The concern that unbalanced sex ratios have a negative effect on family and social outcomes is well established in the literature [1,2]. Intellectual traditions, however, generate different predictions and draw different conclusions regarding the direction of the effect (reviewed in [3]). Of contemporary concern in both the popular and academic literature are the negative consequences of male-biased sex ratios. Commonly cited examples are drawn from India and China where, due to son preference and female-biased infanticide, there is a growing number of extra men (termed 'bare branches' [2]). Because men are more likely than women to be both victims and perpetrators of violence [4], and are typically characterized as the mate-seeking sex [5], their relative abundance at the population-level is expected to elevate conflict among males over partners, thus disrupting the formation of families, destabilizing pairbonds, and leaving many men unable to find a mate [2,6].

Given that sex-biased patterns of migration and mortality are currently altering demographic profiles in many regions of the world [7], the possible negative consequences of populations with too many men is of real, and not just academic concern. However, recent theoretical and empirical research challenges the expectation that male-biased sex ratios are associated with higher rates of male conflict, reproductive skew and family instability [8,9]. Central to this growing body of mating market research is that men’s willingness to marry and commit to a family is context-specific and responsive to pay-offs to varying reproductive strategies, in line with economic principles of supply and demand [1,8,10].

Here we evaluate family formation in the U.S. to determine whether male-biased populations are indeed associated increased instability. Our goals are first to investigate under which conditions men are more or less likely to marry and be part of a family and second to reconsider current concerns for social insecurity in populations with skewed sex ratios.

To test the competing theoretical predictions (see Table 1) we use county-level U.S. Census data [28]. U.S. data is ideally suited to evaluate our models for several reasons: 1) Counts are reliable and largely unhampered by many of the concerns of, for example, Chinese census data regarding biased reporting and unreliable measures [29]. 2) Predictor and response variables relating to marriage and family formation are publicly available. 3) Because most Americans either have married or plan to marry (only ~5% of adults are uninterested in ever marrying [30]), marriage counts are a reliable indicator of relationship preferences. 4) Women in the U.S. have autonomy when choosing their partners, and so family outcome measures are expected to vary with ASR values (bias in this association is likely present when using data from populations with a history of male patriarchal control of female reproductive options [31]).

Our analysis yields three main results. First, women are more likely to be married in counties where men are relatively abundant rather than rare (B = 0. 0031, SE = 0. 0002, p < 0.001; Table 3). Income also is positively associated with marriage, but we find no significant association with education. When evaluating the random effects, marital patterns vary by state (Fig 1). To explore clustering in our dataset across states, we calculate the intraclass correlation coefficient (ICC). The ICC is a measure of variance and describes how strongly those within a group resemble one another (0 not all, 1 identical [37]). The ICC is .34, indicating low to moderate clustering of counties by state.

Our second result is that the percent of married men likewise increases with male-biased ASRs (B = 0. 00085, SE = 0. 00021, p < 0.001). Men are more likely to be married when women are rare, rather than abundant. This suggests that when men are faced with partner abundance they alter their strategy and are less willing to enter into a committed relationship with a single partner. Thus, proportionately, unmarried men are more common at female-biased rather than male-biased sex ratios. With respect to the additional fixed effects, again income is positively associated with marriage, but education is unassociated, and marital outcomes vary at the state-level (Fig 2; ICC = .28).

Third, using two frequently reported measures of family stability, we find that the frequency of both nonmarital fertility and female-headed households are highest in states with female-biased ASRs (B = -0.0038, SE = .0006, p < 0.01; B = -0.0018, SE = 0.0001, p < 0.001; Figs 3 and 4, respectively). Therefore, fewer children are born out of wedlock and households are less likely to be headed by single women in states with male-biased sex ratios. Income and education are both negatively and significantly associated with family stability measures. While the clustering of counties within states is evident for the outcome female-headed household (Fig 3; ICC = .26), it is much less important for the outcome nonmarital fertility (Fig 4; ICC = .08).

In sum, our analyses support two conclusions. First, the ASR is significantly associated with all family outcome measures, even after accounting for additional fixed and random effects. Second, for all measures of family formation, mating market predictions are supported. When sex ratios are male-biased, men and women are more likely to be married, fewer children are born out of wedlock, and fewer households are headed by women.

