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Predicting the optimal preygroupsize from predator

huntingbehaviour

WillCresswell

1

* and JohnL. Quinn

2

1School of Biology, University of St. Andrews, Bute Building, St Andrews, Fife KY16 9TS, UK; and2Edward Grey Institute,

Department of Zoology, University of Oxford, Oxford OX1 3PS, UK

Summary

1. How group size affects predator attack and success rate, and so prey vulnerability, is important

in determining the nonlethal consequences of predation risk on animal populations and communi-

ties. Theory predicts that both predator attack success rate and the dilution effect decline exponen-

tially with group size and that selection generates optimal group sizes at a risk threshold above

which antipredation benefits are outweighed by costs, such as those owing to higher attack rates.2. We examined whether flock size risk thresholds for attack rate, success rate or dilution differed,

and therefore whether the strength of selection for group size differed for these three factors, using

a system of redshank Tringa totanus flocks being hunted by Eurasian sparrowhawks Accipiter

nisus. We also asked which of the three thresholds, on their own or in combination, predicted the

most commonly observed group size.

3. Mean redshank flock size increased with a very gradual quadratic function (i.e. approximately

linearly) with population size, although at a rate half that possible; when population size was not

limiting, individuals almost always avoided flocks of less than 30 and birds were frequently in

flocks up to at least 80. Sparrowhawk attack rate showed a quadratic relationship with flock size

and peaked at 55 redshanks. Sparrowhawk attack success rate, however, declined exponentially,

becoming less steep at flock sizes of about 40 and remaining uniformly low (a 95% decrease) by 70.

Combined with dilution, individual risk of death per attack decreased by 95% when group size

reached 30 (20 for the dilution effect alone).

4. Redshanks most commonly formed group sizes that gained the maximum individual predation

risk reduction. They also commonly formed group sizes far above any further substantial advanta-

ges from the dilution effect or from reducing attack rate, but that continued to reduce predation

risk by lowering attack success rate. Individuals did not always form the largest groups possible

which we suggest is because individual variation in risk-taking subdivides the population. This

places a constraint on the ability of individuals to compensate for predation risk and will have a

variety of important effects on animal populations.

Key-words: group living, hunting success, nonlethal effects, predation risk, trait-mediated inter-

actions

Introduction

How animals respond behaviourally to increased predation

risk is a key part of understanding how trophic interactions

structure ecosystems (Lima 1998; Agrawal 2001; Werner &

Peacor 2003; Abrams 2010). Prey behaviour in general, and

behavioural responses to predators specifically, can deter-

mine the immediate outcome of an encounter between preda-

tor and prey (e.g. Cresswell & Quinn 2004; Quinn &

Cresswell 2004), but they can also determine population

dynamics and community structure indirectly through nonle-

thal, trait-mediated effects as prey respond to the fear of

predation (e.g. Cowlishaw 1997; Schmitz, Krivan & Ovadia

2004; Minderman, Lind & Cresswell 2006; Owen-Smith &

Mills 2006; Ripple & Beschta 2006; Creel et al. 2007). Group

size is one of the main behavioural mechanisms used by

animals to manage their vulnerability to predation risk (Kra-

use & Ruxton 2002; Caro 2005) and has a major influence on

the outcome of predatorprey interactions (Abrams 1993;

Lima 1998; Brown, Laundre & Gurung 1999; Cresswell

2008). However, despite the marked prevalence of this strat-

egy in animal populations, explaining the role of predation in*Correspondence author. E-mail: [email protected]

Journal of Animal Ecology 2011, 80, 310319 doi: 10.1111/j.1365-2656.2010.01775.x

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predicting the group sizes observed in nature remains a major

gap in our knowledge of how populations are structured.

Theory and empirical data suggest that optimal group size

reflects a dynamic interplay between a diverse range of costs

and benefits associated with joining a group. Important costs

of grouping include competition, kleptoparasitism andincreased conspicuousness to predators, while common bene-

fits include gain of foraging information, group defence, vigi-

lance and dilution of risk (Krause & Ruxton 2002). Despite

intensive study for several decades, empirical data linking

observed group sizes to costs and benefits, in terms of influ-

encing probability of predation, are lacking from natural sys-

tems (Lima 2002; Lind & Cresswell 2005; Roth, Lima &

Vetter 2006), so limiting our ability to predict optimal group

size, the ability of animals to compensate for increased preda-

tion risk via grouping or avoidance (e.g. Anholt & Werner

1995, 1998), and so the lethal and nonlethal effects of preda-

tion risk on animal populations (see Werner & Peacor 2003).

