Hierarchical development of dominance through the winner-loser effect and socio-spatial structure

In many groups of animals the dominance hierarchy is linear. What mechanisms underlie this linearity of the dominance hierarchy is under debate. Linearity is often attributed to cognitively sophisticated processes, such as transitive inference and eavesdropping. An alternative explanation is that it develops via the winner-loser effect. This effect implies that after a fight has been decided the winner is more likely to win again, and the loser is more likely to lose again. Although it has been shown that dominance hierarchies may develop via the winner-loser effect, the degree of linearity of such hierarchies is unknown. The aim of the present study is to investigate whether a similar degree of linearity, like in real animals, may emerge as a consequence of the winner-loser effect and the socio-spatial structure of group members. For this purpose, we use the model DomWorld, in which agents group and compete and the outcome of conflicts are self-reinforcing. Here dominance hierarchies are shown to emerge. In the model, we apply analytical methods previously used in a study on dominance in real hens including an analysis of behaviourial dynamics and network triad motifs. We show that when in the complete model one parameter, representing the intensity of aggression, was set high, the model reproduced the high linearity and many patterns of hierarchical development typical of groups of hens. Yet, when omitting from the model the winner-loser effect or spatial location of individuals, this resemblance decreased markedly. Our results demonstrate that the spatial structure and the winner-loser effect provide a plausible alternative for hierarchical linearity to processes that are cognitively more sophisticated. Further research should determine whether the winner-loser effect and spatial structure of group members also explains the characteristics of hierarchical development in other species.

and the outcome of conflicts are self-reinforcing. Here dominance hierarchies are shown to emerge. 23 In the model, we apply analytical methods previously used in a study on dominance in real hens 24 including an analysis of behaviourial dynamics and network triad motifs. 25 We show that when in the complete model one parameter, representing the intensity of aggression, 26 was set high, the model reproduced the high linearity and many patterns of hierarchical 27 development typical of groups of hens. Yet, when omitting from the model the winner-loser effect or 28 spatial location of individuals, this resemblance decreased markedly. 29 Our results demonstrate that the spatial structure and the winner-loser effect provide a plausible 30 alternative for hierarchical linearity to processes that are cognitively more sophisticated. Further 31 research should determine whether the winner-loser effect and spatial structure of group members 32 also explains the characteristics of hierarchical development in other species. 33 Introduction 34 Dominance hierarchies are a near universal pattern of social order in group-living animals. High 35 dominance rank is supposed to be adaptive for access to resources and protection from predators (1-36 5). The hierarchy is often (near) linear in small groups of up to 10 individuals in a wide range of species, 37 including mammals, fish, birds, crustacean and insects (6,7). Yet, what proximate mechanism causes 38 linearity is under longstanding scientific debate. 39 For the formation of a dominance hierarchy mainly two mechanisms have been proposed. First, prior 40 attributes of individuals such as body size or personality characteristics, have been suggested to 41 directly determine dominance rank. This theory is well supported by empirical data on pair-wise 42 dominance interactions (8), but it has been rejected in a theoretical study because hierarchies are 43 (near) linear and this would require difficult mathematical conditions, especially in larger groups (9-44 11). Second, the self-reinforcing outcomes of a fight may result in hierarchy formation (12). The self-45 reinforcing effect implies that, the winner of a dominance interaction becomes more likely to win 46 again, whereas the loser becomes more likely to lose again, the so-called winner-loser effect (13)(14)(15). 47 The winner-loser effect is effective in a wide variety of species. Most evidence comes from contests in 48 experimental studies of isolated pairs, rather than in groups (11). An exception is a study by Lindquist 49 and Chase (16) of small groups of hens. Here the authors tracked the development of the dominance 50 hierarchy with novel analytical methods. They showed that the hierarchy became highly linear and 51 stable and it developed fast. Attacks in pairs of hens often occurred in series of attacks in the same 52 direction (bursts) and those network states occurred most often that either contained an individual 53 that dominated all others, or that comprised only triads that were transitive (shown in a triad motif 54 analysis of the network). 55 Additionally, the authors mathematically represented three models of hierarchy development based 56 on the winner-loser effect. Namely, the Bonabeau model (17), the Dugatkin model (15) and the 57 Hemelrijk model, called DomWorld (18). However, Lindquist and Chase ignore that DomWorld is an 58 individual-based model with a spatial representation of individuals (16). They investigated whether 59 their mathematical abstractions reproduce some aspects of the hierarchy formation in hens. Since they 60 did not sufficiently reproduced observations, they concluded that hens are likely aware of the group 61 hierarchy and actively strive for it to become linear. 