Leaders of war: modelling the evolution of conflict among heterogeneous groups

Abstract

War, in human and animal societies, can be extremely costly but can also offer significant benefits to the victorious group. We might expect groups to go into battle when the potential benefits of victory (V) outweigh the costs of escalated conflict (C); however, V and C are unlikely to be distributed evenly in heterogeneous groups. For example, some leaders who make the decision to go to war may monopolize the benefits at little cost to themselves (‘exploitative’ leaders). By contrast, other leaders may willingly pay increased costs, above and beyond their share of V (‘heroic’ leaders). We investigated conflict initiation and conflict participation in an ecological model where single-leader–multiple-follower groups came into conflict over natural resources. We found that small group size, low migration rate and frequent interaction between groups increased intergroup competition and the evolution of ‘exploitative’ leadership, while converse patterns favoured increased intragroup competition and the emergence of ‘heroic’ leaders. We also found evidence of an alternative leader/follower ‘shared effort’ outcome. Parameters that favoured high contributing ‘heroic’ leaders, and low contributing followers, facilitated transitions to more peaceful outcomes. We outline and discuss the key testable predictions of our model for empiricists studying intergroup conflict in humans and animals.

This article is part of the theme issue ‘Intergroup conflict across taxa’.

1. Introduction

War, defined as violent intergroup conflict [1], is one of the most conspicuous and destructive behaviours exhibited by Homo sapiens. Human warfare is highly variable, encompassing both small-scale skirmishes between bands of hunter–gatherers [2,3] and the more organized, industrial conflict characteristic of the past century [3]. Although sometimes considered a uniquely human enterprise [4–6], war has analogues in intergroup conflict observed across the animal kingdom, from territorial border contests between chimpanzees (Pan troglodytes) [7,–9] to the battle lines of banded mongooses (Mungos mungo) [10,11] and mass colony raids in army ants [12]. Such violent behaviours might only be expected to evolve when the fitness costs, e.g. serious injury or death [9,11,13], are outweighed by the potential benefits of victory, e.g. the expansion of territory [9,14], access to limited resources [8,11,13,15,16] or increases to prestige, status and reputation ([17]; for a review see [18]). However, this simple understanding—that war should evolve when the benefits are greater than the costs—becomes more complicated when considering heterogeneous groups [19].

Social groups are intrinsically heterogeneous [20], with members that may differ in leadership status [21], social rank [14,20–23], sex [13,20,21,24,25], size [20], personality [20,26,27] or age [20,21,24], among other factors. This heterogeneity is likely to lead to individual differences in the risks and rewards of fighting [13,20,25,28–30]. For example, in African lions (Panthera leo), there are consistent differences between individuals in their willingness to engage in territory disputes, as some ‘laggard’ females consistently hang back and exploit the fighting effort of others [26,30,31]. Similarly, in many primates such as vervet monkeys (Chlorocebus pygerythrus) [23], blue monkeys (Cercopithecus mitis) [32], Japanese macaques (Macaca fuscata) [24] and Verreaux's sifakas (Propithecus verreauxi) [33], individuals contribute more towards intergroup conflict the higher their social rank and position in the dominance hierarchy. This is different from modern human societies in which studies of the US military have shown that the risks of sustaining physical combat injuries [34,35], or experiencing poor mental health [36,37], both decrease with increasing military rank. How inter-individual differences in the risks and rewards of conflict affect evolved levels of conflict effort and conflict initiation has been little studied to date. However, see [25,30] (both from this issue) for a consideration of how sex and personality differences influence conflict behaviours.

Two recent evolutionary models [13,29] have examined how within-group heterogeneity affects the evolution of intergroup conflict. Gavrilets & Fortunato [29] asked how heterogeneity influences individual levels of investment in conflict effort between heterogeneous groups. They modelled intergroup conflict as a collective action problem in which individuals pay personal fitness costs to increase the probability of winning an intergroup fight. Specifically, they examined the evolution of conflict effort when group members occupied different social ranks, which determined priority of access to a contested resource. ‘Leaders’—who were assumed to be high-ranking individuals—benefited from priority of access and so received a higher value from the contested resource relative to low-ranking individuals. Given this disparity between ranks, low-ranking individuals were found to evolve low levels of conflict effort, but this reduction was more than compensated by elevated investment from high-ranking individuals [29]. Surprisingly, this leads to outcomes at which low-ranking individuals obtain higher fitness than high-ranking individuals. This is because the non-participatory followers are able to free-ride and benefit from the ‘heroic’ leadership and increased conflict effort of their leaders [29].

