Elise Huchard
email: elise.huchard@cefe.cnrs.fr

Sinead English

Matt B V Bell

Nathan Thavarajah

Tim H Clutton-Brock

Competitive growth in a cooperative mammal

In many animal societies where hierarchies govern access to reproduction, the social rank of individuals is related to their age and weight [1][2][START_REF] Heg | Strategic growth decisions in helper cichlids[END_REF][START_REF] Spong | Factors affecting reproductive success of dominant male meerkats[END_REF][START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] and slow-growing animals may lose their place in breeding queues to younger 'challengers' who grow faster than they do [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Reeve | Dispersal of first "workers" in social wasps: causes and implications of an alternative reproductive strategy[END_REF] . The threat of being displaced might be expected to favour the evolution of competitive growth strategies, where individuals increase their own rate of growth in response to increases in the growth of potential rivals. While growth rates have been shown to vary in relation to changes in the social environment in several vertebrates including fish 2,3,7 and mammals [START_REF] Dantzer | Density triggers maternal hormones that increase adaptive offspring growth in a wild mammal[END_REF] , it is not yet known whether individuals increase their growth rates in response to increases in the growth of particular reproductive rivals. Here we show that, in wild Kalahari meerkats (Suricata suricatta), subordinates of both sexes respond to experimentally induced increases in the growth of same-sex rivals by raising their own growth rate and food intake. In addition, when individuals acquire dominant status, they show a secondary period of accelerated growth whose magnitude increases if the difference between their own weight and that of the heaviest subordinate of the same sex in their group is small. Our results show that individuals adjust their growth to the size of their closest competitor and raise the possibility that similar plastic responses to the risk of competition may occur in other social mammals, including domestic animals and primates.

Recent studies have revealed the extent to which aspects of the social environment can affect growth in several vertebrates. In some social fish, the risk of conflict with dominant individuals reduces the growth rates of subordinates 2,3,7 while, in some mammals, prenatal growth increases in response to physiological stress levels in pregnant mothers in high-density environments [START_REF] Dantzer | Density triggers maternal hormones that increase adaptive offspring growth in a wild mammal[END_REF] . However, studies have not yet investigated whether adolescents or adults can adjust their growth rates in relation to changes in the size of specific rivals who may displace them in reproductive queues. In many cooperatively breeding mammals, subordinates of both sexes queue for reproductive opportunities in breeding groups, sometimes for several years [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Hauber | Bateman's principle in cooperatively breeding vertebrates: The effects of non-breeding alloparents on variability in female and male reproductive success[END_REF] .

Rank in these queues is usually determined by relative age and weight, and previous research has produced some evidence of strategic adjustments in growth. In mole-rats and meerkats, adult females that acquire the dominant breeding position commonly show a period of secondary growth [START_REF] Russell | Adaptive size modification by dominant female meerkats[END_REF][START_REF] Young | Morphological divergence of breeders and helpers in wild damaraland mole-rat societies[END_REF][START_REF] Dengler-Crish | Phenotypic plasticity in female naked mole-rats after removal from reproductive suppression[END_REF] which may allow them to increase their fertility or consolidate their status [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Clutton-Brock | Structure and function in mammalian societies[END_REF] . Here, we describe experiments that investigate whether subordinate meerkats queuing for breeding opportunities also engage in competitive growth.

Meerkats live in groups of 3-50 individuals where 90% of reproduction is monopolised by a single dominant pair [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] . Subordinates of both sexes contribute to costly cooperative activities, including pup-feeding, babysitting and raised-guarding [START_REF] Clutton-Brock | Evolution and development of sex differences in cooperative behavior in meerkats[END_REF] . Within groups, subordinates of the same sex are ranked in a hierarchy based on age and weight [START_REF] Thavarajah | The determinants of dominance relationships among subordinate females in the cooperatively breeding meerkat[END_REF] . If the breeding female dies, the oldest and heaviest subordinate typically replaces her, and subordinate females occasionally displace breeders [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] . Unlike females, most males leave their natal groups voluntarily when they are 2-4 years old in small parties of 2-6 individuals, and attempt to displace males in other groups [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Doolan | Dispersal and extra-territorial prospecting by slendertailed meerkats (Suricata suricatta) in the south-western Kalahari[END_REF] . If they are successful, the oldest and heaviest male in the party may often assume the breeding positionIf they are successful, the oldest and heaviest male usually assumes the breeding position [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Doolan | Dispersal and extra-territorial prospecting by slendertailed meerkats (Suricata suricatta) in the south-western Kalahari[END_REF] . Data presented here are derived from a twenty-year study of wild meerkats that has encompassed more than sixty groups in which all individuals were recognisable. Most individuals were trained to climb onto electronic balances and were weighed three times a day (dawn; after three hours of foraging; and dusk) on approximately ten days a month throughout their lives [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] . Changes in the weight of individuals between the beginning and end of morning foraging sessions provide a measure of their food intake. Using 14 groups of habituated meerkats, we manipulated the growth of subordinates of both sexes by provisioning particular individuals and measuring effects on the growth and food intake of individuals of the same sex immediately above them in the age-related hierarchy.

We identified pairs of same-sex littermates belonging to two distinct age classes: juveniles (aged 4-7 months), who had recently reached nutritional independence (n=12 female and 19 male litters from 12 groups), and young adults (aged 12-24 months), who had reached sexual maturity and were able to compete for any breeding vacancies that occurred [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] (n=8 female and 9 male litters from 14 groups). In each pair, we fed the lighter individual, later referred to as the 'challenger', with half a hard-boiled egg twice per day for three months. We subsequently compared the growth of unfed littermates, referred to as 'challenged' individuals, with those of unfed control individuals of the same age from other litters over the same period (Extended Data Figure 1). Challenged individuals of both age classes responded to increases in the growth of fed challengers by increasing their average weight (both in absolute terms and relative to controls) over the course of the experiment. Growth from the start to the mid-point of the experiment was greater in challenged than in control individuals (Figure 1a-b 1), suggesting that challenged individuals adjusted their growth response to the growth of their rival. Increases in the growth of challenged individuals were associated with increases in food intake: food intake was greater for challenged than for control individuals in the first half of the experiment (Figure 1c-d Social mechanisms other than competitive growth could conceivably contribute to increases in the growth of challenged animals, but we were unable to find any evidence that this was the case. It is unlikely that potential increases in the contributions of fed challengers to cooperative activities in the first half of experiment reduced the contributions of challenged animals and so increased their weight gain. First, juveniles contribute little to cooperative activities, so accelerated growth in challenged juveniles cannot be mediated by changes in cooperative behaviour. Second, challenged adults maintained their investment in raisedguarding and pup-feeding in the same period relative to control animals (Wilcoxon signedrank paired-test, raised-guarding: V=52, df=17, P=0.156, pup-feeding: V=30, df=14, P=0.095). Finally, adult fed challengers increased their contributions to raised guarding but not to pup-feeding (Wilcoxon signed-rank paired-test: raised-guarding: V=143, df=17, P=0.013, pup-feeding: V=67, df=14, P=0.719).

