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1 Title: Too Many Men: The Violence Problem? 2 Authors: Ryan Schacht (1*), Kristin L. Rauch (1) & Monique Borgerhoff Mulder (1-3) 3 4 (1) Department of Anthropology, University of California at Davis, Davis, CA 95616, USA 5 (2) Graduate Group in Ecology, University of California at Davis, Davis, CA 95616, USA 6 (3) Center for Population Biology, University of California at Davis, Davis, CA 95616, USA 7 *Corresponding author: Schacht, R. ([email protected]) 8 9 1 10 Abstract (120/120 words) 11 Are males more likely to engage in violent forms of competition when mates are limited or abundant? We 12 review the theory behind parental investment and mating market models, emphasizing recent reformulations 13 within sexual selection theory integrating both groups of models. The relationship between sex ratios, the 14 intensity of sexual selection, and parental investment is clarified, particularly regarding violent behavior in 15 human populations. We explore conflicting trends within the evolutionary, sociological and economic 16 literatures, and evaluate empirical evidence for the different models of sexual selection. In short, we find that 17 the “more men more violence” expectation derives from a simplistic interpretation of Trivers’ original paper, a 18 failure to appreciate recent theoretical developments, and the very loose use of the term ‘competition’. 19 Main Text (3500/3500 words) 20 More men more violence 21 Recent high-profile cases of violence, such as the notorious 2012 Delhi gang rape case, have the public, 22 journalists and researchers alike all searching for explanations. A popular explanation centers on male-biased 23 sex ratios, with specific examples coming from both India and China where there are growing numbers of extra 24 men (often termed “bare branches”) due to son preferences and daughter-biased infanticide and elective 25 abortion [1]. Because, on average, men are more violent than women it is argued that more men will necessarily 26 lead to more violence. This argument is not new to the scientific literature and has become central to how many 27 understand sexual selection. Essentially, when there are more males than females in a population, males are 28 expected to compete vigorously for the limited number of mating opportunities available. In applying this idea 29 to humans, it is appealing to attribute elevated rates of violent crime to high sex ratios and a shortage of women 30 [e.g., 2, 3]. While this reasoning is intuitive, we question both its underlying theoretical basis and its empirical 31 support. Put plainly, are males more likely to engage in violent forms of competition when mates are limited or 32 when they are abundant? We tackle this issue by focusing primarily on human societies. We explore conflicting 33 trends within the evolutionary, sociological and economic literatures, and in particular we highlight recent 2 34 reformulations within sexual selection theory that challenge our intuitions and generate very different 35 predictions, rather more in line with recent empirical findings. 36 37 The “more men, more violence” prediction is derived from a long-standing model of sexual selection, laid out 38 by Trivers [4] and developed by Emlen and Oring [5] and Clutton-Brock and Vincent [6], the former with the 39 concept of Operational Sex Ratio (OSR) and the latter with Potential Reproductive Rate (PRR) (see Box 1 for 40 Acronyms Defined). Essentially, according to the traditional parental investment (PI) model, when one sex is 41 tied up with parental care, or more generally with activities that lower its PRR, the other sex competes over this 42 limited resource, leading to the prediction that the sex in abundance competes more intensely for mates than 43 does the rarer sex, and the ancillary expectation that this will generate more violence in the more abundant sex. 44 There is however a different model for thinking about mate competition – the mating market model – that 45 emerged within the social sciences decades before the traditional parental investment model [e.g., 7, 8]. Its roots 46 lie in the supply and demand models of economics. Becker [9] argued that an increase in the sex ratio raises the 47 demand for wives, giving women greater bargaining power and requiring men to invest more efficiently in the 48 traits that make them attractive as long-term partners [see also 10, 11]. Mayr [12] first raised this idea in 49 biology, in his discussion of sex ratios and mating systems in birds, and Noë & Hammerstein [13, see also 14] 50 reintroduced these ideas into behavioral ecology. 51 52 These two perspectives have coexisted for over four decades yet make strikingly different predictions, under 53 many conditions, regarding the mating strategies of the more numerous sex. Given the apparent logic, utility 54 and empirical support for both perspectives, the persistent disconnect between these approaches is troubling. 