Download Games among cannibals: competition to cannibalize and

doi:10.1111/j.1420-9101.2005.00941.x
Games among cannibals: competition to cannibalize and
parent-offspring conflict lead to increased sibling cannibalism
J. C. PERRY & B. D. ROITBERG
Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, Canada
Keywords:
Abstract
game interactions;
parent-offspring conflict;
sibling cannibalism;
sibling rivalry;
trophic eggs.
Sibling cannibalism occurs in many species, yet understanding of sibling
cannibalism as an adaptation currently lags behind understanding of other
antagonistic interactions among siblings. Observed sibling cannibalism phenotypes likely reflect the interaction between competitive games among
siblings and parent-offspring conflict. Using a game-theoretic approach, we
derive optimal offspring cannibalism behaviour and parental modifiers that
limit or facilitate cannibalism. The results are compared to contemporary
frequency-independent analysis. With the addition of game interactions
among siblings or parent-offspring co-evolution, our model predicts increased
cannibalism (compared to the frequency-independent prediction), as offspring
compete to eat siblings. When infertile eggs are present – strengthening
competition – offspring risk eating viable siblings in order to gain access to
infertile eggs, intensifying parent-offspring conflict. We use the results to make
new predictions about the occurrence of sibling cannibalism. Additionally, we
demonstrate the utility of trophic egg laying as a maternal mechanism to
promote egg eating.
Introduction
Although there is typically a high degree of relatedness
among siblings, antagonistic sibling interactions are
frequently observed. Selfish sibling interactions may be
broadly categorized by whether they involve competition
for resources or cannibalism (Mock & Parker, 1997). As
an example of resource-based competition, many nestling birds compete for limited parental investment (Mock
& Parker, 1997, and refs therein). In the extreme case,
there may be selection to eliminate competitors via
siblicide (e.g. O’Connor, 1978). In contrast, for cannibalistic interactions, obtaining a meal (in the form of a
relative) is generally the driving selective pressure.
Sibling cannibalism occurs across diverse taxa, and
illustrative species may be found within insects (e.g.
Michaud & Grant, 2004), other invertebrates (e.g. Iida,
2003), birds (refs within Stanback & Koenig, 1992),
Amphibia (refs within Crump, 1996) and fish (e.g.
Fitzgerald & Whoriskey, 1992).
Correspondence: Jennifer C. Perry, Department of Zoology, University of
Toronto, 25 Harbord St., Toronto, ON, Canada M5S 3G5.
Tel.: 416-978-0387; fax: 416-978-8532;
e-mail: [email protected]
Theory for resource-based sibling rivalry (SR) has been
well developed (O’Connor, 1978; Stinson, 1979; Dickins
& Clark, 1987; Parker et al., 1989; Godfray & Harper,
1990; Godfray & Parker, 1992; Forbes, 1993; Rodrı́guezGironés, 1996; Mock & Parker, 1997; Mock et al., 1998),
and the expected limits to selfishness in resource-based
competition have been clearly outlined. These models
have generally required a game-theoretic approach to
predict optimal selfishness, because it is necessary to take
into account the strategies of other offspring in order to
predict optimal selfishness for a sibling. As an example
(paraphrasing Parker et al.’s (1989) remarks), consider a
senior nestling ‘A’, which must decide what fraction of
resources to leave for a junior sibling ‘C’. The usual
assumption is that if A leaves a food item, another senior
sibling ‘B’ might consume that food item, rather than
leaving it for the intended C. In this case, A’s best option
might be to eat the item itself, rather than allowing B to
have it. Thus, the best strategy for a senior sibling to
adopt towards vulnerable juvenile siblings depends on
what other senior siblings do. In contrast, current
understanding of sibling cannibalism as an adaptation
(reviewed in the following section; Eickwort, 1973;
Crespi, 1992; Dong & Polis, 1992; Pfennig, 1997) is based
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
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J. C. PERRY AND B. D. ROITBERG
on a ‘simple’ optimization approach (sensu Mock et al.,
1998), in which the optimal strategy (to eat a sibling or
not) does not depend on the actions of other siblings in
the same clutch. Yet it is clear that, when offspring
interact in groups, victim siblings themselves become a
resource over which cannibal siblings compete (Mock
et al., 1998). Such competition may change the benefit
thresholds for sibling cannibalism from the current
prediction.
Furthermore, current models of sibling cannibalism do
not incorporate parental interests in the degree of
cannibalism among their offspring. It can be optimal for
parents to facilitate or to limit selfish interactions among
offspring, depending on the benefit that an offspring
receives from a selfish act towards a sibling, relative to
the cost of the act for the target sibling (O’Connor, 1978).
Because the thresholds for parents and offspring to
benefit from cannibalism differ (as described below),
parent and offspring interests may overlap or conflict.
Mothers have several tactics available for managing
cannibalism among offspring. For example, hatching
synchrony may limit sibling egg cannibalism (e.g.