Additional analyses suggest that adults that acquire dominant positions may also adjust their growth rates in a strategic fashion. In both sexes, the lifetime breeding success of dominant meerkats depends on the length of time they hold the dominant position [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] which, in females, increases with the difference between their own weight and the weight of the heaviest subordinate of the same sex [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] . Since subordinates engage in competitive growth, we examined whether individuals that have recently acquired the dominant position adjust the magnitude of their subsequent increase in weight to the relative weight of their closest rival. We first analysed whether newly dominant males and females increase their growth rate following dominance acquisition by comparing their weight in the month prior to dominance acquisition and in the four months following dominance acquisition. New dominants of both sexes increased in weight after acquiring dominance (analysis of variance with repeated measures, effect of month post-dominance acquisition on weight: F 4,184 =16.81, P<10 -4 , Figure 2a, Extended Data Figure 3a). The extent of growth following dominance acquisition did not differ between the sexes (analysis of variance with repeated measures, interaction between sex and month post-dominance acquisition: F 4,184 =1.22, P=0.31) and occurred primarily in the two months following dominance acquisition (see Extended Data Table 2 for the results of the post-hoc tests). This growth response may not solely reflect improved access to resources, as food intake remained constant in both sexes during the same period (analysis of variance with repeated measures, effect of month post-dominance acquisition on food intake: F 4,112 =0.34, P=0.850, and interaction between sex and month post-dominance acquisition: F 4,112 =0.09, P=0.986, Extended Data Figure 3b).

The growth of new dominants in the five months following dominance acquisition was more pronounced when the heaviest same-sex subordinate was closer to their own weight at the time of dominance acquisition (Linear Model, estimate±SD=-0.76±0.27, F 1,36 =7.69, P<0.01, Figure 2b and Extended Data Table 3). There was no significant sex difference in this accelerated growth (Extended Data Table 3). Rapid post-dominance growth exacerbated existing weight differences between dominants and same-sex subordinates, with the result that most established dominants were the heaviest individual of their sex in their group (females: 58% of groups, males: 68%). While similar periods of growth after dominance acquisition in female naked mole-rats have been interpreted as a way of enhancing fecundity [START_REF] Young | Morphological divergence of breeders and helpers in wild damaraland mole-rat societies[END_REF][START_REF] Dengler-Crish | Phenotypic plasticity in female naked mole-rats after removal from reproductive suppression[END_REF][START_REF] O'riain | Morphological castes in a vertebrate[END_REF] , the presence of strategic growth adjustments to the relative size of rivals in dominant meerkats of both sexes suggests that these increases may serve to consolidate their status and prolong their breeding tenure [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Clutton-Brock | Structure and function in mammalian societies[END_REF] .

Our findings suggest that subordinates can track changes in the growth and size of potential competitors, perhaps using physical contact as well as visual, vocal or olfactory cues, and react by adjusting their own growth. While the physiological correlates of increased growth rates in challenged individuals are not yet known, hormonal changes associated with heightened threat of competition may increase growth and food intake. Acceleration in growth following dominance acquisition is probably associated with the sudden lifting of reproductive suppression and a re-orientation of life-history strategy. The hormonal profile of dominant meerkats is distinct from that of subordinates, with higher plasmatic levels of oestradiol and progesterone in breeding females and of cortisol in breeders of both sexes [START_REF] Russell | Adaptive size modification by dominant female meerkats[END_REF][START_REF] Carlson | Hormonal correlates of dominance in meerkats (Suricata suricatta)[END_REF][START_REF] Young | The causes of physiological suppression among female meerkats: a role for subordinate restraint due to the threat of infanticide?[END_REF] . Sex steroids are known to regulate the production of critical actors in the insulin/growth factor pathway in the mammalian reproductive tract and associated tissues [START_REF] Dantzer | Mediation of vertebrate life histories via insulin-like growth factor-1[END_REF] , which may result in the up-regulation of anabolic genes involved in growth. Strategic increases in growth rates could be constrained by energy and fitness costs [START_REF] Arendt | Adaptive intrinsic growth rates: An integration across taxa[END_REF] . Allocation of additional resources to growth by challenged individuals may depress immune function and reduce longevity as a result of increases in oxidative stress and telomere shortening [START_REF] Metcalfe | Compensation for a bad start: grow now, pay later?[END_REF] while increases in time spent foraging may raise predation risk, which is high in meerkats [START_REF] Clutton-Brock | Predation, group size and mortality in a cooperative mongoose, Suricata suricatta[END_REF] .

Our results suggest that competitive growth may represent an important component of the developmental strategy of individuals. Recognition of this process may alter classic perspectives on mechanisms of social competition, which frequently suggest that the phenotype of interacting individuals determines the outcome of competitive interactions rather than vice versa. As reproductive queues are widespread in social mammals and the size and weight of individuals often affect their status and breeding success [START_REF] Clutton-Brock | Social competition and selection in males and females[END_REF] , competitive growth may occur in many other social species, possibly including domestic mammals, nonhuman primates and humans.

References and Notes

Methods

Study site and population

Data were collected between 1996 and 2013 as part of a long-term study of wild meerkats at the Kuruman River Reserve, South Africa. The site experiences a hot-wet season (October-April) and a cold-dry season (May-September), with extensive inter-annual variation in rain [START_REF] Clutton-Brock | Predation, group size and mortality in a cooperative mongoose, Suricata suricatta[END_REF] . Rainfall was measured daily (in millimetres) using a standard gauge 25 . Details about the site and population are published elsewhere [START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF][START_REF] Clutton-Brock | Evolution and development of sex differences in cooperative behavior in meerkats[END_REF][START_REF] Clutton-Brock | Predation, group size and mortality in a cooperative mongoose, Suricata suricatta[END_REF] .

Meerkats were habituated to humans and individually recognizable by dye marks.

Groups were visited about three times a week, so life-history events (births, deaths, emigrations, changes in dominance) were known to an accuracy of about 3 days (refs 5, 14).

Pregnancy status was inferred from parturition date and affects female weight from the midpoint of gestation, lasting approximately 70 days (ref 26). Females were considered pregnant from 40 days before parturition or from the first day of detectable pregnancy in cases where abortions occurred. Dominant individuals were identified by their behaviour towards group-mates [START_REF] Spong | Factors affecting reproductive success of dominant male meerkats[END_REF][START_REF] Clutton-Brock | Intrasexual competition and sexual selection in cooperative mammals[END_REF] . They scent-marked more frequently than subordinates, and asserted their dominance over others by anal marking, by rubbing them with their chin, and more rarely by attacking and biting them. Changes in dominance were immediately recognizable, as they were often preceded by a short period (hours to days) of intense fighting, and were accompanied by dramatic changes in behaviour in the contesting individuals. Previous genetic work has shown the absence of incestuous matings within groups [START_REF] Spong | Factors affecting reproductive success of dominant male meerkats[END_REF] . If all immigrant males die, a natal male may become socially dominant in his group. Natal dominant males do not mateguard the dominant female, which is often their mother, and regularly conduct extraterritorial forays for mating opportunities 27 . These males (77/166 dominant males in our dataset) were excluded from analyses.

Weight measures

Individuals were trained to climb onto a laboratory balance in return for drops of water or crumbs of hard-boiled egg, allowing us to record body weight to an accuracy of 1 g. Although individuals were often weighed three times a day, we only used data collected in the morning right after emergence from the burrow and before foraging, to avoid noise created by variation in foraging success throughout the day 25 . Food intake, or morning weight gain, was calculated as the difference between weight collected before foraging activity started, and weight collected after about 3 h of foraging [START_REF] Russell | Adaptive size modification by dominant female meerkats[END_REF] .