62 Their detailed description of the formation of dominance hierarchies in hens offers an opportunity to 63 examine for the first time whether the DomWorld model in its complete form (including the spatial 64 representation of groups of individuals) suffices to generate hierarchical patterns similar to those in 65 hens despite the model's cognitively simple rules (agents are not striving for linearity of the dominance 66 hierarchy). We here investigate the importance of the spatial representation of interactions for the 67 formation of a highly linear and stable hierarchy, because the spatial component of the model in 68 combination with the winner-loser effect has formerly been shown to contribute to the generation of 69 a wide variety of complex patterns of social interaction resembling those in primates, including many 70 aspects of egalitarian and despotic dominance styles of various species of macaques (19,20). 71 Therefore, the aim of the present study is to investigate how the winner-loser effect and the socio-72 spatial structure affect the development of the dominance hierarchy in groups in the model, 73 DomWorld when we use the same analytical methods as Lindquist  The outcome of a fight is self-reinforcing, such that the winner becomes more likely to win subsequent 82 fights and the loser more likely to lose these. Throughout this article we will use the terms 'win' and 83 'lose' for the outcome of dominance interactions and 'initiation' for starting a dominance interaction, 84 also referred to as a fight. 85 A dominance interaction is mediated by dominance values (DOM) that represent each agent's fighting 86 power. The chance Wi of agent i to win a fight against agent j is determined by comparing its ratio of 87 the DOM values to a number drawn from a random distribution (Eq. 1). 88 Afterwards the DOM values are updated depending on the outcome of the fight. The value of the 90 winner (DOMi) increases with 1 minus its relative dominance ratio. The loser decreases its score by 91 the same amount. The change in DOM value is multiplied by a scaling parameter StepDom that 92 symbolises the intensity of aggression (Eq. 2). 93 In the model, DomWorld, agents have been using two strategies of attack (18), obligate and risk-95 sensitive. In the present paper we will only discuss the obligate style of attack, as risk-sensitivity in 96 general did not influence the patterns of hierarchy formation and was used in the work by Lindquist 97 and Chase (16). When agents are meeting an individual in their personal space and are set to always 98 attack it, this is referred to as an obligate strategy of attack (19). If an agent attacks only if it assumes 99 it will win from the opponent, this has been called risk-sensitive attack. Here, an agent assumes it will 100 win from the opponent if wins all mental fights, which it performs against a potential opponent, 101 according to equation 1. A more extensive description of DomWorld can be found in Hemelrijk (21). 102

Setup
Starting from the parameter setting from the work by Hemelrijk in 1999 (21), we tuned the model 104 DomWorld to match several aspects of competition among real hens observed by Lindquist and Chase 105 (16). We used the same number of groups (14), the same group size (4 females) and the same average 106 number of interactions (518) as reported for the study of hens(8). 107 To obtain the same average linearity of the hierarchy in the model as reported in hens, we increased 108 the value of a single parameter, StepDom, representing a higher intensity of aggression, thus, 109 increasing the average linearity of the hierarchy in the model (Fig 1). 110 of StepDom that matched this target, which is a value of StepDom of 9. 120 To gain understanding of the effects of spatial structure and the winner-loser effect we studied results 121 not only in DomWorld in its complete form, but also in DomWorld without spatial structure (by 122 selecting interaction partners at random) and without the winner-loser effect (by using fixed DOM 123 scores of agents based on the final DOM scores of the simulations with the full model). 124 Data collection 125 We calculated the various measures in our data-analysis using scripts written in Python (version 3.6.8), 126 see the section Analysis below. The python package DHDAT of many of these measures is freely 127 available, see ( triads. Individuals in motif F can be ranked. Therefore, motif F is transitive. Individuals in motif G cannot 169 be ranked and therefore, it is intransitive (cyclic). 170 In a directed network with 4 individuals there are 4 triads and 41 different states of these 4 triads, plus 171 1 state with no relations among the individuals, which is not included (Fig 3). States are categorised in 172 groups with the same number of dyadic relations in the network, the so-called link-group. In a link-173 group states are categorised in classes (indicated by a letter). States in the same class share a network 174 structure such that a pair-flip can change the network state to another one in the same class, but not 175 to a network state in a different class (or link-group). If there is an individual that is dominant over all 176 others (indicated as DAO) in the group, its node is marked with a 'D'. The node of an individual that is 177 submissive to all others (SAO) is marked with an 'S'. The development of the network is traced over 178 time by recording its state after each interaction. 