Frechette & Coderre, 2000), whereas hatching asynchrony (e.g. Polis, 1981) and trophic egg laying (the
production of infertile eggs as food for offspring, Crespi,
1992; Perry & Roitberg, 2005) facilitate egg eating.
Evolutionary games between two sets of family
members – among siblings and between parents and
offspring – may, then, influence observed sibling cannibalism behaviour. This study investigates the effect of
these games on predicted sibling cannibalism behaviour.
We model the co-evolution of sibling cannibalism and
two maternal tactics – hatching synchrony or asynchrony
and trophic egg production – for managing cannibalism
among offspring. Given the complexity of a co-evolving,
multiple-trait system, there is a large set of possible
solutions. Here, we use stochastic simulation models
(Goldberg, 1989) to determine the evolved outcome. In
separate experiments, we investigate how three factors
alter the expected frequency independent thresholds: (1)
a SR game; (2) the co-evolution of, or constraints on,
parent and offspring traits; and (3) infertile eggs, which
were introduced to intensify the competitive game
among siblings. We use the results to make new
predictions about expected patterns of sibling cannibalism behaviour. The study also has implications for the
evolution of trophic egg laying.
Current understanding of sibling cannibalism
Eickwort (1973; see also Crespi, 1992; Pfennig, 1997)
used Hamilton’s rule to investigate the conditions
favouring sibling cannibalism. To review the argument,
consider a senior offspring (‘A’) with a probability of
survival, P, in a two-offspring clutch. If A cannibalizes its
junior sibling (‘C’), it receives an increase in survival, P¢,
through reduced starvation risk, and has total survival
(P + P¢). By re-stating Hamilton’s Rule (Hamilton, 1964)
for the spread of a selfish act (Mock & Parker, 1997),
sibling cannibalism is favoured when the relative benefit
to the cannibal exceeds the cost to the victim, weighted
by relatedness – that is, when P¢ > Pr. This can be restated
as
P0 =P > r:
ð1Þ
For example, a cannibal must increase survival by at
least 50% to profit from consuming a full sibling.
Throughout the paper, we refer to the term (P¢/
P) · 100 as the relative benefit of cannibalism (RBC).
As mentioned above, in this model of sibling cannibalism, the optimal phenotype does not depend on the
frequency distribution of phenotypes in the population.
In the model, the probability of survival of the victim C,
PC, is equal to the probability of survival for all offspring,
P*. The optimal cannibalism behaviour of A with respect
to C is then considered, using P* as the basis of the
inclusive fitness cost of eating C. However, if clutch size is
increased to three and there is a second senior offspring,
B, then the true value of PC is modified by B’s phenotype:
PC now depends on the frequency distribution of
phenotypes in the B offspring position. As the frequency
of the cannibalistic phenotype in the population (f)
increases, PC approaches 0:
lim PC ¼ 0
f !1
whereas, if cannibalistic phenotypes are rare, the
approach used above becomes approximately correct:
lim PC ¼ P :
f !0
It is clear, then, that when siblings interact in groups of
more than two, the usual frequency independent analysis may not apply.
From a parent’s perspective, sibling cannibalism provides a net benefit when more offspring are gained from
the increased survival of cannibals than are lost as victims
(e.g. Crespi, 1992). With pairwise sibling interactions,
this occurs when
P0 > P:
ð2Þ
Parents favour cannibalism when the survival of
cannibals is at least doubled through cannibalism (when
RBC > unity).
The model demonstrates that parent and offspring
interests may overlap or conflict, depending on intraclutch relatedness and the relative increase in survival
from cannibalism. Neither parents nor offspring benefit
from cannibalism when RBC < r. When r < RBC < 1, it
is in the interests of offspring to cannibalize siblings and
the interests of parents to prevent cannibalism. When
RBC > 1, parents and offspring agree that cannibalism
should proceed. The model also shows that, for sibling
cannibalism to be beneficial, a noncannibal’s probability
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
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Competition increases sibling cannibalism
In our simulations, individuals were represented as
12-byte strings of information, divided into 4-byte
segments (here, genes) that code for the hatching
synchrony, trophic egg laying, and cannibalism lag time
behaviours. Each individual possessed all three genes,
with the cannibalism gene expressed in offspring and the
hatching synchrony and trophic egg genes expressed in
mothers.
In interactions within clutches, each pair of haploid
parents produces one clutch of 16. The number of trophic
eggs (0–15) is determined by the mother’s trophic egg
allele; ‘trophic’ status is assigned randomly. The remaining viable offspring hatch over 16 time units, in a pattern
determined by the mother’s allele for hatching synchrony
(Table 1). For example, all offspring might hatch within
one time unit, or hatching might be spread out over time.
