat; open triangles are the standing crop of

periphyton in the refuge.

Open Habitat Use

2
AFDW (mg/cm)

0.8

0.6

0.4

0.2

Earhl

48

 

 

 

 

0.25 1.0

4.0

 

 

 

 

 

 

i I

0.25 1.0

Daily Mortality

 

4.0

0.8

0.6

0.4

0.2

Late

 

 

 

oi

0.25 1.0

 

 

 

Daily Mortality

 

 

49

was low by the first sampling date (day 3) and remained at that low level through the
experiment (Figure 10).

I examined more closely the temporal pattern of habitat use and periphyton
responses to mortality risk by plotting the responses over time. I used the F-Ratio of
regression analyses (Ho: slope=0) performed on the relationship between mortality and
snapshots of habitat use (two-day means, N=7) and open-water periphyton (N =3 sample
dates) as an index of the strength of response (Cohen 1988). This analysis clearly shows
that while both habitat use and periphyton were related to predation risk, the strength of
the responses changed over time (Figure 11). At no point during the experiment did both
habitat use and periphyton show simultaneous responses to predation risk. Instead, the
responses mirrored each other, and snail habitat use and periphyton standing crop
responded at different time scales to the risk of mortality.

DISCUSSION

This study demonstrates that @6313 change their habitat use when confronted with
the risk of predation, and this change in the habitat use of P_the_lla can affect the
abundances of their periphyton resources. Further, there is a strong spatial
correspondence between the habitat use of Ma and the standing crop of periphyton.
The habitats that were used least by M contained the highest levels of periphyton.
However, the correspondence of habitat use and resource levels did not exist at any one
point in time: behavioral effects were strongest early in the experiment, while the

periphyton abundance effects were strongest late in the experiment.

50

Figure 11. The F-ratio of linear regressions (Ho: slope=0) performed on the relationship
between mortality level and habitat use (solid circles) and periphyton standing crop (open
triangles) over the course of the experiment. Habitat use data are two day means. Dashed

line represents F0,05,,,,4=4.60. Solid line is a cubic spline interpolation.

51

 

12h e

F—Ratio

 

 

 

 

 

 

0 5 10 15

Days Following Experiment Initiation

52

While the temporal segregation of behavioral and periphyton abundance effects may
seem at first to be counterintuitive, it is predicted by current theory (Gilliam and Fraser
1988, Chapter 3). Consider a forager population with the following characteristics: 1)
foragers regulate resource levels within habitats, 2) individuals assess habitat-speciﬁc
feeding rates and mortality risks, and 3) foragers select the habitat which offers the best
combination of foraging returns and mortality risk (the best value). If foragers perceive
equal levels of risk in two habitats, their expected distribution should conform to an ideal
free distribution (individual feeding rates in each habitat are equal, Fretwell and Lucas
1970, Fretwell 1972). If, however, one habitat becomes more dangerous (higher
predation risk), then there will be a period of transitory dynamics, eventually leading to
new equilibrium resource levels, and a new distribution of consumers among habitats. The
second habitat (the "refuge") will initially offer foraging returns equal to the open habitat,
and a lower risk of predation, so during the transition the straightforward prediction is that
foragers will move into and spend all of their time in the refuge. If foragers regulate
resource levels (assumption 1 above), the high grazing intensity in the refuge will
eventually cause resources to be depleted to a lower level than resources in the ungrazed,
dangerous habitat. At some point in time resources in the dangerous habitat may become
sufﬁciently abundant (relative to resources in the refuge) to offset the higher risk of
mortality, and some of the foragers will choose to move back out into the dangerous
habitats, trading a higher risk of predation for higher foraging rates (assumption 3). Thus,

given the conditions above, theory predicts that short term behavioral responses to

53

predation risk will be stronger than long-term behavioral responses. Conversely, any
indirect effects of risk on resources will not be immediately manifested, but are predicted
to develop during the transition as resources are differentially depleted. Resource levels in
dangerous and safe habitats should then be maintained at some constant level of difference
by foragers, reﬂecting the relative risk of the two habitats. I have shown here that the
temporal patterns of Mia behavior and the temporal patterns of abundance of their
periphyton resources are consistent with these predictions.

The divergence in resource levels between dangerous and safe habitats occurs
through the differential grazing and growth of periphyton in risky and safe habitats.
Because the length of time needed for resources to diverge sufﬁciently to offset the higher
level of risk in the dangerous habitat depends on the extent to which resources in
dangerous habitats exceed levels in safe habitats, the length of the transition period (the
period during which animals use only the refuge) should be related to the magnitude of
danger. I found that M increased their use of the dangerous habitat over time in all
treatments, but shifted to using the dangerous habitat faster at lower levels of risk (Figure
12). The overall pattern of M habitat use and periphyton abundance suggests that
the snails depleted resources in the two habitats to the point where the dangerous and safe
habitats were of equal value in all treatments, although it took longer for the habitats to
equalize at the highest level of risk.

The "depletion and tradeoff" scenario proposed here to explain the changing pattern

of snail habitat use over time is not the only mechanism which could produce the

54

Figure 12. Use of the open habitat in the 1/4, 1, and 4 snails/day mortality treatments
expressed as a percentage of the open habitat use in the 0 snails/day treatment. Data are

two day means over the ﬁrst eight days of the experiment.