Cooperative behaviour

Three cooperative activities are regularly performed by male and female meerkats 14 : (1) babysitting newborn pups, where an individual stays at the burrow while the rest of the group forages; (2) feeding pups that are old enough to join foraging trips (approximately 1-3 months old); and (3) raised-guarding, where an individual ceases foraging and climbs to a raised position to watch out for potential dangers. The occurrence of babysitting, pup-feeding and raised-guarding was recorded ad libitum as events during observation sessions, allowing quantification of relative rates of helping per individual: that is, the number of occurrences of one cooperative behaviour performed by one individual relative to the total number of occurrences of that behaviour in the group over a given period.

Competitive growth experiment

From 2010 to 2013, we conducted a set of 3-month feeding experiments on adults aged 310-870 days and on juveniles aged 111-215 days to investigate whether unfed littermates (challenged individuals) would increase their growth rate in response to experimentally elevated growth rates of their fed siblings (challengers). We identified pairs containing at least two same-sex littermates and fed the individual that was lightest (or as heavy as its sibling) when the experiment started (mean weight difference (±s.d.) in juveniles: 9.8 ± 30.6 g; in adults: 29.9 ± 28.2 g). The fed individuals received half an egg twice daily four times a week for 3 months. Competitive growth has never been described previously, so no prior information was available for power analyses to establish adequate sample sizes. For 17 fed adults including 8 females, the shortest feeding bout lasted 55 days and the mean ± s.d. feeding duration was 84 ± 11 days. For 31 fed juveniles including 12 females, the shortest feeding bout lasted 21 days and the mean ± s.d. feeding duration was 76 ± 21 days. For one adult female litter and one juvenile male litter, there were three same-sex siblings and the two lightest individuals were very close in weight (that is, their average weight difference was lower than 10 g in the 15 days preceding the experiment); one of them was fed, and the two unfed siblings were included in the cohort of challenged individuals. Experiments were interrupted when a pregnancy was detected in an experimental female (fed or unfed), and corresponding data were excluded from analysis. In other cases where the experiment was aborted (for example, if an individual disappeared), data collected during the shortened period were included in analyses; note that for three juvenile dyads, food supplementation lasted respectively 21, 23 and 26 days, so these individuals were excluded from all calculations related to measures describing the second half of the experiment. Observations and weighing sessions were not subjected to blinding, because weight gained by fed individuals during the experiment was often detectable by observers.

Statistical analysis

To investigate the effect of feeding individuals on the growth of their unfed same-sex littermate, we first calculated the growth and food intake, averaged over the first or the second half of the experiment for challenged individuals, challengers and control individuals. Growth was calculated as the individual difference between weight recorded immediately before the start of the experiment and at the mid-point of the experiment (45 days), or as the individual change in weight from the mid-point to the end of the experiment (90 days). Food intake, calculated in terms of morning weight gain, was averaged for each individual, over days 5-45 of the experiment (the first 4 days were excluded to allow for potential adjustments in challenged individuals) and then over experimental days 45-90. We compared these measures across challenged and control individuals using two-sample Welch's t-tests (for juveniles) and paired t-tests (for adults) after checking that variance was homogeneous across groups using Levene tests (P > 0.05 in all cases). We focused on the contrast between challenged and control individuals: significantly higher growth in challenged individuals over controls would provide experimental evidence for competitive growth, defined as an elevated increase in growth in response to the challenge of a fed rival. Control individuals were selected as any individual from the population during the experimental period (2010-2013) that had a lighter same-sex littermate in their group at the age at which supplemental feeding started in experimental groups (120 days in juveniles, 1 year in adults), to match criteria used to identify unfed individuals in experimental dyads (Extended Data Fig. 1). In adults, where heterogeneity in the age at the start of the experiment was considerable (361-772 days, mean ± s.d. = 496.7 ± 112.9 days), each challenged individual was matched to the same-sex individual of the control cohort that was closest in age (differences in birth dates between challenged individuals and their matched control were small: 2-32 days, mean + s.d. = 11.2 ± 8.4) and present in the population at the time of the experiment.

Matching each experimental individual with a same-age and same-sex control in this way allowed us to control for environmental variation that might otherwise have introduced noise when comparing the weight and growth of individuals that underwent a supplementation at different periods (e.g. during the dry versus the wet season). Individual weight before the experiment was averaged across the 15 days preceding the experiment; weight at mid-point was averaged across days 45-60 of the experiment; and weight at the end of the experiment was averaged across experimental days 90-105.

It was not possible to select such matched control individuals in juveniles, however, as there was no control litter born shortly before or after experimental litters in several cases. Small age differences can introduce important noise when comparing weights among juveniles, because growth rates are relatively high between 4 and 7 months of age, compared with later ages 25 . In the juvenile cohort, age at the start of the experiment was very homogeneous (range: 111-128 days of age, mean ± s.d. = 122.3 ± 4.7), so matching experimental dyads with control individuals by age was deemed less necessary. Individual weight records were averaged across 95-110 days of age (before experiment); 170-185 days of age (after about 45 days of experiment); and 215-230 days of age (after about 90 days of experiment), and growth was calculated between these time points.

We further ran a linear model investigating the relationship between the growth of challenged individuals and the growth of their fed challenger to test whether the growth responses of challenged individuals were adjusted to the weight gain of their fed challenger.

Growth was the response variable, and was calculated as the weight difference between the start and the mid-point of the experiment (since the above analyses suggested that competitive growth was highest at this time). Explanatory variables included sex, age at start of experiment and cumulative rainfall in the previous 9 months, which was previously found to influence the growth of individual meerkats 25 . Results and sample sizes are presented in Extended Data Table 1 and Extended Data Fig. 2.

We investigated the influence of the experiment on pup-feeding and raised-guarding rates in the adult cohort only, because helping is rare before 6 months of age [START_REF] Clutton-Brock | Evolution and development of sex differences in cooperative behavior in meerkats[END_REF] . We did not consider babysitting because fewer than half of the experimental groups exhibited babysitting during the experiment. For each observation session, we measured the observed proportion of raisedguarding events performed by the focal individual relative to the total number of events recorded for the group. We then calculated individual deviation from the proportion expected under the null hypothesis, where each individual contributes equally, calculated as the inverse of the number of helpers in the group. We averaged this deviation across all observation sessions for each individual during the first half of the experiment (10-120 sessions per individual, median = 19). Thus, mean deviation gives an indication of the extent of cooperative behaviour relative to average contributions in the group: individuals with a larger, more positive deviation have higher cooperative behaviour. We compared the mean deviations between challenged individuals and their matched controls using paired Wilcoxon signed-rank tests, as the response variable was not normally distributed. We used the same approach to test for differences in individual contributions to pup-feeding between challenged and control individuals.

When investigating changes in weight following dominance acquisition, we considered individuals that maintained dominance for at least 6 months, to avoid biasing the sample towards short and unstable tenures. We averaged weight records for each individual (n = 42 females and 30 males) across the 30 days preceding dominance acquisition (labelled 'month 0') and then across days 0-30, 30-60, 60-90 and 90-120 following dominance acquisition (respectively labelled 'months 1, 2, 3 and 4'). Weights recorded during pregnancies were excluded. We then retained only individuals with no missing data in any of these five 1-month blocks (n = 21 females and 27 males) to ensure a balanced design. Thus, we could evaluate the significance of weight differences between 1-month blocks using a repeated-measures analysis of variance with multiple factors. Factors included sex, proximity to dominance acquisition (with five levels: month 0, 1, 2, 3 and 4) and the interaction between sex and proximity to dominance acquisition, to test if the temporal dynamics of post-dominance growth differed between males and females. Post-hoc tests were conducted using paired ttests with adjusted P values to compare within-individual changes in weight before dominance acquisition to each of the 4 months after acquisition; as well as between each month of the 4-month period following acquisition of dominance. A Bonferroni correction was applied to correct for multiple testing. These results are presented in Extended Data Fig. 3a and Extended Data Table 2.