In each time unit, the hatching offspring (if any) was
selected randomly. After an offspring hatches, it waits
some number of time units (1–16, determined by its allele
for ‘cannibalism lag time’) before seeking an egg to eat
within its clutch; victims were selected randomly from
remaining unhatched eggs. A delay of 16 time units
permits all viable siblings to emerge. After time 16,
offspring may continue to consume any trophic or
infertile eggs present (to a maximum of one egg per
offspring). Thus, an offspring’s opportunity to cannibalize
depends on the availability of unhatched eggs when it
emerges and the combination of its hatch time and delay
time. For example, an offspring that hatches at time 5 and
has a lag time of 12 will seek an egg to eat at time 17,
when all potentially viable eggs will have hatched.
of survival must be low. For example, if P > 2/3,
individuals cannot be selected to eat full siblings due to
the constraint that (P¢ + P) £ 1. Similarly, for parents to
favour sibling cannibalism survival must be less than
50%, else eqn 2 cannot be satisfied.
The models
In computer simulations, we modelled sibling egg cannibalism and maternal influence of cannibalism over
many generations, allowing coded ‘genes’ for the behaviours to evolve according to the success of the coded
strategy. To describe the ecological situation of interest in
general terms, we consider sibling interactions within
clutches of more than two offspring, with potential egg
cannibalism, no parental care, and dispersal of offspring
after egg cannibalism. Within a clutch, we assume that
offspring hatch more or less synchronously, with the
degree of synchrony under maternal control. We assume
that cannibal offspring consume, at most, one egg.
Cannibals may consume a potentially viable sibling, or
an infertile or trophic egg. Infertile eggs are produced by
constraint (i.e. mothers cannot avoid producing them),
whereas trophic eggs are produced according to a
mother’s trophic egg gene. We assume that viable,
infertile and trophic eggs provide equal food value. We
assume that cannibals do not discriminate between
viable and inviable eggs; there is apparently no such
discrimination in several well-studied empirical systems
(e.g. Pienkowski, 1965; Baur & Baur, 1986). Mothers
produce only one clutch, after mating once.
Table 1 The range of hatching synchrony phenotypes tested in simulations, expressed as the number of offspring that hatch in each time
period. Mothers produce clutches with the hatching pattern indicated, based on the allele they possess.
Time period
Allele value
Possible cannibalism events*
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
1
2
3
4
5
6
7
8
8
8
8
8
8
8
8
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
6
7
8
9
10
11
12
13
14
15
16
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Blank cells signify zeroes.
*Derived for a clutch size of 16 and the condition that offspring eat, at most, one egg. Alleles closer to 16 allow maximal cannibalism at a wider
range of offspring cannibalism delay phenotypes.
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
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J. C. PERRY AND B. D. ROITBERG
For each generation, interactions within two hundred
clutches were simulated simultaneously and independently. When time ended (i.e. when no further hatching
or egg eating could occur within a clutch), successfully
hatched offspring had a probability of surviving starvation that was dependent on number of eggs consumed
(0 or 1). From the survivors, 200 pairs of individuals were
randomly selected as parents of the next generation.
Thus, fitness was assigned indirectly: successful alleles
made more copies of themselves and were proportionally
more represented in the pool from which reproducing
individuals were drawn.
The algorithm that we used, often referred to as a
genetic algorithm, introduced new alleles – from which
to search for optimal strategies – through mutation- and
crossover-like processes during reproduction. The chance
of mutation (i.e. changing a 1 to 0 or 0 to 1) was 1% at
each byte locus. When crossover occurred (in 10% of
offspring) the parental chromosomes were spliced at a
random location anywhere along the string. High rates
are used to quickly generate the variation from which
optimal solutions may be found (as in, e.g. Browning &
Colman, 2004). For some simulation sets, we conducted
replicates with mutation and crossover (MC) rates set to
zero to ensure that the introduction of new alleles did not
influence the results. By incorporating these two natural
selection-like processes – differential success of inherited
traits and the testing and re-testing of strategies through
the introduction of new alleles – the algorithm finds the
evolutionarily optimal phenotype for each behaviour
considered. Because genetic algorithms can quickly
search a large strategy set, they are a valuable technique
for complex co-evolutionary games (e.g. Forrest, 1993).
To initialize simulations, a population of 400 randomly
drawn strategies was created (i.e. the aforementioned
12-byte strings). For each parameter set examined, we
conducted five simulation runs with different random
number seeds. Simulations ran for 1000 generations; gene
values stabilized after approximately 100 generations.
Control simulations: frequency independence
In a set of control simulations, we tested that our model
reached the same conclusions as the frequency-independent model (outlined in the introduction) when the
assumptions were identical.
First, we tested the cannibalism lag time gene when
competition among cannibals was prevented, there was
no parent-offspring co-evolution and no happenstance
infertile eggs. To prevent the SR game, we randomly
paired offspring at the beginning of within-clutch interactions. The first-hatching offspring within each pair
could consume only the egg it was paired with; if the
paired egg was not consumed, no other offspring
was permitted to eat it. To prevent parent-offspring
co-evolution, we permitted only one gene to evolve per
simulation set. The other genes were fixed for one allele
value in all individuals, and mutation was prevented
within these genes. In these simulations, the cannibalism
lag time gene evolved, while trophic egg laying was
prevented and hatching was maximally asynchronous.
Thus, offspring could potentially consume viable siblings,
creating selection on the cannibalism lag time gene, with
the direction of selection pressure dependent on the RBC
value.
