Original Paper
The evolution of social play by learning
to cooperate
Adaptive Behavior
1–14
Ó The Author(s) 2015
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DOI: 10.1177/1059712315608243
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Sabine Durand1 and Jeffrey C Schank1,2
Abstract
Social play is common in mammals but its adaptive significance is not well understood. A commonly held hypothesis is
that social play allows juveniles to learn skills and rules for cooperation as adults. On this view, the adaptive benefit of
social play derives from the benefits of cooperation as adults. However, cooperation is only beneficial if it is used in
populations of predominantly cooperators; otherwise, it is a costly strategy. We investigated the latter problem by modeling the link between social play and subsequent adult cooperation using an agent-based model. In our model, agents
had a play gene with allelic social play states (i.e., play or not play). Juveniles with a play gene learned to cooperate by successfully engaging in social play with another juvenile agent with a play gene. As adults, agents played the stag hunt game
with other adults to obtain resources for reproduction. Those that learned to cooperate by playing as juveniles cooperated in the stag hunt game. When agents aggregated into small groups, we found that social play could evolve by facilitating the learning of cooperation. Our theoretical results also show that social play is a novel mechanism for the indirect
evolution of cooperation.
Keywords
Evolution of cooperation, social play, learning to cooperate, evolutionary simulations, fairness, population structure
1. Introduction
Social play is common in mammals (e.g., Bekoff, 1974;
Gomendio, 1988; Hayaki, 1985; Mackey, Makecha, &
Kuczaj, 2014; Thor & Holloway, 1985; Vidya &
Sukumar, 2005; Watson, 1998) and comes in many
forms such as chasing, wrestling and play-fighting, and
in some species more complex forms of social play such
as sociodramatic play in human children (Graham &
Burghardt, 2010). From an evolutionary perspective,
social play has potential costs such as increased exposure
of young animals engaged in social play to predators,
injuries, and energy costs (Graham & Burghardt, 2010).
There are several hypotheses regarding the adaptive benefits of social play, including play as practice for adult
behaviors (e.g., fighting or mating) and play as a way to
develop motor skills (Graham & Burghardt, 2010).
Evidence both for and against these hypotheses has been
found but there are no definitive explanations for the
adaptive benefits of play (Caro, 1980; Nunes et al., 2004;
Sharpe, 2005). It is likely that play serves many functions. In this model, we focus on one functional hypothesis: social play as a means by which juveniles learn the
skills and rules needed for cooperation in adulthood.
Social play theorists have hypothesized that social
play gains delayed adaptive benefit by facilitating the
learning of adult social skills such as cooperation by
practicing the skills required to socially interact and
cooperate as adults (Bekoff, 2001; Bekoff & Pierce,
2009; Fagen, 1981; Lee, 1983; Pellis & Pellis, 2007;
Sussman, Garber, & Cheverud, 2005). During social
play, individuals may learn rules of conduct and gain
an understanding of what is and is not acceptable to
others—skills that may later be applied in cooperative
contexts (Dugatkin & Bekoff, 2003). Indeed, cooperative play has evolved in a number of species (Bekoff,
1995; Bekoff & Allen, 1998; Fagen, 1981; Power, 2000).
For example, animals may learn how roughly they can
interact with others and how to solve conflicts during
play (Dugatkin & Bekoff, 2003). For social play to be
adaptive, the delayed benefits of learning to play must
outweigh the costs of social play. However, cooperating in a population of non-cooperators is costly. If the
1
Department of Psychology, University of California, Davis, California,
USA
2
Animal Behavior Graduate Group, University of California, Davis,
California, USA
Corresponding author:
Jeffrey C Schank, Department of Psychology, University of California,
One Shields Ave., Davis, CA 47405, USA
Email: [email protected]
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Adaptive Behavior
benefits of adult cooperation are to explain the evolution of social play, then social play must evolve in a
way that facilitates the success of adult cooperation.
Here, we focus on how an evolutionary positive feedback loop can emerge in which the evolution of social
play facilitates the success of adult cooperation and the
success of adult cooperation feeds back to facilitate the
evolution of social play.
The potential fitness costs of social play are clear.
For example, Harcourt (1991) found that South
American fur seal pups only spend about 6% of their
time playing, yet 85% of seal pups that were taken by
predatory sea lions were playing at the time they were
captured. When engaged in play behavior, marmots
have been found to take longer to respond to predators, resulting in greater predation risk (Blumstein,
1998). Injuries are not uncommon during play. Bighorn
sheep incur injuries by impaling themselves on cactus
spines and elephants often get trapped in mud during
play (Berger, 1980; Douglas-Hamilton & DouglasHamilton, 1975). With regard to energy costs, Miller
and Byers (1991) have found that playing in fawns
consumes approximately 20% of their daily energy
expenditure in excess of resting metabolic rate and
growth. Domestic kittens were estimated to spend
approximately 4–9% of their total daily energy expenditure, excluding growth, on play (Martin, 1984).