Animals commonly form groups because an individual

usually has a lower probability of predation in a group

(Krause & Ruxton 2002; Caro 2005). Decreased predation

risk in groups arises because of the dilution effect (Foster &

Treherne 1981; Krebs & Davies 1981), enhanced predator

detection (Pulliam 1973; Elgar 1989) and the confusion effect

(Neill & Cullen 1974; Parrish 1993; Schradin 2000; Ioannou

et al.2008). All of these factors predict exponential declines

in predation risk as group size increases, and therefore, above

a particular group size threshold, only very small decreases in

predation risk are expected (Pulliam 1973; Elgar & Catterall

1981; Krakauer 1995; Roberts 1996). This means that the

predation risk for individuals in all groups above a moderatesize will be similar, and so the selective advantage in terms of

predation risk for individuals to form larger groups, when

already in a large group, will be low. Measuring both the

strength of the relationship between group size and predation

risk, and the point at which further increases in group size no

longer give antipredation benefits (or incur net costs), deter-

mines the degree to which behavioural compensation can

mediate predation risk and therefore the strength of lethal

and nonlethal effects.

Grouping is also generally associated with costs (Milinski

et al. 1991; Krause & Ruxton 2002), and when these costs

are significant, selection will act on individuals to choosethose groups that give the lowest predation risk relative to

the number of individuals in the group (Pulliam & Caraco

1984). The most important costs of grouping in the context

of predation include direct competition for food, interfer-

ence competition and enhanced attack rates from predators

(Krause & Ruxton 2002). For example, larger groups are

more conspicuous (Vine 1973) and generally attract higher

attack rates from predators (Lindstrom 1989; Cresswell

1994b; Botham et al. 2005; Carere et al. 2009; but see Fitz-

gibbon 1990; Fernandez-Juricicet al.2004 for the opposite),

so selecting for smaller group size. Consequently, animals

should only join a larger group than the one they are in if it

increases antipredation benefits. Beyond a certain group size

(hereafter called the risk threshold), no further benefits will

arise because predation risk will remain relatively uniform.

Assuming no other benefits for increasing group size and

that animals are risk minimizing, the optimal flock size will

occur at the risk threshold where maximal antipredation

benefits accrue while incurring the lowest possible costs. In

this paper, we explore this prediction by examining whethera bird species that gains no foraging or other benefits from

grouping (Sansom et al. 2008) usually forms flocks that are

no larger than the risk threshold and therefore how optimal

group size arises from predation risk.

The determinants of optimal group size in the context of

predation risk can be summarized for an individual as fol-

lows:

Predation risk 1 Group attack rate 2

Attack success rate 3 Individual attack rate

(1) Groups of different sizes are likely to be attacked at dif-

ferent rates because they vary in conspicuousness (Vine

1973). Generally, larger groups attract higher attackrates because of predator functional or numerical

responses, although this may reach an asymptote if pre-

dators suffer interference competition (Sutherland

1996). Selection therefore acts initially to reduce group

size (Fig. 1a).

(2) As individuals join larger groups, however, there is usu-

ally a reduction in the likelihood of any attack on the

group being successful (e.g. Kenward 1978; Cresswell

1994b, 1996; Krause, Ruxton & Rubenstein 1998; Fun-

ston, Mills & Biggs 2001; Roth & Lima 2003; Cresswell

& Quinn 2004). This arises through a number of mecha-

nisms, for example because of shared vigilance, where

the probability of any animal scanning and so detecting

a predator at any one time increases (Pulliam 1973; El-

gar & Catterall 1981; Roberts 1996). The confusion

effect is also important, where predators find it hard to

track multiple moving targets (Krakauer 1995). Both

vigilance and confusion predict exponential increases in

effect with group size (Fig. 1b) and therefore an expo-

nential decline in attack success with group size

(Fig. 1c).

(3) Individual risk correlates negatively with group size

because of the dilution effect (Krebs & Davies 1981). If

all individuals have an equal chance of being targeted,

then the probability that an individual will be killed onattack will be 1group size, and so an exponential

decline in predation risk with group size will occur

(Fig. 1d).

Therefore, negative selection on group size is expected to

minimize attack rate, but positive selection is expected

because of attack success reductions and the dilution effect.

Because both attack success rate and dilution effect decline

exponentially with flock size, there should be a clear risk

threshold above which predation risk becomes reasonably

constant. If there is negative selection owing to the attack rate

relationship (e.g. foraging costs with increasing group size),

this risk threshold should predict the group size chosen by

most individuals (i.e. optimal group size; Fig. 1).

Optimal group size and predation risk 311

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Optimal group size should, however, depend on the rela-

tive strength of the differing selection relationships. For

example, see Fig. 1 and compare the effects of arbitrary

differences in risk threshold between the relationships that

comprise predation risk on the likely observed group size.

If attack rate was the main factor determining predationrisk, optimal group size will be as small as possible, assum-

ing only antipredation benefits to grouping (Fig. 1e). For

example, for a large animal such as a baleen whale ( Mysti-

ceti sp.) hunting krill (Euphausiacea sp.), where the entire

group is easily engulfed so removing any variation in cap-

ture success with group size, or the dilution effect, then

selection would lead to smaller groups that would be able

to escape detection, or that would be uneconomic for a

whale to pursue.