Next, we tested the two maternal genes when parentoffspring co-evolution was prevented and there were no
infertile eggs. In the second set of control simulations, we
allowed hatching synchrony to evolve with cannibalism
lag time fixed at minimal (creating selection on mothers
to manage cannibalism among their offspring) and
trophic egg laying prevented (constraining them to
respond with hatching synchrony alone). Finally, we
allowed the trophic egg gene to evolve with cannibalism
lag time fixed at minimal and hatching at completely
synchronous. In these simulations, mothers could not
prevent sibling cannibalism, but could facilitate egg
eating by laying trophic eggs.
After confirming that our simulations could generate
the frequency-independent predictions for optimal offspring and maternal behaviours, we conducted three
experiments (described below) that introduced game
interactions, parent-offspring co-evolution, and intensified competition. We compared the predicted evolutionarily stable mean phenotypes from these models to
those of the controls.
Experiment 1: a sibling rivalry game
To introduce SR, eggs were not paired as described above.
Any hatched offspring could consume any unhatched
egg. To ensure that the introduction of variability
through MC did not affect the results, we ran simulations
with MC rates set to 1 and 10%, respectively, or to 0%.
The response variable of interest was the optimal cannibalism lag time. We compared the optimal lag time from
these simulations to the first set of control simulations, in
which the competitive game among siblings was prevented. As in the first set of control simulations, both
maternal genes were fixed, with hatching at maximally
asynchronous and trophic egg laying prevented.
In further simulations, we permitted either the hatching synchrony or trophic egg laying genes to evolve with
the other genes fixed (as described for the second set of
control simulations) and with competitive interactions
among offspring. These simulations are used for comparison with experiment 2.
Experiment 2: parent-offspring co-evolution
Parent-offspring co-evolution was introduced by permitting all three genes to evolve at once. We tested whether
co-evolution affected the optimal maternal and offspring
phenotypes by comparing the results of these simulations
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
Competition increases sibling cannibalism
to those of experiment 1, in which a competitive game
among siblings was present but co-evolution was prevented.
We introduced happenstance infertile eggs (i.e. unavoidable infertility, in contrast to trophic eggs under a
mother’s genetic control) to intensify the competitive
game among siblings. Simulations were conducted in
which all clutches contain such eggs (2 per clutch of 16),
and in which SR and co-evolution were also present. We
tested the effect of infertile eggs on optimal maternal and
offspring traits, compared to the optimal phenotypes
from experiment 2. In these (and all) simulations,
offspring could consume infertile eggs after all viable
siblings hatched, if lag times were long enough.
Statistical analyses
We took the evolutionarily stable mean phenotypes to be
the mean allele value of each gene for the last 200
generations, averaged over all individuals in the parent
population and taken every 10th generation. Allele
values and phenotypes correspond: the cannibalism lag
time allele represents the average number of time units
that offspring wait before attempting to eat an egg; the
trophic egg allele equals the number of trophic eggs in a
clutch; and the hatching synchrony allele corresponds to
the hatching patterns in Table 1. To test for an effect of
treatment (in experiment 1, presence or absence of
competition among siblings; in experiment 2, presence or
absence of co-evolution; in experiment 3, presence or
absence of infertile eggs), we included the factors RBC,
treatment, and the RBC · treatment interaction in
A N O V A models using the program JMP 5.0. In experiment
1, the additional factor of ‘MC’ – prevented or allowed –
was included, along with two-way interactions (the
three-way interaction term was not significant and was
therefore dropped from the final model). The response
variables were the evolutionarily stable mean phenotypes for the responding genes (for experiment 1,
cannibalism lag time; for experiments 2 and 3, all three
genes). We used the Tukey–Kramer post hoc tests to test
for differences between groups. Least-squares means,
which account for variation in the response variable
caused by all other factors in the A N O V A model, are
presented.
Results
The results from control simulations, in which competition among potential cannibals was prevented, match the
frequency independent prediction. As expected from
eqn 1, when there was no competition among offspring,
the evolutionarily stable cannibalism lag time declined
sharply and significantly at RBC values above 50%
*
14
Cannibalism lag time
Experiment 3: happenstance infertile eggs
16
*
1527
*
12
10
8
6
4
2
0
0
25
30 40 44 50 60 75 90 100 125
Relative benefit of cannibalism (RBC)
Fig. 1 Optimal cannibalism lag time phenotype when there is
competition among siblings to cannibalize (open squares) or when
such competition is prevented (filled circles), for a range of values of
relative benefit from cannibalism (RBC; i.e. the per cent increase in
survival from eating one egg). A delay of 16 time units before
cannibalism permits all viable siblings to hatch, whereas a delay of
one time unit (the minimum) means that a potentially viable sibling
will be eaten. When a competitive game among offspring was
prevented, our simulated cannibals obeyed the 50% threshold for
sibling cannibalism predicted from a frequency-independent application of Hamilton’s Rule (see text, Eickwort, 1973; Pfennig, 1997).