179 The degree of transitivity is measured as the proportion of states that are completely transitive 184 (without any cyclic triad) out of all states with at least one complete triad. We also calculated the 185 transitivity, Ttri, as described by Shizuka and McDonald (26). It is the proportion of complete triads that 186 are transitive, normalised by the proportion transitive triads that are expected on average in a random 187 network. Because a state can also be partially transitive, in theory this proportional measure of 188 transitivity has a higher resolution than its binary definition of a state being either completely transitive 189 or cyclic. Since results for the binary and proportional definition of transitivity were similar for the 190 settings in the present paper, we only show the proportion of transitive states, Ttri. 191 The occurrence of each network state is examined using two measures: the Class Occurrence 192 group and the class with the number of recorded interactions to indicate the degree of accuracy (Fig  198   7). 199 Statistical analysis 200 We tested the effects of removing space from the model and of removing the winner-loser effect using 201 a generalized linear model (GLM) for each measure in Table 1. Other predictor variables included the 202 identifier of the run, and for rank-changes that correlated with pair-flips (item 2 in Table 1)   Results from the post-hoc Tukey tests are shown as letters (a, b, c) in superscript. If a letter is not 214 shared between two values this indicates a significant difference between these values. For instance, 215 the proportion of rank-changes (item 1 in Table 1) is significantly lower in the full model than in the 216 model without winner-loser effect. If a letter is shared, there is no significant difference between 217 these groups, e.g. considering the proportion of rank changes, between the full model and that 218 without the spatial component. In hens the hierarchy was highly differentiated and stable. Rank changes were few and happened 231 mostly during the first stage of hierarchy formation, for instance, a top-ranking individual often 232 emerged early on and subsequently maintained its position. Rank changes in a pair were not preceded 233 by a reversal in the direction of attack in that pair (a pair-flip, see next section for a definition), but 234 were supposed to result from one of the members of the pair attacking others lower in rank with as 235 consequence that it surpassed an individual ranking above itself. 236 Rank development in DomWorld (full model) is characterized by its stability (point 1 in Table 1) and a 237 strong differentiation of the hierarchy (4 in Table 1). The top-ranking individual often (in 10 of the 14 238 runs, see appendix 2) emerged early in the run, maintaining its rank throughout the run. Rank changes 239 that involved individuals at lower rank positions are distributed more evenly over time (Fig 4). 240  Table 1). Additionally, without a spatial representation when meeting others randomly, 248 rank changes more often involve all rank positions over the entire length of the run (appendix 2), and 249 result in a hierarchy that is less steep than in the full version of the model and the model without the 250 winner-loser effect (4 in Table 1). 251 In all model versions more than half of the ascensions in rank occurred during the first 60 interactions 252 (3 in Table 1). In the leadup to a rank change, the increase in the dominance value of the individual 253 that will ascent in rank comes about by a combination of attacking lower ranking individuals and 254 attacking the individual ranking immediately above itself with which it will swap rank, but not often by 255 attacking others that are much higher in rank (Fig 4, also see appendix 2). Only one in six rank changes 256 in the full model is directly preceded by a pair-flip (2 in Table 1). When removing the winner-loser 257 effect from the model, rank changes more often correlate with a pair-flip than in the full model (2 in 258 Table 1). 259

Pair-flips
260 An interaction is classified as a pair-flip when a loser from an interaction wins from the same opponent 261 in the subsequent fight. Hence a lower frequency of pair-flips indicates a more stable hierarchy. In 262 hens, pair-flips were reported to be scarce, and half of them occurred during the first 60 interactions. 263 Pair-flips were often quickly followed by another pair-flip indicating immediate retaliation of 264 aggression. 265 In the full DomWorld model pair-flips occurred about half as often as in the model without space or 266 without the winner-loser effect (5 in Table 1). In contrast to the pattern in hens, pair-flips in DomWorld 267 (all versions) were not concentrated during early hierarchy formation (6 in Table 1) and were usually 268 not directly followed by a counter pair-flip (Fig 4). 269  Table 1), with a maximum length of about 10-11 consecutive interactions (8 in Table  277 1). Without space in DomWorld, the percentage of interactions involved in bursts is halved and the 278 maximum length of a burst reduces to approximately 4 interactions. In all model versions the average 279 number of interactions in a burst was higher the greater the dominance of the attacker (Fig 5). 280 Even though a group size of 4 individuals is small, a spatial structure still emerges in which the 284 dominant individual is more often in the centre of the group, while the lower ranking individuals are 285 on average further away from it (Fig 6). 286 for each link-class in Fig 7). Also, the developmental path through the possible network states until a 298 completely connected state (6-links) was reached, varied greatly among runs. Therefore, we will focus 299 only on states with 6 links. 300 Of the 4 states with 6 links (Fig 3), state 38 is the only one that is fully transitive, with 4 transitive triads. 307 State 39 and 40 comprise 1 cyclic triad and 3 transitive triads, and state 41 has 2 cyclic triads and 2 308 transitive triads. State 38 and 39 are the only states that have an individual that dominates all others 309 (DAO), whereas state 38 and 40 contain an individual who is submissive to all others. 310

Bursts
The frequencies of triad motifs in the original model and its two derived versions are similar (Fig 7B).