If attack success rate was the main factor determining pre-

dation risk, and again assuming only antipredation benefits

to grouping, optimal group size will always be above the risk

threshold of the attack success rate relationship (Fig. 1f,

dashed line). For example, consider a colonially breeding

bird attacked by a mammalian predator. In this system,

attack rate might not depend on group size because a breed-

ing colony of any size is always conspicuous, nor the dilution

effect because the predator always targets the weakest indi-

viduals identified during the attack. Selection would then act

to promote groups that minimized capture success per attack

(i.e. above the risk threshold). If there was a cost to grouping,

such as competition for food or nest sites, resulting in selec-

tion for smaller groups, then we would predict that group

sizes would converge around the risk threshold, the exact

location dependent on the relative strength of the costs andbenefits to grouping (Fig. 1f, solid line).

If the dilution effect was the main factor determining pre-

dation risk, and again assuming only antipredation benefits

to grouping, optimal group size will always be above the risk

threshold of the dilution effect relationship (Fig. 1g, dashed

line). For example, a migratory ungulate crossing a river,

where any individual or group is highly conspicuous to a

crocodile Crocodylus niloticus attacking from below and

where the prey have no effective escape behaviour. Again if

there are costs to grouping, such as large groups interfering

with each other as they crossthe river, reducing their speed of

travel, then we would again predict that group sizes wouldconverge around the risk threshold, the exact location depen-

dent on the relative strength of the costs and benefits to

grouping (Fig. 1g, solid line).

This paper explores the importance of group sizedepen-

dent attack rate, attack success rate and individual attack

rate in predicting group size in an animal population under

natural conditions. We recorded daily mean group size in

wintering redshanks Tringa totanus in a system where the for-

aging benefits from shared vigilance are cancelled by interfer-

ence competition, leading to no net effect of group size on

foraging success among redshanks (Sansom et al. 2008).

Therefore, optimal group size is probably entirely determined

by variation in predation risk, and so the group size selected

by most individuals should reflect this. We then measured the

attack rate and attack success rate relationship with group

size for Eurasian sparrowhawks Accipiter nisus attacking and

killing groups of redshanks (see Cresswell & Whitfield 2008

for an overview of the system), and along with the dilution

effect relationship, we determined the likely location of the

risk threshold for all three factors. Finally, we examinedwhether the risk threshold matched the most favoured group

size. First, we tested the general prediction that risk thresh-

olds should predict optimum group size by calculating the

overall predation risk relationship (using the equation men-

tioned earlier) and its risk threshold. Second, we assessed

whether any one component attack rate, success or dilution

might have the strongest selective effect on group size by

comparing which individual risk threshold best predicted

group size.

Materialsandmethods

The study area consisted of salt marsh habitat backed by

woodland or dunes at the Tyninghame Estuary, East Lothi-

an, Scotland (see Whitfield 1985 for further study site

details). Data were collected from September to early March,

198992, and 200106. The salt marsh (c. 15 ha) provides a

feeding habitat for wintering redshanks, in particular for first

winter (juvenile) birds (Cresswell 1994a).

O C C U R R E N C E O F R E D S H A N K S I N D I F F E R E N T F L O C K

S I Z E S

Data on the occurrence of redshanks with respect to the flock sizes

they chose were collected by scan samples on the salt marsh during

the winter of 20012 (see Quinn & Cresswell 2004) during 1- to 6-h

observation periods from fixed locations overlooking the whole salt

marsh, except during high tide periods when the salt marsh was cov-

ered (to any degree) by water. During observation periods, the total

number of redshanks and the number of flocks were recorded on the

salt marsh every 30 min, along with a potentially confounding vari-

able affecting predation risk, the mean distance to predator-conceal-

ing cover for each flock. A flock was defined as a cluster of birds in

which the maximum nearest neighbour distance was 25 m and typically varied in size from 1 to 100

birds.

Observations were made on 57 days with 89 07 scan samples a

day. Mean flock size SE was 183 15 birds (n = 57 observa-

tion days), with a mean SE salt marsh population of 387 27

birds available to form flocks (n = 57 observation days). Each set of

focal samples from a sample time had an overall population size (i.e.

the sum of all flock sizes), and this was classified into a population

size class (110,in intervalsof 10 until 91100and then 101150, with

class sizes chosen to equalize the variance in each class). When the

same population size class occurred in more than one focal sample in

a day, a daily mean value for flock size was calculated for that popu-

lation size class. The sampling unit for analysis was therefore the

number of separate days in which that population size class was sam-

pled. We then tested whether there was an optimum flock size by

determining the flock size at which further increases in daily salt-

marsh population size resulted in no further major increases in meandaily flock size.