When game interactions were introduced, sibling cannibalism
became optimal at lower RBC values. The optimal phenotype was
obtained from a population average over the last 200 generations of
each simulation, when gene values had stabilized; five replicates
were conducted for each combination of factor values. Least-squares
means are presented, which account for variation in optimal
cannibalism lag time caused by the other factors of the A N O V A model
presented in Table 2. Asterisks indicate significant differences among
means (P < 0.05), based on Tukey post hoc tests. For clarity, RBC
values are presented as categories.
(Fig. 1). The maternal genes of hatching synchrony and
trophic egg laying also show different trajectories below
and above the 100% RBC threshold (eqn 2) for mothers
to benefit from cannibalism among offspring. At
RBC < 100%, mothers limit cannibalism with synchronous hatching (Fig. 2b). When RBC > 100%, mothers
facilitate egg consumption with asynchronous hatching
(Fig. 2b) or trophic eggs (Fig. 2c).
Experiment 1: sibling rivalry
The addition of game interactions significantly decreased
the RBC threshold at which sibling cannibalism was
favoured (Table 2 and Fig. 1). With the addition of game
interactions, average cannibalism lag times decreased
(compared to control simulations) at 40 and 44% RBC –
before the 50% threshold predicted by the frequencyindependent analysis. Importantly, the interaction
between RBC and game interactions was significant
(Table 2): the effect of SR occurred only at 40–50% RBC
(Fig. 1). At RBC values above the 50% threshold,
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
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J. C. PERRY AND B. D. ROITBERG
cannibalism lag times were minimal with and without
game interactions, as predicted by both models.
Whether MC rates were set to zero or to positive values
(mentioned under ‘The Models’) did not affect the
evolutionary stable cannibalism lag time (Table 2). However, MC rates, in interaction with the factors RBC and
game interactions, affected the evolved cannibalism lag
time (Table 2). This occurred because, without MC, new
alleles were not reintroduced each generation; if a
(a)
16
Cannibalism lag time
d.f.
F Ratio
P
RBC
SR
RBC · SR
MC
RBC · MC
SR · MC
10
1
10
1
10
1
394.1
82.6
35.2
2.4
19.1
6.7
<0.0001
<0.0001
<0.0001
0.1207
<0.0001
0.0107
*
particular allele became fixed, it remained fixed for the
rest of the simulation.
12
10
Experiment 2: co-evolution vs. constraints on traits
8
*
6
4
2
0
25
50
75
90
100
125
(b)
16
*
14
Hatching asynchrony
Source
Whole model: F33,186 ¼ 138.7, P < 0.0001.
14
12
10
8
*
6
Whether maternal and offspring traits co-evolved, or
evolved independently while other traits were fixed,
significantly affected the evolutionarily stable behaviours
for both mothers and offspring (Fig. 2).
Co-evolution of parent and offspring traits caused a
decreased average cannibalism lag time, compared to the
result when only cannibalism delay evolved (Fig. 2a;
F1,56 ¼ 97.5, P < 0.0001). The decrease in lag time was
significantly different at 25 and 50% RBC only, though
lag time was always lower when co-evolution occurred
(Fig. 2a; RBC · co-evolution interaction: F6,56 ¼ 57.0,
P < 0.0001).
The effect of parent-offspring co-evolution on hatching
synchrony depended on the RBC value (Fig. 2b; effect of
co-evolution: F1,64 ¼ 18.9, P < 0.01; RBC · co-evolution
interaction: F7,64 ¼ 143.5, P < 0.0001). At 0% RBC,
4
2
0
25
50
75
90
100
110
(c)
150
*
8
*
Trophic egg laying
Table 2 The effect of the RBC (at levels 0–125%), sibling rivalry
(SR) (present or absent), and mutation and crossover (MC) (rates set
to 0 or 1 and 10%, respectively) on the average cannibalism delay
gene values derived from simulations.
6
*
4
2
0
0
25
50
75
90 100 110 125
Relative benefit of cannibalism (RBC)
150
Fig. 2 The effect parent-offspring co-evolution on optimal maternal
and offspring phenotypes that influence sibling cannibalism.
Co-evolution was permitted by allowing both parent and offspring
genes to evolve (open squares), or prevented by having each trait
evolve alone (filled circles) as described in the text. Of interest is the
change in optimal phenotype as the relative benefit of cannibalism
changes (RBC; see the caption for Fig. 1). Asterisks indicate significant
differences among means (P < 0.05) by Tukey post hoc tests. (a)
Optimal cannibalism lag time for offspring; longer delays indicate less
willingness to cannibalize viable siblings (see text). (b) Hatching
synchrony phenotypes are given in Table 1. Low values indicate more
synchronous hatching and, thus, an attempt to prevent cannibalism
among offspring. (c) Values for the trophic egg phenotype correspond
to the optimal number of trophic eggs produced in a clutch of 16. It
was never optimal to produce more than eight trophic eggs, because
offspring could consume one egg at most. The factor ‘co-evolution’
significantly affected optimal phenotypes for all three behaviours
(P < 0.01; see text). Optimal phenotypes were calculated as described
in the caption of Fig. 1. Least-squares means are presented, which
control for variation in optimal phenotypes caused by the RBC and the
RBC · co-evolution interaction.