55

 

 

 

 

 

 

1‘3 //
5 100
O
I
c
(1)
O.
O
‘5
<1) 80 —
(f)
D /
"O I
<1)
.E‘
E .
O Level of Mortality
2 so ~ 2 I 0.25/day
B A 1/day
(I)
O 4/day
l l i
2 6 8

Days Since Experiment Initiation

 

56

pattern observed. One alternative explanation is that snails initially responded to the
crushed snail cue, but then habituated to the cue after several days, and perceived a lower
level of mortality. While it is difficult to know with certainty the motivations of snails for
behaving as they do, there are data supporting the assumptions underlying the depletion
and tradeoff mechanism. First, several studies have shown that freshwater snails, including
Ma, control the abundance of their periphyton resources (Doremus and Harman
1977, Lowe and Hunter 1988, Bronmark 1989, Osenberg 1989, Barnese and Lowe 1990).
In this experiment I found that M spent 45% of their time grazing on the two tile
substrates, even though the two tiles comprised just 2% of the available substrate. Such
an intense concentration of snail foraging activity on the tiles lends support to the notion
that PpLsila interacted strongly with their periphyton resources.

Second, in two separate experiments I found that M can assess habitat-specific
predation risk and foraging rate, and that they will trade safety for food. Both experiments
were conducted in the same pools, in the same manner, and using the snails from the same
source population, as the experiment above. Habitat use analyses were done on mean
habitat use over the course of the experiment (N=8 days for experiment 1, N =9 days for
experiment two). In the ﬁrst experiment I manipulated overall food level (tiles in open and
refuge depleted by grazing prior to experiment versus tiles in open and refuge undepleted
by grazing) and predation risk (two levels: 0 crushed snails/day and 3 crushed snails/day) .
I found that Ma habitat use was affected by food level (F 1’,2=5.2, £<.05) and

mortality level (F ,,,2=22.2, £5.01). Physella used the open habitat less in response to both

57

higher food levels and higher predation risk (Figure 13, top), demonstrating that they
assess and consider both food and predators when selecting habitats. I tested the
hypothesis that Mela will trade increased risk of predation for higher foraging rates by
conducting a second experiment in which I manipulated food level only in the open habitat
(spinach added, no spinach added) and predation risk (5 snails crushed/day versus 0 snails
crushed/day). I found a strong main effect of predators on Physell_a habitat use (F 113:1 17,
_E<.01), but the response to predators depended on food level (F,,6=5.6, 2:05). In the
high risk treatment M ventured into the dangerous habitat most often at high food
levels (Figure 13, bottom), demonstrating that they will trade safety for food. Thus, while
I can not prove that the change in M habitat use through time in the main experiment
was due to habituation to the mortality cue, data available from other experiments show
that snails have the ability to assess food rewards and predation risk and that they will

accept higher risk in return for more food.

58

Figure 13. The effects of food and predation risk on the habitat use of ﬂryaalla Top:
Food added to both open and covered habitats. Use of open habitat is shown under two
levels of predation risk (absent, present) and two levels of food (periphyton covered tiles
added to both habitats). Bottom: Food added to open habitat only. Use of open habitat is
shown under two levels of predation risk (absent, present) and two levels of food in the
open habitat (no spinach added, spinach added). The perception of risk was manipulated
by pairing each pool with an aquaria housed in an adjacent laboratory. The predation cue
was then generated by feeding ﬁve Bag/£112; daily to pumpkinseed sunﬁsh housed in
aquaria, and adding one liter of water from these aquaria, along with untreated water from
control aquaria, daily to predator and no-predator pools. For both experiments "Use of
Open Habitat" is the mean proportion of the population in the open habitat (j; 1 SE) over

the course of the experiment, N=4

Open Habitat Use

Open Habitat Use

0.6

59
'fifgfzgiiigigg N o F o o d Ad d e d

 

m Food Added—Both Habitats

 

1.0

(18

(I6

0.4

 

Predation Risk Predation Risk
Absent Present

 

N 0 F0 0 d Ad d e d
m Food Added—Open Habitat

Predation Risk Predation Risk
Absent Present

60

I have argued that the increase in periphyton standing crop in the Open habitat in
high mortality treatments is due to a reduction in snail foraging. An alternative
explanation is that crushing snails increased nutrient input and thereby increased
periphyton abundance. Two lines of evidence argue against this. First, snail growth was
negatively related to mortality level, which is consistent with the idea that differences in
snail grazing is the mechanism responsible for the positive relationship between risk of
mortality and periphyton abundance in the open habitat. Lower snail growth at high levels
of risk reﬂect lower average feeding rates at high levels of risk and coincides with higher
periphyton standing crop at high levels of risk. Further, snails spent a disproportionate
amount of time foraging on the small periphyton-bearing tiles, suggesting that the tiles
were very important food sources. Second, if nutrient input (and not snail grazing) was
the predominate factor affecting periphyton standing crop, there should be a positive
relationship between mortality level (number of snails crushed) and periphyton abundance
in the refuge habitat. I found no relationship between mortality level and periphyton
abundance in the refuge, although other factors (e.g. light levels) may have limited
periphyton growth in the refuge habitat.