A second model by Johnstone et al. [13] examined how a different form of leadership (decision making, not dominance) affected the probability of escalated conflict between groups. Specifically, Johnstone et al. [13] adapted the classic hawk–dove (HD) model [38] to investigate the evolution of conflict-escalating behaviours when leaders control decisions about whether their group fights or not. This model predicts that where leaders receive a disproportionately large reward, or are at a disproportionately low risk, they are more likely to lead their group into escalated fights with other groups [13]. Such ‘warmongering’ behaviour evolves because fighting increases the individual fitness of war leaders (who made the decisions), even when it leads to negative consequences for their followers [13]. It is for this reason that exploitative warmongering behaviour has been hypothesized to be responsible for amplified levels of violence in both non-human animal [13] and human societies [39,40]. This model is supported with empirical data from banded mongooses [13], where dominant females are thought to selfishly lead male followers into violent and dangerous intergroup encounters in search of extra-group mating opportunities for themselves [13,41]. By contrast to Gavrilets and Fortunato's model [29], the exploitative leadership model predicts that leaders should obtain much higher fitness payoffs than the followers as a result of intergroup conflict.

These two modelling approaches thus focus on two related but distinct aspects of the question of how heterogeneity affects conflict behaviour: Gavrilets & Fortunato [29] focus on the evolutionarily stable strategy for investment in conflict effort, whereas Johnstone et al. [13] focus on the decision of whether to initiate and escalate conflict. What emerges from these two frameworks is a continuum between two extreme types of war leaders: ‘heroic’ leaders, who invest much more in conflict than low-ranking followers, versus ‘exploitative’ leaders, who initiate conflicts but invest relatively little.

Our aim here is to provide a more general model of the evolution of intergroup conflict behaviour, and to generate ecologically relevant predictions regarding conflict investment and escalation in heterogeneous groups. In the process, we synthesize and generalize the two theoretical approaches introduced above. Our model allowed fighting investment to evolve such that individuals could exhibit greater or lesser contribution to the conflict. This is consistent with the approach taken by Gavrilets & Fortunato [29], and unlike the Johnstone et al. model [13], in which all followers had enforced participation in fighting. We adopted heterogeneity of decision making from Johnstone et al. [13]. Specifically, only leaders were responsible for conflict decision making, which is consistent with leadership as defined in the relevant literature [22,30,42]. In keeping with both Gavrilets & Fortunato [29] and Johnstone et al. [13], we assume that leaders benefit more from the rewards of fighting. However, we also test the model with a full range of benefit distributions, biased either for or against the leaders (see also sharing rules in [43]).

We use the model to explore key ecological and demographic conditions that can favour different forms of conflict leadership. We also focus on scenarios where populations evolve relatively peaceful versus hostile interactions. The outcome is a set of novel, testable predictions relevant for empiricists studying intergroup conflicts in both human and non-human animal systems.

2. Methods

(a) . Broad overview of model

See figure 1 for a graphical representation of the model. We simulate intergroup encounters using a finite population of distinct groups consisting of a single leader and multiple followers (initialized with number of groups in starting population (Ngr) = 200 groups of N = 20 individuals; table 1; see row 1 in figure 1). Upon meeting, the leaders of each group decide to play a ‘hawk’ (aggressive) or ‘dove’ (peaceful) strategy [38]. Costs C (modelled as mortalities) and benefits V (modelled as births) are distributed to winning and losing groups (see row 2) based upon their strategy played (table 2), and, if conflict escalates, a summed fighting effort of the group (figure 2). Following the resolution of encounters, a sequence of events takes place to mimic natural population dynamics [28]. First, random births and deaths are applied to re-establish a stable carrying capacity (row 3). Second, possible group fission takes place, where larger groups are more likely to split [44–50] (row 4). Finally, possible migration between groups can occur (row 5). This process is then repeated with the surviving groups for N = 20 000 rounds.

Figure 1.

Schematic of model process in simplified population of three groups. All rows are discussed in greater detail in §2. Row 1: Population as it stood following the previous round (for the first round see §2a). Groups each have one leader (purple), multiple followers (green) and a group ID (numbered). Row 2: Encounters are generated and payoffs are then resolved (table 2). Row 3: Random deaths or births are applied with equal probability for each member of the population to re-establish the same population size. Row 4: Fission. Row 5: Migration. Row 6: New population will feed back into row 2, for the next round. There were N = 20 000 rounds in each of our iterations of the model. Each iteration was repeated 15 times for a distinct set of parameters.

Table 1.

Parameter table. Default values for each parameter are in bold. Default values define the value taken for each variable when exploring other parameters in non-bold. V and Ni remained fixed and are investigated as relative to C and Ngr, respectively. Parameters, including defaults, were chosen to illustrate a wide range of resulting outcomes (based on preliminary findings). We encourage researchers to use our code to explore other values and/or data-driven parameterization of the model: www.github.com/sankeydan/leadersOfWarModel.

parameter	short form	parameter values or calculation
round	n.a.	20 000
number of groups in starting population	Ngr	100, 200, 300, 400, 500
size of each group in starting population	Ni	20
maximum group size	Max	40, 50, 60, 70, 80, 90
mutation strength	Mut	0.005, 0.01, 0.015, 0.02, 0.025
migration probability	Mig	0, 0.01, 0.02, 0.03, 0.04
value of resource	V	6
cost of escalated conflict	C	2, 4, 6, 8, 10
pyrrhic constant	Pyr	0, 0.15, 0.3, 0.5, 1
encounter rate	Er	1, 2, 3, 4, 8
reproductive skew in favour of leader	Skew	0.5, 1, 2, 3, 4

Table 2.

