Strategic heuristics underlie animal dominance hierarchies and provide evidence of group-level social knowledge

Strategic heuristics underlie animal dominance hierarchies and provide evidence of group-level social knowledge

Elizabeth A. Hobson Dan Mønster Simon DeDeo


The question of what animals understand about their social worlds is fundamental to studies of the evolution of sociality, cognition, and animal culture. However, the presence and extent of social knowledge in individuals is difficult to detect, and when detections have been made, differences in methodology make cross-species comparisons difficult. We present a new method for detecting social knowledge. This method infers individual-level strategic rules for aggression in dominance hierarchies where rank differences between individuals may structure decision-making. We apply this method to a data from 172 social groups across 85 species in 22 orders. By looking for heuristics that depend upon knowledge of group-level facts, we can back-infer the types of knowledge individuals possess. Summary measures then place groups within a taxonomy, providing a “social assay” of group-level knowledge. This assay allows the identification of consensus strategies at the group level. The majority of animal groups in our dataset (112 groups, 65%) follow a downward heuristic, spreading aggression relatively equally across lower-ranked opponents. An additional 50 groups (29%) use strategies that are indicative of more detailed rank knowledge. Different groups within the same species can use different strategies, indicating that the choice of heuristics may be contextual and that the structuring of aggression should not be considered a fixed characteristic of a species. Instead, individuals may be able to plastically respond to changes in environmental or social conditions by changing their strategies. Our approach to studying animal conflict provides new opportunities to investigate the extent of rank knowledge across species, compare the evolution of social knowledge, and better understand the effect of social knowledge on individual behaviour in within-group conflict.

Keywords: Animal sociality, animal conflict, dominance hierarchy, self-organizing system, social cognition, social feedback, social complexity, heuristics


Biologists have long been interested in within-group conflict and dominance hierarchies [1, 2, 3, 4, 5, 6, 7]. These structured conflicts have attracted research attention because they are taxonomically widespread across the animal kingdom [5, 8, 9], biologically relevant to individuals within social groups [10, 11], and strikingly similar in basic structure even across very different species [12]. This surface-level similarity makes the aggression networks underlying hierarchies one of the most promising social network types for comparative analyses across a wide range of species and social systems.

However, aggression does more than construct and maintain dominance hierarchies. It is also possible for the dominance hierarchy itself to play a critical role in conflict in a top-down fashion. Hierarchies are emergent, group-level facts, that contain information about the extent to which knowledge about rank can explain the ways in which individuals direct that aggression. The complex relationships between rank and aggression are part of this hidden structure.

Because of this connection between rank and behaviour, dominance hierarchies can provide critical insight into the cognition underlying social decisions. As we shall show, in many animal groups, the group-level summary statistics that emerge from individual-level decision-making describe aspects of the dominance hierarchy. Information about the hierarchical structure and individuals’ ranks in the hierarchy can then be detected and used by individuals to make future decisions about who to fight. The presence of this feedback between individual behaviour and group characteristics serves as a critical link between the social and the cognitive features underlying behavioural decisions.

The emergence of between-level feedback makes animal conflict a cognitive process which is informed by whatever knowledge an individual has: whether this is knowledge about its own abilities, the relationships it has with others, or the structure of the group-level dominance hierarchy. Given the complexity of quantifying the full structure of the dominance hierarchy, we expect individuals to rely on simpler rules that require neither full knowledge nor fully optimized strategies. In the literature on judgement and decision-making in humans, these simpler rules are known as heuristics [13, 14]. The use of heuristics is now understood to be a major factor that structures human social behaviour and decision making. Characterization of these heuristics and the advantages and disadvantages of their use has allowed economists and psychologists to explain previously mystifying features of human behaviour (see, e.g., [15, 16]).

Here, we apply these two ideas—of socio-cognitive feedbacks which create knowledge of rank and of the heuristics which facilitate use of this knowledge—to animal dominance hierarchies. We present a method to detect the presence and use of knowledge in animal groups, and apply it to observational data from fighting and dominance interactions within 172 independent social groups across 85 species in 22 orders.

Previous research has shown that aggression networks underlying dominance hierarchies in species across the phylogenetic tree are remarkably similar when decomposed into basic network motifs [17]. Here, we take the opposite approach, and analyse high-level strategies of aggression across entire groups. We present two measures to quantify the extent to which aggression is contingent on rank. Focus quantifies the extent to which individual aggression patterns are related to its rank relative to potential opponents and quantifies the extent to which individuals use knowledge about relative rank differences. Position quantifies the relative location in the dominance hierarchy at which aggression is focused and indicates how individuals use rank knowledge as a basis for forming dominance strategies or heuristics to guide their conflict decisions.