We compared changes in food intake (measured as morning weight gain) following dominance acquisition using the same approach. As described above, we retained only individuals with no missing data in any of the five 1-month blocks (n = 9 females and 21 males) to evaluate the significance of differences in food intake between 1-month blocks using a repeated-measures analysis of variance with multiple factors. As above, factors included were sex, proximity to dominance acquisition and their interaction. These results are illustrated in Extended Data Fig. 3b.

To investigate the effect of competition on growth following dominance acquisition, we ran a linear model, with weight gain within 150 days following dominance acquisition (calculated as weight 150 days after dominance acquisition minus weight at dominance acquisition, each averaged across all weights for 10 days before and after the time-point of interest) as our response variable. We focused on a 5-month period after dominance acquisition, because previous analyses had revealed that growth rates were elevated in the 2 to 4 months following dominance acquisition. We included all new dominant females that retained dominance for longer than 6 months and had at least one subordinate female in their group that was older than 6 months when they became dominant. Six months is the age of the youngest female that ever reached dominance. Weights recorded during pregnancies were excluded. We included all new dominant males that had at least one non-natal subordinate male in their group that was older than 6 months when they became dominant. Natal subordinate males were not considered as rivals because they hardly ever reproduce or fight for dominance [START_REF] Spong | Factors affecting reproductive success of dominant male meerkats[END_REF] . Explanatory variables included sex, rainfall (averaged over the 150 days following dominance acquisition), a sinusoidal term describing season of dominance acquisition 25 , age at dominance acquisition, and absolute weight difference with the same-sex rival (that is, heaviest subordinate at the time of dominance acquisition). In addition, the interaction between sex and absolute weight difference with the same-sex rival tested whether the effect of the weight difference with the main rival differed between sexes. We used the absolute value of weight difference because graphical exploration of the data suggested that dominant growth rates increase when the main same-sex rival is either slightly heavier or slightly lighter, but not when the rival is much lighter or much heavier. In cases where a rival is much heavier but fails to win fights over dominance, he or she may have poor competitive abilities for other reasons and may not represent a threat to the dominant. The results and sample sizes are presented in Extended Data Table 3. acquisition (respectively labelled '1', '2', '3' and '4'). Whiskers show all data points that are no further away from the box than half the interquartile range.

Additional references of the section describing methods

1

  Hoogland, J L, The black-tailed prairie dog: social life of a burrowing mammal. (University of Chicago Press, Chicago, 1995).

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Competitive growth in dominants. Panel a: example growth trajectories of a male

25

  English, S., Bateman, A. W., and Clutton-Brock, T. H., Lifetime growth in wild meerkats: incorporating life history and environmental factors into a standard growth model. Oecologia 169, 143 (2012).

  Figure 1 506

Sharp, S. P, English, S., and Clutton-Brock, T. H., Maternal investment during pregnancy in wild meerkats. Evol. Ecol.

27, 1033 (2013).

Extended Data Figure2

Acknowledgements. We are extremely grateful to the many volunteers, field managers, PhD students and post-docs who have contributed to data collection over the past 15 years, and to D. Gaynor, I. Stevenson, P. Roth, J. Samson, R. Millar, E. Cameron, J. du Toit and M. Haupt for invaluable support. We are grateful to M. Manser for her contribution to the organization of the Kalahari Meerkat Project (KMP). We also thank Dom Cram for comments on previous drafts, and Andrew Bateman, Alexandre Courtiol, and Mick Crawley for statistical advice. Northern Cape Conservation and the Kotze family kindly provided permission to work in the Kalahari. Our work was approved by the Animal Ethics Committee of the University of Pretoria (Project number: EC010-13). The KMP is supported and organized by the Universities of Cambridge and Zurich. This research was supported by the Natural Environment Research Council (grant RG53472) and the European Research Council (grant 294494)..

Author contributions. EH implemented the analysis and drafted the results; THCB, SE and MB planned the experiments which were conducted by NT and other members of the Kalahari Meerkat Project; EH, SE, MB and THCB wrote the paper. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to ehuchard@gmail.com.

Extended data


Dieter Lukas
email: dl384@cam.ac.uk

Keywords: infanticide, mammals, phylogeny, social system, mating system, reproductive skew, dominance tenure, polyandry Species MaleInfanticide Reference Acinonyx_jubatus

Male mammals may commonly kill conspecific offspring. The benefits of such infanticide to males, and its costs to females, likely vary across mammalian social and mating systems. Here we use comparative analyses to show that infanticide primarily evolves in social mammals where reproduction is monopolized by a minority of males. It has not promoted social counter-strategies such as female gregariousness, pair-living, or changes in group size and sex-ratio but is successfully prevented by female sexual promiscuity, a paternity dilution strategy. These findings indicate that infanticide is a consequence, rather than a cause, of contrasts in mammalian social systems affecting the intensity of sexual conflict.

One Sentence Summary

Infanticide by males is an evolutionary consequence, rather than a cause, of contrasts in mammalian social systems and reflects the intensity of sexual conflict.

Main text

Infanticide by males is widespread in mammals and may represent the main cause of infant mortality in some populations [START_REF] Palombit | The evolution of primate societies[END_REF]. It has long been viewed as a sexually selected strategy that increases mating opportunities for killer males by shortening postpartum infertility in the victim's mother [START_REF] Hrdy | Male-male competition and infanticide among the langurs (Presbytis entellus) of Abu, Rajasthan[END_REF][START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF]. This is supported by natural observations across taxa showing that males target unrelated infants and often impregnate the victim's mother afterwards [START_REF] Palombit | The evolution of primate societies[END_REF][START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF][START_REF] Ebensperger | Strategies and counterstrategies to infanticide in mammals[END_REF].

Attempts to explain the taxonomic distribution of infanticide have however been mainly limited to investigations of the life-history correlates of male infanticide [START_REF] Janson | Infanticide by males and its implications[END_REF][START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Blumstein | Infanticide by Males and Its Implications[END_REF][START_REF] Van Schaik | Infanticide by Males and Its Implications[END_REF], showing that it rarely occurs where it does not accelerate the mother's return to sexual activity, as in seasonal breeders who cannot resume cycling before the next breeding season [START_REF] Van Schaik | Infanticide by Males and Its Implications[END_REF].

Several scenarios have linked the distribution of infanticide across species to the evolution of social organization and mating systems in mammals, and they remain largely untested or disputed [START_REF] Lukas | The evolution of social monogamy in mammals[END_REF][START_REF] Opie | Male infanticide leads to social monogamy in mammals[END_REF]. According to the sexual selection hypothesis, the distribution of infanticide is expected to be modulated by contrasts in social systems that affect the intensity of male intrasexual competition [START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF][START_REF] Janson | Infanticide by males and its implications[END_REF][START_REF] Van Schaik | Infanticide by Males and Its Implications[END_REF]. Male infanticide should thus be prevalent in species where a few males mate with multiple females and monopolize most reproductive opportunities.