312 W. Cresswell & J. L. Quinn

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Population size was frequently limited duringa scan andprecluded

theformation of large flocks. We,therefore, analysed a subsetof scan

samples where the total population of redshanks on the salt marsh

exceeded 100. This gave 21 observation days, with mean SE

27 05 scans and 89 18 flocks recorded per day. We then cal-

culated the total number of birds recorded per day in 12 flock size

classes (1, 35, 610, 1115, 1620, and then increments of 10 until

80, 81100: increments defined in this way to be consistent with those

used to calculate capture success). We divided these totals for each

day by the number of scan samples for each day to obtain compara-

ble relative frequencies across days. We then summed the number of

birds recorded across days within each flock size class. We deter-

mined the existence of a flock size class most favoured by redshanks

by determining whether there was a quadratic relationship between

thefrequency of redshanks withinthe flock size classes and flock size.

Relative flock availability with respect to sparrowhawk attack rate

was calculated by pooling flock size records into the same 12 flock

size classes as used previously and summing the total number of

flocks recorded in eachsizeclass in a day.The proportion of the over-

all total that each flock-size-class total represented was then calcu-lated for each day (i.e. standardizing daily relative flock size class

availability because of variable daily sample effort). The daily pro-

portions were then summed for each flock size class across the

57 days sampled. The overall mean relative abundance was then

scaled to the abundance of group size 1 (e.g. if the abundance of

group sizes 1 and 10 was 15 and 5, respectively, relative abundances

were calculated as 1515 = 1and 515 = 033).

S P A R R O W H A W K A T T A C K D A T A

Sparrowhawk attacks were seen on 288 separate days over 8 winters,

198992 and 200106 (mean SE = 2 5 03 attacks per day on

days when attacks were recorded). During the initial more intensivestudy in the first three winters (2557 h spent at the study site), it was

estimatedthat at least six sparrowhawksattackedduringeach winter.

Some individuals were probably recorded across winters (see

Cresswell & Whitfield 1994). The 16-year period over which observa-

tions took place, however, makes it likely that many different birds

were involved.

An attack was defined as a rapid flight directed towards a flock or

a single bird. A kill was recorded when the raptor captured a

redshank. For each attack, flock size and distance from predator-

concealing cover were estimatedwhen possible. Flocks almost invari-

ably contained only redshank; the presence of additional birds was

ignored in flock size estimates, and the attack was not considered if

other species were targeted, which happened very rarely. Markers

were placed at regular intervals around the edge of the salt marsh to

facilitate estimating distances. Flock size and distance to cover were

usually recorded before attacks. For some attacks, details were

obtained from videos (see Quinn & Cresswell 2006). In total, we saw

641 surprise (where sparrowhawks attacked directly from concealing

cover see Cresswell 1996) attacks where flock size was accurately

recorded, resulting in 101 captures. All attacks were included where

we had a measure of flock size; usually, this was recorded before any

escape response had occurred because flocks were under continuous

observation. After theattack, we confirmed theflock size by counting

the flock again. Sample sizes of attacks and captures are larger than

those in Cresswell, Lind & Quinn (2010) because flock size informa-

tion could almost always be recorded accurately during an attack,

whereas distance to cover could not be for some attacks, where fore-shortening, or an unclear view of the entire flock before flight

prevented an accurate and unbiased estimate of initial distance from

cover.

Attack success rate was calculated by pooling into the same 12

flock size classes used for flock availability above, with class sizes

determined to spread captures as equally as possible between classes.

The relationship between sparrowhawk attack success rate and flock

size may be confounded by distance to cover, which also strongly

affects capture success rate in our system (Cresswell 1994b; Cresswell

& Quinn 2004). However, any variation in attack rate arising from

distance to cover was uniform with respect to group size and should

not bias our estimates of the relationship between hunting behaviour

and flock size. On average, there was no significant variation in dis-

tance to cover across group size for attacking sparrowhawks (e.g.

KruskalWallisv211 = 126, P = 032 data pooled withinthe 12 clas-

ses of increasing flock size).

G E N E R A L S T A T I S T I C A L M E T H O D S

Analyses were carried out in R (R Development Core Team 2009),

predominantly using linear models (lm command in R); all finalmodels met the assumption of normally distributed data and

homogeneity of variance as demonstrated by the (plot) command

in R and according to criteria in Crawley (2007). Relationships

between variables were modelled with the three most likely biologi-

cal models: a linear relationship (continuous increase), a quadratic

relationship (a peak or optimum) and a logarithmic relationship (a

rapid increase becoming gradual). Where biologically appropriate

(i.e. flock size must be zero when population is zero), models were

constrained to pass through the origin. Models were compared

using AICC values because of small sample sizes (Burnham &

Anderson 2002). For the relationship between flock size and popu-

lation size, a logarithmic relationship was not expected and there-

fore tested because flock size must always be less than or equal to

population size. For the relationship between attack rate and flock

size, attack rate was adjusted for variation in overall availability of

the different flock size classes by dividing attack rate by the relative

abundance of the different flock size classes. Variation in attack

success across flock size classes was further tested using Chi-square

tests (summary command in R) and using logistic regression (glm,

family = binomial, command in R) to determine how attack suc-

cess (capture or escape) was dependent on flock size and distance

to cover in the unpooled data.

