Conceived and designed the experiments: CJT AB IDC. Performed the experiments: CJT AB IDC. Analyzed the data: CJT AB IDC. Wrote the paper: CJT AB IDC.
The authors have declared that no competing interests exist.
Understanding cooperation in animal social groups remains a significant challenge for evolutionary theory. Observed behaviours that benefit others but incur some cost appear incompatible with classical notions of natural selection; however, these behaviours may be explained by concepts such as inclusive fitness, reciprocity, intra-specific mutualism or manipulation. In this work, we examine a seemingly altruistic behaviour, the active recruitment of conspecifics to a food resource through signalling. Here collective, cooperative behaviour may provide highly nonlinear benefits to individuals, since group functionality has the potential to be far greater than the sum of the component parts, for example by enabling the effective tracking of a dynamic resource. We show that due to this effect, signalling to others is an evolutionarily stable strategy under certain environmental conditions, even when there is a cost associated to this behaviour. While exploitation is possible, in the limiting case of a sparse, ephemeral but locally abundant nutrient source, a given environmental profile will support a fixed number of signalling individuals. Through a quantitative analysis, this effective carrying capacity for cooperation is related to the characteristic length and time scales of the resource field.
One of the key challenges facing evolutionary theory is understanding how cooperation and communication evolve in social systems. In many situations cooperation leads to higher net benefits to all, but a population of cooperators is vulnerable to invasion from exploitative strategies. When foraging, aiding others through sharing information can lead to an advantage to a collective of communicating individuals. How this behaviour can be maintained and resist invasion without centralized control or policing is currently not clear. In this work, we examine a social foraging system where individuals evolve to signal to conspecifics when they locate a resource. We show that in some environments, cooperative signalling is sustained through a form of indirect reciprocation, as a signalling phenotype is more likely to be the beneficiary of a signal from a conspecific in the future. This effect naturally occurs as a result of the foraging dynamic and, depending on the environment, such as how resources are distributed and how difficult they are to track, will compensate for relatively large costs of signalling. Through simulations and a simplified model we examine the parameters driving this process and identify the mechanisms required for cooperation to evolve in such a system.
In many systems subject to evolutionary pressure, there exists a discrepancy between behaviour that is adaptive at the individual level and that which would be most beneficial for higher levels of social or biological organization. When individual self-interest runs counter to the best interests of the collective, it can lead to what is known as the
Despite this issue, examples of altruism and cooperation abound in the natural world
Locating and exploiting resources is an ever present challenge for all organisms, and it is an area where cooperative strategies can greatly improve the probability of success. Social foraging theory has shown animals in groups are able to acquire more information about their environments than if they were to forage alone
Effective and honest communication in these situations would clearly improve foraging efficiency since it provides individuals with an additional level of reliable information
The study of information in an ecological context is an active and important area of research, encompassing learning, communication, exploitation through informational parasitism, and strategic social interaction
As an alternative to the ICH, Richner and Heeb proposed the recruitment centre hypothesis (RCH)
Several studies based on evolutionary game theory and numerical simulations
Active recruitment of conspecifics to resources is observed in several species, and when not attributed to indirect fitness benefits (see e.g.
The purpose of this work is to investigate the conditions where signalling can be maintained due to the nature of the resource environment. Through a numerical study of evolution in a two dimensional turbulent environment we show that, within a certain region of parameter space, a cooperative signalling strategy is stable. A reduced model that retains the essential features of the full simulation is then analyzed and the mechanisms that drive the evolutionary dynamic are explored.
The underlying biological and physical processes that shape environmental conditions often result in patchy and heterogenous landscapes
The summary effect of these processes is the presence of steep local gradients in nutrient concentration. Fluctuations and stochasticity in an organism's position relative to the resource, are therefore capable of significantly affecting both nutrient uptake and perception of the resource. Perturbations, either due to the nature of the advective carrier flow, or to the random motion of the organism, may result in sharp decreases in the experienced resource concentration and the loss of an unexploited food patch. In this situation social interactions can be greatly beneficial as the effective sampling size of the organism is increased, and when a resource is lost it may be relocated by following others
In our model individuals forage within a chaotic environment and freely evolve the ability to do so cooperatively, by signalling to others when they have located a region of high nutrient availability. It is assumed this is an active behaviour as opposed to inadvertent social information (ISI)
To generate a realistic stochastic environment a synthetic turbulence model was used
The flow field is used to advect a concentration field
We fix the length scale of the largest energy mode to be equal to the system size
(A) Size of source,
Individuals foraging in the generated environment follow simple behavioural rules corresponding to two distinct and discrete strategies. The two categories of individual are signallers (S), a strategy that may be equated to the cooperate strategy of traditional game theoretic models, and non-signallers (NS), which equivalently are considered analogousto defectors. When signallers locate a favourable nutrient region, they actively recruit others through some form of communication. If an individual is within range of a signal and is not currently located in a preferred region, this individual becomes attracted to the source of the signal.