These measures provide a social assay that can detect how much individuals use knowledge of relative rank differences between themselves and potential opponents to structure their observed behaviour. Combined, we use focus and position to delineate three conflict heuristics that are informed by different types of knowledge about rank: (1) the downward heuristic, where individuals aggress equally against all lower-ranked individuals; (2) close competitors, where individuals aggress preferentially towards those ranked just below themselves in rank; and (3) bullying, where individuals aggress preferentially towards those ranked far from their own rank. Each strategy allows individuals to preferentially engage with a certain subset of others based on different types of knowledge about the relative rank difference between themselves and potential opponents. The use of a particular strategy also allows us to back-infer the type of knowledge individuals must have in order to use the strategies that they do.

Combined, our new quantitative methods, our model-fitting procedure, and our detection of social rules governing hierarchies provides new insight into how animals structure their social relationships and how they make decisions about who to fight.


Empirical data sources

We used a large empirical dataset of aggression and dominance hierarchies that is openly accessible ([12], Dryad doi: We excluded two groups due to apparent errors in the presentation of data in the original papers (Table 4, Nest 39 in [18] and Table 3 in [19]). We supplemented this dataset with data from aggression and rank in monk parakeets ([20], Dryad doi:, data from study quarters 2-4 for groups 1 and 2).

These datasets contain the number of times each individual “won” against each other individual. These “wins” could be the outcome of aggressive contests, show the directionality of aggressive events, or indicate a submission display towards a dominant individual. They do not have information on which individual started a fight, only the outcome of the interaction. We use the general term “aggress” to describe the actions individuals take in these datasets, and focus here on the perspective of the winners as initiators of aggression, although all of our analyses apply equally well to cases where the initiator of the fight chooses to start a fight that it ultimately loses.

Rank and distribution of aggression

For each group, we find individual ranks using eigenvector centrality. In particular, we compute the probability that each individual attacks each other individual, and then add a small regularization term, (see SI for a Bayesian calculation of the optimal value of this term); the eigenvector centrality of the resulting matrix allows us to extract the relative ranks of individuals that are implicit in the patterns of aggression [21].

Plotting the overall distribution of real aggression in each group by relative rank differences enables us to determine whether the distribution of aggression is structured by rank differences among individuals, whether individuals in the group focus their aggression on a subset of individuals based on relative rank differences, and where in relative rank distance space aggression is focused.

Our two measures are focus and position. We compare their values quantified from real-world data with those from a set of different agent-based models which allows us to determine minimal models for group-level aggression strategies used in a particular group.

Calculating focus

A group’s focus is is high when individuals strongly concentrate their aggression towards opponents with a particular range of relative rank differences; it is low when aggression is spread across the entire group.

To define focus we first construct the relative-aggression distribution, , which measures the level of aggression between individuals separated by steps in relative rank. If we define as the set of all pairs where is ranks above , then is defined as


where is the total number of pairs in the set. In words, is the average amount of aggression directed rank-steps away. When is positive, measures the average aggression directed ’down’ the hierarchy, from a higher-ranked individual to a lower-ranked individual.

Figure 1: Distribution of aggression of real groups showing how patterns are consistent with (panel a) or diverge from (panels b and c) patterns of aggression artificially generated by the downward heuristic. Panels show data from (a) mule deer [22], where the real aggression followed the downward heuristic, (b) monk parakeet [23], where real aggression followed a close competitor pattern, and (c) vervet monkey [24], where real aggression followed a bullying pattern. Shading around lines indicated 95% confidence intervals.

In other words, is a measure of the fraction of events that are directed between individuals separated by steps in relative rank, given the total aggression in the system that could have been directed steps away. A plot of as a function of tells us a great deal about the flows of aggression through the system. Fig. 1 provides an example; most aggression is directed “down” the hierarchy towards lower-ranked individuals (positive ), although in Fig. 1b and c, aggression is more widely distributed than Fig. 1a, indicating that in these systems, more aggressive events are directed “up” the hierarchy (negative ).