Furthermore, play behavior can impede the acquisition
of food. Caro (1995) found that playing in cheetah cubs
significantly decreased maternal hunting success, as the
cubs’ play alerts prey of their mother’s presence. If
social play is beneficial, its benefits must outweigh costs
due to exposure of young animals to predators, injuries, and energy expenditure.
As the costs of social play are suffered early in development, the benefits delayed until adulthood must be
substantial. But even if the benefits of adult cooperation are substantial, they are only reaped if other adults
successfully cooperate. If an individual attempts to
cooperate in a population of non-cooperators, there is
a net cost to cooperation rather than a benefit (Axelrod
& Hamilton, 1981). Thus, contrary to the adaptive benefits of cooperation hypothesis for the evolution of
social play, it appears that cooperation is unlikely to be
beneficial unless a population already has evolved
cooperation.
There is some evidence suggesting that juvenile animals learn to cooperate and behave fairly through
social play (Bekoff, 2001). During social play, juveniles
must learn social behaviors and rules that are acceptable to others, or risk being excluded by other juveniles
from play (Bekoff, 1974). In canids, pups avoid playing
with individuals that are too rough (Brosnan &
de Waal, 2012). As a result, juveniles often engage in
fair play behaviors during social play (Dugatkin &
Bekoff, 2003). Individuals will sometimes exhibit selfhandicapping behavior, in which they voluntarily put
themselves in vulnerable positions, giving their play
partners the advantage (Bauer & Smuts, 2007). For
example, red-necked wallabies modify their play behavior based on their playmate’s age, using gentler play
behavior with their younger, less experienced, playmates (Watson & Croft, 1996). Many rodent and primate species have been observed to forgo the inclusion
of a defensive maneuver in their attacks when playfighting, unlike in serious fight scenarios, allowing their
play partner an opportunity to counterattack (Pellis,
Pellis, & Reinhart, 2010). Play partners that are on the
receiving end of the attack may also be slower on the
defense during play fights, allowing their play partner
to take the advantage (Pellis et al., 2010). The rules of
conduct and understanding of fairness and cooperation
learned during social play may carry over to future
social interactions, such as cooperative interactions, in
adulthood (Bekoff, 2001).
Several studies have provided evidence suggesting
social play experiences in early development are important for establishing competent social skills in adulthood (Einon et al., 1978; Hol, Van den Berg, Van Ree,
& Spruijt, 1999; Pellegrini, 1992; Pellis & Pellis, 2007).
Rat pups deprived of social play were found to display
significantly reduced social behavior as adults (Hol
et al., 1999; Van den Berg et al., 1999). Social play
deprivation in rats is also associated with difficulty
coordinating movements with a partner in adult social
interactions and a tendency to exhibit hyperdefensiveness in response to an approaching rat (Pellis
& Pellis, 2007; Pellis, Field, & Whishaw, 1999).
However, socially isolated rats that were permitted
short daily play sessions exhibited relatively normal
social behaviors in adulthood (Einon et al., 1978).
Though little research has been done in humans,
Pellegrini (1992) found that children who engaged in
more rough and tumble play tended to exhibit better
social problem solving abilities. Social play has been
found to be relevant in the development of a variety of
social skills—including initiating social interactions,
coordination with a partner, and the ability to act
appropriately around peers—that are likely necessary
for adult cooperation (Pellegrini, Dupuis, & Smith,
2007). Yet, there is also evidence against the hypothesis
of social play as learning for adult cooperation. For
example, grizzly bears and orangutans engage in social
play extensively during their juvenile stage, but are solitary animals that typically do not cooperate with one
another in adulthood (Burghardt, 1982). Baldwin and
Baldwin (1974) found that squirrel monkeys can
develop normal social organization and social behavior
in the absence of social play, though individuals that
engaged in more social play were found to have
improved social skills.
Empirical results suggest that juveniles can learn to
cooperate and behave fairly by engaging in social play
and that what they learn can facilitate adult cooperative
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Durand and Schank
3
behavior. There are, however, theoretical problems with
the cooperation hypothesis. If social play is introduced
in a population of non-cooperators at low frequency
and social play derives its benefits from social cooperation, it would appear theoretically impossible for social
play to evolve. Moreover, if social play is introduced at
low frequency into a population, how do juveniles find
other juveniles that will engage them in social play so
that they learn to cooperate as adults? The theoretical
problem of explaining social play via adaptive benefits
of adult cooperation appears to be a vicious circle: there
must be sufficiently many juveniles with heritable disposition for social play, but if cooperation as adults is not
favored at low frequency, the number of individuals
with a disposition towards social play cannot increase.
To break this circle, we show that population structure
together with social play can result in small spatial clusters of agents with high frequencies of juveniles that can
engage in social play and cooperate as adults. To investigate this possible explanation, we developed an agentbased model of the evolution of social play that links
social play to cooperation via social learning during
development.