At the individual level no search strategy exists and no form of taxis occurs. Instead a solitary individual performs a correlated random walk through the environment at constant speed, so that their average nutrient uptake is equal to the mean concentration. While there are many asocial strategies that result in a nutrient exposure greater than this mean value (see e.g.
In our model all individuals are advected by the flow and propel themselves at a constant speed along their axis of orientation,
The signal and response dynamic is stochastic with the probability of performing a certain behaviour determined by both phenotype and external conditions. At each time step, the probability of emitting a signal is
It is worth noting at this point, individuals only interact when a signal has been given. In the absence of signalling all foragers are effectively invisible. While responding to non-signalling conspecifics may be beneficial
The signalling cost may arise as a result of various factors, the most obvious being the energy expended in producing the signal. While this may seem slight, the energy budget for free-living birds is often finely balanced
Regardless of the nature or source of the immediate cost of signalling, in a well mixed, highly mobile population, any behaviour that benefits others is essentially costly since it will increase local competition for mates, territory or preferred breeding sites. The act of signalling must therefore be understood in the context of the direct advantage it conveys to the actor.
The within generation process is defined by the environment and the behavioural rules outlined above. The foraging success of each individual is dependent on their phenotype, the behaviour of others and the statistical properties of the resource field. Simulations of the foraging process were performed, then a roulette wheel algorithm was used to select individuals to contribute to the next generation according to their fitness. Here fitness is defined as normalized foraging success less the cost paid through signalling. Cost is levied at a constant rate, not on a per signal basis, although both are statistically equivalent.
The steady state absolute number of signalling individuals for a range of parameter values are shown in
Results are for a range of mean velocities,
(A–B) Relative uptake,
These plots demonstrate the existence of a fixed density of signallers that is robust to invasion by the non-signalling phenotype and that is dependent upon the statistical properties of the resource field. The region of parameter space which supports the cooperative phenotype is characterized by intermediate patch size and flow velocity. In this regime the resource field is not widely distributed or well mixed, and there exists a high variance in concentration. When the patch source size,
In
From these data it can be observed that once a threshold number of signallers is reached, the strategy outperforms non-signallers. Under selection pressure this advantage leads to an increase in the number of individuals adopting the signalling strategy until a certain equilibrium density is attained. At this point both discrete strategies have on average equal fitness and an evolutionarily stable polymorphic population exists. The value of this stable density is a function of the cost attributed to emitting a signal, and the temporal and spatial correlation lengths of the resource. From
The reason for this outcome lies in the manipulative effects of the signalling individuals. Effectively a signaller increases the local density of conspecifics in its immediate vicinity, meaning it is more likely to subsequently benefit from the behaviour of other signallers in the population. To understand how the properties of the resource field influence this dynamic, we now introduce a simple model representation that is amenable to an analytical treatment and a fuller exposition of the underlying mechanisms.
For analytical tractability we now consider a reduced, but qualitatively equivalent model, in which individuals follow analogous behavioural rules, but instead forage in an environment with a simple resource distribution and no advective forces. In this environment (see
Individuals move at constant speed and are unable to stop when locating a resource patch. This constraint is enforced so that the model is consistent with the full simulations described above. When chaotic, advective forces are present an individual cannot simply maintain its position in a region of high resource concentration; instead maintaining this position is an active process that requires constant processing of environmental and social cues or signals. Since in our reduced model there is no advection, we capture this effect by imposing the constant velocity condition, effectively ensuring there is a non-zero relative velocity as is the case when the resource and/or individuals are subject to stochastic advective forces.
In combination, the constant individual velocity and intermittent relocation of the resource patch capture the dynamics of the full model. The spatial variance of the resource determines the range over which uptake rates can vary, i.e. more localized, high concentration regions lead to a greater difference between an effective search strategy and random motion. However, the role of the temporal dynamics is more complex. The aim of this section is to understand this role by isolating the essential features of the full model. We do this by coarse-graining the spectrum of the turbulent velocity fluctuations into two processes that operate at different time scales. The first is characterized by the frequent occasions on which the resource is lost by the collective. This is equivalent to the resource relocation in the reduced model, and to large scale fluctuations in the full model. The second process operates over the short term and involves the loss of the resource by individuals, imposed by forcing individuals to move through the patch in the reduced case, and by the constant, small scale fluctuations in the full simulations.
Our model therefore has only two relevant parameters, the spatial correlation length of the resource,
Each figure shows a unique patch persistence time, (A)
To more quantitatively understand this process four steps are required, each involving a certain degree of approximation, but which in combination provide a heuristic and intuitive explanation of the underlying mechanisms which link the statistical properties of the environment to the evolutionary dynamic. In summary these steps are
Firstly time is discretized and it is assumed the future state of the system depends only its state in the current time interval and not on previous history.
Secondly, transition probabilities are determined for an individual to enter or exit the resource patch depending on whether a signal has been given or not.
Next the dynamic is divided into two distinct temporal regimes. The first occurring immediately after the resource has been lost and continuing until a stable cohort of signallers have located it. The second regime begins when this stable cohort emerges and continues until the resource again relocates.