Focus, , is defined as how “sharp” this distribution is:


where is the -weighted variance of ,


and is the -weighted mean of ,


The normalization term is chosen so that a uniform (flat) distribution of aggression, i.e., “rank ignorant”, gives a focus of zero. If focusing is very strong—e.g., if all individuals direct their aggression towards the individual two ranks down from them in the hierarchy, is 1. As aggression is more evenly distributed, decreases. In the case that aggression is completely uniform across all ranks, then the normalization is chosen such that will be precisely zero. (In rare cases, where the aggression is “overdispersed”, it is possible to have negative focus.)

Position of focused aggression

If rank knowledge is present and is used, and we can detect this via focus, then knowing the position of the peak of aggression gives us information about the specific relative rank-based strategy that individuals are using. For example, individuals with focused aggression could direct most of their aggression towards those that are ranked directly beneath themselves in the hierarchy. Alternatively, individuals could focus their aggression on the very lowest ranked individuals in the group. These two cases could result in similar levels of focus in aggression, but could be differentiated from each other by differences in their position values. In the first case, position would be closer to each individual’s own rank (and closer to 0) while in the second case, position would move towards 1 as aggression is directed at individuals many ranks distant from an individual’s own rank.

We define the position of focused aggression as the average of the distribution of normalized aggression for each social group; i.e., for each individual, we compute the probability that the individual’s attack is directed at an individual rank away, , and then average these probabilities over all individuals, formally,


This accounts for the effects of both individual aggression levels and the number of potential aggressive targets as a function of rank, and allows us to capture the extent to which decision-making on the individual level is sensitive to relative rank position.

Modelling the structural rules of dominance hierarchies

The simplest rank-based rule governing aggression in a hierarchy is a rule we term the “downward heuristic”. Here, individuals aggress only against those ranked below themselves, and lose against all those ranked above. This is the simplest rank-based rule because individuals follow a binary decision rule: attack those of lower ranks and avoid those with higher ranks; in essence, individuals perfectly follow the most basic structure of the dominance hierarchy.

We use this simple rule to recreate aggression patterns for each group, and compare it with the real observed aggression patterns. We do this using an ensemble of agent-based model simulations to create a set of artificial aggression networks. These models preserve some of the real data structure while permuting other aspects. We used these artificial aggression networks to determine which values of focus and position we should expect to be generated if animals in the group were only using this basic downward heuristic.

We use each individual’s rank, calculated from the real dataset, and then allow individuals to aggress as much as they do in the real data, but change who they fight against. In the pure downward heuristic case, individuals fight randomly but only with individuals ranked below themselves in the hierarchy. This process allowed us to remodel the real data at the event level. This process is consistent with recent best practice recommendations for network permutation, which supports event-level permutations of social interactions rather than relationship strengths [25].

Formally, given the aggression matrix , and the ranks . The first-ranked individual, , has equal to one, and indicates that is lower ranked than . Then, for each individual , the row is then mapped to where


and is equal to one when the subscript is true (i.e., when then is lower ranked than ) and zero otherwise.

Due to mistakes by the participants, real systems may be somewhat noisy and may not follow a pure downward heuristic. To account for this, we introduced the possibility of randomness in aggression direction; mathematically, we allow for an probability that the individual simply directs aggression at a random individual,


We conducted a parameter sweep of the downward aggression heuristic in , gradually increasing the amount of randomly-directed aggression from equal to zero (perfect downward aggression) to unity (completely random behaviour), then examined how increasing randomness affected focus and position values.

Fig. 1 shows the effect of replacing the actual aggression patterns with aggression artificially generated by the downward heuristic; as can be seen, non-zero aggression ( positive) is now (almost) entirely found at positive . (A small amount of upwards aggression persists, because the rank orders () are measured on the original data, and that order changes slightly when the rule is enforced.)

Assignment of Heuristics

Our artificial aggression networks generated by the downward heuristic serve as randomized reference models [26] to which we can compare the real observed datasets, and as a form of null model for the downward heuristic: we fail to reject the downward heuristic as a plausible generating rule of focus and position in the real datasets if the real focus and position values fall within the range that can be produced by our artificial data. For real groups that fall outside of the region that could be generated by the downward heuristic, we categorize these groups into strategies other than the basic downward heuristic.

Figure 2: Examples of strategy assignment to (a) downward heuristic (mule deer, [22]), (b) pure close competitors (monk parakeet, [23]), and (c) pure bullying (vervet monkey, [24]). Diamond points show real focus and position values for each group ( 1SD). White points indicate focus and position values ( 1SD) of artificial dataset generated with agent-based models including 0% (upper right) to 100% (lower left) randomly directed events.