2. Model
Our agent-based modeling approach emphasizes modeling generic properties of organisms relevant to the theoretical problem of interest (Schank, Smaldino, & Miller,
2015), which more broadly can be characterized as synthetic ethology (MacLennan & Burghardt, 1993). From
this perspective, we begin by supposing that agents go
through two developmental stages: a juvenile stage and
an adult stage. During the juvenile stage, juveniles that
have a genetic disposition for social play can engage in
play with one another and learn to cooperate via bouts
of mutual social play. As adults, agents with the necessary social play experience cooperate with other adults
in obtaining resources. Suppose that (1) at both juvenile
and adult stages, agents attempt to aggregate with others of the same developmental stage, (2) when adult
agents achieve sufficient resources, they can reproduce,
and (3) dispersal of their offspring is limited. These conditions will produce structured populations of groups
of agents. Because it takes at least two agents to engage
in social play as juveniles and thereby learn to cooperate, cooperators will also likely be in spatiotemporal
proximity with each other as adults. In such a scenario,
small groups of two or more cooperators may occasionally appear (via learning to cooperate by social play)
and spread throughout the population.
2.1 Adult cooperation
Consider a population of adult agents that play the stag
hunt game (SH) for resources. The SH is based on a
scenario first described by Jean-Jacques Rousseau, in
which two individuals go hunting (Rousseau, 1992).
They can each hunt a small hare on their own for a
small meal, but if they would like a stag for a larger
meal, the two individuals must join forces. If both players cooperate and hunt stag, both gain the highest payoff possible, but if one defects and hunts a hare instead,
the other is left with nothing for its efforts. The SH is a
type coordination game in which agents must coordinate their behavior to achieve a cooperative gain and is
most appropriate for the initial evolution of cooperation in a population (Skyrms, 2004).
More formally, we assume non-cooperators each
receive a benefit b each time they play minus a cost c.
By cooperating, their joint gain is increased by a factor
x. If two cooperators (C) play, they split their cooperative gains, xb, and each receive xb/22c units of
resource. If two non-cooperators (N) play, they do not
cooperate and each gains b2c, which is the quantity of
resources they can gain on their own. If a cooperator
and non-cooperator play, the non-cooperator gains
b2c because it does not cooperate, but the cooperator
receives only –c, which is no resource minus the cost.
When x.2, two evolutionarily stable strategies
(ESS) exist for the SH. This implies that there exists a
fixed point, p, below which the frequency of cooperators evolves to p=0 and above which the frequency of
cooperators evolves to p=1. To find this fixed point we
let p represent the frequency of cooperators in a population and then write a differential equation specifying
how p evolves over time
dp
= p(E(C) E(N))
dt
ð1Þ
where E(C) is the expected payoff for cooperators and
E(N) is the expected payoff for non-cooperators. The
expected payoffs are given by Equations 2 and 3.
xb
c ð1 pÞc
E ðC Þ = p
2
ð2Þ
EðN Þ = pðb cÞ + ð1 pÞðb cÞ = b c
ð3Þ
By substituting Equations 2 and 3 into Equation 1 we
obtain
dp
xb
= pð1 pÞ p b
dt
2
Solving for
ð4Þ
dp
= 0 yields the fixed points p=0, p=1,
dt
2
if x.2.
x
For our simulations, we set b=1, c=0, and x=4
with an unstable fixed point of p=1/2. If the proportion of cooperators, p, is less than 0.5 (i.e., in the ESS
zone for non-cooperation), the frequency of cooperators will decrease to the stable fixed point p=0. If the
proportion of cooperators, p, is greater than 0.5 (i.e., in
and p =
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Adaptive Behavior
the ESS zone for cooperation), the frequency of cooperators will increase to the stable fixed point p=1.
If agents can play any other agent in the population
with equal probability, cooperators cannot invade a
population of non-cooperators when introduced at low
frequencies. However, consider a population of agents
that on each round of play randomly play another adult
agent from an adjacent cell rather than an agent from
the population as a whole. Agents in this population
play other agents in their spatial proximity. Thus, even
when cooperators are introduced at low frequencies in
a population, random drift and mutation can result in
spatial regions that have higher frequencies of cooperators than others. In such regions, cooperators do relatively better.
2.2 Space and movement
learn to cooperate. The more they engage in social
play, the more likely it is that they cooperate as adults.
The adult stage lasts Li2D.
2.4 Learning to cooperate
When juvenile agents mature into adults, their probability of cooperating in the SH depends on the cooperation they have learned by repeatedly engaging in social
play (Figure 1). Learning to cooperate by engaging in
social play was modeled using a version of RescorlaWagner (1972) learning model given by Equations 5
VCP ðt = 0Þ = 0
VCP ðtÞ + a½1 VCP ðtÞ if social play
VCP ðt + 1Þ =
if no social play
VCP ðtÞ
ð5Þ
Agents are located in an X 3 Y square grid of cells with
periodic boundaries. Each agent occupies only one cell;
no two agents can occupy the same cell. On each round
of play, agents search nearby cells (with radius SR
around the agent) for other agents of the same developmental stage (adult or juvenile). An agent remains in its
current cell if it is next to another of the same developmental stage. If an agent is not next to another agent, it
will move to a randomly selected empty cell next to
another agent of the same developmental stage that is
within it search radius, SR. If there are no other agents
at the same developmental stage within its search
radius, the agent will move one cell using a zigzag random walk (Smaldino & Schank, 2012).