The pattern of resource depletion in safe and dangerous habitats in this experiment
offers insights into the nature of the decision rules utilized by snails when balancing
predation risk and foraging rates. If a population of foragers divides its time among
habitats offering equal fitness returns, but varying combinations of predation risk and

foraging rates, then the amount by which food in dangerous habitats exceeds the amount

61

of food in safe habitats at one level of risk represents the energetic equivalent of that level
of predation risk. Two hypotheses have been put forward regarding how animals might
make this comparison. Gilliam and Fraser (1987, 1988) suggested that, given certain
assumptions (most notably the presence of a foodless refuge), foragers will choose the
habitat with the lowest ratio of mortality to feeding rate (i.e. minimize u/f). If foragers
deplete resources and have a linear functional response, they will deplete resources such
that the ratio of resources in safe and dangerous habitats matches the ratio of the predation
risk (Figure 14, tOp). Abrahams and Dill ( 1989) countered with the suggestion that
foragers compare the absolute difference in resource levels when selecting habitats, not the
ratio of resources (Figure 14, bottom). As risk of mortality increases, the difference must
be larger in order to lure foragers into the dangerous habitat (Figure 14, bottom). Both
Gilliam and Fraser (GF) and Abrahams and Dill (AD) present experimental evidence to
support their respective decision rules; however, the two decision rules have never been
tested on a single data set.

The relationship between relative resource levels and mortality risk in the experiment
described here can be used to test the two decision rules. GF predicts that the ratio of
resources in dangerous and safe habitats will be positively related to risk, but that the
difference probably won't be (a fortuitous correlation is possible, depending on the pattern
of depletion across treatments). In contrast, AD predicts that the difference will be related

to risk, but it is unlikely that the ratios will be. I tested both hypotheses and found that the

62

Figure 14. Hypothetical switching curves at five levels of relative risk as suggested by
Gilliam and Fraser (top) and Abrahams and Dill (bottom). Curves represent the
combination of resource levels in habitats one and two which are predicted to yield equal
value to foragers under 5 levels of relative predation risk in the two habitats. Curve 1
represents equal risk in each habitat; curves 2 through 5 represents the effect of increasing

risk in habitat two relative to habitat one.

63

Ratio Hypothesis

 

 

Resource Standing Crop — Dangerous Habitat

Resource Standing Crop — Safe Habitat

2

5 4 3
Difference Hypothesis

Resource Standing Crop — Safe Habitat

 

 

Resource Standing Crop — Dangerous Habitat

64

difference in resource levels was related to mortality (linear regression, _13 < .01), but that
the ratio of resource levels was not related to mortality (1_’ > .10), supporting the
Abrahams and Dill hypothesis.

The models contrasted above predict how individuals balance predation risk and
foraging rate when selecting habitats, but do not address the related question of how a

population of foragers will assort itself among habitats of equal value, but offering varying

- _ _

l
combinations of predation risk and foraging gains. In Chapter 3 I develop a three trophic :

level model which uses the individual decision rules proposed by Gilliam and Fraser (1987)

ﬁﬁ: .

and Abrahams and Dill (1989) to predict population level distributions of foragers among
habitats, and their growth dynamics within habitats. The model shows that if foragers
assort themselves among habitats such that they maintain high resource levels in risky
habitats and low resource levels in safe habitats, thereby maintaining habitats of equal
value to individual foragers, then the proportion of the grazer population in each habitat
depends on how much grazing activity is needed to maintain resource levels at that level
(Turner, Chapter 3). The equilibrium number of foragers in each habitat depends on
habitat specific resource productivity and feeding rates. For those resource production
and feeding rate functions yielding stable equilibria, more foragers are required to maintain
resources at lower levels (Noy-Meir 1975, May 1977). The model thus predicts that
foragers will occupy both dangerous and safe habitats, but that the density of foragers will
be higher in safer habitats. Note that this result is not a direct effect of predators on

forager habitat use, but instead is mediated through the indirect effects of predators on

65

resource levels and productivity.

The predictions above concerning the long-term effects of predation risk on forager
habitat use and resource levels can be synthesized to predict the response of forager
growth to predation risk. If individual foragers within a population differ in their
willingness to trade safety for food (e.g. Turner and Mittelbach 1990), then foragers will
specialize. Some foragers will spend a disproportionate amount of time in risky habitats,
and others will spend more time in safe habitats. Those foragers that utilize risky habitats
will reap growth benefits from higher resource levels, while those that use safer habitats
will suffer a growth penalty. The overall effect of increasing risk in one habitat relative to
another will be to increase the variance in population growth rates (Turner and Mittelbach
1990). In this experiment I found no evidence for specialization by Mia; variance in
growth was independent of risk level.

What then, is the predicted effect of increasing risk on the mean growth of a forager
population? In Chapter 3 I show that increasing the risk of one habitat relative to a second
in a two habitat system always results in lower growth rates of foragers: the higher feeding
rates foragers enjoy while foraging in the risky habitat is always more than offset by lower
feeding rates in the safe habitat. The results of this experiment are consistent with this
prediction: M growth at the highest level of mortality was only 59% as high as its
growth at the lowest level of mortality (Figure 8). However, the magnitude of this growth
penalty will be highly dependent on the overall balance of foragers and their resources

(Chapter 3). In a system where resources are lightly grazed (total forager density low)

66

increasing risk will have strong negative effects on forager growth. In contrast, in
overgrazed systems (total forager density high) increasing risk is predicted to have little
effect on forager growth. Abrams (1992) makes similar predictions using a different
modeling approach. The notion that the growth penalty associated with predation risk will
vary in a predictable way with overall forager density (or inversely, underlying resource
productivity) has not yet been tested, but the Ma - periphyton system used here looks
promising.

The strong interactions among snails, their predators, and their periphyton resources
has been documented by several investigators (Osenberg 1988, 1989, Bronmark et al.
1992), but these studies focused on the numerical interactions among trophic levels. Here
I have shown that snail predators can strongly interact with periphyton by changing snail
behavior. Predation risk and m habitat use were negatively correlated, as was
ﬂyglla habitat use and periphyton standing crop. This pattern, typical of top-down
effects, was mediated completely by behavior. These results have important implications
for the interpretation of predator manipulations: behavioral mechanisms may be as
important or more important than mortality mechanisms in mediating the effects of top
predators on lower trophic levels.