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
Competition increases sibling cannibalism
hatching was, on average, less synchronous when
co-evolution with offspring occurred (Fig. 2b). A likely
explanation is that, when cannibalism lag times could
evolve, lag times quickly increased to avoid sibling
cannibalism at 0% RBC; hence mothers did not need to
prevent sibling cannibalism with synchronous hatching.
When RBC ¼ 150%, hatching was, on average, more
synchronous with co-evolution (Fig. 2b), indicating that
mothers did not attempt to facilitate as much sibling
cannibalism with co-evolution.
More trophic eggs were produced when the trophic
egg-laying gene evolved alone, compared to the
(a)
16
Cannibalism lag time
14
*
12
10
8
6
4
2
0
10
25
50
75
90
100 110 125 150
(b)
Hatching asynchrony
12
10
8
6
Experiment 3: nonevolved infertile eggs
When we strengthened the competitive game among
siblings by introducing infertile eggs, offspring became
more willing to risk cannibalizing viable siblings. The
average cannibalism lag time decreased significantly
(Fig. 3a; F1,80 ¼ 10.2, P ¼ 0.002), compared to results
from experiment 2 in which game interactions occurred
without infertile eggs. The difference was detectable at
10% RBC (Fig. 3a; RBC · infertile eggs interaction:
F9,80 ¼ 4.8, P < 0.0001). At RBC values above 50%, the
delay until cannibalism was minimal in the presence and
absence of infertile eggs.
Mothers produced more synchronously hatching clutches when infertile eggs were present (Fig. 3b; F1,80 ¼
6.8, P < 0.05). The difference in synchrony in the
presence and absence of infertile eggs was not detectable
at any RBC level (Fig. 3b), though the interaction term
was significant (RBC · infertile eggs interaction: F9,80 ¼
3.0, P < 0.01).
Unsurprizingly, fewer trophic eggs were produced in
the presence of infertile eggs (Fig. 3c; F1,80 ¼ 133.4,
P < 0.0001). The difference was detectable at RBC values
from 75 to 125% (Fig. 3c; RBC · infertile eggs interaction: F9,80 ¼ 5.6, P < 0.0001).
Our results indicate that games among family interactors
affect both the extent of selfishness expected among
siblings and parental attempts to facilitate or limit selfish
interactions among offspring. We have elaborated on the
4
0
10
25
50
75
90
100 110 125 150
6
*
Trophic egg laying
co-evolution simulations (F1,72 ¼ 37.1, P < 0.0001); the
difference was significant for RBC values of 125 and
150% (Fig. 2c; RBC · co-evolution interaction: F8,72 ¼
46.6, P < 0.0001). The opposite pattern occurred at 75%
RBC; then the trophic egg allele was higher when
co-evolution occurred.
Discussion
2
(c)
1529
4
*
*
*
*
2
0
0
10 25 50 75 90 100 110 125 150
Relative benefit of cannibalism (RBC)
Fig. 3 The effect of infertile eggs on optimal maternal and offspring
phenotypes related to sibling cannibalism, for a range of values of
the relative benefit of cannibalism (RBC; see text). Infertile eggs
were introduced to strengthen the competitive egg-eating game
among siblings; clutches had either no infertile eggs (filled circles) or
two per clutch of 16 (open squares). Asterisks indicate a significant
difference among means (P < 0.05) by Tukey post hoc tests. (a) In the
presence of infertile eggs, optimal cannibalism lag time decreased
even at low RBC values – that is, cannibals were more willing to
cannibalize potentially viable siblings. (b) Hatching was significantly
more synchronous in the presence of infertile eggs (P < 0.05; see
text), though this difference was not detectable at any given level of
RBC. (c) The optimal number of trophic eggs (for a clutch of 16
offspring) decreased when infertile eggs were present. Optimal
phenotypes were calculated as described in the caption of Fig. 1.
Least-squares means are presented, which control for the variation
in optimal phenotypes caused by factors other than ‘infertile eggs’.
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
1530
J. C. PERRY AND B. D. ROITBERG
usual predictions of optimal cannibalism behaviour
towards siblings, which are derived for the frequencyindependent case. Below, we discuss our predicted
optimal behaviours in parents and offspring (especially
where these differ from frequency-independent predictions) and, where possible, compare our qualitative
predictions with natural systems. The results of the
model are directly applicable to species in which offspring
interact within a confined physical space (a nursery, sensu
Mock & Forbes, 1995) for some small portion of their
lives – small because extended interactions likely involve
resource-based competition and, thus, an additional
selection pressure favouring siblicide. Our results apply
when clutch size exceeds two, and when there is the
possibility of competition among siblings for cannibalism
opportunities (i.e. at least two offspring are capable of
eating a third); when these conditions do not exist, the
frequency-independent prediction likely applies. Furthermore, our results may be extended to any selfish acts
among family members in which the benefit of selfishness accrues to one individual only, such that individuals
may compete to reap that benefit.
