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Conceived and designed the experiments: LL. Performed the experiments: LL. Analyzed the data: LL. Contributed reagents/materials/analysis tools: LL. Wrote the paper: LL.

The author has declared that no competing interests exist.

Intraspecific coalitional aggression between groups of individuals is a widespread trait in the animal world. It occurs in invertebrates and vertebrates, and is prevalent in humans. What are the conditions under which coalitional aggression evolves in natural populations? In this article, I develop a mathematical model delineating conditions where natural selection can favor the coevolution of belligerence and bravery between small-scale societies. Belligerence increases an actor's group probability of trying to conquer another group and bravery increase the actors's group probability of defeating an attacked group. The model takes into account two different types of demographic scenarios that may lead to the coevolution of belligerence and bravery. Under the first, the fitness benefits driving the coevolution of belligerence and bravery come through the repopulation of defeated groups by fission of victorious ones. Under the second demographic scenario, the fitness benefits come through a temporary increase in the local carrying capacity of victorious groups, after transfer of resources from defeated groups to victorious ones. The analysis of the model suggests that the selective pressures on belligerence and bravery are stronger when defeated groups can be repopulated by victorious ones. The analysis also suggests that, depending on the shape of the contest success function, costly bravery can evolve in groups of any size.

Coalitional aggression between groups of individuals occurs not only in humans but is prevalent in other vertebrates and invertebrates as well. For instance, colonies of army ants battle against each other to increase the size of their territory

Coalitional aggression is a group level strategy, which allows individuals within groups to acquire reproduction enhancing resources from other groups. This strategy might have played a central role in human evolution

While the analytics of the proximate causes of raiding is well developed

But repopulation of defeated groups is not the only plausible demographic benefit that may lead to the evolution of coalitional aggression. An alternative situation is that resources are captured from defeated groups by victorious ones, which, when used by the the individuals of victorious groups may result in an increase in their local carrying capacity. For instance, due to its high nutritional value, meat of all sorts was contested among hunter-gatherers

The aim of this paper is to analyze the co-evolutionary dynamics of belligerence and bravery under this alternative demographic scenario, where victorious groups can expand in size as an outcome of warfare. These two traits are likely to be involved in coalitional aggression as belligerence increases an actor's group probability of trying to defeat another group and bravery increases an actors's group ability to defeat another group. In order to be able to contrast the selective pressure on belligerence and bravery under the two aforementioned demographic scenarios, I present a mathematical model, which takes both scenarios into account and allows me to contrast how different assumptions may lead to similar or different selective pressures on the evolution of these two traits when interaction occurs between small-scale, pre-state societies (“hunter-gatherer” warfare). The analysis of the model suggests that the selective pressure on belligerence and bravery are stronger when defeated groups can be repopulated by victorious ones.

The population is assumed to consist of an infinite number of groups, which are connected by random dispersal (i.e., infinite island model of dispersal;

In each generation, the following events occur in sequence. (1) Each adult individual in a group produces a large number of juveniles. Juveniles mature and become subadults. (2) Each subadult disperses with probability

Each different connected series of edges starting at the root node (top of the figure) provides a demographic outcome. Different outcomes may lead to similar demographic events, which are denoted by

(i) Defeated group repopulation scenario (DGR). Here, in groups that have not been defeated, only subadults from that group compete against each other for access to breeding spots vacated by the death of adults. By contrast, in groups that have been defeated, subadults from both the victorious and defeated group compete against each other for vacated breeding spots. With probability

This DGR scenario is essentially a haploid version a the model mentioned above

(ii) Victorious group size expansion scenario (VGE). Here, instead of repopulating a fraction

In order to be able to directly compare this VGE scenario to the DGR scenario described above, I assume that the extraction of resources from defeated groups leads to an increase in the number of individuals reaching adulthood in victorious groups by

One may also suppose that warfare occurs at different timings in the life cycle of the individuals. For instance, subadults within groups may wage war before their dispersal instead of after dispersal so that stages (2) and (3) in the life cycle are interchanged. This case will also be investigated below.