The behavioral decisions made by individual animals regarding where to forage may
have repercussions which are expressed at lower trophic levels, and then feed back up the
food web. Many animals alter their behavior in response to some change in the

environment (e.g. predation risk or food availability). It is possible that these ﬂexible

-g. c.-.
- .n

67

behavioral responses of animals to food or predators play an important role in determining
the nature and strength of food web interactions (e.g. Power et al. 1985, Huntly 1987,
Turner and Mittelbach 1990). "Behavioral Indirect Effects" may cascade through the food
web, and have effects as strong as the numerical effects of predators on lower trophic
levels (Werner 1992). Only further empirical work in which the effects of behavior are
clearly isolated from numerical effects will establish whether behavioral effects are of

general importance in shaping communities.

 

CHAPTER 3
THE EFFECTS OF PREDATION RISK ON

CONSUMER HABITAT USE AND FEEDING RATES

68

 

69

INTRODUCTION

Predators have strong effects on both prey densities and prey behaviors, and these
effects have been shown to cascade through food webs, indirectly affecting non-adjacent
trophic levels (reviews in Kerfoot and Sih 1987, Abrams 1994). However, while there is
an abundant literature on density-mediated indirect effects, there is little understanding of
the potential ecological consequences of behavioral indirect effects. Consider the example
of the freshwater snail ﬂyaalla gj'ma. Where ﬂyilla coexists with the molluscivous
pumpkinseed sunfish (M M) it inhabits the underside of covered substrates,
where it is relatively safe from pumpkinseed predation (Chapter 1). If invulnerable
competitors are absent resources will become very abundant in open habitats, and walla
will then venture forth and spend some of their time foraging in the more dangerous but
proﬁtable habitat, trading a higher risk of predation for a higher feeding rate (Chapter 2).
Thus, snails in this situation divide their time between two habitats offering similar ﬁtness
returns: a safe habitat offering low foraging returns, and a more dangerous habitat offering
higher foraging returns. However, there are two fundamental questions associated with
this common situation that are not addressed by current ecological theory. First, what
proportion of their time do we expect snails to spend in each habitat? Second, how do we
expect snail feeding rates in predator-absent treatments to compare to snail feeding rates in
predator-present treatments?

In this chapter I will ﬁrst review theoretical predictions regarding how individuals

balance foraging gains and mortality risks when selecting habitats, and review how two

4 _._ 'A'- un- W
I

7O

decision rules have been used to predict patterns of resource depletion among habitats that
differ in mortality risks. I then construct a three trophic level model aimed at predicting
the distribution of consumers among habitats of equal value, but offering varying
combinations of predation risk and feeding rate. The expected distribution of consumers
among habitats is then synthesized with the expected resource levels among habitats to
predict how consumer feeding and growth rates will respond to variation in habitat-
specific predation risk. Finally, I compare these predictions to the results of experiments

in which I manipulated habitat speciﬁc predation risk.

EFFECTS OF PREDATION RISK ON RESOURCE LEVELS

Many species of animals are capable of assessing both habitat specific predation risk
and foraging rates (e. g. Chapter 2, review in Lima and Dill 1990), and a number of studies
demonstrate that animals will forage in relatively dangerous habitats if food is sufﬁciently
abundant, i.e. animals will trade a higher risk of mortality for a higher foraging rate
(Gilliam and Fraser 1987, Abrahams and Dill 1989, Nonacs and Dill 1990, Todd and
Cowie 1990, Kotler et al. 1991, Chapter 2). If resource levels within habitats are
insensitive to variation in consumption (e. g. donor-controlled systems), then predator
induced changes in habitat use will not affect resources levels. In this case, individual
consumers should choose the habitat which offers the highest ﬁtness, and the choice of
habitats will not be affected by the density of consumers or the choices made by other

consumers. The equilibrium distribution of consumers simply reﬂects the sum of their

H - ‘.~--_-

 

71

individual decisions. However, if foragers control resource levels within habitats (Sih et
al. 1985), then predator mediated changes in forager habitat use will affect resource levels.
In this case, the speciﬁc patterns of resource depletion among habitats should be
predictable from a knowledge of the way in which individual consumers balance energetic
gains against mortality risks when choosing habitats.

There is a large body of theory which specifies how individual consumers should l .
balance energetic gains against mortality risks when selecting habitats (e.g., Gilliam 1982,

Gilliam and Fraser 1987, Clark and Levy 1988, Mangel and Clark 1988, Abrahams and

‘1'
I

Dill 1989, Ludwig and Rowe 1990, Rowe and Ludwig 1991). While experimental tests of
this theory are still rare, Gilliam and Fraser (1987) and Abrahams and Dill (1989) both
have found that foraging ﬁsh can assess both mortality risks and energetic gains when
selecting habitats, and that a higher risk of death in an area does not preclude its use.
Gilliam and Fraser developed and tested a model which, given certain assumptions (most
notably the presence of a foodless refuge), predicted that foragers will choose the habitat
with the lowest ratio of mortality to feeding rate (i.e. minimize ,u/f). Abrahams and Dill
(1989), on the other hand, suggested that foragers compare the absolute difference in
resource levels when selecting habitats, not the ratio of resources. These two contrasting
models can be used to illustrate how individual decision rules might affect resource
depletion among habitats.