Payoffs for different focal versus opponent strategies.

focal strategy	opponent strategy	focal win/lose escalated conflict	costs (number of mortalities to focal group)	benefits (number of reproductions to focal group)
hawk	hawk	win; escalated	(C x Pyr)	V
hawk	hawk	lose; escalated	C	0
hawk	dove	win; non-escalated	0	V
dove	hawk	lose; non-escalated	0	0
dove	dove	draw; non-escalated	0	V/2

Figure 2.

Contributions: a trade-off between group fighting success and individual mortality. Illustration of how escalated conflicts are resolved between two groups (each group N = 5) (escalated conflict occurs when both groups play a ‘hawk’ strategy). Leaders are coloured (red or blue), while followers are black. Group membership and identity are consistent throughout the three panels. (a) Each individual is positioned according to their LC score (fighting effort if the individual is a leader) or FC score (fighting effort if the individual is a follower), such that higher values represent individuals who contribute more to the fight and are positioned closer to a figurative ‘battle line’. The group on the left side of the battle line is described as having a ‘heroic’ leader (LC higher than group mean FC), whereas the group on the right side of the battle line have a more ‘exploitative’, low contributing leader (LC lower than group mean FC). (b) A sum of each group's contribution score (leaders' LC and all followers' FC) determines their group's combined fighting strength (ordered from lowest to highest contribution scores). Here, the group with the ‘heroic’ leader has a greater summed score and would win the fight. (c) Each individual's contribution score also determines their individual risk of death when mortalities are suffered as a result of escalated conflict (ordered from lowest to highest contribution scores). This mortality probability is an individual's contribution score, divided by the summed score of their group.

The leader of each group is chosen at random in the first round, and randomly re-assigned if the present leader dies. The rest of the group are assigned as followers. All individuals are assigned three fixed genes on a continuous scale between 0 and 1: (i) hawk–dove score (HD, probabilistic propensity to play ‘hawk’ rather than ‘dove’ if the individual is leader); (ii) leader contribution (LC, fighting effort if the individual is leader); and (iii) follower contribution (FC, fighting effort if an individual is a follower). Importantly, all individuals are assigned values for all three genes, but which genes are expressed depends on their status as a leader or follower, which may change over time. For example, a leader will express their HD and LC gene but will also carry a dormant FC gene to pass on to offspring. Likewise, followers' HD and LC genes remain dormant unless they become a leader. Each individual in the starting population is initialized with HD, LC and FC scores of 0.5. From this starting point, a mutation value is applied with each offspring created (mean = parent value; with standard deviation Mut applied; table 1), but each gene is bounded to take a value between 0 and 1. Asexual reproduction is assumed for simplicity [51,52].

(b) . Intergroup encounters

Groups randomly encounter one another in pairwise interactions according to the encounter rate (Er), which determines the mean number of encounters per group per round of the model (see row 2, figure 1). The random generation of encounters allows multiple interactions between the same groups while other groups possibly avoid interaction altogether (in a given round). Encounters are resolved sequentially in the order in which they were generated. If a participating group becomes extinct in a prior interaction within the same round (e.g. if all group members die in the previous conflict) then all this group's following interactions are cancelled.

Encounters begin with the focal and opponent leaders each making the binary decision whether to play an aggressive ‘hawk’ strategy with probability HD, or peaceful ‘dove’ strategy with probability (1 − HD). For example, a leader with a HD score of 0.8 would play ‘hawk’ 80% of the time. All encounters beside hawk–hawk (i.e. hawk–dove, dove–hawk, dove–dove) are resolved without escalated conflict according to the payoffs listed in the interaction table (table 2). For example, if an aggressive ‘hawk’ group encounters a peaceful ‘dove’ group, then the hawk group will obtain all the benefits of the resource (V), which is left uncontested by the fleeing dove group.

If two ‘hawks’ meet, then the encounter escalates to a conflict where only one group can obtain the resource V. The other group will pay a cost for losing an escalated conflict, which we define as C for the losing group. Winners are determined by totalling the fight contribution scores of each participating group (i.e. leaders' LC + all followers’ FC scores), with the greater score determining the winner (figure 2a,b). We thus treat all group members as ‘perfect substitutes’, meaning that they are all equal in their capacity to contribute towards their group's fighting effort [53,54]. ‘Perfect substitutes’ is the most widely used group impact function when modelling intergroup conflict [28,54,55].