Results

G R O U P S I Z E F R E Q U E N C Y

Mean daily flock size on the salt marsh varied typically from

1 to 60 (mean SE = 183 15). Flock size was best pre-

dicted by a shallow quadratic relationship with population

size [(056 004 SE) population size]) [(00015

000042 SE) population size2]; population size, F1,9 =

12673,P < 0001; population size2,F1,9= 125,P= 0006;

adjustedR2 = 099: Fig. 2. A linear function gave a poorer

fit (DAICC= 79).

When population size was not constraining on the salt

marsh (i.e. more than 100 birds available), the observed flock

size in which bird frequency peaked occurred at about 75

(Fig. 3). The total number of birds found in a flock size classwas best predicted by a logarithmic relationship which



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Atta

cksuccessrate

Strong selection

for larger

groups

Weak selection forlarger groups

Attack success rate

RT

Frequency

Group sizeRT

Strong selection for small groups

Frequency

Predation risk

group attack rate(a)

(c)

(b)

(d)

Likely observed number

of individuals(e)

Frequency

RT

0 20 40 60 80 100

0 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100

0 20 40 60 80 100

0 20 40 60 80 1000

1

Weak selection for

larger groups

Strong

selection

for

larger

groups

Relativeprobabilityofflock

beingattacked

Probability

ofindividualbeingattacked

wh

enaflockisattacked

Group size

Dilution

RT

0 20 40 60 80 10000

05

10

Probabilityofdetection

ormaximal"confusion"

(g)

(f)

Fig. 1.Graphs showing predicted values of

howgroup attackrate (a), attacksuccess rate

(c) and the dilution effect (d) (where individ-

ual risk of being targeted is 1group size)

should vary with group size, and how corre-

sponding selection pressure should lead to

preference of certain group sizes by individu-

als minimizing predation risk, and so greater

observed frequencies of individuals in less

risky flocks (eg).Graph (a) shows two pote-

ntial functions linking attack rate and group

size; others are possible, but all predict that

attackrate increases initially with group size.Attack success and dilution both have a

threshold (risk threshold labelled RT)

where further change in the function makes

little further difference to predation risk.

Correspondingly, we predict that there will

be strong selection for individuals to avoid

risky flock sizes below these thresholds (lead-

ing to the dashed line distributions in f and

g). If there is also strong selection from

attack rate to minimizeflocksize (a), we pre-

dict a peak of preference for individuals in

flock sizes close to the risk threshold (leading

to the solid line distributions in f and g).

Inset graph (b) shows how the probability of

detection and confusion changes with groupsize leading to the predicted exponential

change in attack success rate function with

group size.

0 20 40 60 80 100 1200

10

20

30

40

50

60

28

27

3326

3130 24

18

1111

17

Meanflock

size(+1SE)

Mean population size

Flock size observed

Flock size maximised

Fig. 2.Mean flock size as a function of the total population of red-

shanks available (pooled into population size classes). Overall mean

flock size values (acrossall days that a population size class was sam-

pled) were then plotted, withn being the number of separate days in

which that population size class was sampled (shown by the numbers

above each point). The line plots the quadratic function of best fit

(F2,9= 6400, P < 0001, Adj. R2 = 099).

0 20 40 60 80 1000

50

100

150

200

250

300

350

400

Frequenc

y

Flock size

Fig. 3.The frequency of individual birds in each flock size class for

scan samples when the population of the salt marsh exceeded 100

birds. Scans were carried out on 30 separate days, and each days

samples were weighted so each day contributes equally, irrespective

of sampling effort. The line plots the logarithmic function of best fit

(F1,11= 1233, P < 0001, Adj. R2 = 091).



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showed that very few birds were in flock sizes of less than 30,

with a gradually increasing frequency of birds in flocks above

this flock size [total number of birds = (556 50

SE) ln (flock size); F1,11 = 1233, P < 0001, adjusted

R2 = 091]: Fig. 3. A quadratic relationship that peaked at

about flock size 80 was a poorer (DAICC= 15), although

also reasonable, predictor of the relationship (flock size,

B = 69 14 SE, F1,10 = 1081, P < 0001; flock size2,

B = )0044 0020,F1,10= 52,P = 0045;F2,10 = 567,

P< 0001, adjusted R2 = 090). A linear function gave a

much poorer fit (DAICC = 49).