However, females may respond to infanticide by developing counter-strategies that may refine patterns of associations across species. Social counter-strategies may include the evolution of female sociality [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Pradhan | Infanticide-driven intersexual conflict over matings in primates and its effects on social organization[END_REF][START_REF] Teichroeb | Infanticide risk and male quality influence optimal group composition for Colobus vellerosus[END_REF], of permanent male-female associations [START_REF] Van Schaik | The evolution of monogamy in large primates: a new hypothesis and some crucial tests[END_REF][START_REF] Borries | Social monogamy and the threat of infanticide in larger mammals[END_REF][START_REF] Van Schaik | Infanticide risk and the evolution of male-female association in primates[END_REF], or of changes in the group sex-ratio [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Pradhan | Infanticide-driven intersexual conflict over matings in primates and its effects on social organization[END_REF][START_REF] Teichroeb | Infanticide risk and male quality influence optimal group composition for Colobus vellerosus[END_REF][START_REF] Van Schaik | Infanticide risk and the evolution of male-female association in primates[END_REF] because females may form coalitions with other females or with resident males to defend their progeny against male invaders. Additionally, females may mate with multiple partners to confuse paternity and dissuade infanticide [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Van Noordwijk | Infanticide by Males and Its Implications[END_REF][START_REF] Wolff | Promiscuous females protect their offspring[END_REF], which may thus be absent in species with pronounced sperm competition. The evolutionary arms race between the sexes driven by male infanticide has generated confusion and controversy regarding the role of infanticide in the evolution of mammalian societies, calling for more integrative studies.

Here we use information gathered on 260 mammal species including 119 species with, and 141 without infanticide (Figure 1) to identify how variation in social organization and mating systems may have favoured or prevented the evolution of infanticide by males using phylogenetic analyses [START_REF]Material and Method is available on Science Online[END_REF]. Specifically, we test if infanticide has primarily evolved in species where females breed throughout the year and some males have high reproductive monopoly, and if it has selected for social and sexual counter-strategies, including transitions towards female gregariousness, permanent male-female associations, changes in group size or sexratio or increases in female sexual promiscuity. We included infanticide records from wild populations for which the killer was unambiguously identified as an adult male. Species for which infanticide had never been observed were included only if natural observations on females and juveniles were available over more than 3 reproductive seasons, to minimize the risk of misclassifying them as "non-infanticidal". The phylogenetic relatedness between species was inferred from the updated mammalian supertree [START_REF] Fritz | Geographical variation in predictors of mammalian extinction risk: big is bad, but only in the tropics[END_REF] and analyses were also replicated in primates exclusively, which confirmed results obtained across mammals (see supplementary results).

The distribution of male infanticide is closely associated with the absence of seasonal or 'annual' breeding (defined as an average inter-birth interval of 360-370 days). Infanticide occurs in a majority of non-annual breeders (76% of 97 species), compared to 28% of 134 annual breeders (lambda=0. 67, t=-4.0, p<0.001). A long lactation (relative to gestation) and the absence of a postpartum oestrus, two life-history traits affecting the time to cycling resumption in mothers of killed infants, are also associated with male infanticide, though their association disappears when controlling for annual breeding (for both traits, p as estimated by MCMCglmm (pMCMC)>0.08 while pMCMC for annual breeding <0.001). While previous studies have used the ratio of the duration of lactation to that of gestation to estimate infanticide risk [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Blumstein | Infanticide by Males and Its Implications[END_REF][START_REF] Van Schaik | Infanticide by Males and Its Implications[END_REF], our results reveal that this association is weak: lactation exceeds gestation in 25 of 45 mammal species with infanticide, and in 38 of 89 species without infanticide. Other aspects of life-history were not associated with male infanticide (longevity: n=210 species, pMCMC=0.08; litter size: n=230 species, pMCMC=0.07; relative offspring weight at birth: n=191 species, pMCMC=0.59), suggesting that infanticide evolution is not determined by a species' pace of life. Overall, the possibility for females to breed throughout the year is the only life-history trait examined that significantly explains the distribution of infanticide, confirming previous work and suggesting that infanticidal males gain extra mating opportunities due to earlier cycle resumption of the victim's mother in non-annual breeders. Such males are thereby redirecting maternal investment from unrelated offspring towards their own future offspring.

Comparing the occurrence of male infanticide across social systems, we find that males commit infanticide more frequently in stable mixed-sex groups (66% of 112 species) than in solitary species (40% of 78 solitary species, pAN=0.01), in species with female-only groups (23% of 31 species, pAN=0.006) and in pair-living species (18% of 39 species, pAN<0.001).

Phylogenetic reconstructions confirm that variation in social organization is a key determinant of the evolution of male infanticide, which is more likely in stable bisexual groups than in any other social system (see supplementary table 1). In addition, social groups contain, on average, 1 male per 2.5 females in species with male infanticide (SD= 1.7, n=56 species), but only 1 male for 1.3 females in species without infanticide (SD= 3.2,n=19 species,Figure 2a;lambda=0.47,p=0.002; this is not an effect of differences in group sizes, as group size is similar in both sets of species: p=0.28). Phylogenetic reconstructions suggest that a biased group sex-ratio is a determinant, rather than a consequence, of the evolution of male infanticide: the strongest female biases are observed just before or at the transition towards male infanticide, while there are few or no subsequent changes once infanticide has evolved (see supplementary results).

In line with this, infanticide occurs more frequently where reproduction is monopolized by a few males (Figure 2b): the median percentage of offspring sired by the alpha male is 67% (SD=19.9, n=15 species) in species with infanticide, compared to 35% (SD=22.2, n=5) in species without (lambda=0. 75, t=3.9, p=0.001). Finally, males retain their dominant position for shorter durations in species with infanticide (Figure 2c): on average, dominance tenure covers two inter-birth intervals (if the females were to successfully wean each litter) (SD=1.0, n=34 species), compared to four in species without infanticide (SD=1.2, n=6) (lambda=0.0, t=-3.4, p=0.001). These correlations hold after controlling for the effect of annual breeding, which may also affect male ability to monopolize females (Supplementary Table 2). Overall, these findings indicate that a high male monopolization potential favours transitions towards infanticide by allowing males to maximize their reproductive output in systems where the costs of holding dominance shorten their breeding tenures [START_REF] Lukas | Costs of mating competition limit male lifetime breeding success in polygynous mammals[END_REF].

Male infanticide has been proposed to alter social evolution by favouring female gregariousness or permanent male-female associations or by promoting a higher number of resident males that may help mothers to protect their infants from male intruders. We found no support for any of these scenarios. Infanticide risk is low in solitary species, the ancestral mammalian social organization [START_REF] Lukas | The evolution of social monogamy in mammals[END_REF], and as such is unlikely to motivate evolutionary transitions from a solitary lifestyle to other social organizations. Phylogenetic reconstructions confirm that male infanticide is significantly more likely to evolve after transitions towards group-living than in their solitary ancestors (see above). The presence of male infanticide does not increase the likelihood of a transition from solitary living to social monogamy, to female gregariousness or to group living (see supplementary table 1). In addition, among species living in stable bisexual groups, male infanticide is not linked to changes in the degree of female sociality (5.5±5.1 females per group in 56 infanticidal species compared to 8.9±4.0 in 13 non-infanticidal species; pMCMC=0.93). These findings indicate that infanticide by males did not trigger important transitions in mammalian social evolution. Population studies have nevertheless highlighted relationships between infanticide rates and group size (e.g., [START_REF] Crockett | Infanticide by males and its implications[END_REF], suggesting that the social consequences of infanticide may differ within populations versus across species, or that selection exerted by infanticide is insufficient at inducing major shifts in mammalian social organization.