2.3 Agents
An agent has a lifespan, Li, consisting of social play followed by adult play with the SH. The lifespan of each
agent is determined by generating a number from a
random normal distribution with mean L, standard
deviation SDL, and rounding it to the nearest integer.
The standard deviation, SDL, was selected to approximate a survival curve from the Gompertz standard
model commonly used to represent age-dependent mortality rates in a wide variety of species (Easton &
Hirsch, 2008). When adult agents reach the end of their
lifespan, they die, as do their juvenile offspring, as we
assume that juvenile development depends on parental
resources. Adult agents may die earlier if they run out
of resources.
During the lifespan of an agent, the juvenile stage
lasts exactly D=50 rounds. During the juvenile stage,
agents receive a proportion, pc, of their parent i’s
resources, Rit on each round of play. They also have
the opportunity to engage in social play with other
juvenile agents, but they can only engage in social play
if both have at least one allele for social play. If two
juvenile agents successfully engage in social play, they
where a is learning rate and VCP(t) is the strength of
association (1<VCP(t)0) between cooperation as an
adult and bouts of social play. VCP(t) can only increase
when two agents engage in social play and the probability, pc, of an agent cooperating as an adult is the value
of VCP(t=D) at the end of the juvenile developmental
period.
2.5 Reproduction and social play
At any time during the adult stage, if an adult agent
acquires sufficient resources to reach or surpass the
reproductive threshold, RT, it attempts to reproduce a
juvenile agent in an empty cell next to it. Agents can
only reproduce if the current population size is less
than the maximum population size, Nmax. If an agent
successfully reproduces, it provides its offspring with a
proportion, pI, of its resources (i.e., initial parental
investment), and then subsequently provides a percentage, pc, of its resources to all of its juvenile offspring
during each round of play until each offspring matures
to adulthood.
We investigate both asexual and sexual reproduction. For asexually reproducing agents, offspring
inherit a social play gene with two allelic states (i.e.,
play or not play). If the social play gene is in the play
state, then a juvenile agent attempts to engage in social
play with other juvenile agents that it is next to. If the
social play gene is in the not play state, then it does not
attempt to engage in social play. At the time of reproduction, mutations occur at rate r and a mutation flips
the social play gene into the opposite allelic social play
state of its parent.
Sexually reproducing agents are hermaphroditic and
an agent can assume either a female or male role (but
not both) during each pairwise reproductive episode.
Hermaphroditic agents are used to investigate the role
of sexual reproduction on the evolution of social play
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Durand and Schank
5
and cooperation while at the same time maintaining
populations with effective population sizes similar to
asexually reproducing agents. Upon acquiring sufficient
resources to reproduce, a randomly selected adult agent
assumes a female role and searches for an available
mate (another adult agent nearby that has also satisfied
the minimum resource requirement for reproduction)
to assume the male role. If a mate is successfully found,
each agent contributes one allele. Each allele can
mutate at rate r, which flips the allele into the opposite
social play state of its parent. Thus, when a juvenile offspring is produced, it inherits one social play allele from
each parent; each allele has one of two states (i.e., play
or not play).
For sexual reproduction, we modeled three types of
allelic interactions: dominant, recessive, and additive.
For the dominant case, if a juvenile has at least one
social play allele, it will attempt to engage in social play
with other juveniles and can learn to cooperate. In the
recessive case, a juvenile must have both social play
genes to engage in social play and learn to cooperate.
In the additive case, juvenile agents with one social play
allele engage in social play with probability 0.5, whereas
juvenile agents with both social play alleles engage in
social play with probability 1.0.
For sexually reproducing agents, parental investment
can be either uniparental (i.e., only the agent assuming
the female role contributes resources to the offspring) or
biparental (i.e., both parents contribute resources to the
offspring). For the uniparental case, the agent assuming
the female role provides its offspring with a proportion,
pI, of its resources (i.e., initial parental investment), and
then provides a percentage, pc, of its resources to the
juvenile offspring on each time step. In the biparental
care case, both reproducing agents provide juvenile offspring with a proportion, pI/2, of their resources followed by a percentage, pc/2, of their resources to their
juvenile offspring on each time step.
2.6 Events
On each time step of an agent’s life span, it is either a
juvenile or an adult (Figure 2). If it is a juvenile, it dies
if it has no parent(s) to provide resources. If it is old
enough, it matures into an adult. If it has the play allele,
it next searches for another juvenile agent with which to
play; otherwise, it does nothing. If it searches and finds
another agent that has not played, it attempts to engage
in social play. If the other agent has the social play
allele, they both engage in social play; otherwise, they
do not. If it engaged in social play, it incrementally
learns to cooperate as an adult.