55 This paper will review the theory behind PI and mating market models and evaluate empirical (primarily 56 human) evidence for both. We outline innovations in sexual selection theory [15-18], which offer promising 57 ways to integrate the two groups of models and develop a sharper understanding of the relationship between sex 3 58 ratios, the intensity of sexual selection, and parental investment, with a view to shedding more light on the 59 occurrence of violence in humans. 60 61 Parental Investment Models 62 Building on Bateman’s [19] demonstration of greater sexual selection in males than females, Trivers [4] 63 proposed that the relative PI of the sexes is a key variable controlling the operation of sexual selection. The 64 higher-investing sex becomes a limiting resource for the sex that invests less, leading to escalated levels of mate 65 competition in the latter. Often, and especially for mammals, females invest more in parental care than do 66 males, therefore males face higher levels of competition for access to the limited number of females. 67 68 Emlen and Oring [5] added the concept of OSR. The OSR is the ratio of sexually active males to sexually 69 receptive females and is highly influenced by patterns of parental investment. Higher investment by females 70 decreases the amount of time they are ‘receptive’ to fertilization. Such sex differences in the availability of 71 gametes skew the OSR towards males leading to the claim that males face a greater intensity of sexual selection 72 on the traits that make them competitive for relatively scarce females. Insofar as relative PI is typically an 73 important factor contributing to variations in OSR between species and/or populations, Clutton-Brock and 74 Vincent [6, see also 20] proposed that PRRs of males and females can be used to predict patterns of competition 75 between the sexes. 76 77 According to this perspective, when males are in abundance they are expected to compete vigorously for mating 78 opportunities, often with the implications of intense physical struggles and violence. Insofar as some males are 79 more successful than others in monopolizing these opportunities as a result of heritable traits [e.g., 21], this is 80 expected to lead to intensified levels of sexual selection on males. 81 82 Mating Market Models 4 83 Mating markets operate by the principle of supply and demand. The rarer sex has more bargaining power in the 84 marketplace than the more common sex, and can leverage their scarcity to realize their preferred mating 85 strategies. The more common sex, as a consequence of their abundance, must cater to the preferences of the 86 rare sex in order to acquire a mate. 87 88 Economists and sociologists regularly employ mating market theories. While much of their research is not 89 explicitly based on sexual selection it is, nonetheless, consistent with evolutionary reasoning. In a famous book 90 entitled “Too Many Women” Guttentag and Secord [11] draw from historical accounts and quantitative 91 analyses to demonstrate how sex ratios affect the many aspects of the relationships between men and women. 92 They show that in societies with a surplus of women, men find themselves in demand and can leverage their 93 scarcity, behaving promiscuously and offering little parental investment; whereas when women are in short 94 supply, marriage and a commitment to family are highly valued. A more recent example comes from Colombia 95 [22], where high male mortality rates in some regions have led to an abundance of women, decreased marriage 96 rates and high incidences of men involved in concurrent relationships. Much cross-cultural work corroborates 97 these findings and has shown that female-biased sex ratios are associated with lower levels of male parental 98 investment and higher rates of female headed households [23]. Conversely, when there are too many men the 99 nature of relationships change. For example Angrist [24] found that among immigrants to the U.S., high sex 100 ratios had a large positive effect on the likelihood of female marriage and a large negative effect on female 101 labor force participation due to higher rates of male investment. In general, male biased sex ratios are 102 associated with less promiscuity [23] and greater conjugal stability [25]. 103 104 A Reformulation with implications for violence and sex ratios 105 In a recent model Kokko and Jennions [18] implicitly integrate the two veins of thought, by including both the 106 importance of PI and the frequency-dependent nature of mating strategies. Accordingly, the adult sex ratio 107 (ASR) becomes a key predictor of sex-differentiated behavior. For example, due to poor odds of remating in a 5 108 crowded market, a male-biased ASR discourages male desertion in search of additional matings and instead 109 favors increased male care [18] and less intense sexual competition [26]. According to this reformulation the 110 intensity of sexual selection is driven by intrasexual variability in quality [16], paternity certainty [15, 17], and 111 crucially for our argument here, the relative abundance (or shortage) of either sex [18], such that when one sex 112 is in oversupply both sexes respond by strategically altering their preferences and behavior, as in a mating 113 market [14]. Central to understanding this shift in thinking is the reevaluation of several variables and their 114 relationship with the intensity of sexual selection (Box 2), including the concept of OSR which has until 115 recently structured our understanding of sexual selection [26]. 