Infanticide risk may also lead to the evolution of sexual counter-strategies by females, who might prevent infanticide by mating with many males to dilute paternity [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Van Noordwijk | Infanticide by Males and Its Implications[END_REF][START_REF] Wolff | Promiscuous females protect their offspring[END_REF]. To test this hypothesis, we investigated evolutionary relationships between infanticide and testis size, an indicator of the intensity of sperm competition [START_REF] Soulsbury | Genetic patterns of paternity and testes size in mammals[END_REF][START_REF] Harcourt | Testis weight, body weight and breeding system in primates[END_REF]. In support of the paternity dilution hypothesis, phylogenetic reconstructions indicate that relative testis size is larger in lineages in which more time has elapsed since the evolution of infanticide. State-dependent diversification models [START_REF] Beaulieu | Modeling stabilizing selection: expanding the Ornstein-Uhlenbeck model of adaptive evolution[END_REF] show that increases in testis size follow rather than precede transitions to infanticide as they are not detected on branches immediately before transitions to infanticide, suggesting that infanticide exerts directional selection on relative testis size [START_REF]Material and Method is available on Science Online[END_REF]. In addition, infanticide is subsequently lost in lineages where testes have grown large (Figure 3; pMCMC=0.02; see supplementary results), indicating that infanticide may disappear where female attempts to prevent male sexual monopolization are successful.

Our findings support key predictions of the sexual selection hypothesis: males primarily kill the offspring of rivals in stable bisexual groups where a few males monopolize reproduction over short periods. Increased testis size following evolutionary transitions to infanticide and secondary loss of infanticide in species with large testes suggests that female paternity dilution strategy efficiently reduces infanticide risk, and emphasizes the reversible nature of infanticide, which may appear and disappear according to the evolutionary arms race between the sexes. While past studies failed to find comparative evidence for sexual counterstrategies to infanticide [START_REF] Blumstein | Infanticide by Males and Its Implications[END_REF][START_REF] Van Noordwijk | Infanticide by Males and Its Implications[END_REF], our sample spanning all mammals, combined with phylogenetically controlled analyses, and our focus on testis size to index female sexual promiscuity may explain divergent results.

Our analyses build on five decades of field observations to understand the distribution of species differences in the occurrence of infanticide by males across mammalian societies. The evolution of infanticide is largely determined by variation in the intensity of male-male contest competition and has not promoted major switches in mammalian social organization.

However, it has impacted the evolution of mating systems by increasing female sexual promiscuity as a paternity dilution strategy. These findings suggest that the distribution of infanticide across mammals is a consequence of contrasts in social and mating systems, and closely reflects variation in the intensity of intra-and inter-sexual conflict. and seems to have evolved independently multiple times. It mostly occurs in social (dark grey branches), less in solitary (light grey branches), and least in monogamous species (black branches). Animal drawings are from phylopic.org (for full credit see ( 18)).

Figure 2: Infanticide is associated with polygynous mating systems

Male infanticide occurs in species in which (a) social groups contain more females per male, (b) dominant males obtain a higher share of reproduction in a given season, but (c) maintain their dominant position for shorter periods (here measured as the average number of interbirth intervals).

Figure 3: Loss of male infanticide occurs in species with large testes

In some lineages in which males commit infanticide, testes appear to increase in size (relative to body mass) and subsequently, male infanticide is lost when testes are relatively large.

Old World

Relative testes size

data unambiguously showed that the individual committing infanticide was an adult male.

From databases and reviews we extracted information on life-history (seasonal breeding, lactation and gestation length, inter-birth interval, longevity, body mass at birth, litter size [START_REF] Ernest | Life history characteristics of placental nonvolant mammals[END_REF][START_REF] Jones | PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals[END_REF][START_REF] De Magalhães | A database of vertebrate longevity records and their relation to other life-history traits[END_REF] and postpartum oestrous [START_REF] Van Schaik | Primate males: causes and consequences of variation in group composition[END_REF]), on mating system (reproductive skew [START_REF] Soulsbury | Genetic patterns of paternity and testes size in mammals[END_REF], length of dominance tenure in males [START_REF] Lukas | Costs of mating competition limit male lifetime breeding success in polygynous mammals[END_REF], testis size as an index of multiple male mating by females [START_REF] Harcourt | Testis weight, body weight and breeding system in primates[END_REF][START_REF] Kenagy | Size and function of mammalian testes in relation to body size[END_REF][START_REF] Glander | Morphometrics and testicle size of rain forest lemur species from southeastern Madagascar[END_REF][START_REF] Hosken | Sperm competition in bats[END_REF][START_REF] Stallmann | Size matters: the (negative) allometry of copulatory duration in mammals[END_REF][START_REF] Iossa | Sperm competition and the evolution of testes size in terrestrial mammalian carnivores[END_REF][START_REF] Orr | Does delayed fertilization facilitate sperm competition in bats?[END_REF]) and on sociality (social organization [START_REF] Lukas | The evolution of social monogamy in mammals[END_REF], group composition [START_REF] Lukas | Costs of mating competition limit male lifetime breeding success in polygynous mammals[END_REF][START_REF] Carnes | Effects of the distribution of female primates on the number of males[END_REF]). We classified the social organization of a species as solitary if breeding females tolerate the proximity of adult conspecifics only during the mating season; as monogamous if a single breeding female and a single breeding male share a territory, potentially including nonbreeding offspring; as female-only groups where stable groups of breeding females associate permanently and males only join for mating; and as stable mixed-sex groups if two or more breeding females associate permanently with one or more male [START_REF] Lukas | The evolution of social monogamy in mammals[END_REF]. Seasonal breeding was defined as an interbirth interval comprised between 360 and 370 days, and we used data on intra-annual variability in temperature [START_REF] Botero | Environmental harshness is positively correlated with intraspecific divergence in mammals and birds[END_REF] to verify that yearly breeding thus defined is associated with ecological seasonality (yearly variance in temperature 38.7, compared to 27.5 for non-seasonal breeders; lambda=0.92, t=-0.1, p<0.001). We chose to exclude species reproducing always at the same season but less than once a year on average from the seasonally breeding species, as infanticide is likely to provide males with benefits in this context if a female resumes cycling one year earlier than she would if her infant was alive. We provide a full data file in text format at the Knowledge Network for Biocomplexity (https://knb.ecoinformatics.org).

We relied on the updated mammalian supertree [START_REF] Fritz | Geographical variation in predictors of mammalian extinction risk: big is bad, but only in the tropics[END_REF] to reflect the phylogenetic relatedness between species. The tree was truncated to match our sample using functions of the package 'ape' [START_REF] Paradis | APE: analyses of phylogenetics and evolution in R language[END_REF] in the statistical software R [START_REF] Ward | Life-history of the feathertail glider, Acrobates pygmaeus (Acrobatidae, Marsupialia) in South-Eastern Australia[END_REF]. We resolved polytomies randomly for all analyses that require bifurcating trees, and repeated each analysis with three independent resolutions, which in all cases gave consistent results. Phylogenetic reconstruction of discrete traits were performed across trees with dated branch lengths, across ultrametric trees in which all tips have the same distance to the root and branch lengths are proportional to the number of descendants [START_REF] Grafen | The phylogenetic regression[END_REF], and across trees in which all branch lengths were transformed to equal one.