If an agent is an adult, it dies if it has no resources.
Otherwise, it attempts to engage another agent next to
it that has not yet played the SH that time step. The
likelihood that both agents cooperate is a product of
how much cooperation each agent learned as a juvenile.
Figure 1. An illustration of juvenile learning rates during social
play. During the juvenile period, agents with play genes engage in
social play and depending on their learning rate, α, they increase
their probability of cooperating as adults as a function of the
number of bouts of social play.
Whether or not an agent plays the SH, it can reproduce
if it has sufficient resources. If it has sufficient
resources, the population size is not at maximum Nmax,
and there is an empty cell next to it, it can reproduce
either asexually or sexually.
3. Evolutionary simulations
The simulation model was written in Java using
MASON, a multi-agent simulation package (Luke
et al., 2005). Mason’s simulation engine supports asynchronous updating of agents, where the order of agent
updating is randomized for each time step (see Table 1
for all fixed parameter values).
3.1 Initial conditions
All simulations began with a population of adult agents
that was half the maximum population size. Agents
were placed randomly on a 50 3 50 2D space with periodic boundaries. The starting age of each agent was
determined as described above. The starting resources
of each agent were determined by generating a number
from a random normal distribution with mean SR, standard deviation SDSR, and rounding to the nearest integer (see Table 3 for initial condition values).
3.2 Experimental conditions
We systematically simulated two reproductive conditions: sexual and asexual reproduction. Within the sexual reproduction conditions, we systematically varied
the rate of learning, maximum population size (or density, holding grid size constant), mode of inheritance
(dominant, additive, and recessive), and type of parental care (biparental or uniparental) for a total of
5 3 3 3 3 3 2=90 conditions (Table 2). For the asexual
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6
Adaptive Behavior
Figure 2. Flowcharts depicting adult-agent (a) and juvenile-agent (b) decision rules for each time step. At the beginning of a time
step, all agents increase one unit in age. When adult agents reach the end of their lifespan or have no resources, they die. When
juvenile agents reach the end of their juvenile period, they become adults. If a juvenile agent’s parent(s) dies before it becomes an
adult, the juvenile agent dies.
Table 1. Fixed parameters.
Description
Parameter
Values and/or descriptions
Payoffs
Base life span
Standard deviation
Reproduction resource threshold
Resource cap
Parental investment
C
T, D
S
L
SDL
RT
Rc
pI
Parental care
pc
Mutation rate
Grid size
Aggregation threshold
Search radius
r
X×Y
AT
SR
Juvenile development
D
2 – Cooperator payoff
1 – Temptation and defector payoffs
0 – Sucker’s payoff
250 – Time steps
30 – The standard deviation for L
100 – The resource level required for an agent to reproduce.
300 – Maximum resources an agent can have
0.1 – The percentage of parent resources initially invested when producing an
offspring
0.01– The percentage of parent resources a juvenile offspring receives each
time step
0.01
50 × 50 – Spatial dimensions in cells
1 – The minimum number of agents an agent to contact attempts to contact
2 – The distance in cells, an agent searches for other agents when attempting
to aggregate
50 – Rounds of play
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Durand and Schank
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Table 2. Parameters sweeps.
Description
Parameter
Values
Learning rate
Population size
Reproduction
For sexual
reproductive cases:
Allelic interaction
α
Nmax
0.04, 0.06, 0.08, 0.1, 0.2
250, 500, 1000
Sexual, asexual
Recessive, additive,
dominant
Biparental, uniparental
Parental care type
Table 3. Initial conditions.
Description
Parameter
Values
Average starting age
Standard deviation for starting age
Average starting resources
Standard deviation for starting resources
Initial population size
SA
SDSA
SR
SDSR
N
150
50
75
30
pmax/2
reproductive conditions, we systematically varied the
rate of learning and maximum population size (or
density–holding grid size constant) for a total of
5 3 3=15 conditions (Table 2). For each condition, we
ran 100 runs of 100,000 time steps each.
3.3 Population structure control conditions
Because small groups of agents formed over time due
to active aggregation and limited dispersal, group selection emerged in these simulations (Figure 3). To eliminate the effects of group selection; a second set of
control simulations was also conducted. These simulations were identical to the simulation conditions in the
previous section except that on each round of play, all
agents of the same developmental stage randomly
swapped locations with each other. This eliminated
spatial associations among agents (Figure 3). These
simulations allowed us to assess the role of population
structure in the evolution of social play.