Previous predictions of the threshold for benefit from
cannibalizing a sibling (Eickwort, 1973; Crespi, 1992;
Dong & Polis, 1992; Pfennig, 1997) considered the
frequency-independent case. Incorporating game interactions among siblings – a competition for the resource of
consumable eggs – decreases the predicted benefit
threshold (Fig. 1). Sibling games appear to drive the
evolution of higher cannibalistic tendency than would
otherwise be optimal.
A second evolutionary game – parent-offspring conflict
over sibling cannibalism – also affected optimal maternal
and offspring behaviours. Cannibalism lag time was
reduced in simulations in which parental and offspring
behaviours co-evolved (Fig. 2a), compared to simulations in which maternal traits were constrained (i.e.
mothers could not prevent cannibalism with synchronous hatching, nor facilitate egg eating with asynchronous
hatching and trophic eggs). A possible explanation is that
co-evolution intensified the SR game. When maternal
genes were permitted to evolve along with cannibalism
lag time, hatching became synchronous at RBC values
less than 50% – perhaps strengthening competition for
rare cannibalism opportunities. In effect, maternal
attempts to limit cannibalism among offspring may
intensify their cannibalistic tendencies. An alternative
explanation is that, with the reduced opportunity for cannibalism due to synchronous hatching (at RBC < 50%),
selection against sibling-eating individuals may have
weakened. However, this second hypothesis is not
supported by the results: in the co-evolution simulations
of experiment 2, at RBC values of 25 and 50%,
cannibalism lag times decreased from the random
initialization average of 7.5 time units. This pattern
indicates strong directional selection, rather than weakened selection and drift.
The effect of co-evolution on hatching synchrony and
trophic egg production – decreasing asynchrony and
trophic egg production at RBC values exceeding 100%
(Fig. 3b, c) – is easily understood. At RBC > 100%, when
both maternal genes were permitted to evolve, mothers
used a combination of asynchronous hatching and
trophic eggs to facilitate egg eating among offspring.
More particularly to our next argument, mothers did not
use hatching asynchrony alone. It may seem counterintuitive that a mother’s best option is to produce a
trophic egg (e.g. Dixon, 2000), when instead, she could
increase hatch asynchrony so that eggs may continue
development if they escape cannibalism. In our simulations, it was not, in fact, better to increase hatching
asynchrony than to produce trophic eggs. We suggest
that mothers produce trophic eggs in order to ensure that
egg eating occurs. If hatching asynchrony alone is used,
there is some chance that delayed-hatch eggs will hatch
first.
The control and experiment 1 simulations – in which
some traits were prevented from evolving – may be
similar to natural systems in which offspring or parental
traits are constrained. For example, in predatory insects,
offspring may experience strong selection for early
predatory ability. Genetic correlations may prevent
selection from separating the behaviours of attacking
prey and cannibalizing siblings soon after emergence.
Furthermore, mothers may be unable to make hatching
perfectly synchronous, if egg formation and deposition
are not perfectly precise processes. The presence of
constraints gives control of the occurrence of sibling
cannibalism to the unconstrained party. Thus, in natural
systems, the observation of sibling cannibalism does not
imply that parents experience a net fitness benefit from
cannibalism; they may simply be unable to prevent it.
Empirical predictions
The results allow several predictions about patterns of
sibling cannibalism in natural systems. First, a key
prediction from the model is that, when there is
competition among cannibals for victims, sibling cannibalism should occur when the RBC is less than 50%; the
precise threshold favouring sibling cannibalism should
depend on the strength of competition among cannibals.
In contrast, the frequency independent model (outlined
in the introduction) predicts sibling cannibalism only at
RBC > r, the coefficient of relatedness. Testing this
prediction requires quantitative estimates of the increase
in survival from eating a sibling, relative to survival
probability under normal food conditions without cannibalism. Most useful would be systems in which the
RBC < relatedness among siblings. However, most
observations of sibling cannibalism are qualitative (e.g.
Byrne, 1996; Frechette & Coderre, 2000; Rienks, 2000;
Margalida et al., 2004). We know of six quantitative
studies of sibling cannibalism (Table 3). Of these, RBC
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
Competition increases sibling cannibalism
1531
Table 3 Quantitative studies of sibling cannibalism. The RBC refers to the increase in survival that cannibals experienced, relative to survival
without cannibalism in the food conditions indicated.
Species
Coccinellidae
H. axyridis
H. axyridis
H. axyridis
C. maculata lengi
S. bisellata
Menochilus sexmaculatus
Coleophora inaequalis
Coccinella repanda
Other taxa
Subsocial burrower bug Admerus triguttulus
Land snails Arianta arbustorum
RBC (%)
Comparison
Source
16
226
114
25
37
70
84
135
Noncannibals at high aphid (prey) density
Noncannibals at low aphid (prey) density
Unfed larvae with access to water
Unfed larvae without water
Unfed larvae without water
Unfed larvae without water
Unfed larvae without water
Unfed larvae without water
Osawa (1992)
Osawa (1992)
Kawai (1978)
Pienkowski (1965)
Ng (1986)
Ng (1986)
Ng (1986)
Ng (1986)
Unfed larvae
Noncannibals given access to same vegetable diet as cannibals
Kudo & Nakahira (2004)
Baur (1990)
75
75
values less than 50% were reported for three species.
