Conceived and designed the experiments: SAR. Performed the experiments: SAR. Analyzed the data: SAR. Wrote the paper: SAR.
The author has declared that no competing interests exist.
Although social behaviour can bring many benefits to an individual, there are also costs that may be incurred whenever the members of a social group interact. The formation of dominance hierarchies could offer a means of reducing some of the costs of social interaction, but individuals within the hierarchy may end up paying differing costs dependent upon their position within the hierarchy. These differing interaction costs may therefore influence the behaviour of the group, as subordinate individuals may experience very different benefits and costs to dominants when the group is conducting a given behaviour. Here, a state-dependent dynamic game is described which considers a pair of social foragers where there is a set dominance relationship within the pair. The model considers the case where the subordinate member of the pair pays an interference cost when it and the dominant individual conduct specific pairs of behaviours together. The model demonstrates that if the subordinate individual pays these energetic costs when it interacts with the dominant individual, this has effects upon the behaviour of both subordinate and the dominant individuals. Including interaction costs increases the amount of foraging behaviour both individuals conduct, with the behaviour of the pair being driven by the subordinate individual. The subordinate will tend to be the lighter individual for longer periods of time when interaction costs are imposed. This supports earlier suggestions that lighter individuals should act as the decision-maker within the pair, giving leadership-like behaviours that are based upon energetic state. Pre-existing properties of individuals such as their dominance will be less important for determining which individual makes the decisions for the pair. This suggests that, even with strict behavioural hierarchies, identifying which individual is the dominant one is not sufficient for identifying which one is the leader.
Dominance hierarchies could offer interacting animals a quick way to settle disputes without having to use too much effort. However, individuals may pay a price for acknowledging their position within the hierarchy, which could influence how they choose to behave within the group. Consequently, the actions of the group may be shaped by the effects of the hierarchy on each of the group’s members. I consider the behaviour of a pair that consists of a dominant and a subordinate individual, where the subordinate pays an energetic cost when it interacts with the dominant. I show that having to pay this cost affects the behaviour of the pair. I also demonstrate that, although a social hierarchy is imposed, the behaviour of the pair is not determined by the dominance relationship, but is instead influenced by the energetic reserves of the pair, where the decision-maker may just be whoever is the hungriest.
Animals can gain many benefits from associating in groups
Differing effects of dominance upon the behaviour of interacting individuals have been integrated into a number of theoretical studies. Some have concentrated upon how dominance affects the order of access to resources, where dominants may have priority or exclusive access to a foraging resource
As well as effects upon foraging ability and group composition, living in social hierarchies can impose differing costs on individuals
The way in which this socially mediated interference cost was implemented within the spatially-explicit individual-based framework of
The model followed here builds on the dynamic foraging game described by Rands
As well as the risk of starvation if an individual doesn’t forage, there is also the risk of predation, which depends on the actions of
The model I describe here builds further on this framework. Although Rands
when both it and the individual who does not pay a cost (which I refer to as the ‘dominant’) are foraging together (which could for example be a proximity or vigilance cost, or simply a reduction in foraging efficiency due to direct competition from the dominant);
when both the dominant and the subordinate are resting (which again could be a proximity cost, or perhaps an energetic cost due to the subordinate expending energy providing a service such as grooming to the dominant);
when the subordinate is foraging on its own (which could be through social anxiety at not knowing where the dominant individual is, or through an increased cost of scanning for food, predators, or the dominant);
when the subordinate is resting on its own (which again could be through social anxiety at not knowing where the dominant individual is).
In (
The model considers a dynamic game between pair of players consisting of a dominant and a subordinate individual. This dynamic game builds on solution procedures outlined in
Where the current model differs from that presented in
In order to consider the effects of dominance on behaviour, I replace the
If the individual is dominant, I assume
If the focal individual is subordinate, I instead assume
Apart from the novel interference cost terms (described below), terminology here follows
For simplicity, both dominant and subordinate individual were assumed to have identical probabilities of incurring given gains and costs, and share identical predation risks when conducting particular activities (so
Once stable behavioural policies for subordinate and dominant individuals had been identified, forward iterations using Markov chain processes
Having identified both the optimal policies for dominant and subordinate members of a pair, as well as the stable distribution of paired energetic reserves within the population, I was therefore able to calculate the proportion of the dominant and the subordinate population that would be foraging during a period.