(c) . Costly victories

So far in our model, the average payoff for hawks is equivalent to the classical formulation of the HD game where hawks meeting hawks receive a payoff = (V−C)/2 [38]. However, we also consider a modification to the payoff structure by including a parameter whereby winning groups also pay a cost of conflict determined by a pyrrhic Pyr parameter (table 2). Such scenarios are reminiscent of a costly pyrrhic victory, originally named after the devastating casualties suffered by the victor King Pyrrhus against the Romans in the Battle of Asculum in 279 BC [56]. This parameter reflects the reality that even victorious groups will often suffer casualties during a fight (this is also true of individual contests; [57]). As a real world example, we provide data from banded mongooses (data collected from 13 mongoose groups between February 2000 and January 2020), where 4 of 34 deaths attributed to intergroup conflict occurred within winning groups (data provided in electronic supplementary material, table S1; 78 battles either ended in no deaths, or none were recorded). Pyr is bounded in our model between 0 and 1 and is used to calculate the winning group's mortality cost (C x Pyr, table 2). Banded mongooses would be modelled with a Pyr of 0.13 (calculated from the ratio of 4 : 30; above), and we used a rounded 0.15 as the default parameter in our model (table 1). The conflict mortality rate observed in banded mongooses is similar to that of both chimpanzees and humans [13], although values of Pyr are unobtainable from these data. When Pyr = 1, both winners and losers suffer the same costs of fighting. In extreme instances, this could lead to pyrrhic victories where the costs of fighting, even if successful, negate most or even all of the benefits obtained from the resource (V). Importantly, we can still recapture payoff structures comparable to the classic HD model by simply allowing Pyr = 0 (winning groups pay no costs).

(d) . Payoff resolution

Payoffs are resolved after each intergroup encounter according to the outcome table (table 2). Values of V and C are directly translated into reproductions and mortalities, respectively. Payoffs are resolved such that mortalities take place first, and then any reproductions occurring afterwards do so from among the surviving group members. For example, if a victorious group suffers costs of C x Pyr = 4 and wins a payoff of V = 6, the group will lose four group members through mortality, and then gain six new members through reproduction (how mortalities and reproductions are distributed between individuals in the group is explained below in §2d(i) and §2d(ii), respectively). Mortalities represent either direct mortality during combat, or those that occur indirectly, such as through infected wounds or from loss of access to resources ([9], for a review see [18]). Reproduction represents how the spoils of war, such as increased territory size or access to food and mating opportunities, can directly be translated into increased reproductive output ([15], for a review see [18]).

(i) . Distribution of costs (mortalities)

The value of C (or C x Pyr) equates to the number of mortalities that the group will suffer. If C x Pyr is not an integer, the fraction is converted into a probability that another individual will perish. (For example, if C x Pyr = 3.5, the winning group will suffer three or four mortalities with equal probability.) Mortalities are applied sequentially and distributed proportional to the effort that group members contributed towards the fight. Therefore, individuals that are most influential in contribution towards a group victory (figure 2b) are also the most likely to die when the group suffers mortalities (figure 2c). More specifically, the probability of death within a group is determined as the effort of the individual divided by the summed effort of the group (also figure 2a,c), meaning the costs are dependent on the actions of all group members (also see [30]):

$$\mathrm{leader\prime s}\hspace{0.17em}\mathrm{probability}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\mathrm{death}=\hspace{0.17em}\hspace{0.17em}{\displaystyle \frac{LC}{\left({\sum }_{i=1}^n{FC}_i\right)+(LC)}}$$

and

$$\mathrm{follower}\hspace{0.17em}x\text{′s}\hspace{0.17em}\mathrm{probability}\hspace{0.17em}\mathrm{of}\hspace{0.17em}\mathrm{death}=\hspace{0.17em}{\displaystyle \frac{{FC}_x}{\left({\sum }_{i=1}^n{FC}_i\right)+(LC)}\hspace{0.17em}}$$

where n is the number of followers in the group, LC is the LC score of the leader and FC_x is the FC score of the focal follower x.

If the number of mortalities a group receives exceeds the number of contributing group members (LC or FC > 0) then, once mortalities have been applied to contributing group members, mortalities are applied at random among non-contributing group members (LC or FC = 0). At any point, if groups consist of fewer than two individuals (one leader and one follower) then they are considered extinct and removed from the population.