116 117 While some of the empirical findings consistent with the traditional model are recovered in the reformulated 118 model, albeit by employing the new logic, [27], in general predictions are strikingly different. All else being 119 equal (to which we return), traditional models predict an abundance of men to lead to greater sexual 120 competition, violence, crime and paternal absenteeism, while reformulated models, in general, contradict these 121 expectations. According to the reformulated perspective men, when they are in abundance (and not therefore in 122 demand), will cater to women’s preferences for investment and fidelity in order to attract and retain limited 123 mating opportunities. 124 125 Turning to humans 126 To obtain a clearer understanding of how mate competition varies within species we need to know about the 127 relationship between sexual selection and ASR. To take an empirical approach to this question in humans we 128 worked through two networks of anthropologists [28, 29], using both published sources and personal 129 communications, to examine across 15 populations the relationship between ASR and the opportunity for sexual 130 selection (Is; Box 3). The relationship between the Is of males and sex ratio of the mating pool is negative, 131 suggesting greater sexual competition among men in female-biased than in male-biased populations. Clearly 132 this is a preliminary empirical demonstration, of primarily illustrative significance, but it does raise the 6 133 possibility that, across this small subsample of human populations, when men are scarce they show greater 134 variance in fitness than when they are in abundance. 135 136 How does this relate to the patterning of violent competition across societies? We turn now to an examination of 137 the relationship between the sex ratio and different forms of behavior that might be seen as indicators of 138 competition to determine whether or not they are negatively associated, as the reformulated model would 139 predict. As is quickly observed from Table 1, the results are mixed. In some cases male-biased sex ratios are 140 associated with higher rates of violence and crime and in some cases with lower. Why might this be? While 141 methodological differences play a role (see notes in Table 1), this table reveals there is no simple pattern of 142 violence in relation to mating competition. 143 144 A closer look at ‘competition’ and how it varies with ASR 145 Given the variety of forms that mate competition can take (see Box 4), it is incorrect to assume that violent 146 competition is the only male response to a shortage of opposite sex mates – both theoretical [a male-biased ASR 147 favors male care; e.g. 18] and empirical [male mate guarding in response to mate shortage; e.g. 30] findings 148 counter this assumption. This is perhaps the most fundamental reason why violence is not necessarily 149 attributable to “too many men”. More generally, competition is used with a variety of distinct meanings, both in 150 the human and nonhuman sexual selection literature, and it is often unclear how it relates to mating effort (e.g., 151 are males competing to be selected as long-term or short-term mates?). Clarifying this relationship is key to our 152 understanding of the role of sexual selection and for making predictions of patterns of violence and criminal 153 activity. 154 155 We can venture explanations for some of the variable patterning of violence with sex ratio shown in Table 1. In 156 line with the reformulated model, comparative studies in the US and cross-nationally find an abundance of 157 males associated with lower rates of rape and sexual assault [31, 32], and a shortage of men associated with 7 158 higher rates of male-male homicide victimization [33]. On the other hand, female homicide victimization rates 159 seem to counter predictions of the reformulated model: there is a positive relationship with ASR in the U.S. [34, 160 35]. However, when women have the advantage in the mating market this may favor female sexual strategies, 161 such as mate sampling [36], that lead to male sexual jealousy [37]. Mate guarding, in response, is one strategy 162 used by males when in abundance to ensure paternity certainty [30, 38] and may be carried to extremes in some 163 cases. These examples highlight a key point - not all violence is due to sexual competition, mate retention 164 strategies may also be violent. Therefore, “violence” may be