Both socio-demographic and mating market approaches emphasize the importance of sex-ratios in shaping family and societal outcomes [2,6,17,38]. Socio-demographic approaches predict that a male-biased sex ratio leaves many young men unable to find a mate and have a family. Mating market approaches, in general, predict the opposite. Men will be more willing to marry and have a family when partners are rare, and less willing to do so when they are abundant. Our results for all measures of family formation are consistent with mating market theory. Drawing from a multi-level dataset, we find that men are more likely to marry, be part of a family, and be sexually committed to a single partner when women are rare.

Below we discuss (i) the speculative nature of concerns that male-biased sex ratios generate family instability; (ii) support for our findings from nonhuman animal sex ratio research; (iii) implications for predicting male behavior, particularly that of unmarried men; (iv) applications of this study to future research.

Because the negative impacts of male-biased sex ratios, especially in Asian societies, tend to be based on anecdotal and historical accounts [2], the association between male abundance and family instability may be overstated [15]. Additionally, recent research in China suggests that the position of women has been elevated due to increased bargaining power in response to their relative rarity. Families are now having to provide more resources to enhance the attractiveness of sons [39] and divorce and remarriage rates for women are on the rise as women select more desirable partners [40]. These findings of positive outcomes for women in response to male abundance are not universal. However, they highlight the context-specific nature of mating strategies and the need to understand constraints to female autonomy by studying reproductive decision making comparatively. For example, male patriarchal control of women in parts of India seems to have intensified with a relative male abundance due to limitations on educational and economic opportunities for women [41]. Thus, while increasing evidence shows that marriages are more common and families are more stable in response to a shortage of women, the role women play in these decisions varies across populations.

Additionally, while female trafficking and prostitution in response to male-biased sex ratios are of public concern, supporting data are lacking. In China, areas with the least sex ratio bias have the highest proportions of sex workers [42]. Economic growth and socioeconomic inequality are better predictors of sex industry growth than a male-biased sex ratio. Moreover, STD rates are lowest in male-biased populations [43].

The socio-demographic approach emphasizes that the number of unmarried men will increase with female rarity. However, we find that percentages of men and women married are highest in U.S. counties with an excess of men. We interpret this to indicate that men are flexible in their desire to marry and are less willing to do so when they are rare and potential partners are abundant. These findings are in line with those from other studies across diverse animal taxa, including a recent analysis of 187 bird species [44], showing that male-biased sex ratios are associated with higher rates of pairbonding [45–49]. Consistent with mating market expectations [1] and frequency-dependent reformulations within sexual selection theory [8,50], males appear to leverage their rarity and pursue multiple partners when they are available. However, when potential partners are rare, males focus on acquiring and maintaining a single partner.

While an individual’s marital status is an important predictor of relationship strategy, not all single men are equally risk-prone and violently competitive. For example, recent work in China finds no evidence that unmarried men in male-biased areas are more violent. Instead unmarried men are more shy, withdrawn, and likely to be depressed [51]. This study suggests that unmarried males living in male-biased sex ratios are of much less concern when it comes to violence and other negative societal consequences than unmarried males living in female-biased sex ratios. When males are abundant and surrounded by competitors, rather than aggressively competing with each other, unmarried men may alternatively benefit from appealing to female preferences by investing in behaviors that signal their willingness to commit to marriage and parenting [52]. Indeed, recent research from China concludes that women have become increasingly demanding regarding a partner’s investment ability in response to an abundance of potential partners [39].

Although men may respond to female preferences when partners are rare, some concerns of ‘more males, more violence’ [2] are supported empirically [3]. Following mating market theory, we outline four predictions in which male-biased sex ratios would be associated with elevated levels of family and social instability.

First, understanding why a population is sex-biased and the conditions under which men and women seek relationships are key to predicting mating behavior. For example, many young men migrate to the U.S. state of Alaska for short-term labor opportunities. If temporary immigration self-selects for males who are not seeking committed relationships, they may pursue mating strategies that differ from males in other male-biased populations. Social stability may be very real in populations of itinerant males (e.g., areas of seasonal or temporary employment). Thus, we predict that male-biased populations, composed of short-term resident males, will be associated with higher rates of male aggression and violent conflict and lower rates of family stability than male-biased populations composed of long-term residents.