Figure 3. An illustration of initial conditions (a, b) and agent
swapping (c, d). Initially, agents are non-cooperators (solid red),
lack play alleles, and are randomly distributed in unique locations
in space (a). Early in a simulation, agents aggregate into groups of
varying sizes (adults are solid and juveniles are open circles) and
a few juvenile agents have the social-play gene by mutation (blue
circle; b). Later in the simulation, small clusters of cooperators
(shaded blue according to their probability of cooperating) of
varying sizes with cooperators, non-cooperators, and offspring
with and without the play gene emerge (c). To illustrate location
swapping, on the next round, the agents in (c) randomly swap
locations with agents in their developmental class (d).
the recessive case, if both alleles are cooperative, agents
cooperate with probability 1.0; otherwise, they cooperate with probability 0.0. For the additive case, agents
with one cooperative allele cooperate with probability
of 0.5, agents with two cooperative alleles cooperate
with probability 1.0, and agents with no cooperative
alleles cooperate with probability 0.0. For the dominant
case, agents with at least one allele always cooperate
with probability 1.0; otherwise, they cooperate with
probability 0.0.
4. Results and discussion
3.4 Cooperation control conditions
4.1 Social play population structure
In a second set of control conditions, we systematically
investigated the evolution of cooperation without social
play. For both sexual and asexual reproduction, cooperation alleles were inherited in the same manner as play
alleles. We ran 18 conditions corresponding to the sexual reproduction conditions and three conditions corresponding to the asexual reproduction conditions in
Section 3.2 (varying the rate of learning was not applicable here). For sexual reproduction, we defined the
probabilities for cooperation in the SH as follows. For
Social play evolved by facilitating the learning of adult
cooperation in population structures characterized by
the formation of spatial clusters or groups of agents,
and evolved even when the rate of learning was relatively low (Figure 5). In contrast, in the cooperation
control conditions (where agents cooperated only if
they inherited a cooperation gene), cooperation evolved
infrequently in most conditions and only evolved in
slightly more than 50% of the simulations in the sexually reproducing dominant allele condition with low
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8
Adaptive Behavior
Figure 4. A succession of snapshots of the evolution of social play and adult cooperation over 100,000 rounds for a small
population size (Nmax=250) under the sexual, uniparental care condition. Juveniles with a play gene are illustrated with open blue
circles and juveniles without a play gene are illustrated with red open circles. Adults that have learned to cooperate are represented
by shaded-blue circles (i.e., shaded blue according to their probability of cooperating) and non-cooperators represented by solid red
circles. In the early stages of evolution, the social play gene (and learned cooperation) increase in small regions of space. When the
frequency of cooperation in these small regions exceeds the fixed-point p=0.5, cooperators can then expand as illustrated in the
bottom two rows.
population density (Figure 6). In general, cooperation
without social play evolved much less frequently and at
much lower frequencies than cooperation facilitated by
social play (cf. Figures 5 and 6).
For cooperation to evolve in the SH, the frequency
of cooperators must exceed the fixed-point frequency
of 0.5 (i.e., ESS zone for the evolution of cooperation).
Because populations began with no cooperators and
low mutation rates, the frequency of cooperators was
well below the unstable fixed point making it effectively
impossible for cooperation to increase in panmictic
populations, which is exactly what we found in the
swapping control conditions (Figure 7). With population structure (i.e., agents actively aggregate and offspring locally disperse), however, the frequency of
cooperators varied over local regions of space (Figure
4). Occasionally, the frequency of cooperators in a
region of space exceeded the fixed point and gradually
expanded throughout the whole population (Figure 4).
This was most likely to occur for relatively small
population size, sexual reproduction with dominance,
and uniparental care (Figure 5). Conditions with
smaller maximum population size (or density) tended
to evolve cooperation more often because clusters of
agents were more likely to be isolated from one
another, which promoted group selection (Figures 5
and 6).
By adding social play, adult cooperation dramatically increased (Figure 5). The explanation of this effect
is that the negative effect of cooperating in a population of non-cooperators is masked at low frequencies
by social play. When a play gene exists at low frequencies in a population, the frequency of adult cooperators
is close to zero because the likelihood that two or more
juveniles with the play gene are next to each other is
low. In a structured population characterized by spatially isolated groups, this can facilitate (by genetic
drift) increases in the frequency of a social play gene
within small regions of space (Figure 4). As mutation
and drift increase the frequency of play genes within
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9
Figure 5. The frequency of simulations for which the average probability of cooperating was greater than 0.5 (i.e., the
evolutionarily stable strategies zone for cooperation). The learning rate, α, was varied from 0.04 (weak) to 0.2 (strong) as illustrated
on the horizontal axes. The first column (a, c, e) contains graphs of parameter sweeps for the sexual biparental care conditions. The
second column (b, d, f) contains graphs of parameter sweeps for sexual uniparental care conditions and the asexual condition. Each
row contains graphical results for different population sizes: the first row (a, b) is for a population size of 250, the second row (c, d)
is for a population size of 500 and the third row (e, f) is for a population size of 1000.
these regions, the frequency of juveniles with the play
gene can become sufficiently high so that agents begin
to learn to cooperate. Because agents that play together
as juveniles tend to stay in the same place as adults, the
likelihood of one cooperator finding others like it are
relatively high in these regions of space. Thus, small
regions emerge in which cooperators do relatively well
when their frequency is greater than the fixed-point
value of p=0.5 and thereby out reproducing regions
with non-cooperators, and quickly spread throughout
a population (Figure 4).