Similarly, knowing stable paired states and policies also allowed us to calculate the proportions of the population where both members of a pair foraged during a period (
Having calculated the proportions of the population conducting the four types of paired behaviour, I quantified the amount of behavioural synchronisation during a period as (
Rands & Johnstone
Given that a dominant or a subordinate can choose to conduct one behaviour during a period, the stable population and policies calculated above could be used to calculate the proportion of the population where the individual then conducts the same behaviour in the following period. Tracking repetition over time, I also calculated the repeatability of paired behaviours: this was taken to be the mean number of periods until at least 50% of the population had conducted at least one different pair of behaviours to that which they were engaged in at the initial period recorded.
he mean energetic reserves of the dominant and the subordinate individuals were calculated from the stable population distributions calculated above.
Due to the stochastic nature of the system, it was possible that both the dominant and the subordinate individual could end up having the highest energetic reserves. I calculated the mean length of time that dominants or subordinates maintained the rôle of ‘heaviest individual’ within the pair.
I explored the effects of the costs by randomly generating 1,000 sets of other model parameters, and then calculating optimal policies and population distributions for all possible combinations of the four socially-mediated interference costs.
Variable | Description | Value |
|
Largest cost possible | 4 state units |
|
Extra energetic cost paid by subordinate when both it and the dominant are foraging | 0 or 1 |
|
Extra energetic cost paid by subordinate when it is resting and the dominant is foraging | 0 or 1 |
|
Extra energetic cost paid by subordinate when it is foraging and the dominant is resting | 0 or 1 |
|
Extra energetic cost paid by subordinate when both it and the dominant are resting | 0 or 1 |
|
Maximum gain during a period | 6 state units |
|
Error in decision making | 0.0000001 |
|
Population adjustment constant | 0.1 |
|
Predation risk when foraging alone | exp(-25 |
|
Predation risk when resting | |
|
Predation risk when foraging together | |
|
Mean cost of foraging | ( |
|
Mean cost of resting | ( |
|
Mean gain from foraging | (4 |
|
s.d. of energetic gain when foraging | (0.5)0.5 state units |
|
Maximum state possible | 40 state units |
|
s.d. of energetic gain when foraging | (0.5)0.5 state units |
|
s.d. of energetic gain when resting | (0.5)0.5 state units |
Where these are not discussed in the text, refer to
The model considers four possible interference costs to a subordinate individual, all of which could potentially have a separate effect upon its energetic turnover during a period dependent upon the behaviour of the pair. Therefore, I was interested in the interactions of the costs, as well as each of the costs themselves. To explore this, standard analysis of variance was used to generate
The statistical model considered includes two-, three- and four-way interactions, as these were biologically feasible within the framework considered. The results of these interactions are presented in full in
Subordinate pays extra cost when | proportion of time dominant forages | proportion of time subordinate forages | proportion of time both players forage | proportion of time dominant forages, subordinate rests | proportion of time dominant rests, subordinate forages | proportion of time both players rest | synchrony coefficient |
|
both players forage (FF) | + | + | + | – | + | – | – | – |
the dominant forages, and the subordinate rests (FR) | NS | + | + | – | + | – | + | NS |
the dominant rests, and the subordinate forages (RF) | + | + | + | – | + | – | + | NS |
both players rest (RR) | + | + | + | – | + | – | – | + |
|
||||||||
FF × FR | NS | + | + | * | NS | NS | – | NS |
FF × RF | + | + | + | * | NS | – | – | – |
FR × RF | NS | + | + | – | + | – | * | NS |
FF × RR | + | + | + | NS | + | – | – | – |
FR × RR | * | + | + | NS | NS | – | * | * |
RF × RR | * | + | + | NS | NS | – | + | * |
FF × FR × RF | * | NS | NS | * | * | NS | * | NS |
FF × FR × RR | NS | * | * | * | NS | NS | * | NS |
FF × RF × RR | * | * | * | * | * | * | NS | NS |
FR × RF × RR | * | * | * | NS | NS | * | * | NS |
FF × FR × RF × RR | * | * | NS | NS | NS | * | * | NS |
This table reports the significance and direction of change for these result sets, based on ANOVA models containing all four costs of dominance and all possible interactions between these costs. Assuming a significance term of
Subordinate pays extra cost when | likelihood dominant repeats behaviour | likelihood subordinate repeats behaviour | length of time a paired behaviour is repeated | energetic reserves of dominant | energetic reserves of subordinate | length of time dominant heaviest | length of time subordinate heaviest |
both players forage (FF) | + | + | NS | + | – | NS | – |
the dominant forages, and the subordinate rests (FR) | NS | + | + | + | + | – | + |
the dominant rests, and the subordinate forages (RF) | NS | + | + | + | – | + | – |
both players rest (RR) | – | – | – | + | – | NS | – |
|
|||||||
FF × FR | NS | NS | NS | + | – | * | NS |
FF × RF | * | + | * | NS | – | * | NS |
FR × RF | NS | + | NS | + | + | * | NS |
FF × RR | + | + | NS | NS | NS | * | – |
FR × RR | NS | + | NS | NS | + | – | * |
RF × RR | NS | + | NS | NS | – | + | NS |
FF × FR × RF | NS | NS | NS | NS | NS | NS | NS |
FF × FR × RR | * | * | NS | * | NS | NS | * |
FF × RF × RR | NS | * | NS | NS | NS | NS | NS |
FR × RF × RR | NS | NS | NS | NS | NS | NS | NS |
FF × FR × RF × RR | NS | * | NS | NS | NS | NS | NS |
See
All individual increases in dominance cost led to an increase in the amount of foraging behaviour shown by the subordinate (
The increases in individual foraging behaviour were also echoed in the paired behaviours (
Paired costs led to increases in both individuals foraging together, and (apart from the case where the subordinate always paid a cost when the dominant was foraging), decreases in resting together. The paired interactions when the members of the pair were conducting differing behaviours were mostly non-significant, although there were increases in cases where the dominant rested and the subordinate foraged when the costs experienced by the subordinate occurred when the pair differed in their behaviour.