present in both high and low sex ratio conditions, 165 making identifying a particular violent act and how it relates to mating competition of critical importance for 166 understanding the strength and direction of sexual selection in a particular ASR. 167 168 Our consideration of how violence is patterned in relation to ASR points to three things. First, the patterning is 169 complex, and likely reflects multiple interacting factors not yet modeled by theoreticians. Key factors may be 170 the degree of intrasexual variation in quality, and the shape of the Bateman gradients that capture the marginal 171 returns to agonistic competition [39]. Second, violent crime statistics need to be more precisely disaggregated in 172 order for the ideas suggested above to be testable (e.g., avoid combining multiple measures). We need to know, 173 for example, whether a particular type of crime, or specific violent act, is: sexual effort or competition over 174 resources for parental care [e.g., higher rates of property crime when men are in abundance, 40]; an 175 exemplification of within or between sex conflict; restricted to certain sectors, or socioeconomic brackets, of the 176 population. For example one man might commit theft and another man may go to the office, with both gaining 177 the resources to attract a mate; similarly some men might display their good genes through violence, others 178 through artistic expression. In both examples, the motivation and outcomes may be the same, but the context 179 can impose constraints on behavioral options and influence patterns of crime. Third, social scientists have not 180 yet properly delineated the behavioral options available. For example, in response to high ASR, unmarried men 181 might migrate to regions with more women, patronize prostitutes, resort to polyandrous marriage, or even set up 182 bachelor households and “bachelor villages” as reported for contemporary China [41]. 8 183 184 In short, our understanding of how men compete for women, how women’s reproductive strategies vary, and 185 how these are affected by sex ratio, is greatly under-theorized. It is clear, however, that the uncritical 186 acceptance of the “more men, more violence” expectation of traditional theory is unwarranted. 187 188 More theory to the rescue 189 Modelers have already anticipated the variation in the relationship between sex ratio and violence we see in 190 Table 1, and from them we can identify potential avenues towards a more precise understanding of the 191 patterning of violence across human societies. First, Kokko & Jennions [18] show that, counter intuitively, a 192 particular behavior may be selected for even when it increases mortality rates. This is because frequency 193 dependent selection selects against care in the rarer sex, and mortality patterns will influence which sex is rare. 194 So, if competition entails a higher risk of mortality, then the competing sex will remain the rare one, favoring 195 competition among those who survive. If caring (whether as a form of mate competition or not) brings a higher 196 mortality risk, the caring sex will become the rare sex and thus the opposite sex is now abundant and favored to 197 provide care due to poor odds in the mating pool [27]. Thus empiricists committed to explaining the patterning 198 of human violence should be quantifying the relative mortality costs associated with caring and mate 199 competition across different human societies, a difficult task to be sure. 200 201 Second, modern sexual selection theory identifies two additional factors other than ASR that influence male 202 strategies, therefore complicating simple (“all else equal”) predictions about the effect of ASR on violent 203 behavior: the extent of variation in quality among males and females, and paternity certainty [15]. Where there 204 are differences in male quality that affect the future likelihood of mating, paternal care may be unlikely for two 205 reasons. First, already mated males are likely to desert because they face very good odds of remating by virtue 206 of the qualities that gained them mating success in the first place. Second, unmated males have no choice but to 207 remain in the mating pool since they have no offspring to care for. Similarly where males have low paternity 9 208 certainty, even at high ASR high paternal care will not be favored. These factors can vary independently of 209 ASR between populations, and can interact, as when low paternal care favors female strategies that reduce 210 paternity certainty. 211 212 The third important factor that intersects the relationship between ASR and male violence is the criteria on 213 which females choose mates. If females choose males on their provisioning qualities, and provisioning does not 214 entail violence, then consistent with Kokko & Jennions’ [18] model the lowest levels of violence would indeed 215 be observed at highest ASRs. However, if successful provisioning depends on the control of resources, and 216 resource access entails physical competition, high ASRs may indeed be associated with violence. Furthermore, 217 male violence might be selected even at high ASRs if females choose mates based on indirect benefits to 218 offspring, affording their sons a potential advantage in violent competitive environments [42, see also 43]. 