(ii) . Distribution of benefits (reproductions)

In our model, the probability of reproduction does not depend upon individual fight contribution scores (LC or FC). Some studies have suggested that highly contributing fighters are more attractive and expected to benefit from increased reproductive success, e.g. ‘sexy soldiers’ [15,18,58,59], whereas others have argued that the costs of fighting decrease the reproductive success of fighters relative to non-combatants, e.g. ‘worn-out warriors’ [18,60–62]. Rather than arbitrarily choosing a position on this argument, the probability of each individual reproducing in our model (i.e. sharing rule [43]) is distributed through the group evenly except for leaders, which exhibit a skew that reflects their share of reproduction relative to the followers. We test a range of conditions from Skew < 1 (leaders reproduce less and have lower fitness than followers, e.g. lions [26] and theoretical models [63,64]) through Skew = 1 (everyone reproduces roughly equally e.g. plain zebras and bottlenose dolphins [21]) to Skew > 1 (leaders have higher likelihood of reproducing, e.g. meerkats, hyenas and white-faced capuchins [21]). Consistent with both Gavrilets & Fortunato [29], and Johnstone et al. [13] we chose a positive skew as default (Skew = 2; table 1).

(e) . Population dynamics

(i) . Finite population modelling

At the end of each round, after all paired encounters have been resolved, we simulate biologically relevant changes to the population structure. Our model assumes that population size is limited by resources in the environment and tends toward a stable carrying capacity [65,66] (see row 3, figure 1). Therefore, after resolving all payoffs from intergroup encounters in a given round, we apply additional reproductions or mortalities to ensure that the population size remains stable and prevent it from either depleting to zero or increasing to unsustainable levels. Both outcomes are possible in this model because of encounters with asymmetric payoffs, whereby one group gains a different amount (in reproduction) from what is lost by the other group (in mortality). At this step, both reproduction and mortality are applied equally and randomly, despite any differences in leader status or genotype scores. Any new individuals born inherit a follower status in the same group as their parent.

(ii) . Fission

Next, we incorporate group splits, which become more likely with increasing group size and for which there is empirical [44,46,48,49] and theoretical [45,47,50] evidence (see row 4, figure 1). In our model, splitting is inevitable if groups are at or above the maximum group size parameter Max (table 1) and impossible for group sizes fewer than four, because two is the minimum viable group size for each daughter group (i.e. one leader and one follower). Group splitting for groups between four and Max individuals is governed by a standard exponential increase, meaning splitting has a low probability that increases exponentially as group size approaches Max. In nature, the size of each subgroup after splitting can be highly variable, from evictions of small subgroups [67] to larger (relatively even) group splits [68,69]. Our model does not bias between large or small group splits, and so determines the size of the daughter group from a uniform distribution with a minimum group size of two and a maximum of one half times the total group size (rounded down in the case of decimals). When a group splits, the leader remains in position to lead the larger, parent group (if daughter and parent groups are the same size, then the leader is assigned to a daughter/parent group at random. A new randomly selected leader—chosen among followers—is assigned to lead the daughter group. Leadership has been demonstrated to arise spontaneously from previously identical individuals through a runaway process starting with minimal stochasticity [63], which validates this choice within our model.

(iii) . Migration

Intergroup migration is the final step in each round of the model (see row 5, figure 1). Migration dynamics have a large effect on population structure and relatedness, which in turn can predict pro-social behaviours towards own group members [28,70,71] and hostility towards other groups [28,71], such as the willingness to fight [28,72,73], which we investigate here. Therefore, a migration parameter is an appropriate inclusion. All followers can migrate (i.e. change groups) at the end of each round. The probability that any follower will migrate in each round is determined by Mig (table 1). When migrating, an individual emigrates to another group at random and with equal probability.

(f) . Model iterations

We ran 15 iterations of each set of parameters tested in our model (table 1) to understand the influence of each parameter on the emergent population. During the simulation, for each group, in each round, we output the leader's HD and LC scores, and one mean FC value from all their followers (but see electronic supplementary material, figure S1 for output using the FC of each individual follower). For analysis, a mean of the population phenotype for each trait was calculated from the last 5000 rounds (representing 25% of the model) and taken for further analysis. Waiting for 15 000 generations allowed the model to stabilize beyond the point at which no more changes to the phenotype were observed (which was typically prior to 5000 generations).

3. Results

(a) . Follower and leader contributions

We found that both ‘heroic’ leader outcomes (high LC, low FC) and ‘exploitative’ leader outcomes (low LC, high FC) emerged readily within our model, in addition to another condition that we term a ‘shared effort’ outcome (high LC, high FC).

Varying the maximum group size (Max) was found to greatly influence LC and FC, with increasing group size causing a shift in outcome from all individuals contributing highly (shared effort), to a ‘exploitative’ leader outcome, and then to a ‘heroic’ leader outcome (figure 3a). Similar trends were also found with increasing values of the cost of escalated conflict C (figure 3b), and migration rate Mig (figure 3c), whereas increasing the encounter rate, Er, resulted in a transition in outcomes in the opposing direction (figure 3d). At low values of reproductive skew (Skew) leaders contributed more than followers and vice versa at higher values (figure 3e).

Figure 3.