We categorized groups into four aggression strategy types: downward heuristic, close competitors, bullying, and undefined. We used iterative fitting of agent-based models, with increasing levels of randomness, to delineate the focus and position parameter space in which these summary measures could be consistent with those produced by the downward heuristic. We drew a polygon around this entire space, using the extremes of error bars to set the edges of the polygon (Fig. 2). Real data that intersected this downward heuristic polygon were scored as consistent with that model if any of the error bars for the real data overlapped with the polygon (Fig. 2a). Fig. 2 provides an example of these assignments; the same value of focus and position may be categorized as “close competitors” in some groups and “downward heuristic” in others, because larger group sizes may provide additional signal-to-noise for null rejection.

We defined the close competitors strategy as having a lower position value than that produced by the downward heuristic model (i.e. aggression focused more towards near-ranked individuals, Fig. 2b) and bullying as having a higher position value than the modelled data (i.e. aggression focused more towards the bottom of the hierarchy, Fig. 2c). The undefined strategy groups had focus values lower than those expected in fully random systems. Real data that were fully contained within the polygon space of the close competitors, bullying, or undefined strategies were scored as “pure” for that strategy. Real data with 3 error bars falling within a single strategy were categorized as “mostly” close competitors, bullying, or undefined.

We also used the downward heuristic agent-based models to determine the likely level of hierarchical structuring in the real datasets. We determined the extent to which focus values were affected by increasing the amount of randomly directed events in the artificial downward heuristic data.

Code to enable running all analyses will be released in an R package, on publication of the paper.


Structured aggression

Most of the animal social groups in the dataset had well-structured dominance hierarchies. We assessed the level of structure by comparing real focus values to the focus values generated by our model of the downward heuristic rule with increasing levels of randomly-directed events. Most groups had real focus values consistent with low levels of randomly-directed aggression: 39% of groups () were most similar to modelled data with 10% or less randomly-directed events; 72% of groups () were most similar to modelled data with 30% or less randomly-directed events. Only 20 groups (12%) had focus values most similar to modelled data with 80% or greater randomly-directed events; of these, none were categorized as a pure close competitor or pure bully strategy type. Only 12 groups (7%) had focus values closest to modelled data with totally random aggression, which corresponds roughly to previous results with this dataset which found over-representation of transitive configurations, an indication of structured hierarchies, in all but 3% of groups [12].

Focus and position

When we simulated the downward aggression heuristic, we found that artificial datasets had a mean focus value of 0.79 (range 0.67 to 0.93) and a mean position of 0.42 (range 0.3 to 0.48). Focus values in our artificial datasets responded strongly to the amount of randomly-directed events included in the rule. We found a strong negative relationship between the amount of randomly-directed aggression events in our modelled data and the resulting value of focus (mean correlation , range to , all -values ).

Real focus and position values in our dataset were much more varied than the artificially-generated values (Fig. 3). Mean focus in real groups was 0.53 (range to 0.95) and mean position was 0.34 (range to ). These values were not strongly associated with phylogenetic relatedness.

Group-level rules structuring aggression

Figure 3: Focus and position values for observed social groups, coloured by strategy assignment.

The majority of animal social groups in the dataset had clearly detectable strategies that structured aggression (Fig. 3). Almost all groups (94% of groups, ) could be categorized without ambiguity to one of three main aggression strategies: downward heuristic (65%), close competitors (16%), or bullying (13%). Only 10 groups had less defined strategies, and of these, only 5 (3%) were classified as undefined.

We found no evidence that these strategy types were phylogenetically constrained. All three strategies occur in orders across the range in the dataset (Fig. 4).

Figure 4: Strategy types are not phylogenetically restricted to particular orders nor affected by the size of social groups.

Where a single species had multiple independent social groups in our dataset, we found that different groups of the same species often followed a mix of strategies rather than a single consistent strategy. For the 32 species for which two or more groups had pure detectable strategies (either downward heuristic, pure close competitors, or pure bullying), 53% of species had groups that followed more than one strategy (Fig. 5). For example, yellow baboons were evenly split between 5 groups which used a basic downward heuristic and 5 groups that used the more complex close competitors strategy. Three species, African elephants, Harris’s sparrows, and horses, had groups that followed all three pure strategies.