219 Finally, much of the above reasoning assumes that females are able to exercise choice. Model predictions about 220 levels of violence must be modified accordingly when females are not able to express their mate preferences 221 [44]. Additionally, recent findings have shown that assuming a tradeoff between parenting effort and mating 222 effort is problematic [45]. Indeed, parental care can be a mate competition strategy [two-spotted goby, 223 Gobiusculus flavescens; 46]. 224 225 Conclusion 226 Humans are a good species in which to investigate how violent competition and other traits are related to sex 227 ratio because we have such variable mating systems, from harem polygyny attained through violence among 228 men against women [e.g., Yanomamo, 47], through resource defense polygyny attained through economic 229 competition among men who are chosen by women or their kin [e.g., Kipsigis, 48], to situations where men and 230 women choose each other on the basis of individual qualities [e.g., Tsimane, 49]. This review has suggested that 231 violence is not structured according to simple predictions from the traditional parental investment model, nor 232 intuitive reasoning. A major reason is that measures of violence are simply proxies for what the models are 10 233 actually trying to gauge: the intensity of sexual selection. When we measured the intensity of sexual selection 234 directly (using Is), the findings assembled in Box 3 are in line with reformulations in sexual selection theory, 235 pointing to the importance of ASR as a predictor of the relative opportunities for sexual selection. 236 237 The belief that violence and crime are exacerbated in human populations by an excess of males is 238 oversimplistic. We show in Table 1 that the patterning of violent crime shows no simple association with the 239 sex ratio, the patterning is complex. We discuss reasons why current understandings of sexual selection are as 240 yet inadequately articulated to deal with a number of the critical intervening factors we have identified. We also 241 recognize that empiricists have failed to quantify some of the key parameters needed for such modeling, such as 242 the relative costs of care competition and the role of violence in attaining mates. Finally, we point to a need for 243 a much richer ethology of human violence – the data is primarily drawn from police reports and/or national 244 statistics that, for the most part [for a remarkable exception see 50], combine inter and intra sexual attacks, 245 crime directed at people and property, and crime emanating from different sectors of the population. 246 247 The simple message to take from this review is that the often related claim that when males are more numerous 248 than females (high ASR) males will create a potential social problem [e.g., 51], rests (as we can now see) on a 249 very specific set of assumptions about the nature of male-male competition and the extent to which females can 250 make choices over mating. There are policy applications of this research, with serious practical implications for 251 people’s lives. Recommendations that a low sex ratio will alleviate problems of male violence, while well- 252 intentioned, could actually exacerbate the problem [e.g., attempting to reduce bullying by lowering a 253 classroom's sex ratio, 52]. Likewise, “tough on crime” policies that incarcerate increasing numbers of men may 254 actually be contributing to rates of violence, rather than alleviating them, through the resulting sex ratio 255 imbalance in highly policed communities [e.g., 53]. Similarly appeals to abolish polygyny because of the 256 dangerous emergence of a class of unmarried men rely on equally flawed logic [2]. In short, the “more men 11 257 more violence” expectation derives from a simplistic interpretation of Trivers’ original paper, a failure to 258 appreciate more recent theoretical developments, and the very loose use of the term competition. 259 260 Acknowledgements 261 For financial support we thank the University of California, Davis (RNS) and the Wissenschaftskolleg zu Berlin 262 (MBM); for discussions and comments on the manuscript our colleagues in the HBE and Cultural Evolution 263 labs at UCD, and for secondary data the generous anthropologists whose populations are included in Box 3. 