4.2 Sexual reproduction and parental care
Social play was more likely to evolve under the dominant and additive sexual reproductive conditions than
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Adaptive Behavior
Figure 6. The frequency of simulations for which the average probability of cooperating was greater than 0.05 (i.e., the
evolutionarily stable strategies zone for cooperation) by population size in which agents did not learn to play but instead but instead
evolved cooperation via a cooperation gene. On the left (a) are the sexual biparental care conditions. On the right (b) are the sexual
uniparental care conditions and the asexual case.
the asexual and recessive conditions (Figure 5).
Sexually reproducing agents with a recessive play gene
did the worst because they required two copies of the
play gene for the expression of social play. For both
the dominant and additive cases of sexual reproduction, cooperative agents did quite well because only
one gene was required for full or partial expression.
A freeloading effect emerged for both the dominant
and additive cases. Freeloading is straightforwardly
explained in the uniparental care condition. In this condition, one agent assumes the role of the care-giving
parent (CG) and provides all of the parental care, while
the other agent only provides a genetic contribution. In
a population with a low frequency of cooperators, an
offspring with a cooperative CG parent would be at a
disadvantage to an offspring with a non-cooperative
CG parent. However, if the genetic-contribution-only
(GCO) parent happens to be a cooperator and the CG
parent is a non-cooperator, then the GCO parent may
pass on the social play gene to their offspring—and the
offspring will not incur any costs associated with having a cooperative GCO parent in a predominately noncooperative population. Furthermore, the cooperative
GCO parent will not be burdened with providing parental care, and hence will have the resources necessary
to reproduce again shortly afterwards. Thus, it is possible for a cooperator parent to reproduce two or more
juvenile offspring with a play allele in quick succession,
thereby increasing the frequency of play allele offspring
in a particular group to the levels needed for cooperation and social play to take off. In the case of biparental care, both parents contribute equal resources. If an
offspring with the play allele has a cooperator and a
non-cooperator as parents, it will benefit from the noncooperator parent when adult cooperation is low, but
not as much as in the uniparental case. A cooperative
parent may also be more likely to reproduce multiple
offspring with a social play allele in a short time period,
though it will not be able to reproduce as quickly as in
the uniparental case, due to the required parental care.
Figure 5 illustrates that both dominant and additive
conditions did very well under both biparental and uniparental care. The biparental dominant and additive
conditions did slightly better than the same uniparental
conditions only for low learning rates and high population size (or density). The opposite was true for the
asexual and recessive conditions.
In the asexual condition, there was no freeloading
effect as offspring with a cooperator parent only
received resources from that cooperator parent and
therefore incurred a significant cost when the population was predominantly non-cooperative. Cooperative
parents were also much less likely to have the opportunity to reproduce multiple offspring consecutively. This
could explain why asexual cases did not often evolve
cooperation (Figures 5–7).
Finally, the freeloading effect is frequency dependent. Freeloading is only beneficial to the evolution of
cooperation and social play when a population is predominantly non-cooperative and adult cooperators
receive no payoff the majority of the time. Once cooperation has spread throughout a population, cooperators
obtain the cooperative payoff the majority of the time
and there is no longer a benefit to freeloading on noncooperative parents. Freeloading is a two way street
when cooperators are common; it becomes detrimental
to cooperation because offspring without the play allele
can freeload on cooperative parents.
5. General discussion
We found that social play gains delayed adaptive benefit by facilitating the learning of adult cooperation. For
adults playing the SH, cooperation can evolve from
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Figure 7. The frequency of simulations for which the average
probability of cooperating was greater than 0.5 (i.e., the
evolutionarily stable strategies zone for cooperation) by learning
rate, α, for agent location swapping, which eliminated group
effects. This graph shows the results for a population size of
250. For all other population sizes investigated, cooperation
frequencies were lower than shown here.
very low initial frequencies when population structure
is characterized by the formation of spatial clusters of
agents. Social play as a necessary requirement for cooperation, in our model, allows juveniles to learn to cooperate only when there are other juveniles present that
engage in play. Because agents remain at the same location so long as they are in contact with at least one
other agent, it is likely that an agent that learned to
cooperate by engaging in social play will remain next to
agents that also learned to cooperate when they enter
adulthood. Thus, agents that engage in social play as
juveniles are more likely to benefit from higher cooperative payoffs as adults, resulting in selection for social
play. Our theoretical results support the hypothesis that
social play could evolve by promoting the learning of
cooperation when starting with populations of entirely
non-cooperative agents.
Our model and results provide a novel solution to
the problem of the evolution of cooperation, a notoriously difficult problem to explain. For the SH, for a
wide range of parameter values, cooperation cannot
invade a population of non-cooperators. For cooperative games such as the prisoner’s dilemma, several
mechanisms have been found that support the evolution
of cooperation including retaliatory strategies such as
tit-for-tat (Axelrod & Hamilton, 1981), walking away
from defectors (Aktipis, 2004; Smaldino & Schank,
2012), and spatial aggregation (Smaldino, Schank, &
McElreath, 2013; Traulsen & Nowak, 2006). We have
shown that social play in conjunction with spatial
aggregation could be a very powerful mechanism for
the evolution of cooperation.