As would be expected, pairs become more synchronised when there are costs involved with not being paired, and become less synchronised when there are costs to conducting the same action as each other (
The
Both the dominant and subordinate individuals tended to increase their repetition of behaviour when there was an extra cost to the subordinate of foraging at the same time as the dominant (
The subordinate individual also tended to repeat its own behaviour more often when there was a dominance cost associated with conducting the opposite behaviour to the dominant individual (note here that this means an overall increase in the subordinate repeating a behaviour irrespective of what the dominant is doing, rather than a statement that the subordinate is increasing conducting the opposite behaviour to the dominant). Most of the interactions shown for the subordinate individual also indicate a positive trend. Paired behaviours were also repeated more often when these costs were incurred. These increases are likely to be due to the increase in synchronisation behaviour seen when there is an extra cost to being non-synchronised.
As would be expected, incurring an extra cost of dominance to the subordinate meant that its energetic reserves tended to be reduced (
The length of time that the subordinate remained heaviest (when it managed to reach that state of being) was in most cases reduced by imposing a cost of dominance (
This model demonstrates that if a subordinate pays energetic costs when it interacts with a dominant individual, this has distinct effects upon the behaviour that it shows, and subsequently it affects the behaviour of the interacting dominant individual. Considered independently, both individuals tended to increase the amount of foraging behaviour they conducted when there were interaction costs. Considered together, the behaviour of the pair was driven by the subordinate individual. Costs imposed when the subordinate forages tend to increase paired foraging behaviour.
In the model presented here, the subordinate individual tended to be the lighter individual for longer periods of time when interaction costs were imposed. This lends support to the suggestion that the lighter individual acts as the decision-making ‘pace-maker’ of the group
Therefore, imposing direct energetic costs of dominance should lead to effects upon the paired behaviour of foragers, lending support to the rules proposed for larger groups by Rands
Furthermore, the current model makes a simplifying assumption by assuming that the subordinate paid additional costs (and indeed, being subordinate is solely defined by paying these costs within the model). We could conceivably see a situation where the dominant individual also pays additional costs for being dominant. If these costs are less than those paid by the subordinate, these could simply be subsumed into the general metabolic costs paid by individuals, giving us a similar model structure to that described. However, if the dominant and the subordinate individual paid different levels of cost for different behaviours such that both paid more than the other for at least one of the four behavioural pairs, then this would be a situation not covered within the current model. For example, we could imagine a situation where the dominant paid the higher metabolic cost when foraging at the same time as the subordinate (such as through having to be aware of the subordinate’s foraging actions, and through expending energy in forcing the subordinate away from resources), whilst the subordinate could show a higher metabolic cost than the dominant when it was foraging on its own (such as through raising vigilance levels to spot both predators and in anticipation of the currently absent dominant individual). In this hypothetical example, the current model is not sufficient, and an extended version would need to be considered where costs to the dominant individual are also modelled. I would suggest that this exercise might be useful if exact predictions are needed for a well-defined system (such as tying the model in with an empirical system), but investigating a more general model would be unlikely to yield more tangible results than described in the simpler model I present here.
As well as behavioural interactions leading to subordinates gaining less energy during an interaction, physiological processes may also mean that they spend more energy, and could be mediated hormonally, such as through stress responses by individuals. Studies on many species have demonstrated that social stress and dominance interactions have effects upon body mass and composition
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Rufus Johnstone, Guy Cowlishaw, Richard Pettifor, Marcus Rowcliffe, Cédric Sueur (the handling editor) and three anonymous reviewers are gratefully thanked for helpful discussion and comments on drafts of this work.