264 12 265 TABLE 1. Sex ratio and violence: a literature review* Reference Sample Sex Ratio Measure (1) Measure of violence (2) [33] 100 countries; UN Complete sex ratio Homicide [34] U.S.; FBI 70 countries; INTERPOL Female homicide victimization Murders, rapes & violent assaults Positive [32] Men and Women (18+) Men and Women (15-64) [54] Review Mixed Historical accounts Positive [55] Massachusetts; NIBRS U.S.; FBI [56] India; Government data Simple & aggravated assault Male-on-female partner violence Homicide Unassociated [37] Men and Women (18-23 & 24+) Men (18+)/Women (18-34) Complete sex ratio [40] China; Government data HRAF Violent and property crime Warfare mortality Positive [57] Men and Women (16-25) Complete sex ratio [58] Review Mixed Historical accounts Positive [59] U.S.; State data Complete sex ratio [60] 56 countries; WHO & UN Complete sex ratio Homicide & suicide rates Homicide [53] 153 U.S. cities; FBI & Census 45 nation sample; WHO & UN U.S.; Census & FBI Men and Women (15-59) Complete sex ratio Murder & robbery Negative Homicide Negative Five-year groupings Rape Negative India; Crime in India database 46 nations; WHO & UN Complete sex ratio Homicide Complete sex ratio Homicide Negative Men and Women (18+) Unmarried men & women (18-44) Homicide Negative [65] 46 nations; World Values Survey U.S. Counties; FBI & Census Homicide Unassociated [35] U.S. Cities (n=217); FBI Complete sex ratio [66] Chinese Cities (n=37); community level data [61] [31] [62] [63] [64] Female homicide victimization Men (17-23), women Forced sex (15-21) Relationship SR/Violence Negative Negative Positive Positive Negative Mixed Negative Positive Positive Positive 266 13 267 *We performed a literature search for violence and sex ratio in humans on Web of Science (April 3, 2013, 268 n=64). Some search results were excluded due to redundancies, lack of empirical data (e.g. book reviews), or 269 irrelevance to the question at hand (e.g. studies looking at the sex ratio of criminal offenders without reference 270 to the population sex ratio). This table summarizes the results of the remaining papers (n=21), highlighting 271 inconsistencies in the relationship between the sex ratio and violence as well as critical methodological 272 differences. 273 (1) Measures of sex ratio vary widely, and there is no evidence that the scale of the sex ratio measurements 274 (ranging from national level to village level data) is appropriate to capture the relevant mating pool. 275 (2) Measures of violent crime range quite widely: in some cases all homicides are included, some just female 276 victims and others include a mix of physical assault and property crime. 14 277 BOX 1: Acronyms and Definitions 278 Operational Sex Ratio (OSR): the ratio of sexually active males to sexually receptive females in a population 279 280 Potential Reproductive Rates (PRR): the hypothetical maximum number of independent offspring produced by males and females per unit time 281 Adult Sex Ratio (ASR): the ratio of adult males to adult females in a population 282 High sex ratio: more males than females in a population 283 Low sex ratio: more females than males in a population 284 15 285 BOX 2. Changing the direction of the causal arrow between parental investment and sexual selection 286 The traditional PI model has been influential in the development of sexual selection theory but it is logically 287 flawed. The reasoning goes that because females produce large, costly eggs, male fitness is constrained by 288 access to mates, producing (in most cases) female-biased care and male-biased competition. However, shortly 289 after Trivers [4] presented this argument, criticisms of the model began to mount. (I) Sex differences in PI 290 cannot be taken as a determinant of the intensity of sexual selection as this entails committing the faulty logic of 291 the “Concorde Fallacy” [18, 67]. Past investment alone is irrelevant to decisions about future behavior. (II) As 292 with Maynard Smith’s [68] classic model relating parental care evolution to sex differences in mating 293 opportunities, Trivers’ verbal model lacks internal consistency, violating the requirement of equal average 294 fitness for females and males and effectively making females exogenous to the model [16]. While males do 295 have higher PRRs [6], it is actual and not potential rates that matter in terms of selection [69]. To make the 296 model self-consistent the additional paternity of deserting males must be accounted for, and comes at a cost to 297 the paternity of other males [i.e. the extra mates of successful males must come from somewhere; 17]. (III) In 298 the traditional PI model a male-biased-OSR leads to more intense intrasexual selection and greater competition 299 among males due a shortage of females [5]. However, male biased OSRs do not necessarily lead to greater 300 intensity of sexual selection. Klug et al [70] show how OSR only accurately predicts sexual selection under a 301 limited set of circumstances, most specifically when mate monopolization is strong. In fact a wise strategy for a 302 male who may face a long wait time in between reproductive events if he were to desert would be to instead 303 stay with his current partner [18]. Thus the OSR can equally be thought of as a frequency dependent mechanism 304 that selects for care in the sex that is in abundance. 