Figure 5: Occurrence of pure strategies by species with multiple social groups. Sorted by number of groups, then strategy, then alphabetically

We found no strong evidence that the conditions under which groups were sampled (whether the group was a captive or wild group) affected observed values of focus or position, or which strategy type the group followed. Focus and position values were similar in wild and captive groups, and both wild and captive groups had similar proportions of strategy types (Fig. A2.1). At the order level, not enough groups from the same orders were sampled in both wild and captivity to make any general conclusions about whether living conditions, and captivity in particular, affected the changes of a group using a particular strategy (Fig. A2.2).


Biologists have been fascinated by dominance hierarchies in animal groups for nearly a century. Previous research found strikingly similar patterns in micro-structural elements of aggression networks across a wide range of species [17], but the reasons for this widespread similarity have remained unclear.

This paper has taken a complementary approach by addressing hierarchical structures from a macro-structural perspective. Instead of looking at the building blocks of hierarchies, we looked at the aggression rules that structure decisions behind them. These rules represent strategies based on feedback from group-level social facts, not just network structure, and are based explicitly on detecting the use of rank-based social knowledge. We developed new methods to detect and categorize these group-level consensus strategies that structure within-group aggression and conflict. These consensus strategies are detectable because they are followed by the majority of individuals in the group. Each strategy relies on different kinds of social knowledge, and the use of a consensus strategy indicates that the social group has access to that knowledge.

Our methods enable us to assay historical datasets to detect group-level structural rules that guide behavioural decisions within dominance structures and to develop a taxonomy of social systems using different types of knowledge to structure aggression. Many groups have aggression structures consistent with the downward heuristic, the most basic dominance hierarchy rule, but some groups use multi-faceted strategies such as preferentially attacking close competitors or bullying bottom-ranked animals. We detected all three strategy types across most of the orders in our dataset and found that the strategies employed by specific social groups could vary even within species.

Social knowledge and rank-based strategies

These results about the strategies animals use to structure their interactions and the types and extent of social knowledge that underlie these decisions provide novel insight into the social knowledge contained within groups. For species that have more detailed knowledge of rank, and use a close competitors or bullying strategy, we can take a closer look at that species to differentiate between cases where it can follow that strategy via a simple underlying rule that allows easy detection of relative rank differences, or whether the ability to use rank knowledge is based instead on memories of past outcomes and individual recognition. This approach allows us to identify those species that could have more complex social assessment and memory abilities than we previously expected, and can serve as a guide for future research on a particular species. While models can make predictions about which cognitive processes may underlie sociality, in-depth understanding of the natural history of the species (memory acuity, recognition abilities, and perceptive abilities) are needed to fully understand how knowledge is used, what knowledge is present, how it is formed, and what kinds of cognition allow for the entire process.

The presence of a rank-informed aggression strategy in a group is evidence that individuals in the group are capable of perceiving the information needed to use that strategy. However, the use of a strategy in a particular group is not necessarily an indication of whether that strategy is commonly used by other groups of the same species, or an explanation of the cognitive methods individuals use to manage the necessary underlying information. Similarly, not finding evidence for a particular rank-informed strategy in a particular group cannot be used to determine whether the knowledge is present but not being used, or whether, conversely, the animals themselves are incapable of synthesizing the type of knowledge necessary to use the strategy. As such, it is important to note that the absence of a rank-based strategy cannot be used a positive confirmation that a species is unable or unwilling to use a particular rank-based strategy.

Potential plasticity of social strategies

We show here that groups of the same species can exhibit different macro-level strategies. While overall levels of conflict correlate with the phylogenetics of the species in question [27], it appears that the strategies that a species deploys have as much variance within clades as they do between them. The variability we find in strategy use within species shows that these social rules should be thought of as facts about particular groups, rather than rigid species-level characteristics.

Many species are able to respond to changes in ecological or social dynamics by dynamically altering their behaviours, interactions with group members, and group-level social structures. Factors such as resource availability and distribution, environmentally-mediated constraints, and direct environmental influences on physiology can all result in changes to individual aggression and group dominance structures (reviewed in [28]). Under different social, ecological, or environmental conditions, different aggression strategies may be optimal. A species that is able to respond to changes in conditions by altering its aggression strategy may be more successful than a more socially rigid species. Temporal shifts in the behaviours underlying dominance interactions have been documented in human groups, where dominance strategies, and the behaviours used to mediate dominance interactions, change with age [4]. Dominance strategies can even change over time in the same social group, as we previously documented in aggression in parakeets [20].