We used different approaches and methods to assess our hypotheses according to the type of prediction and data. Initially, we compared values of currently living species in which male infanticide is present to those in which male infanticide is absent without taking phylogeny into account by using Wilcoxon-tests. When assessing whether the distribution of a trait differed between species that were grouped into discrete categories while taking phylogeny into account, we used phylogenetic Anova as implemented in the R-package 'geiger' (40; indicated as pAN in the manuscript). We tested whether the presence or absence of infanticide explains variation in quantitative traits using phylogenetic generalized least squares regressions as implemented in the R-package 'CAPER' (41; indicated in the manuscript by listing the lambda-, t-, and p-value of the model) and examined whether changes in the traits most likely co-occur on the same branches by calculating phylogenetic independent contrasts using functions of the R-package 'ape'. To examine whether variation in continuous traits explained the distribution of infanticide across species we ran regression models in the R-package 'MCMCglmm' ( 42) that corrected for phylogenetic relatedness (indicated as pMCMC in the manuscript), using a fixed prior [START_REF] Hadfield | MCMCglmm: Markov chain Monte Carlo methods for Generalised Linear Mixed Models[END_REF]. The significance of factors in explaining variation in the dependent trait was assessed by the p-values [START_REF] Hadfield | MCMCglmm: Markov chain Monte Carlo methods for Generalised Linear Mixed Models[END_REF]. In addition to their presentation in the main manuscript, we also list all statistical results in Supplementary Table 2.

Both the phylogenetic generalized least squares regression and the MCMCglmm method estimate the extent of the phylogenetic signal, and thereby can correct for phylogeny to the appropriate degree (including the possibility of no phylogenetic signal).

There are two traits, longevity and litter size, for which Wilcoxon tests returned a significant difference between species with and without infanticide that were not supported in analyses that controlled for phylogeny. We discuss these in the supplementary results below. In addition, to control for the possibility that some effects identified across all mammals might differ from patterns occurring within particular lineages of mammals, we repeated all analyses including only the 90 primate species in our sample. The significance of all the correlations reported are the same using the main dataset and the restricted, primate-specific dataset (see Supplementary Table 3). However, when only including primate species, we do not have sufficient power to investigate the evolutionary sequence of changes in group sex ratio and testis size in relation to transitions towards presence or absence of male infanticide.

In order to decipher causal associations between two traits that could be coded as binary (absence versus presence) we compared inference models in Bayestraits Discrete [START_REF] Pagel | Inferring the historical patterns of biological evolution[END_REF][START_REF] Pagel | Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo[END_REF]. In Discrete, we compared the evolution of male infanticide against the evolution of each type of social organization (solitary, socially monogamous, harem, multi-female multi-male group) in separate models. We first checked for each association whether models that assume a dependent evolution between male infanticide and a particular type of social organization were better supported compared to models that assume an independent evolution of the traits. If the inference suggested a dependent evolution, we ran further models to investigate the potential directionality of the association: first, we tested whether models in which transitions in social organization were constrained to occur at identical rate in both the presence and the absence of male infanticide were less supported (which would indicate that transitions in social organization might depend on the presence of male infanticide); second, we assessed whether models in which transitions in male infanticide were constrained to occur at equal rates independent of the social organization were less supported (which would indicate that the evolution of male infanticide depends on a particular type of social organization). We assessed significance between dependent and independent models by comparing the likelihood ratio statistic against a chi-squared distribution with four degrees of freedom [START_REF] Pagel | Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo[END_REF]; unconstrained models were considered to explain the data significantly better if the likelihood ratio statistic exceeded a chi-squared distribution with one degree of freedom.

To investigate causal relationships between male infanticide and continuous traits (testis size relative to body size and group sex ratio) we applied flexible Ornstein-Uhlenbeck models of trait diversification [START_REF] Beaulieu | Modeling stabilizing selection: expanding the Ornstein-Uhlenbeck model of adaptive evolution[END_REF]. Ornstein-Uhlenbeck models assume that a trait is under stabilizing selection toward a single or multiple adaptive optima. Specifically, we predicted that models that assume that relative testis size and group sex ratio evolve towards different values in lineages in which male infanticide is present compared to absent are statistically better supported than models that assume that relative testis size and group sex ratio evolve independently of the presence or absence of male infanticide. We performed the Ornstein-Uhlenbeck model reconstructions using functions of the R-package 'OUwie' [START_REF] Beaulieu | OUwie: Analysis of evolutionary rates in an OU framework[END_REF]. We first reconstructed the evolution of male infanticide. Next, we assessed two possible ways in which the presence of male infanticide could influence either relative testis size or group sex ratios: first, the presence of infanticide could speed up or slow down the rate of change, but average values of testis size and sex ratio are about the same; second, while the rate of change is the same, the presence of male infanticide could be associated with a different peak value of testis size or sex ratio. Peak values, in comparison to averages, take into account the possibility that the value might only have been reached

once male infanticide has been present for a sufficient amount of evolutionary time. Any association that shows that peak values of either testis size or group sex ratio differ between lineages in which male infanticide is either present or absent could however also be the consequence of the reversed directionality: male infanticide evolves in lineages in which either testis size or group sex ratio have already reached extreme values. To differentiate the direction of causality in such cases, we performed two further sets of analyses. First, we compared the estimated peak values to the observed average values for extant species which either do or do not show male infanticide. If infanticide evolves only when the value of a given trait is already high (or low) but does not subsequently influence the evolution of this trait, the average value is expected to be similar to the peak value, because infanticide evolves when the condition matches. If, in contrast, infanticide does influence the evolution of the trait, then the peak value should be more extreme than the average value observed in extant species, because these likely include a number of species where infanticide has only evolved recently and where the trait has not yet reached its peak value. Second, we checked whether directional selection favouring a different value of the trait had already started before infanticide evolved. For these analyses, we included the branches just before the nodes at which infanticide most likely first evolved, in lineages associated with the presence of male infanticide. If the presence of male infanticide leads to a shift in the peak value, the inclusion of these additional branches should decrease or obscure any signal. If, alternatively, male infanticide only evolves in those lineages characterized by an extreme trait value, the inclusion of these additional branches should increase the strength of the signal. We report the results below.

Supplementary results

Inference of non-phylogenetic model differs from that of phylogenetic model

For longevity and litter-size, Wilcoxon-tests of the raw species values indicate a difference between species in which male infanticide is present as compared to absent. This difference does not hold in analyses controlling for phylogenetic relatedness. While including phylogenetic information could have introduced a bias if longevity and litter-size where to evolve in a more complex way than approximated by the shared co-ancestry between species, this scenario is unlikely because these two life-history traits generally show a strong phylogenetic signal. Instead, it appears that the association between male infanticide and longevity/litter-size is indirect, mediated by another trait that is approximated by the phylogenetic component and better explains the variance in longevity/litter-size. The factor mediating the relationship between male infanticide and longevity/litter-size is most likely group-living, which has a significant phylogenetic signal.

This interpretation is supported by non-phylogenetic multivariate analyses which show that the presence of male infanticide no longer predicts variation in longevity/litter-size across species when controlling for the social organization (see Supplementary Table 2).

Analyses including only the primate species in our sample

The significance of all the correlations we report is the same when including only primate species in the analyses (90 of the 260 species are primates; see Supplementary Table 3). However, we do not have sufficient power with the more limited sample of species to investigate the evolutionary sequence of change of group sex ratio and testis size in relation to transitions in male infanticide. Here, the AIC values of models assuming that species with male infanticide are associated with different values of group sex ratio and testis size compared to species in which infanticide is absent are within 1.5 of the AIC values of models assuming similar values. In addition, the multivariate analyses suggest that, in primates, annual breeding and postpartum oestrus is closely linked, and postpartum oestrus is a better predictor of male infanticide than is annual breeding.