Consider a two habitat system with resources (R, and R2) in each habitat, and a

forager population that consumes R, and R2, but is free to choose between the two

72

habitats. The way in which consumers balance mortality risks and energetic gains when

selecting habitats (i.e. their decision rules) can be represented by switching curves on a

graph of R, versus R2 (Gilliam and Fraser 1988). These switching curves show the

combination of resource levels in habitat one and two which yield habitats of equal value

to foragers under a given level of relative risk (Figure 15). For example, if consumers

perceive equal levels of risk in the two habitats, they should conform to an ideal-free I
distribution among habitats (i.e. individual feeding rates in each habitat are equal; Fretwell
and Lucas 1970, Sutherland and Parker 1985), and resource levels will be maintained at i
equal levels in the two habitats (slope of switching curve = 1; Figure 15). If, however,

habitat 2 becomes more dangerous, all consumers should initially shift to using the safer

habitat (habitat 1). Over time, the higher consumption rates in habitat 1 will cause

resources to be depleted there, while resources in the ungrazed habitat 2 increase in

abundance (Figure 15). At some point resources in the dangerous habitat may become

sufficiently abundant, relative to resources in the safe habitat, to offset the higher risk of

mortality. When resources reach the new switching curve, habitats are of equal value and

consumers should use both dangerous and safe habitats, depleting resources along the

switching curve. Resource populations in the riskier habitat thus experience a positive

indirect effect of the predator, while resources in the safer habitat experience a negative

indirect effect. This positive, indirect effect of predators on resources, mediated through

changes in consumer behaviors, has been shown to be an important force in natural

communities (e.g. Turner and Mittelbach 1990, Chapter 2, see Abrams 1994 for a review).

73

Figure 15. Hypothetical switching curves of consumers under two levels of relative risk,
and the resource depletion trajectories produced by these behaviors. Switching curves are
those combinations of resource levels in habitats 1 and 2 which yield habitats of equal
value to consumers under a given level of relative risk. Dashed line represents equal risk
in habitats 1 and 2, solid line represents habitat 2 more dangerous than habitat 1.
Consumers are predicted to deplete resources from the point shown by the open circle to
the point shown by the ﬁlled circle when habitat 2 becomes more dangerous than habitat 1.
Top: the pattern of habitat selection behavior and resource depletion when consumers are
using the ratio rule developed by Gilliam and Fraser (1988). Bottom: the pattern of
habitat selection behavior and resource depletion when consumers are using the difference

rule developed by Abrahams and Dill (1989).

74

Ratio Hypothesis

 

 

Resource Standing Crop — Dangerous Habitat

Resource Standing Crop — Safe Habitat

 

Difference Hypothesis

 

Resource Standing Crop — Dangerous Habitat

 

Resource Standing Crop — Safe Habitat

75

Behavioral rules utilized by individual foragers when selecting habitats can therefore
determine the pattern of resource levels among habitats: safe habitats will have low
resource levels and dangerous habitats will have high resource levels (Chapter 2).
Consumer behavior effectively links together the dynamics of resources in isolated
habitats: by exercising adaptive habitat selection behavior, consumers deplete resource
levels to the point that habitats are of equal value. I now turn to the next question: what is l .
the distribution of consumers among habitats with differing combinations of risk and

resource levels, but of equal value to consumers? i “

THE DISTRIBUTION OF CONSUMERS AMONG HABITATS OF EQUAL VALUE
The general approach here is to describe resource natality and mortality in two
isolated habitats, and then use the decision rules reviewed above to express resource levels

in one habitat as a function of resource levels in the second (Figure 16). One can then
solve for the particular distribution of consumers between habitats which produces
mortality functions yielding zero resource growth (Figure 16). In the following analysis I
assume that: 1) resources renew logistically, 2) there is no numerical response by
consumers (i.e. consumer generation times are long relative to that of resources and the
frecuency of habitat switching), 3) each habitat contains a single resource population (R,),

4) consumer feeding rates are linearly related to resource density (Type I functional
response), and 5) underlying resource productivity (r and K) is the same in both habitats.

76

Figure 16. Resource production and harvest functions as a function of resource standing
crop. Humped curve represents the population birth rate of resources and the function is
assumed to be equal in the two habitats. The two linear functions are the rate at which
consumers in each of the two habitats harvest resources, and their slope is dependent on
the distribution of consumers among habitats. The intersection of the production and
harvest curves gives the equilibrium resource standing crop in each habitat (R,°, R;). The
model (equation 6) solves for the proportion of the consumer population needed in each
habitat to maintain R,’ and R2. at the level of difference speciﬁed by the individual decision

rule.

77

 

 

 

i K
\JI
DH
2 <
V R p
O
r
C
g
m
........................ V i..R d
mil.
0
LIL
S
e
C
. Fl
. U
n O
u S
" e
” DH
< <
O
0

USE Epic: pco cozospoca coSOmcm

78

Resource dynamics are then

7-1-RZ(1--k—)-aR2N(l-P,) (2)

where P, is the proportion of the consumer population (N) feeding in habitat 1, a is the
consumer attack rate on resources, r is the per capita growth rate of resources in the
absence of competition, and K is the carrying capacity for the resource.

Consumer behavior links resource dynamics in habitat one to resource dynamics in
habitat two. Two versions of the model are developed, one using the ratio rule of Gilliam
and Fraser (1988), and one using the difference rule of Abrahams and Dill (1989). By
contrasting the predictions yielded by each version, I can evaluate how sensitive the model
predictions are to the nature of the individual decision rule employed. In each case the
variable 0 represents the energetic equivalent of a given level of relative risk. The ratio
rule specifies that consumers will structure resources such that R, = 0R2, where Q
=(,u,/,uz), while the difference rule speciﬁes that resources will be structured such that R, =

Q+R2.