Finally, the relative advantage of the signalling strategy is calculated during the transient first regime. During the second regime both strategies perform equally, hence the overall advantage to signallers is calculated by weighting the transient advantage according to the relative lengths of the two regimes.
In the analysis that follows we assume events occur at discrete time intervals. Within a given interval an individual forager may make the transition from a state of being external to the food patch to being within the resource, and vice versa. The most natural choice for the length of this time step is the time required for an individual to cross the resource patch at its widest point,
Further to this, it is assumed the probability of the system transitioning to a given state at the next discrete time interval is dependent only on the current state, and not on any previous history, i.e. the process exhibits the Markov property
We define
Since the time interval,
Therefore, the probability to enter the patch given that a signaller is present,
However, if no signaller is present in the patch, an individual within the outer ring may still enter the patch within the next time step due to its random motion. This probability,
To find
We note two distinct regimes in the dynamics of the system. When the patch first appears in a new location it typically has a high probability to be unoccupied or only intermittently located before being lost again. Eventually a small cohort of signallers will form upon the patch, where they are able to leverage their mutual interactions to stay on the patch and remain there until it moves. In this second phase signallers and non-signallers alike arrive at the same rate, have little chance of losing the patch and enjoy equal resource uptake.
However, the nutrient uptake during the first regime is greater for signallers as compared to non-signallers. For this reason we calculate the relative length of these regimes. To do so, we consider a three state system,
State
The transient phase is divided into two states, the first
The final, absorbing state,
State
We calculate
Now that we have solved for the length of the transient phase we turn to the relative uptake between signaller and non-signallers during this regime. We reduce this regime to a two state system with the patch initially unoccupied, and focus on two representative individuals employing each strategy.
It is assumed that once inside the patch a single individual will leave at the next time step unless another signaller enters. Therefore a signaller will leave if not able to attract at least one of the other
We can construct analogous matrices for the non-signaller, but the probabilities are dependent on whether or not a signaller is already within the patch,
Using these transition matrices we solve for the equilibrium patch occupation probabilities,
The occupation probability for the patch is proportional to the mean uptake of resources for the individuals during the transient phase. We now weight the occupation probabilities by the relative time spent in the transient regime,
Many organisms share information, either inadvertently or through some form of active communication. When communication is honest and appears to benefit the recipient of the information but not the donor, it is often considered a form of cooperative behaviour. The purpose of this work is to further our understanding of the mechanisms that lead to the evolution and stable existence of such behaviour.
One example of recruitment signals occurring in nature is the food calling observed in species of the cliff dwelling swallow,
We have shown that signalling that a food source has been located is indeed an adaptive strategy. We go beyond speculation and provide a mechanistic explanation for the evolution of this behaviour. Signallers raise the local density of fellow signallers around them, this enables a collective response to the resource and hence strongly influences foraging performance. When conditions are appropriate, this effect is sufficient to offset relatively large costs imposed on signalling.
The simulations of the full turbulence model we present demonstrate the existence of a region of parameter space in which the cooperative, signalling strategy is stable. At first glance the key mechanisms that create this outcome are unclear, but by introducing a reduced model we relate the properties of the environment to the stable density of signallers. This reduced model effectively displays two separate time scales. By enforcing each individual to move at a fixed speed, a time scale at which the resource is lost is created, thereby giving an advantage to cooperation. This time scale is defined by the average time taken to traverse the resource, if a signal from a conspecific isn't received within this time frame, the resource will be lost.
The second time scale is defined by the time between relocation events, when the resource is entirely lost. In the full simulations, this is equivalent to the infrequent events when large velocity fluctuations cause all individuals to lose track of the resource. The reduced model effectively has a bimodal distribution of stochasticity, while in real dynamical systems a continuous spectrum exists, but this difference is not important. What matters is that on a shorter timescale, cooperation is beneficial (how beneficial depends on the local variance of the resource i.e. its spatial correlation), whereas infrequent, but more severe fluctuations, put an effective time limit on the period signallers may be exploited, weighting the benefit towards those that contribute to the collective effort early, and thus restricting the evolution of a defector strategy.
These mechanisms can be related to the processes involved in other studies of information use in ecology, notably those concerning the information or recruitment centre hypotheses for colonial living birds
To facilitate comparison to such works (e.g.
Important distinctions are that the finder's share is conditional on recruitment, hence recruitment does not only reduce the information producer population as in
Our results suggest signalling strategies may have evolved in a wide range of scenarios. Diffuse resource fields scattered by advective flows, as in our full turbulence model, are ubiquitous throughout aquatic and aerial environments. Scavengers and decomposers may face a similar challenge when locating and staying with resources that may be lost due to movement by flows or larger organisms, or through displacement by dominant competitors if insufficient conspecifics are present. Further, organisms constrained to provide information to conspecifics through cues, such as strongly electric fish which use electric fields to capture their food, or other organisms inadvertently displaying stereotyped feeding behaviour (including, for example, hunger or dominance displays
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The authors wish to thank members of the Couzin Lab and three anonymous referees for helpful comments and suggestions.