305 306 In sum, the relative abundance of gametes (i.e. more sperm than eggs) generates the conditions for sexual 307 selection. If selection occurs, patterns of care and competition are an outcome [15]. Therefore, sexual selection 308 is not an outcome of patterns of PI as posed in traditional models, but instead the arrow of causality must be 309 flipped [69]. 16 310 BOX 3. The Sex Ratio and Opportunity for Sexual Selection across 15 populations 311 We calculated the opportunity for sexual selection (Is) of males against the sex ratio of the mating pool for each 312 population, selected from the work of human behavioral ecologists working in non-industrial societies. The Is is 313 a standardized measure of variance in reproductive success (RS) and is calculated by dividing the variance in 314 RS by the squared mean of mating success [71-73]. It represents the upper limit of the potential strength of 315 sexual selection in a given population (importantly, not the actual strength of sexual selection on specific traits). 316 The Is is useful for cross-population comparisons because it is standardized by mean fitness and describes the 317 variation in mating success that drives sexual selection within a population. The Is provides a valuable 318 summary statistic to describe mating systems [74] because it offers a concise description of the distribution of 319 fertilizations [75] and does not rely on vague descriptions of variation in the distribution of matings that labels 320 such as ‘monogamy’ and ‘polygyny’ often do [76]. Below we show how the opportunity for sexual selection is 321 associated with the sex ratio of the local mating pool across 15 populations. 322 17 323 The regression line (calculated using maximum likelihood estimation) shows a negative relationship between 324 the sex ratio of a population’s mating pool and the Is among males (dashed line) and the 95% confidence limits 325 (displayed in pink for female-biased sex ratios and blue for male-biased sex ratios). The slope is negative, 326 suggesting that traditional assumptions regarding a positive relationship between the abundance of males and 327 the intensity of sexual selection is flawed. Rather, as the sex ratio decreases the opportunity for selection among 328 males increases [see also (77) for a similar conclusion for human populations but based on normative mating 329 system categorizations]. 330 18 331 BOX 4. Empirical Ambiguities: The Term ‘Competition’, and ‘Violence’ as Proxy 332 The specific form that mate competition takes is central to the question of sex ratios and violence. Here we 333 propose a working taxonomy: 334 335 (1) Demographic competition: In a simple demographic sense, there is ostensibly a higher degree of mate 336 competition among the more common sex when sex ratios are imbalanced; this is indeed the inference from 337 OSR. The term “competition” here is used simply to depict the fact that, under most conditions, not all 338 individuals find a partner due to the number of competitors. Note that the term is neutral with respect to 339 competitive behavior, and with respect to the implications for the intensity of sexual selection (Box 3), even 340 though it corresponds to OSR (see Box 2). 341 342 (2) Courtship competition: These behaviors are usually directed at opposite sex individuals, and are 343 “competitive” due to mate selection. Females in some species (including humans) have considerable autonomy 344 with respect to their choice of mates [see 78]. Accordingly competition among males may take the form of 345 providing what females and their relatives want [e.g., a bridegroom’s labor 79] , and among females in 346 providing what males want [chastity, 80]. This might entail accumulating resources [48], advertising paternal 347 proclivities and abilities [81], or demonstrating genetic fitness [82]. 348 349 (3) Agonistic competition: This type can, of course, also occur behaviorally among and between both sexes 350 irrespective of ASR. Focusing here just on males it can take many forms, as in bellowing displays in bison 351 [83], fighting over the control of breeding or nesting territories as in red-winged blackbirds [84], or forced 352 copulations as in orangutans [85]. In humans this kind of competition might entail physical attacks to eliminate 353 (or character attacks to denigrate) male competitors [86], direct sexual attacks on women [44], or property 354 crimes [40]. In many cases this type of competition is directed at same sex individuals, but not always, as in 355 rape and sexual assault [87]. 19 356 It is clear from these simple categories and examples that not all mate competition is violent, and not all 357 violence is mate competition – a problematic reality for empirical analyses that use violence as a proxy for the 358 intensity of sexual selection. For instance, a female shortage might decrease violence by favoring more 359 courtship competition among males. 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