 

79

Using the ratio rule, resources dynamics in habitat two can be expressed in terms of

resource levels in habitat one:

an, QRl
7-,QRlu- K )-.QR,N(1-P,) (3)

 

Setting eqs. 1 and 3 equal to zero and solving for the equilibrium yields

R2
rR,(l-E—)-aR2N(l-P,)=0

 

01'
R, - (3:2) (r-aNP,) (4)
K- 2R

{Q :2 '-aQN(1-P,)=o (5)

The proportion of the consumer population in habitat 1 (P,) can be solved for by
substituting eq. 4 into eq. 5. After making this substitution, and rearranging, we ﬁnd that
the equilibrium distribution of the consumer population among habitats is speciﬁed by the

following:

P _ aN-r(l -Q)

6
' aN(l+Q) ( )

Clearly, only certain values of a, N, and r yield a positive equilibrium for resources.

Stability analysis shows that there is a single, stable non-zero equilibrium point for

 

80

resources in each habitat (Appendix 2):

R,’ = K - aNP,K / r (7)

For r < 1/2 aN, consumers always drive resources extinct, while for r > 1/2 aN there is a
single stable equilibrium solution. With the presence of a stable equilibrium established, the
main question of interest here can be tackled: How does the distribution of animals among
habitats vary as a function of the relative predation risk of the two habitats?

This model makes the simple prediction that increasing the risk of predation in one
habitat relative to another will result in a lower equilibrium number of foragers in the more
dangerous habitat. Figure 17 illustrates the effect of increasing relative risk in a habitat on
the equilibrium number of foragers in that habitat. In addition, analysis of equation 6
shows that the results illustrated in Figure 17 holds for all parameter values: the first
derivative of P, with respect to Q is negative, and the second derivative is positive.

The strength of the habitat shift depends on how intensely consumers graze their
resources. When resources are lightly grazed, due to low consumer population size, low
consumer attack rates, or high resource growth rates, consumers feed only in the safest
habitat unless relative risk is very near unity (Figure 17, "low consumption" curve).
Consumers in this situation will not appreciably deplete resources in the safe habitat
relative to the dangerous one, and hence will not be in a position to trade higher mortality
risk for higher foraging rates. Conversely, if resources are heavily grazed, the model
predicts that consumers will use both habitats over a broad range of relative risk values

(Figure 17, "high consumption" curve). Thus, the sensitivity of consumers to predation

 

81

Figure 17. The proportion of a consumer population feeding in habitat 1 as a function of
the level of risk in habitat 1 relative to habitat 2. Relative risk is the ratio of mortality risk
in habitat one to the mortality risk in habitat two (0 = [ll/[12), and is assumed here to be
equal to the ratio of resources in habitats 1 and 2 (R,=OR2). Equal risk corresponds to a
relative risk value of 1. In this hypothetical example a = 2 and r = 3. I show the model
predictions for two densities of consumers: N = 10 consumers for the "low consumption"

curve, and N = 30 consumers for the "high consumption" curve.

Proportion of Consumers in Habitat One (P1)

82

 

 

 

1.00
0.75 -
< """""" Low Consumption
0.50 —< ------------------ . High Consumption
E \i

0.25 —
0.00 if ,

0 1 2

Relative Risk in Habitat One

 

83

risk will depend on the degree to which consumers hold resources below their carrying
capacity. The prediction that the magnitude of the habitat shift associated with predator
avoidance varies in a predictable way, depending on the relationship between consumers
and their resources, is currently untested.

Substituting the difference rule for the ratio rule does not substantially change the
model predictions. Proceeding exactly as above, except letting R, = Q-i-R2 instead of R, =

0R2, the equilibrium distribution of consumers is given by

‘ 'Q (8)

p.—.._-
' 2 KaN

 

This version of the model also predicts that foragers will gradually shift out of the more
dangerous habitat, and that the shift is more abrupt when resources are lightly grazed than
when they are heavily grazed (Figure 18). The pattern shown in Figure 18 is globally true:
the ﬁrst derivative of P, with respect to Q is negative, and the second is 0. The overall
pattern of habitat use predicted by the difference rule is remarkably similar to the pattern
predicted by the ratio rule, illustrating that the predictions are not overly sensitive to the
nature of the specific decision rule used.

It is important to keep in mind that this model predicts the long-term equilibrium
distribution of consumers among habitats. There should be a period of short-term
transitory dynamics associated with changes in relative risk, illustrated in Figure 15, in
which consumers will occupy the safer habitat until it depleted sufficiently to make a trade-

off worthwhile (e. g. Chapter 2). The long-term solution addresses the question "how

84

Figure 18. The proportion of a consumer population residing in habitat 1 as a function of
the level of risk in habitat 1 relative to habitat 2. Relative risk is assumed here to be equal
to the difference between resources in habitats 1 and 2 (R,=Q+R2). Equal risk
corresponds to a relative risk value of 0. In this hypothetical example a = 2 and r = 3. I
show the model predictions for two levels of grazing pressure: N = 10 consumers for the

"low consumption" curve, and N = 30 consumers for the "high consumption" curve.