Influence of ecological or demographic parameters on fighting contribution scores. Follower contribution (FC; green) and leader contribution (LC; purple) (mean (dots) ± s.e. (bars); see raw data in electronic supplementary material, figure S3). All other variables not on x-axis are set at default values (highlighted in bold in table 1). Each unique combination of parameters ran 15 times, with each model run representing one datum (population mean of followers' FC or leaders’ LC for final 5000 rounds of an iteration).

(b) . Evolution of hostile interactions

We found that HD score was highly correlated with FC (figure 4a,b), such that aggressive ‘hawk’ strategies were more common when groups had higher FC scores (Pearson correlation coefficient = 0.999; correlation between models displayed in figure 4a with those in figure 4b, N = 150). This is a strikingly high correlation when considering that the two genes evolved independently and suggests a possible causal relationship. However, HD score (as well as FC) also decreased when there were higher costs (C—figure 4a; and Pyr—electronic supplementary material, figure S2). Therefore, a valid alternative hypothesis to a causal relationship between leader HD and follower FC is that costs of conflict are driving both leader HD and follower FC. To further investigate the effect of FC on hawkishness independent of fighting costs, we fixed the values of C and Pyr at default values (table 1) and changed other variables known—from our results (figure 3; electronic supplementary material, figure S3)—to favour high or low levels of FC (table 3, figure 4c) and then measured the outcomes.

Figure 4.

Hawk–dove decision (HD) driven by low costs and high follower contribution scores. (a) HD score (mean ± s.e. for 15 iterations) as evolved under parameters fixed at the default values except for cost (C), which varies on the x-axis. (b) (As in (a)) except showing evolved follower contribution FC score (mean ± s.e. for 15 iterations). (c) HD score when parameter values favoured different levels of follower contribution (FC). This shows that even when costs C and Pyr were frozen at default values (6 and 0.15, respectively), mean hawkishness (HD score) of populations increased from low FC, through default, to high FC conditions (table 3; N = 15 replicated iterations for each condition), suggesting that FC has an independent causal influence on HD.

Table 3.

Comparison of low FC, default and high FC starting conditions. Parameters not shown take the same values as the defaults in table 1.

parameter	low FC conditions	default conditions	high FC conditions
max group size (Max)	90	70	50
migration probability	0.04	0.02	0.01
encounter rate	1	2	3
reproductive skew in favour of leader (Skew)	1	2	4

We found that HD score could still covary with FC, despite fixing costs (C and Pyr) (figure 4c). When the model was parameterized with conditions known to favour high FC, HD score increased (table 3; figure 4c). When conditions favoured low FC, HD score decreased (table 3; figure 4c), although not to zero because hawks can always invade pure dove populations through frequency-dependent selection [38].

4. Discussion

We have used a single-leader–multiple-follower evolutionary model to explore the effect of ecology and demography on conflict initiation and conflict participation in warfare between heterogeneous groups. Our results suggest that demographic and ecological parameters can shift the population between three classes of outcomes: from ‘heroic leadership’ with low contributing followers, through ‘exploitative leadership’ with high contributing followers and ‘shared effort’ outcomes, with both leaders and followers participating in conflict. For example, when (i) the maximum group size is high, (ii) intergroup encounters are infrequent, (iii) leaders reproduce less than followers, (iv) the costs of escalated conflict are high or (v) follower migration rates are high, then leaders contribute more during conflict relative to followers (‘heroic’ leaders). These outcomes—where followers are less willing to participate—are associated with relatively more peaceful intergroup encounters at the population level, and the evolution of conflict avoidance strategies. By contrast, outcomes with high participation levels among followers are strongly correlated with increased intergroup aggression and hostility.

(a) . Evolution of conflict investment

In order to explain the different range of outcomes from our model it is useful to invoke the framework of multi-level selection [51,74–76]. Here, changes to parameters either emphasize intergroup conflict (and selection at the level of the group) or intragroup conflict (and selection at the level of the individual). Within-group altruism (e.g. high fight contribution) is more likely to evolve with high intergroup and low intragroup conflict [77–79]. As a first example, consider changes to the intergroup encounter rate, which directly encodes higher rates of intergroup conflict into the model. With increased encounter rates, high participating ‘cooperative’ groups outcompete lower participating ‘selfish’ groups (which tend toward extinction). As a result, both follower and leader participation increase at higher intergroup encounter rates (figure 3d). Conversely, increased migration rates are known to enhance intragroup competition and undermine cooperation [80–82]. This is because high-participating groups are vulnerable to invasion by selfish individuals who participate very little but can free-ride on the efforts of a cooperative group. Another factor promoting intragroup conflict is maximum group size. It is well known that larger group sizes can result in increased susceptibility to collective action problems [19,83,84], with each individual shying away from sharing the costs necessary to produce a public good (in our case, victory in intergroup conflict).