Because a focal group in a focal generation may either attack or not attack another group, fight or not fight a battle when it attacks another group, be attacked or not be attacked by another group, and win or loose any of the possible battles, several different outcomes may affect the fitness of an adult individual from a focal group (

Under the DGR scenario, a demographic event determines the expected number of groups in which the individuals of a focal group may reproduce. For the events

The demographic events experienced by each group may also change across generations. A focal group may experience a certain demographic event, say

Following earlier models for the evolution of warfare in small scale societies, individuals within groups are assumed to express two different traits

Although both belligerence and bravery increase group success, both traits are assumed to reduce the probability that an individual expressing them survives up to the stage of density-dependent competition (stage 4 of the life cycle). Since clonal reproduction is assumed, the average phenotype of an offspring is the same as that of its parent. One can then express the relative number of juveniles, which reach the stage where they compete for breeding spots, and that are produced by a focal adult individual with level of belligerence

The evolutionary dynamics of belligerence (

The change in the frequency

Although such an ESS approach does thus not give a full picture of evolution, it allows one to obtain explicit analytical approximations, which would otherwise be out of reach, and that have repeatedly shown to provide good predictions for long-term phenotypic evolution and/or the direction of selection under a wide spectrum of biological applications involving local genetic drift under complex demographies with weak assumptions about the distribution of mutant's deviating phenotypic effects

For the DGR scenario, group size is the same in each group in the population in each generation. There are also no correlations between the demographic events experienced by a group from one generation to the next, and the occurrence of warfare is independently distributed across generations. The selection gradient on the trait

Owing to the infinite island model assumptions, individuals from different groups (with phenotype

For the VGE scenario, group size may fluctuate across generations and correlations between demographic states may develop over time. The selection gradient

I will present the derivations of the fitness function

In order to evaluate

Owing to the infinite island model of dispersal assumptions introduced above, I assume that the probability that the focal group with subadults expressing average level of belligerence

Alternatively to the situation described by eq. 2, one may also assume that warfare occurs right before the dispersal of juveniles, in which case the average phenotype among subadults is the same as that among adults so that

The exact functional relationship relating

From these assumptions, the probability that the focal group engages into a fight locally is given by

Eq. 4 gives the probability that a focal group engages in a fight. But we also need an expression for the probability that it wins the ensuing battle. I assume that the probability that the focal group, where subadults express average level

In this winning probability,

Equation 5 is a so-called contest success function

In order to evaluate

It is convenient to write the fitness function as

The fitness functions corresponding to each demographic event are evaluated by following the life cycle assumptions presented in the main text and standard calculations for the infinite island model

When the focal group has been conquered,

If warfare occurs before the dispersal of subadults; that is, stages (2) and (3) of the life cycle are interchanged but every other assumption of the model is the same, the above fecundity functions still apply. These fecundity functions can be applied to both warfare occurring before or after the dispersal of subadults, because in both cases regulation occurs after dispersal and warfare and it is the number of offspring reaching the regulation stage that determines fitness. Hence, we can use the same fitness functions to analyze the two different timings of warfare by making use of eq. 3 and the analogous equation for bravery (

Gathering all the above terms and taking into account the fact that, when the focal group conquers another group, the focal individual has descendants in the focal group and in the conquered group gives

In order to evaluate

Substituting eqs. 9–11 into eq. 7 and simplifying yields the fitness of a focal adult as

In order to compare the demographic benefits that accrue to a focal group under the DGR scenario to that obtained under the VGE scenario, it is useful to note that the reproductive value

Having an explicit expression for the fitness function

After simplification, eq. 15 reduces to

Substituting the direct fitness function (eq. 12) and the probability of identity-by-descent (eq. 18) into eq. 1, using belligerence as the focal trait (

Because

The left member of eq. 22 is the marginal decrease

The increase in fitness stemming from defeating a group is given by

When the right-hand-side of eq. 22 is higher than the left-hand-side, a higher level of belligerence is selected for, because the relatedness times the fitness benefits exceeds the fitness costs. When the right-hand-side of eq. 22 is lower than the left-hand-side, a lower level of belligerence is selected for. At an equilibrium point both sides of eq. 22 balance each other out. Substituting the explicit value of

A special case of eq. 23 will be useful for comparing different results. This is the weak warfare benefit limit; namely, when

Substituting eq. 12 and eq. 18 into eq. 1, using bravery as the focal trait (

At an evolutionary rest point

The marginal change in the wining probability given by eq. 26 has the interesting feature of increasing with group size,

Using the ratio form of the contest success function gives

An analytical model of selective groups extinction was developed in

Eq. 28 is also related to eq. 3.3 of

In addition, the term

These considerations show that DGR demographic scenario analyzed here is consistent with previous work endorsing closely related assumptions. The main difference with previous work so far is that the qualitative results obtained earlier apply to warfare occurring before and after the dispersal of subadults (the warriors in the model) and the winning and fighting probabilities have been made more mechanistic (e.g., eq. 4 and eq. 5). Further, making these functions more mechanistic has revealed that, depending on the form of the contest success function, costly bravery may actually evolve in large-scale societies and that the fighting probabilities are likely to depend on the level of belligerence in other groups from the population, which was not clear from previous work.