Our results support these earlier conclusions that sociality can vary within a single species. Combined, these results suggest that experimental work on the ontogeny of dominance hierarchies, social knowledge, and aggression strategies is needed to fully understand the conditions under which a knowledge-based strategy, like rank-focused aggression, would emerge and be used in social groups.

Variability in strategy use, or social plasticity, has a further implication. One way that aggression strategies could emerge is through adaptive responses to local conditions. Once established, these strategies could be learned by new individuals joining the group. If individuals could learn these strategies from each other, and the strategies could persist in groups due to social learning, aggression strategies may represent “cultures of aggression”, where the type of aggression strategy in use in a group may be a somewhat arbitrary outcome of prior conditions frozen in by cultural learning. This kind of culturally-based inertia may lead to a divergence between actual and optimal behaviour, and may indicate that the social system is susceptible to complex nonlinear dynamics and potentially to social tipping points [29].

Insight into social cognition

A fundamental question in animal behaviour is how much animals know about their social worlds. Our analyses, which found evidence for social knowledge and rank-focused aggressive behaviour across the animal kingdom, suggests that this question has two parts: first, “how much do they know?”; second, “how do they know it?”. This is because individuals can obtain and act on the same type of knowledge using a broad range of mechanisms that vary widely in their cognitive demands.

Given the widespread nature of social knowledge and its use in the animal kingdom, why don’t all species use a simple cue or rule-of-thumb to infer their own rank and the rank of others in their group? Many species do, in fact, use these simpler methods, and have strongly size-based hierarchies which would allow rank differences to be visible if the individuals could discriminate among these signal differences. But some species do not seem to use these simple solutions to detecting rank differences among individuals.

In previous work with monk parakeets for example, we have not found any easily-observable characteristic that is strongly correlated with rank. Instead, we have found indications that rank knowledge in these groups forms through memory and processing of social interactions, rather than a directly correlative signal [20]. Along similar lines, recent evidence from experiments with sparrows shows that individuals can also change the complexity of the rule they follow. In these sparrows, individuals only use simple rules when interacting with strangers, but rely on individual recognition and memory of past interactions when interacting with known individuals [30]. This kind of change represents a shift from what appears to be a simple rule to one that appears more cognitively demanding.

Social cognition and social complexity

Just as intelligence appears to have evolved independently in different clades [31], social complexity appears to have multiple, independent evolutionary origins. Approaches to studying animal social complexity often attempt to indirectly quantify the extent of social knowledge in social groups, usually through various summary measures such as group size (e.g., Ref. [32, 33]), network size (e.g., Ref. [34]), or the number or diversity of different types of relationships (e.g., Ref. [35, 36]). All of these methods seek to understand how much animals know about their social worlds, and recent work has advocated explicitly quantifying social knowledge when attempting to assess social complexity [35]. However, while we can quantify many aspects of social structure, without additional experimental manipulation (e.g. [37, 38]) it has not previously been possible to determine the extent of knowledge that individuals in groups have of their social worlds. In broader comparisons, it has also been difficult to find a way to quantify social knowledge in a manner that is both feasible and generalizable enough to be used in a wide range of species, as social interactions may differ in their salience and biological meaningfulness across species. By taking a top-down rank-informed approach in our work, we can avoid some of these difficulties.

Our global approach to detecting and studying social knowledge can be used to gain insight into social complexity in groups across many different types of social structures. This is especially important in understanding the conditions under which complex sociality, based on social knowledge, should emerge. Treating social complexity as an emergent property of the group provides a cleaner framework for comparing complexity both within and between species. The information contained in the interactions is complementary to the overall social network structure; our results show that species with different social systems and network structures can have similar levels of complexity.

The tractability and wide applicability of our approach enables comparative analyses that can provide a better understanding of the evolutionary patterns underlying the distribution of social processing skills and complex sociality across taxa. Previous analyses have often simplified many of the driving features of social complexity [32, 33], or were restricted to closely related species, e.g. within primates [39]). Using our approach, we are now able to compare a broad range of species using a high-level summary of group behaviour which enables us to more directly compare the presence and use of social knowledge, and the potential for social cognition, in these groups.