Proportion of Consumers in Habitat One (P1)

1.00

85

 

0.75 —

0.25 —

High Consumption

  

Low Consumption ---------->>

 

0.00

  

 

 

0 10

Relative Risk in Habitat One

20

86

many foragers are needed in each habitat to maintain resources at a level such that habitats
are of equal value to consumers?" The equilibrium number of foragers in each habitat
depends upon habitat-specific resource productivity and consumer feeding rates. It is well
known that for the resource production and feeding rate functions yielding stable
equilibria, more foragers are required to maintain resources at lower levels (Noy-Meir
1975, May 1977). This explains why consumers will move out of a habitat as it becomes
more dangerous: consumers regulate resource levels such that more dangerous habitats
yield higher feeding rates, and fewer consumers are required to maintain resources at
higher levels. Note that this result is not a direct effect of predators on forager habitat use,
but instead is mediated through the indirect effects of predators on resource levels and

productivity.

EFFECTS OF PREDATION RISK ON CONSUMER FEEDING RATES
The effects of predation risk on individual consumer feeding and grth rates can be

predicted from a knowledge of the effects of risk on consumer habitat use and the effects
of risk on resource levels within habitats. Growth rates are typically positively related to
feeding rates, but the nature of the function relating feeding rates to growth rates depends
on a number of factors. Therefore, I take a more general approach here of modeling
consumer feeding rates, and use it as a general predictor of growth. For the purposes of
this analysis, I assume that the feeding rates of individual consumers residing within a

particular habitat are simply (a R,), and the overall feeding rates of consumers moving

87

among habitats are 2 Ri a P,. The effect of predation risk on growth can be predicted by
inserting appropriate values for R,, from the models above. Overall feeding rate of
consumers is an appropriate predictor of individual growth if all individual behave alike,
and each individual allocates its time among habitats as predicted by the model. However,
a number of studies suggest that individuals may vary in their tendency to use risky
habitats (e. g. Turner and Mittelbach 1990). In this situation, some consumers may
specialize in high risk, high growth habitats, while others specialize in safe, low growth
habitats. The habitat specific feeding rates are the appropriate predictors of the growth
rates of habitat specialists.

Using the ratio version of the model, I ﬁnd that any deviation from equal risk results
in reduced growth by the entire consumer population (Figure 19). However, if foragers
are habitat specialists those foragers residing in risky habitats will experience a positive
effect of risk on growth, while those in safe habitats will experience a negative effect of
risk on growth, leading to the prediction that increasing the predation risk of one habitat
relative to another will increase the variance in individual growth rates. This prediction is
consistent with the pattern found by Turner and Mittelbach (1990). The difference version
of the model makes growth predictions that are similar to the ratio version (Figure 20).

The extent to which consumers depressed resources below their carrying capacity
was found to be an important factor inﬂuencing consumer habitat use, and it also has a
strong effect on the growth predictions. Both versions of the model predict that the

growth penalty associated with increasing the risk in one habitat relative to another will be

 

88

Figure 19. The predicted growth dynamics of consumers as a function of the level of risk
in habitat 1 relative to habitat 2. Relative risk is deﬁned by the ratio rule (equal risk = 1).
Overall growth represents the average growth of a population, or the growth of
individuals when all members of a population behave alike. Also shown are habitat-
speciﬁc growth rates, which are appropriate predictors of growth if individuals specialize.
Parameter values are as in Figure 3, except that N=20. Values on Y-axis are consumer

feeding rates (prey eaten / time).

Consumer Growth

89

 

 

 

5.00
Overall Growth
2.50 —
I r
Growth in Habitat Two .
Growth in Habitat One
aoo , ,

Relative Risk in Habitat One

 

90

Figure 20. The predicted growth dynamics of consumers as a function of the level of risk
in habitat 1 relative to habitat 2. Relative risk is deﬁned by the difference rule (equal risk =
0). Overall growth represents the average growth of a population, or the growth of
individuals when if all members of a population behave alike. Also shown are habitat-
specific growth rates, which are appropriate predictors of growth if individuals specialize.
Parameter values are as in Figure 4, except that N = 10. Values on Y-axis are the number

of resource individuals consumed per unit time.

sit

Consumer Growth

6.00

91

 

4.00 ~

Growth in Habitat One

Overall Growth

Growth in Habitat Two

 

 

 

2.00

Relative Risk in Habitat One

3“]

 

92

Figure 21. The predicted pattern of consumer growth as a function of relative risk when
resources are near their carrying capacity (Low Consumption, N=10 consumers) and when
resources are held by consumers further below their carrying capacity (High Consumption,
N=30 consumers). Top: Growth of consumers using the ratio rule, parameter values as in
Figure 3. Bottom: Growth of consumers using the difference rule, parameter values as in

Figure 4. Y-axis is the number of resource individuals captured per unit time.

Consumer Growth

Consumer Growth

93

 

4.00 -

2.00 e

  
    

Low Consumption

High Consumption

 

 

0.00

.I-ﬂ

 

4.00 H

    
 

c
a
,
.
4
u
.
o

Low Consumption

High Consumption

 

 

2.00

 

Relative Risk in Habitat One

 

 

 

94

stronger when resources are lightly grazed (Figure 21). When resources are heavily
grazed, the increase in resource standing crop associated with increased risk will stimulate
resource production, and tend to ameliorate the growth penalty. This is another simple,
powerful, and untested prediction: increasing the relative risk of a habitat should depress
consumer grth rates, but the magnitude of the growth depression depends on how

intensely consumers graze their resources.