A T T A C K R A T E

Sparrowhawk attack rate, relative to the availability of each

flock size class, increased with flock size, with peak observed

values at flock sizes of about 65 (Fig. 4). Attack rate was best

predicted by a quadratic relationship with flock size, with

predicted values peaking at flock sizes of about 55 (attack

rateflock availability = [(00076 0024 SE) flock size]

) [(000068 000027 SE) flock size2] + ( 04 7 040

SE); flock size, F1,9= 78, P = 0021; flock size2, F1,9= 62,

P= 0030; adjusted R2 = 052). A logarithmic function

gave a poorer fit (DAICC = 26) as did a l inear fit

(DAICC= 43).

A T T A C K S U C C E S S

Attack success declined steeply with group size until about

40, after which the decline became relatively shallow (logistic

regression flock size B =)

0029 0

007, P < 0

001,

n = 540 unsuccessful attacks, 101 captures). This relation-

ship was very similar, B = )0026 0007, see Cresswell,

Lind & Quinn (2010), when also including distance to cover,

as would be expected from the equal distribution of all dis-

tances to cover across the flock size classes see Materials

and methods). When data were pooled into flock size classes

to equalize samples of kills attack success was best predicted

by a logarithmic function [attack success rate = ()0-

0063 00086 SE) ln (flock size) + (037 0028 SE);

flock size, F1,10 = 530, P < 0001; adjusted R2 = 083]:

Fig. 5. A quadratic function gave a poorer fit (DAICC= 27)

as did a linear fit (DAICC = 66). Attack success was signifi-

cantly affected by flock size up to 40 birds (v26 = 243,

P < 0001), but not for flock sizes above 40 (v24 = 29,

P = 057).

C O M P A R I N G G R O U P S I Z E T O A T T A C K R A T E , A T T A C K

S U C C E S S A N D D I L U T I O N R I S K T H R E S H O L D S

Almost all (95%) of the decline in risk occurred by flock size

of about 20 for the dilution effect (Fig. 6), by about30 for the

overall individual predation risk relationship (Fig. 6) and by

about 70 for the attack success relationship (Fig. 5). The

0 20 40 60 80 10000

05

10

15

20

25

30

35

Attackrate/flockavailab

ility

Flock size

Fig. 4.The relative attack rate per availability of each flock size class

(scaled to the attack rate for group size 1); sample sizes of attacks as

in Fig. 5. The line plots the quadratic function of best fit (F2,9= 70,

P = 0014, Adj. R2 = 052).

0 20 40 60 80 100

000

005

010

015

020

025

030

035

65

69 7157

54

9782

53

45

24

9

16Attacksuccess

rate

Flock size

Fig. 5.Capture success rate with flock size with attacks pooled into

classes so rates of capture can be calculated; numbers of attacks in

each class are given beside each point. The line plots the logarithmic

functionof bestfit (F1,10 = 530, P < 0

001, Adj. R

2

= 083).

0 20 40 60 80 100

00

05

10

During the whole

study average

flock size was 183

Relativerisk

Flock size

Dilution

Overall individual predation risk function

Attack success

Attack rate

Most birds were in

flocks of 75 95

when population

size allowed

During the whole

study most birds

were in flocks of

40 60

Fig. 6.A summary of the relationships forattack rate, attacksuccess,

dilution and overall predation risk (=attack success attack rate

function 1group size) with group size.



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attack success relationship suggested selection for joining

flocks as large as possible (Fig. 4). Optimum flock size, as

measured by the one adopted by most birds when uncon-

strained by population size, was at least above 30, with most

birds being in larger flocks than this with a possible peak at

around 80 (Fig. 3), above all of the risk thresholds, but clos-est to that of attack success.

Conclusions

W H I C H P R E D A T I O N R I S K F A C T O R D E T E R M I N E S G R O U P

S I Z E ?

Redshanks continued to increase group size as population

size increased, both independently of attack rate and

beyond the threshold predicted by both the dilution effect

and the individual risk of being killed per attack (see

Fig. 2). Redshanks were found most commonly in large

flocks, although there was little increase in the frequency

with which redshanks favoured larger flocks above a flock

size of about 30 (see Fig. 3). This relationship between the

preferred flock size and population size has two possible

interpretations. First, the quadratic fit suggests an optimum

flock size of about 80, but the logarithmic relationship sug-

gests redshanks avoid small flocks (less than 30) but still

attempt to form large flocks at least up until 100 (the maxi-

mum flock size we included). Either way, redshanks clearly

preferred large flock sizes up to around 80100, and the

group sizes most frequently used by birds were therefore

closest to those that might be predicted from the overall

individual predation risk relationship and the attack successrate relationship.

The strength of selection for the dilution effect above flock

sizes of about 30 was minimal predicting few larger flocks if

this were the main driver of group size (assuming no other

advantages of flocking), and this is shown by the reduction in

the strength of increase in the relationship shown in Fig. 3.