Results of the Ornstein-Uhlenbeck model inferences

For both sex ratio and testis size, the presence of infanticide seems to be associated with different peak values, but not with different rates of evolution (in both cases, the likelihoods of these best supported models differ by >3 from the likelihoods of the next models assuming different peak values and different rates, and by >5 from the likelihood of the best supported models assuming equal peak values). These findings match the regression analyses comparing changes in the values of the traits. To disentangle causality, we compared peak values to average values among extant species and investigated whether changes in either sex ratio or testis size most likely originated before or after the transition towards male infanticide.

In contemporary species with male infanticide, the average group sex ratio is 1 male per 2.5 females, whereas it is 1 male per 1.3 females in species without infanticide; these values do not differ from peak values (1 male per 2.4 females in species with infanticide; 1 male per 1.6 females in species without infanticide). In addition, the strength of the association between male infanticide and group sex ratio increased when we included additional branches located immediately before the evolution of male infanticide, as shown by increases in the likelihoods of models supporting two different peak values, relative to models supporting similar peak values. The peak value of group sex-ratio changed to 1 male per 2.8 females in lineages with infanticide, and to 1 male per 1.2 females in lineages without infanticide.

In contemporary species with male infanticide, average relative testis size is 0.20 (indicative of relatively large testes for a given body size), whereas it is -0.02 in species without infanticide; the peak value for species with infanticide appears much higher (0.48), whereas it is identical to the average relative testis size (-0.03) for species without infanticide, suggesting that the evolution of infanticide induces changes in testis size. In addition, the association between relative testis size and male infanticide disappeared when we included additional branches located immediately before transitions to male infanticide, confirming that changes in testis size follow, rather than precede, transitions to male infanticide: in this case the best supported model suggested that peak values for testis size were identical in lineages with or without infanticide.

These results suggest that a male-biased sex ratio is a cause for the evolution of infanticide, whereas testis size increases as a consequence of infanticide.

Credit for animal drawings used in Figure 1 All drawings were downloaded from PhyloPic: http://phylopic.org Picture information is listed as:

Figure 1 :

 1 Figure 1: Distribution of male infanticide across mammals Male infanticide has been reported for about half of all species in our sample (open circles)

  Figure 1

  Figure 2

  Common name listed in figure (taxon identifier for picture on PhyloPic)

Acknowledgements

We are grateful to Tim Clutton-Brock, Peter Kappeler, Guy Cowlishaw, Dan Blumstein and an anonymous reviewer for helpful comments on an earlier draft of this manuscript, and to LARG for insightful discussions. DL received funding from the European Research Council (grant N°294494-THCB2011) and EH from the Natural Environment Research Council (grant number NE/RG53472). Data supporting this study are available in the Supplementary Materials.

Supplementary Materials for

The evolution of infanticide by males in mammalian societies D. Lukas* & E. Huchard contact: dl384@cam.ac.uk This file includes: Data and Methods (pages [START_REF] Palombit | The evolution of primate societies[END_REF][START_REF] Hrdy | Male-male competition and infanticide among the langurs (Presbytis entellus) of Abu, Rajasthan[END_REF][START_REF] Hrdy | Infanticide among animals: a review, classification, and examination of the implications for the reproductive strategies of females[END_REF][START_REF] Ebensperger | Strategies and counterstrategies to infanticide in mammals[END_REF][START_REF] Janson | Infanticide by males and its implications[END_REF][START_REF] Nunn | Infanticide by Males and Its Implications[END_REF] Supporting results for multivariate and the Ornstein-Uhlenbeck models (pages [START_REF] Nunn | Infanticide by Males and Its Implications[END_REF][START_REF] Blumstein | Infanticide by Males and Its Implications[END_REF] Credit for animal drawings used in Figure 1 (page 9) Supplementary Table 1: inferences from Bayestraits' Discrete (page 10) Supplementary Table 2: results from analyses run across all mammals (page 11) Supplementary Table 3: results from analyses run across primates (page 12) Supplementary Table 4: data on distribution of male infanticide (pages [START_REF] Van Schaik | The evolution of monogamy in large primates: a new hypothesis and some crucial tests[END_REF][START_REF] Borries | Social monogamy and the threat of infanticide in larger mammals[END_REF][START_REF] Van Schaik | Infanticide risk and the evolution of male-female association in primates[END_REF][START_REF] Van Noordwijk | Infanticide by Males and Its Implications[END_REF][START_REF] Wolff | Promiscuous females protect their offspring[END_REF][START_REF]Material and Method is available on Science Online[END_REF][START_REF] Fritz | Geographical variation in predictors of mammalian extinction risk: big is bad, but only in the tropics[END_REF][START_REF] Lukas | Costs of mating competition limit male lifetime breeding success in polygynous mammals[END_REF][START_REF] Crockett | Infanticide by males and its implications[END_REF][START_REF] Soulsbury | Genetic patterns of paternity and testes size in mammals[END_REF]

Data and Methods

To determine the taxonomic distribution of male infanticide, we relied on its observed distribution, which is documented for an increasing number of species that have been the focus of detailed and prolonged field studies. We took care to include only species in which this behaviour could have been observed in natural populations because they had been studied continuously over more than 3 reproductive seasons, including observations of females with unweaned juveniles, in order to minimize the risk of introducing noise in the data if some species were misclassified as "male infanticide absent" (see Supplementary Table 4). For the opposite, we only included a species as "male infanticide present" if the Supplementary Table 1: Inferences from Bayestraits' Discrete models investigating correlated evolution between male infanticide and social organization Phylogenetic reconstructions that consider the evolution of male infanticide and social organization suggest that transitions to male infanticide depend on a social system involving bisexual groups (harem or multimale-multifemale). While male infanticide appears to evolve independently from social monogamy (and vice versa), transitions to male infanticide appear significantly more likely in lineages with bisexual groups. Changes in social organization do however not appear to be a consequence of male infanticide, as transitions to group living are equally likely when male infanticide is present or absent. The higher support for a dependent model in the case of group-living species appears to derive from this trait being evolutionarily stable, with transitions to this state much higher than losses of this state (regardless of the presence of infanticide). The values of delta log-likelihood represent the difference between the likelihood of the model presented and the likelihood of the best supported model (in all cases dependent and unconstrained), and values in bold with stars indicate models that are significantly less supported compared to this baseline model (based on a chisquare test comparison correcting for the difference in the number of parameters of each model).

Supplementary Table 2: Summary of the results of the statistical analyses including all species.

The table presents for the non-phylogenetic Wilcoxon tests the test value W and significance value p, for phylogenetic Anova (PhyloAnova) the significance value p, for phylogenetic generalized least squares regression (PGLS) the most likely value for the transformation of the branch lengths lambda, whether this lambda value is significantly different from a value that reflects no phylogenetic signal (p lambda = 0) or a value that reflects that change occurs consistently over evolutionary time (p lambda = 1), for the MCMCglmm regression model the significance value p, and for multivariate regression models in MCMCglmm the significance values p for the two traits analysed simultaneously in one row.

Supplementary Table 3: Summary of the results of the statistical analyses including only primates.

The table presents for the non-phylogenetic Wilcoxon tests the test value W and significance value p, for phylogenetic Anova (PhyloAnova) the significance value p, for phylogenetic generalized least squares regression (PGLS) the most likely value for the transformation of the branch lengths lambda, whether this lambda value is significantly different from a value that reflects no phylogenetic signal (p lambda = 0) or a value that reflects that change occurs consistently over evolutionary time (p lambda = 1), for the MCMCglmm regression model the significance value p, and for multivariate regression models in MCMCglmm the significance values p for the two traits analysed simultaneously in one row.

Supplementary