SUMMARY

Perhaps the most important behavioral choice a mobile animal faces is where to
forage. Early studies used long-term average rate maximization approaches to relate
individual habitat choice to single resources such as mates (Orians 1969, Parker 1978),
and food (Fretwell 1972, Chamov 1976, Milinski 1979, Whitham 1980, Harper 1982,
Pulliam and Caraco 1984). More recent work has shown that animals are often
confronted with conﬂicting demands, and that they may consider several factors when
selecting habitats (Mittelbach 1981, Sih 1982, Werner et al. 1983, Kotler 1984, Power
1984a; review in Lima and Dill 1990). Several studies have now shown that animals will
move into more dangerous habitats in return for a higher feeding rate, thereby balancing
food intake against the risk of mortality (Gilliam and Fraser 1987, Abrahams and Dill
1989, Nonacs and Dill 1990, Todd and Cowie 1990, Kotler et al. 1991). Further, it is well
known that resource levels in a habitat often varies inversely with consumer foraging

intensity (Sih et al. 1985, Kerfoot and Sih 1987). Therefore, the level of predation risk

 

95

may inﬂuence food levels in a habitat through the effects of predators on consumer habitat
selection behavior. The balancing acts animals perform may have major community-wide
repercussions, but the importance of these extended effects are little explored.

The model developed here predicts the long-term distribution and performance of
consumers selecting among habitats that differ in potential feeding rates and predation
risks. The model is built by incorporating a ﬁtness currency based on feeding rates and
mortality rates into an ideal-free distribution framework (Fretwell and Lucas 1970,
Fretwell 1972). Assumptions of the model include 1) a linear functional response of
consumers to resource density, but no numerical response by consumers, 2) that
consumers trade-off mortality from predators for higher feeding rates according to some
measurable rule, and 3) logistic renewal of resources. The distribution of consumers
among habitats is found to depend on 1) relative risk of mortality, 2) potential resource
productivity, and 3) consumer foraging intensity. Speciﬁc predictions are 1) as the relative
danger of a habitat increases, consumers will gradually shift out of that habitat, 2) the
habitat shift is much more abrupt when resources are lightly grazed, 3) there is always a
growth penalty associated with increasing relative risk, and 4) the magnitude of the growth
penalty depends on the relationship between consumers and their resources. These are
questions of fundamental importance. Predicting the effects of predator and nutrient
manipulations in natural communities is a major goal of community ecology, yet
surprisingly little attention has been paid to linking the developing theory of habitat

selection to the dynamics of resources within habitats. This theoretical framework is an

96

attempt to forge a link between the behavior of habitat selection and it's consequences for

community dynamics.

APPENDIX A

SNAIL FAUNA OF EIGHT LAKES WITHIN THE LUX ARBOR RESERVE,

MICHIGAN STATE UNIVERSITY

97

APPENDIX A
Snail fauna of eight lakes within the Lux Arbor Reserve, Michigan State University. X
denotes taxa present in a lake, 0 denotes taxa not found in a lake. Lake coding scheme is
that devised by Elizabeth Smiley (Personal Communication).
Lake LCL MCL LA02 LA08 LA09 LAl6 LA18 LA26
Area (ha) 127 78 0.2 0.3 0.4 0.1 1.0 4.0
Fish Y
Ammcgle m
Laevapex _fu_sc1§

Pseudosuccinea columella

Fossaria humilis

 

 

Physella gyrina
Physella integra

Aplexa elongata

Planorbella trivolvis

 

Planorbella campanulata

Promenetus exacuous

X X X X 0 O X X X X X

0 O O O X O X X X C O 2
O O O X X 0 O O O O O 2
X X O X 0 O X 0 O X X ~<

Gyraulus deﬂectus

O X 0 O O O X X X 0 O X ~<
>< O X O X 0 O X 0 O X 0

O O O O O O O X 0 O O O 2
O X X 0 O O O X 0 O X X <

O O O O

Gyraulus parvus
* LA08 contains fathead minnows (Pimephales promelas), but no other species of fish. All
other lakes marked Y contain a typical warmwater ﬁsh assemblage (largemouth bass
(Micropterus salmoides), bluegills (Lemmis macrochirus), and pumpkinseeds (L. gibbosus)).

APPENDIX B

GROWTH AND STABILITY OF RESOURCE POPULATIONS

98

APPENDIX B
In this appendix I show through analytical methods that there is a single stable equilibrium
density of resources within each patch. Noy-Meir (1975) makes similar arguments using
graphical methods. The birth and death rate of resources are assumed to depend on
resource density in the following manner. Per-capita birth rates decline in a linear fashion
with increasing resource density, and per-capita death rates are assumed to be independent

of resource density (Figure 22). The per-capita growth of resources in patch, is given by

 

dR' (1 R') NP (A 1)
=r -— -a .
R,dr K '

Any positive equilibria (R') must satisfy

R!
r (1 -?)=3N P, (11.2)

Rearranging, we ﬁnd that there is a single equilibrium at

R,'= K-aNP,K/r (A.3)

What values of a, N, and P, result in a positive solution? R,‘ is positive when the following
requirement is met:

r > a N P, (A.4)

Therefore, r < 1/2 aN will never yield a positive equilibrium; consumers always drive

resources extinct.

99

A positive equilibrium will be locally stable if

:1 (1R,
— — < 0 (A5)
dR, R,dt

at equilibrium. Substituting equation A.1 into A.5 yields

4 R1 r
JR, [r(l- K)-3NP,) -K (A.6)

Since r and K are by deﬁnition positive, -(r/K) is always negative, giving the result that
R,’ will always be a locally stable equilibrium point, and that resources will always increase

from low density (given R,‘ > 0).

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