Although this multi-level selection argument explains the contribution patterns of followers, it does not explain why leaders contribute differently from followers across much of the range of parameters we explored. Here, it becomes important how frequently high participation from a leader will be decisive in determining victory for their group. Consider the case where intergroup conflict levels are high, but not extreme, for example Er = 5 from figure 3d. Here, follower participation is large across the population (i.e. FC is close to 1) and therefore all leaders are likely to have highly willing followers. In such cases (with summed fighting strength approximately equal to group size) it would take a meeting of two almost-identically sized groups for a highly participating leader to swing the outcome in their favour. In most cases, the increased risk of mortality (associated with high participation) is enough to outweigh this small probability of benefit, and leaders shirk away from battle as a result. This echoes the result of Johnstone et al. [13] where leaders exploit their high-participating followers. At the other end of the scale, as follower participation declines, the group's success will be highly dependent upon the participation from their leaders, and thus high participation from leaders becomes favourable. Gavrilets & Fortunato [29] found a similar result, whereby high-ranking individuals applied extra effort to offset a collective action problem and overcome the reduced contributions of the lower-ranking individuals.

Our choice to treat all group member contributions as ‘perfect substitutes’ [28,53–55], meaning that all individuals have equal capacity to contribute to a fight, could limit the generalizability of our results across different contexts of intergroup conflict. For example, in some taxa such as wolves and banded mongooses, some individuals (notably older males) have a disproportionate influence on conflict outcomes [85,86]. Extreme examples are provided in the economics literature where a ‘weakest link’ (e.g. high interdependence between group members) and ‘best shot’ (e.g. champion warfare) group impact functions explore only the least and highest contributor, respectively [43,54,55]. Another approach, not explored in our model here, is to differentiate participation on the basis of attack or defence. Models that consider this approach find differential investment depending on whether resources are being defended or attacked [87,88]. Nevertheless, a summed ‘perfect substitutes’ approach, as used in our own model, is the most widely used group impact function [54,55] and its use successfully captures many of the common elements of intergroup conflict (e.g. larger groups are more likely to win).

(b) . Real world relevance of parameters

(i) . Maximum group size (Max)

Our results suggest that in larger groups, high-ranking leaders will contribute more towards battles than followers. Supporting this finding are observations from spotted hyena (Crocuta crocuta) clans, which may contain 90 or more individuals [89]. Within these clans, high-ranking adult females are most often observed at the front line during conflict [21,25,90]. As these individuals are also disproportionately responsible for initiating conflict [90], we would also predict (after accounting for any other differences in other important ecological variables) (i) that larger groups within the population would be more aggressive (electronic supplementary material, figure S4) and (ii) lower levels of conflict in hyena populations with larger clan sizes (e.g. 90+ in Kenya [89,90]) than smaller clan sizes (e.g. 15+ in Namibia [91,92]; electronic supplementary material, figure S4). Conversely, humans do not fit the outcomes of the model, with leaders of larger groups having been shown to contribute less [21]. We suggest that differences in humans could be due to coercion, including but not limited to punishment [93,94], or the spread of cultural ideas from the leaders to followers to induce within-group altruism [95,96]. To test the relevance of our conclusions in humans, the intergroup game we propose could be broadly replicated in experiments involving human participants following methods from a large body of experimental work into contest theory (for reviews see [54,97]).

(ii) . Intergroup migration rate (Mig)

Increased migration rates led to decreased contributions among followers and increased contributions in leaders (figure 2c). As migration rates increase, cooperation can be more easily undermined by faster-reproducing non-cooperators [73]. Followers evolve non-cooperation and leaders ‘pick up the slack’ to remain competitive with other groups and to avoid individual and group extinction, consistent with Gavrilets and Fortunato's conclusion [29]. In animal systems where the potential for intergroup migration is limited, e.g. there are high dispersal costs [98], we would expect to see groups consisting of highly contributing followers and aggressive and ‘exploitative’ leaders. Yellow baboons (Papio cynocephalus) appear to support this prediction, because males are highly vulnerable to predation during solo dispersals [99], and also participate in frequent, and often lethal, intergroup conflict [100,101].

(iii) . Reproductive skew in favour of the leader (Skew)

Our model predicts that increased reproductive skew (biased towards the leader) will select for more cooperative followers and ‘exploitative’ leaders, who are best able to minimize their mortality risk and therefore maximize the length of their reproductive tenures (figure 3e). When leaders have low contribution, competition between groups will favour high contribution from followers. As reproductive skew increases, the FC rise, as they are determined increasingly by the leaders (who will be motivated to sire highly contributing offspring) and less by follower reproduction (who will be motivated to decrease contributions). Different animal systems, with varying degrees of skew, represent ways to test this prediction. For example, in African lions, the relative fitness benefits of intergroup conflict are skewed against the leading females (e.g. Skew < 1) [21], which our model predicts will lead to low contribution scores among followers (figure 3e). This is seen in nature, with observations of ‘laggard’ females who are reluctant to participant in territorial conflicts [26,31]. By contrast, meerkats have a high degree of reproductive skew, with leaders able to monopolize the benefits from intergroup conflict [21]. Given that these leaders are the same individuals that initiate conflicts [14,21], our model provides a direct prediction that we would expect contribution scores among these leaders to be lower than the mean contributions of followers once battles ensue (figure 2e). Furthermore, we might predict that leaders would exhibit ‘warmongering’ behaviour, initiating more conflict than is beneficial for their group [13,14].