Advantages of increasing group size from the attack success

rate function, however, were still substantial, even up to

group sizes of 70, and we found a preference for flocks up

until at least 80, as shown by the continuing increase (or

peak) in number of birds using flocks up to about 80 in

Fig. 3. Some of the threshold estimates were uncertain. Forexample, the attack success threshold may have been as low

as 40, andoptimum group size may nothave been reached by

a group size of 80. This does not, however, greatly change

our conclusions: the group size most commonly used by indi-

viduals was above the risk thresholds of all the antipredation

relationships with group size we examined, suggesting that

even the very small decreases in predation risk accrued by an

individual moving from a large group to a slightly larger

group give fitness benefits sufficient to have led to selection

for this behaviour. Our results also clearly showed that red-

shanks avoided flocks of less than about30 as predicted from

the very large fitness benefits of joining a flock above the

overall individual predation risk threshold of about 30 (see

Fig. 6).

Attack success rate may be an important selective factor

driving the flock size increases above the overall individual

predation risk threshold in redshanks because behaviourally

driven variation in flock vulnerability is the main determi-

nant of attack rate and mortality (Quinn & Cresswell 2004)

and because sparrowhawks are opportunistic, generalist pre-dators (Cresswell 1995). Any reduction in success rate should

encourage a shift to other more vulnerable prey. If sparrow-

hawks attack prey that they can most efficiently catch (i.e. the

smallest number of attacks to gain the largest prey possible),

then their prey choice will be determined by the relative vul-

nerability and size of different prey species. Redshanks are

relatively large prey for sparrowhawks (Newton 1986; Cres-

swell 1995) and so might be preferentially attacked even when

there is a low chance of success. But any reduction in attack

success, even when this is already low, may lead to a sparrow-

hawk shifting prey species, as another prey becomes the most

profitable (Newton 1986), so leading to strong selection on

redshanks to reduce attack success rates as much as possible.

Reducing attack success rate as low as possible should greatly

reduce attack rate, particularly if the prey-switching thresh-

old is passed, although this threshold will be dependent on

the availability and vulnerability of alternative profitable

prey (Jackson et al. 2006).

Although redshanks on the study site were primarily

attacked and killed by sparrowhawks, peregrines Falco pere-

grinus also attacked and killed redshanks frequently (Cres-

swell & Whitfield 1994) and therefore observed flock sizes

may also be influenced by the effects of variation in peregrine

attack rate and success with flock size. The decline in success

rate with group size for surprise attacks was the same forboth predator species; however, peregrines attacked smaller

flocks more frequently than sparrowhawks (Cresswell &

Quinn 2010) and therefore further increase the predation risk

associated with very small flocks, in effect making the

increase in attack rate with flock size illustrated in Fig. 4 shal-

lower. The lack of a strong effect of attack rate on observed

favoured flock size may then partly be a consequence of a

more uniform overall attack rate when all predators are con-

sidered, but this effect is likely to be minor because peregrines

attack redshanks much less frequently than sparrowhawks

(Cresswell & Quinn 2010).

A T T A C K S U C C E S S R A T E

Most previous studies have related attack success rate to

broad flock size categories, rather than to continuous mea-

sures, but have found broadly similar results: attack success

rate drops off very rapidlyfor group size (e.g. Kenward 1978;

Lindstrom 1989; Krause & Godin 1995; Roth & Lima 2003).

Our results show, however, that there are still reasonable

advantages in terms of reduction in attack success rate for

redshanks in flocks up to about 70. This is perhaps surprising

considering that there is unlikely to be any enhanced benefit

in terms of predator detection in groups above 20 birds, both

theoretically (Pulliam 1973; Roberts 1996) and empirically

for redshank (Cresswell 1994b), and also in terms of the



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confusion effect, both theoretically for groups of more than a

few individuals (Krakauer 1995) and empirically for Daphnia

above group sizes of about 30 (Jeschke & Tollrian 2007). Yet

our results show that reductions in attack success do occur

over larger group sizes well above where further vigilance

and confusion benefits should accrue. Why this should be sois not clear, but potential explanations include enhanced col-

lective detection, because accurate and rapid escape

responses rely not only on detection but on simultaneous

detection and response of several flock members (Cresswell,

Hilton & Ruxton 2000; Quinn & Cresswell 2005a), and

increase in the probability of larger flocks containing unusual

or poorly behaving individuals that are identified and prefer-

entially targeted during an attack, thus countering the confu-

sion effect(Ohguchi 1978; Quinn & Cresswell 2006).