Under the VGE scenario, the selection gradients on belligerence and bravery involves more terms because the reproductive value of offspring settling in groups facing different demographic events must be taken into account (compare eq. 1 to eqs. B-1–B-2 of

Nevertheless, it was observed in numerical work that the stationary probabilities of occurrences of the demographic states often take values very close to that of independently distributed probabilities of occurrences across generations, which are the stationary values of the demographic process when

Assuming that the fitness benefits of defeating other groups are small, we can evaluate the selection strengths on belligerence to the first order in

Comparing eq. 31 to eq. 24 highlights that the demographics benefits of belligerence are generally lower under the VGE scenario than under the DGR scenario and that this difference decreases when the level of migration,

The probability of identity

The quasi flat line is the the value of

Assuming that the benefits of defeating other groups are small (e.g.,

The analytical results presented in the last two section (eq. 31 and eq. 32) suggest that the selective pressure on belligerence and bravery is generally stronger under the DGR than under the VGE scenario, especially when migration is limited. However, these analytical results rely on the assumption that the benefits of warfare are small and one may wonder if these results still hold if the benefits of warfare are strong; that is, if

The functional relationships used are

Evolutionary models of social interactions occurring within and between groups of individuals have often emphasized the benefits and conflicts associated with resource exchange within groups

The analysis of the models shows that the condition under which both belligerence and bravery spread in the population under the two demographic scenarios depends on four quantities (see eq. 22, eq. 28, eq. 29, and eq. 32). The first quantity is the relative marginal cost to a focal individual of expressing the trait under scrutiny [

The increase in the probability of defeating other groups from the population (

How different are the selection on belligerence and bravery under the two demographic scenarios? It is worthwhile to emphasize at this point that in order to be initially able to compare the DGR to the VGE scenario, I assumed that the demographic benefits of warfare accruing to a focal group are comparable in magnitude. Although the demographic processes underlying these two models are different, the reproductive value

Under the life-cycle assumptions used in this paper, the main quantitative difference in the selective pressure on belligerence and bravery under the two scenarios stems from the fitness benefits of defeating other groups and relatedness taking different values. Under the DGR scenario, the fitness benefits of defeating another group; namely, the increase in group reproductive value, is equal to

The relatedness coefficient tends to be smaller under the DGR scenario than under the VGE scenario, which now tips the balance in favor of stronger selection on belligerence and bravery under the VGE scenario. This follows from the fact that genetic mixing occurs during repopulation, which decreases the probability of identity within groups, unless groups are completely repopulated (

Combining the effect of relatedness and the fitness benefits of defeating other groups on the selective pressure suggests that selection is stronger on both traits under the DGR than under the VGE scenario. From an evolutionary perspective, this suggests that the possibility to repopulate defeated groups by fission of a victorious one or by its members fertilizing the females of defeated groups leads to higher fitness benefits than the gain of additional resources by conquest, which increase local carrying capacity.

The two demographic scenarios of warfare analyzed here may also occur under different ecological conditions. The DGR scenario may be more consistent with a situation where groups live on or around resources that are concentrated and have static positions in space and time (such as patchily distributed resources, water points, or shelters) and fight over them for monopolization. This may be the case in social insects

As a final point, the DGR and VGE scenarios are mainly relevant for understanding the fitness benefits of warfare in pre-state societies, where interactions occur between individuals that are more likely to share a recent common ancestor than are individuals sampled at random from the population. But the role of and motivations behind belligerence and bravery in the transition from small-scale to large-scale societies remains to be better understood. In the absence of benefits to self or relatives, there should be no naturally selected motivations in the world causing an individual to lay down its life.

Derivation of the fighting probabilities.

(PDF)

Derivation of the selective pressures on belligerence and bravery under the VGE demographic scenario.

(PDF)

The remarks of a referee on a previous version of this paper were very helpful for improving the presentation. I also thank F. Rousset and S. Yeaman for useful comments on the paper.