(c) . Evolution of conflict initiation and hostility between groups

Classic work has shown that the frequency of escalated conflict observed in a population is highly dependent on the costs of fighting [38]. We show that whether groups interact peacefully or are hostile to one another is dependent not only upon these costs, quantified in our model through C (figure 4a) and Pyr (electronic supplementary material, figure S2), but also the contribution of followers (figure 4c). This finding is intuitive, as leaders will be incentivized to escalate more conflicts when they are supported by large numbers of ready and willing followers, compared to when their followers are reluctant to participate in conflict.

In some non-human animal or human societies followers might not have the freedom to individually lower their contributions. This might be the case in banded mongooses, where there are high levels of group synchrony [102] and acting alone is not an option due to predation risk [102,103]. In humans, the presence of coercion and punishment, such as court martials for cowardice as was common during World War I [104], may provide a similar constraint on the evolution of FC, and serve to sustain higher-than-expected levels of aggression. Conversely, if the costs of conflict increase or the contribution levels of followers are chosen freely, then more mixed HD strategies are favoured, and the mean population level of intergroup aggression decreased. This result provides a testable prediction for researchers studying intergroup conflict, namely that for populations with larger maximum group sizes, higher migration rates or lower frequency of intergroup encounters, we would find a lower level of escalated intergroup conflict.

Mixed HD strategies are more peaceful when compared with non-negotiable fighting over every resource, as is the case when populations play purely hawk strategies. However, hawks will continue to succeed when invading majority dove populations [38], eliminating the possibility of entirely peaceful populations (figure 4c). Exploring these mixed strategy populations, we found that, within the same population, larger groups were more likely to exploit their favourable position and behave more aggressively than small groups (electronic supplementary material, figure S4). This difference between the aggression levels of small and large groups increases as maximum group size increases, even as population mean conflict levels decrease. This may be reflected in modern international interactions, whereby larger powerful nations are rarely challenged by smaller ones, and have been found to start more wars [105].

The work presented here provides a base model that may now be extended further to explore whether any conditions can reduce the evolution of intergroup hostility further than we observed here. For example, a classic argument in political theory ([105,106]; [107, pp. 93–130) is that more democratic societies, with more distributed and shared forms of decision making, are expected to evolve to be more peaceful, relative to non-democratic societies (such as the dictatorial one-leader, multiple-follower groups we have presented here). Democratizing the conflict initiation process, e.g. by allowing multiple individuals to ‘vote’ and contribute towards a collective HD strategy, would constitute a simple extension to our model to test this theory directly. We could also start to model the cultural evolution of strategies, allowing for dynamics such as coercion and copying, rather than using fixed genotypes as presented in the model here. Finally, we could allow for alliance formations between groups, which rational actors may seek when conditions are favourable [54,108]. Extending our model in such a way would provide a means to adapt it to different, related questions of interest, in both the animal and human sciences.

5. Conclusion

Our model shows how ecological and demographic conditions influence the evolution of intergroup warfare, both in terms of differential follower and leader participation, and variable rates of aggression. In the process, we have been able to generalize two previous evolutionary models [13,29] of intergroup conflict and generate new ecologically relevant predictions. The parameter values we have chosen, such as maximum group size, intergroup migration rate and intergroup encounter rate, are designed to be tractable and measurable for empiricists, and we encourage other researchers to test the hypotheses implicit in our model directly in their own study systems.

Data accessibility

All code is freely available at www.github.com/sankeydan/leadersOfWarModel.

Authors' contributions

D.W.E.S.: conceptualization, formal analysis, investigation, methodology, supervision, visualization, writing—original draft, writing—review and editing; K.L.H.: conceptualization, formal analysis, investigation, methodology, visualization, writing—original draft, writing—review and editing; D.P.C.: conceptualization, funding acquisition, investigation, writing—review and editing; D.W.F.: conceptualization, funding acquisition, investigation, writing—review and editing; P.A.G.: conceptualization, investigation, writing—review and editing; F.J.T.: conceptualization, data curation, funding acquisition, investigation, project administration, writing—review and editing; R.A.J.: conceptualization, funding acquisition, investigation, writing—review and editing; M.A.C.: conceptualization, funding acquisition, investigation, supervision, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Competing interests

We declare we have no competing interests.

Funding

Work was funded by a NERC standard grant awarded to M.A.C, D.P.C, F.J.T, D.W.F and R.A.J. Grant Reference NE/S009914/1.