In our analyses, none of the strategies we detected were phylogenetically restricted to particular orders. This provides evidence that similar levels of social knowledge could emerge through convergent evolution even if the underlying socio-cognitive methods animals use to process social information and make aggression decisions differ. Without perception, inference, and knowledge, simpler rules based on cues or less cognitively demanding signals can likely explain interaction patterns and hierarchical organization. Without inference and knowledge, group social interactions and resulting social network structure may simply be complicated, rather than complex.


Our analysis has provided a social assay to back-infer what animals may know about their social worlds, based on their decisions about how to interact with each other. Using these new tools, researchers can now categorize groups into a taxonomy of social strategies, where the patterns of aggression in each strategy type are based on different types of social knowledge. The applicability of our quantitative tools allows for a new way to quantify the evolution of social structure across divergent taxa. Combined with recent results from empirical work and an understanding of the cognitive abilities of species, our approach provides new opportunities to investigate the extent of rank knowledge across species, compare the evolution of social knowledge, and better understand the effect of social knowledge on individual behaviour in within-group conflict.


EAH was supported by a postdoctoral fellowship from the ASU-SFI Center for Biosocial Complex Systems, with additional funding from the Santa Fe Institute. DM was funded in part by Independent Research Fund Denmark (grant no. 7089-00017B), Aarhus University Research Foundation, and The Interacting Minds Centre, and gratefully acknowledges the hospitality of the Santa Fe Institute during a sabbatical visit. This research was supported by Army Research Office Grant #W911NF1710502.

1 Appendix

1.1 Appendix 1: the Regularization Term for the measurement of PageRank in Animal Conflict

A basic step in the calculation of focus and average peak position is the estimation of the transition matrix, , a collection of probabilities, from the data. The “naive” way to estimate a probability of an event occurring from a finite number of observations is


While attractive in its simplicity, this estimator has a number of problems (see Ref. [40]); a Bayesian analysis leads to the correction


where is the number of event types, and a regularization parameter (sometimes called a “teleportation term”). When is equal to unity, we have Laplace’s rule; more generally, we can think of as parametrising a Dirichlet distribution that serves as the prior for the possible values of the underlying probabilities  [41, 42].

In the case we have here, is the estimate of the probability that attacks ; by stipulation, the individual can not attack itself. We can then adapt equation 9 to the estimate of the probability distributions in the matrix .

How do we choose ? A natural way to do so is to learn from the data itself; we do so here using -fold cross validation, with set to five. For each dataset, in other words, we compute the probabilities , for some particular choice of , based on a randomly chosen sample of only of the data. We then compute the log-probability per data-point of the remaining “held out” of the data, , using those estimated s,


where is the number of observations in the held-out set (i.e., of the total number of observations). In words, is how well that particular choice of “predicts” the held-out data; the optimal choice of is that which best predicts.

We repeat this process many times, choosing a different hold-out set each time, to get an estimate of the average log-probability of the held-out data. We then choose to maximize this average of . Fig. A1.1 shows an example of this process for the data of Ref. [43]. The peak of this function allows us to pick the optimal epsilon to be around for this dataset, although values between and are largely indistinguishable. Fig. A1.2 shows a scatter plot of the -maximizing for all 161 aggression matrices in our data, as a function of both total number of observations, and number of individuals.

We find that most matrices have optimal values of between and , and that there is no strong correlation between optimal and system size or total number of observations. The average value of epsilon across all datasets is .

Little hinges on the exact value of ; indeed, using the average value in place of the optimal choice for any particular dataset leads to an average (absolute value) shift in the focus measure of only , and in the average peak position of only ; over our data, the two choices have a Pearson correlation of (Focus) and (Average Peak Position). Since finding the optimal is computationally intensive, and since the final results are largely insensitive to this choice, we suggest that use of the average value, , is appropriate for ordinary use, and (for simplicity) we present our analyses here using this choice.

Figure A1.1: Determining optimal through -fold cross validation; an example of equation 10 applied to the data of Ref. [43]. An value of approximately , in this case, best predicts held-out data, but a range of values between and perform similarly well.
Figure A1.2: A scatter plot of optimal epsilons found using equation 10, as a function of total number of observations (left), and total number of individuals in the data (right). The optimal value shows no strong trends with either variable; the average optimal value for is and we use this for simplicity in the calculations in the main text.

Appendix 2: Strategies in wild vs. captive groups

Figure A2.1: Focus, position, and strategy type for wild and captive groups
Figure A2.2: Group size and strategy type for wild and captive groups


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