A T T A C K R A T E

Large flocks (55) were attacked approximately two and a half

times as often as small flocks. Although our data are sparse

for flocks above 55, very large flocks seem to also have been

preferentially avoided by sparrowhawks. Flock conspicuous-

ness is likely to have influenced attack rate: single birds are

often relatively difficult to detect on the salt marsh from the

relatively low vantage points normally used by sparrow-

hawks, particularly when redshanks are feeding in creeks or

depressions (W. Cresswell, pers. obs.). On many occasions,

we witnessed a single redshank flying away after a sparrow-

hawk had flown over the redshank on its way to attack a

group of redshanks further away from it, suggesting that the

closer and more vulnerable redshank (see Cresswell & Quinn2004) had not been detected. But above five or so redshanks,

any group on the salt marsh is conspicuous: redshanks are

very mobile when feeding because of interference competi-

tion (Minderman, Lind & Cresswell 2006) and so are detect-

able to a human observer at a distance of hundreds of metres

(pers. obs.). It therefore seems unlikely that the increase in

attack rate above small flock sizes is driven by conspicuous-

ness. One reason for attacks on large flocks, even when suc-

cess rates are on average low, may be that because

sparrowhawk hunts are very brief (Cresswell 1996), and the

redshanks remain in the general area after attack (Cresswell

& Whitfield 1994), sparrowhawks can probe for weakenedindividuals or even create more vulnerable prey with repeated

attacks (see Charnov, Orians & Hyatt 1976; Lima 1990,

2002; Brown, Laundre & Gurung 1999).

D I L U T I O N E F F E C T A N D O V E R A L L R I S K F U N C T I O N

The dilution effect ensures that any effects of variation in

attack rate and attack success rate are swamped with increas-

ing group size. For example, elsewhere it has been shown in

this system (Cresswell 1994b although with much lower sam-

ple sizes) that individual risk still decreases rapidly even with

elevated attack rates on larger flocks. The dilution effect,

however, relies on an unrealistic assumption that all prey

have an equal chance of being targeted, when in reality

differences in the vulnerability of individuals within flocks

lead to preferential targeting (Quinn & Cresswell 2006).

Therefore, it is perhaps not surprising that flocks above the

threshold for the dilution effect are preferred because any

vulnerable individual is likely to have more vulnerable com-

panions in larger flocks.

W H Y D O N O T R E D S H A N K S A L W A Y S M A X I M I Z E F L O C K

S I Z E ?

Redshanks increased flock size where possible, increasing

average flock size as the pool of available redshanks

increased (Fig. 3). They did not, however, frequently form

one flock when populations were below 80. The most likely

hypothesis for this discrepancy may be because, although we

counted the whole population of redshanks available to form

flocks on the salt marsh, these birds were likely to have varied

in their position on the starvationpredation risk trade-off

continuum (Cresswell & Whitfield 2008; Sansom, Lind &

Cresswell 2009). Some birds may have been prepared to feed

closer to cover and at higher risk than others because their

risk of starvation exceeded their risk of predation. Other

birds that were prioritizing risk avoidance, rather than forag-

ing would notbe prepared to join birds that were taking more

risks (Cresswell, Lind & Quinn 2010). Individual variation in

body condition and starvation risk may inevitably always

lead to a subdivided population which constrains the ability

of all individuals to maximize group size. Similarly, the use of

alternative antipredation strategies linked to personality

(Quinn & Cresswell 2005b) could also lead to the nonrandom

distribution of behavioural phenotypes across groups.

G E N E R A L P O P U L A T I O N A N D C O M M U N I T Y S T R U C T U R E

C O N C L U S I O N S

Our results have several implications for how predatorprey

interactions might influence trophic interactions and commu-

nity structure in ecosystems generally. First, species that are

able to form groups may be able to respond to increased

predation risk without having to avoid areas frequented by

predators, and generalist predators may then switch to more

profitable prey in other areas. This may lead to predation on

populations being inversely density dependent and to Alleeeffects because predators may primarily impact small popu-

lations that are unable to form large groups (e.g. Mooring

et al. 2004; Angulo et al. 2007; Watson, Aebischer &

Cresswell 2007). Second, if a predator has a high attack suc-

cess rate that declines steeply with larger group sizes of prey,

then selection will favour prey that form groups. Formation

of groups will then change the local density of a species so

affecting its competitive interactions with conspecifics and

the prey species with which it shares a food supply, as well as

affecting the spatial availability and distribution of this food

supply (Minderman, Lind & Cresswell 2006). Third, if the

threshold for losing further antipredation benefits from

grouping occurs at low group sizes, then nonlethal effects will

be relatively large because optimum group size is unlikely to



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be constrained by the availabilityof individuals. Fourth, even

when increasing group size may confer substantial advanta-

ges, unless all individuals are prepared to feed in the same

areas (i.e. take the same risks), maximum group sizes will not

occur unless the population is sufficiently large to allow opti-

mal subpopulations to form. Increased variation in condi-tion, dominance or the competitive ability of individuals will

therefore reduce the likelihood of optimal group size forming

and so decrease the strength of nonlethal effects. The precise

manner in which any of these effects arise is likely to be sys-

tem dependent.

Acknowledgements

We thank NERC, the Royal Society and the Leverhulme Trust for funding.

We also thank Philip Whitfield, East Lothian District Council, the Tyningh-

ame Estate and Sue Holt. We thank the Editors, Andrews Jackson and two

anonymous referees for helpful comments.

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Received 1 April2010;accepted18 October 2010

HandlingEditor:Tom Webb



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