Interestingly, social play only robustly evolves by
facilitating adult cooperation under sexual reproduction. Assuming a single play gene that is either dominant or additive for social play resulted in the evolution
of social play even when learning was very gradual and
required a number of bouts of social play to learn cooperation. We argue that sex allows the play gene to freeload on non-cooperator parents when the play gene is
relatively rare. Freeloading frees offspring, to some
extent, from selection on parents that have learned to
cooperate when the frequency of adult cooperators is
low. This allows the play gene to increase by drift in
small clusters of agents. By chance, clusters occasionally
emerge with relative high frequencies of the play gene;
members of these clusters engage in social play and subsequently cooperation. Once a group of agents has over
50% cooperators (i.e., for the payoff structure used in
these simulations, the group of agents enter the ESS
zone for cooperation), it has a fitness advantage over
groups of non-cooperators and cooperation is locally
favored. The evolutionary process by which this occurs
is similar to Wright’s (1932) shifting balance theory.
In our model, we assumed that juvenile agents
engaged in play and that social play was one form of
play with no additional costs. Social play may introduce costs in addition to the costs of other forms of
play. As outlined in the introduction, these potential fitness costs can take several forms. Increased predation
(Blumstein, 1998; Harcourt, 1991), injuries (Berger,
1980; Douglas-Hamilton & Douglas-Hamilton, 1975),
energy costs (Martin, 1984; Miller & Byers, 1991), and
foraging costs (Caro, 1995). Each of these costs can
entered into a model such as ours in different ways. We
have begun to investigate different forms of costs to
social play. For example, in simulations from a new
model we are analyzing, which includes the cost of
social play as increased risk of predation, we have
found that social play still evolve for a wide-range of
parameters reported above when predation risk is as
high as 10% during the juvenile developmental period.
Future research will investigate how the potential costs
of social play affect its evolution.
Our results suggest that the frequency and complexity of social play in juveniles should correlate with the
frequency and complexity of adult cooperation found
in different mammalian species. There is evidence that
juvenile animals learn to cooperate and behave fairly
through social play (Bauer & Smuts, 2007; Bekoff,
1977, 2001; Brosnan & de Waal, 2012; Dugatkin &
Bekoff, 2003; Pellis et al., 2009; Watson & Croft, 1996).
There is also evidence indicating that social play in
early development is important for social skills in adulthood (Einon et al., 1978; Hol et al., 1999; Pellegrini,
1992; Pellis & Pellis, 2007). However, further research
is needed to determine whether the social skills learned
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Adaptive Behavior
during play are used in adult cooperative behavior and
whether these skills translate into adaptive benefits.
Our model also predicts that the evolutionary context
in which cooperation and social play evolved consisted
of populations of small isolated groups, rather than
large, well-mixed populations. This prediction can only
be assessed once we have made progress on the former
question.
Although we have shown that social play could
evolve by facilitating adult cooperation, cooperation is
more complicated and dynamic than mere coordination
of behavior for a cooperative goal (e.g., see MacLennan
& Burghardt, 1993, for a general discussion of the evolution of cooperation in the context of synthetic ethology). We modeled a simple coordination scenario in
which individuals must coordinate their behavior to
achieve a resource. In addition to achieving a cooperative gain, the resource must then be divided, which
introduces the possibility of agents fighting over the
resource or one individual behaving unfairly, taking the
cooperative gain for itself (defecting). This suggests an
important direction for future research. Could juvenile
agents learn social skills during social play for dealing
with defectors? Models could be investigated in which
there is initial variation in the degree to which juvenile
agents are likely to engage in fair play and they subsequently learn to play fairly or not as a function of their
bouts of social play. We know that animals may learn
how to play fairly and solve conflicts during play
(Dugatkin & Bekoff, 2003). If, for example, fair agents
learn to avoid unfair agents (Brosnan & de Waal,
2012), they may have a successful counter strategy for
defectors.
Acknowledgments
This work was inspired by participants in the working group
on Play, Evolution, and Sociality sponsored by National
Institute for Mathematical and Biological Synthesis, an
Institute sponsored by the National Science Foundation
through NSF Award #DBI-1300426 with support from The
University of Tennessee, Knoxville.
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About the Authors
Sabine Durand is a graduate student studying psychology at the University of California,
Davis. She received her B.A. in Psychology and Mathematics at University of California, Santa
Cruz in 2011. She is interested in complex group and social behaviors, particularly cooperation.
Jeffrey C Schank is a professor of psychology at the University of California, Davis. He
received his PhD in the conceptual foundations of science from the University of Chicago in
1991. His primary research tool is agent-based modeling, which he applies to the study of social
behavior, its organization, development, and evolution.
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