319
As to the similarity between aspects of the hierarchy in hens and in groups in the full model, 320 DomWorld, we showed that in DomWorld, groups developed a highly linear and stable hierarchy that 321 featured similar characteristics to those of hens (Table 2). After the value of the model parameter 322 intensity of aggression was increased compared to former settings, that were relevant to macaques, 323 the hierarchical linearity was similar to that in hens (11 in Table 2). Also the frequency of rank-changes, 324 pair-flips and bursts in the model resembled those in hens (2, 5 & 7 in Table 2). The hierarchy in 325 DomWorld developed rapidly whereby most changes in rank occurred early in the development of the 326 hierarchy and soon most network states were fully connected with 6 links. The frequency distribution 327 of the complete network states (with 6 links) in DomWorld resembled that of hens (Fig 8). A difference 328 is that in DomWorld intransitivity is mostly the result of state 40, while in hens intransitivity comes 329 from all states that contain one or more cyclic triads, thus also from states 39 and 41. 330  Table 2) and the immediate retaliation of aggression described for hens were 337 absent (9 in Table 2). Further, pair-flips in DomWorld were more evenly distributed over the length of 338 the run, whereas in hens they clustered during early hierarchy development (8 in Table 2). An 339 explanation for these differences might lie in two methodological problems of matching the behaviour 340 of individuals in our computational model to empirical data. Transitive inference, with which individuals fill in transitive relationships for unobserved relationships, 375 has indeed been found in a wide variety of species, including cognitively simpler species such as hens 376 and recently even insects (28). Where transitive inference was long thought to be the hallmark of 377 human reasoning, the ability of simpler species to solve transitive-inference tasks begs the question 378 whether the mechanism underlying transitive-inference-like behaviour is truly cognitively demanding 379 (29). Yet while cognitively simpler explanations have been proposed based on reinforcement history 380 (30,31), experimental evidence is lacking (32-35). 381 However, it is unclear whether the task commonly used to measure transitive inference is directly 382 relevant to the social context of real animals such as dominance relations in a group (29,36). The vast 383 majority of evidence for transitive inference in animals has been collected with the so-called N-term 384 series task, wherein animals are first trained and then tested using transitive series of arbitrary stimuli 385 such as colours, odours or shapes. A study that illustrates this question, by Takahashi and colleagues 386 (37), finds that three species (tree shrews, rats and mice), which in other studies were shown to solve 387 the N-term series task (38,39), were not able to solve two inference tasks in social context, while a 388 fourth species (capuchin monkeys) could. 389 In the present study we show that the winner-loser effect in combination with a socio-spatial 390 component successfully reproduces many of the characteristics of hierarchy development in hens 391 without the need for cognitively sophisticated processes, such as transitive inference. Thereby it forms 392 a plausible alternative to assuming the need of transitive inference in dominance processes. Removing 393 the winner-loser effect from DomWorld, thus representing fixed individual capacities of winning, 394 reduces the resemblance of the model to interactions patterns in hens to 4 out of 12 patterns (11 395 patterns in Table 2 and one in Fig 8) compared to the full model. Furthermore, by experimenting with 396 the presence of the spatial configuration of group members in the model we show that spatial 397 interaction is essential for the formation of a highly linear and stable hierarchy. 398 On the other hand, even though the model DomWorld shows patterns of hierarchy development 399 resembling those in real hens, it cannot prove the existence of similar processes in real animals. 400 Although challenging, future research should determine to what extent the winner-loser effect shapes 401 dominance hierarchies, a pioneering example is a study with novel statistical methods that provided 402 the first evidence in a wild and uncontrolled population of primates (baboons) for the role of the 403 winner-loser effect in the dynamics of the hierarchy (40). 404 In recent years a broader call has been echoed to investigate the development of social networks over 405 time, arguing that for testing hypotheses relevant for selection, dynamics, development and evolution 406 of social networks, it is necessary to include temporal dynamics and spatial constraints (41-44). Along 407 these lines further research may focus on collecting time-series of data of development of the 408 hierarchy in other species in order to determine whether the combination of the winner-loser effect 409 and the socio-spatial structure can generally explain the formation of linear dominance hierarchies, 410 also in species with different dominance styles than hens. 411