For the ladybird beetle Harmonia axyridis, RBC depended
strongly on local food conditions (Osawa, 1992); it is not
possible to estimate an overall RBC without knowledge
of how frequently individuals encounter different food
environments. Ng (1986) reports RBC values of less than
50% for two other ladybirds, Coleomegilla maculata lengi
(25%) and Spilocaria bisellata (37%; Table 3), in which
sibling cannibalism is common. Average relatedness in
these species is not known; the possibility that offspring
are less than full siblings cannot be excluded. However,
this study measured the benefit of cannibalism relative
to ‘no food’ conditions, and thus overestimates the RBC
experience in natural conditions. Given that offspring
within a clutch have relatedness of ‡0.25, cannibal
C. maculata lengi apparently experience an RBC value
less than relatedness among siblings. Hence, the pattern
is consistent with the hypothesis that game interactions
drive the evolution of increased tendency to cannibalize
siblings, but not with the frequency-independent hypothesis that offspring should cannibalize full siblings only
if RBC > 50%. Additional studies quantifying RBC
values compared to natural conditions would be of
great interest in light of this prediction. Studies of
related taxa in which some species exhibited sibling
cannibalism and others did not (e.g. coccinellids) would
be especially useful, if noncannibal species could be
induced to consume siblings so that the benefit of doing
so may be measured.
A second and related prediction is that sibling cannibalism should be more common in species with game
interactions among siblings, compared to species in
which there is no game. Sibling cannibalism should,
then, be more common in species that produce clutches
of two or more offspring, compared to species in which
clutch size is two. The prediction is difficult to test with a
particular taxonomic group. For example, few insect taxa
produce clutches of only two eggs. While two-egg
clutches are more common in birds, bird nestlings
experience strong resource competition, and cannibalism
in birds is probably driven by the need to eliminate a
competitor rather than the value of siblings as meals
(Fitzgerald & Whoriskey, 1992).
In our model, the presence of infertile eggs strengthened the competitive game among siblings, further
lowering the RBC threshold for sibling cannibalism
(Fig. 3a). In the model, cannibal offspring had the option
of waiting until viable siblings had hatched before
consuming infertile eggs; instead, cannibals risked eating
viable siblings to gain access to infertile eggs first. Thus, a
third prediction is that sibling cannibalism should occur
more frequently in species that produce infertile eggs, if,
as assumed in our model, offspring cannot distinguish
between viable and infertile eggs. This prediction is
complicated by the possibility that infertile egg production is under maternal control – i.e. that the infertile eggs
are trophic eggs. Trophic eggs are expected only when
RBC > 100%, that is, when sibling cannibalism is
favoured even without game interactions. Thus, in
testing this prediction, it will be important to distinguish
infertile eggs produced by constraint from infertile eggs
that serve a trophic function. The presence of infertile
eggs – common in many taxa – has implications for
sibling cannibalism because it strengthens competition
among siblings.
Conclusion
Because sibling cannibalism is found in many diverse
taxa, it is important to understand the selective forces
driving its evolution. Previous understanding of sibling
cannibalism is summarized by Mock & Parker (1997),
p. 6): ‘when a sib is more valuable as food than as a gene
bearer, it should be consumed’. We may now add to this
condition, ‘it should also be consumed if it will be
consumed by another sibling anyway’. Mock & Parker
(1997) highlighted the potential importance, and deficit
of study, of evolutionary games within family units for
J. EVOL. BIOL. 18 (2005) 1523–1533 ª 2005 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
1532
J. C. PERRY AND B. D. ROITBERG
the evolution of selfishness among siblings. Our results
demonstrate that game interactions can indeed contribute new insights to predictions of optimal behaviour for
family members. Moreover, considering such interactions
in a framework of negotiated change leads to new insights
compared to a static optimality approach (McNamara
et al., 1999). There is clearly scope for further work in
modelling how other factors – for example, offspring
potential to consume more than one egg, or to discriminate between viable and infertile eggs – change predictions for optimal behaviour of family members towards
each other.
Acknowledgments
Appreciative thanks are due to J. M. Biernaskie,
F. Breden, K. M. Campbell, B. J. Crespi, L. S. Forbes,
D. B. Lank, B. O. Ma, and an anonymous reviewer for
helpful criticism that greatly improved this manuscript.
This study was supported by grants from the Natural
Sciences and Engineering Research Council of Canada to
JCP and BDR and from the Department of Biological
Sciences at Simon Fraser University to JCP.
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Received 17 February 2005; revised 15 March 2005; accepted 18 March
2005
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