Second, threshold effects for mating strategies might exist at extremely unbalanced sex ratios. At very high male-biased sex ratios, males may shift from a strategy of courtship and appealing to female preferences, to one of antagonistic competition between males. Currently, this is the fear of what could occur in parts of China with a male surfeit [2,53]. While males might shift mating strategies at some sex ratio threshold, we are skeptical that this would occur under contemporary demographic conditions for three reasons. One, because sex ratios across China appear to have recently peaked and begun to decline, concerns for the future may be unfounded [14]. Two, recent work finds that male interest in long-term, committed relationships appears to increase with male-bias, even in populations approaching 150 men for every 100 women [9]. Three, nonhuman animal research finds that at sex ratios of nearly three males for every female, male-male conflict does not increase. Instead, males becomes increasingly willing to sacrifice themselves to be consumed by a female in exchange for a single mating opportunity [45]. Together, these points suggest either that males intensify their commitment to a strategy when abundant or that sex ratios need to be substantially more male-biased than they presently are to reach a threshold where males would pursue more aggressive behaviors.

Third, we predict that males with no chance of securing a partner may be particularly risk-prone and aggressive, regardless of the sex ratio. Such circumstances may arise when political or cultural systems exclude sectors of the male population from mating. In India, for example, the caste system and hypergyny may create a pool of males with no opportunities for marriage [54]. While regions with male-biased ASRs have the highest rates of homicide, these northern areas also rigorously enforce the caste system, complicating straightforward claims of association between sex ratio and violence in India [55,56]. In another example, Greenlaugh argues that governmental policies in China that suppress the marital options of rural bachelor males actually create the very pool of risk-prone, criminal males these policies are attempting to reduce as males must work outside of the law to secure a partner [57]. These examples suggest that behavioral polymorphisms in male mating strategies may also arise in response to access to the mating market, not just to partner availability.

Fourth, while our analysis indicates that males are more willing to be in committed relationships when partners are scarce, they may utilize violence to maintain a relationship. In the animal literature, the defense and control of a partner through male mate guarding can result in males directing violence at females [58]. We predict that intimate partner violence will be more common in populations where women are relatively rare because of more pronounced and frequent male mate guarding behaviors. Some evidence exists that rates of domestic abuse [59] and female homicide victimization by a partner [60] are higher at male-biased sex ratios. We emphasize that male aggression likely manifests itself in different ways across sex ratios because male mate acquisition strategies can take a variety of forms. Disaggregating measures of violence (intimate partner violence from sexual assault for example) may lead to a more productive understanding of the patterning of violent behavior [3].

Finally, we wish to point out that the social effects of female-biased sex ratios are generally under studied. Our analyses show that men are less likely to commit to a partner and family when women are abundant, not rare. It is under these circumstances that males may decrease investment in long-term relationships and focus on short-term mating strategies. When men are rare, rates of homicide and assault tend to be at their highest [61], possibly indicating that men are directing violence against other males over mating or partner opportunities [62]. Hormonal research also suggests that males tend to be more aggressive when they are around more women than men. A recent study found that when male U.S. college students compete in mixed-sex sport events, testosterone levels, which are linked with risk-taking and competitive behavior, vary significantly with team composition. When teams are female-biased men’s testosterone levels increase and when teams are male-biased they decrease, even after controlling for event outcome [63]. Together these studies suggest that productive insights and public policy recommendations could be gleaned from mating market theory. For example, consistent with the points above, ‘tough on crime’ policies in highly policed areas of the U.S. create extremely skewed adult sex ratios [23,24,64]. Our findings support previous research that attributes high rates of unstable families among poor and minority households to exogenous, rather than endogenous, factors. We show that family structure is sensitive to partner availability. Consequently, neighborhoods that are disproportionately affected by high incarceration rates and female-biased sex ratios are expected to express greater levels of family instability.

Socio-demographic and mating market approaches to sex-ratio effects on family formation have important implications for public policy and popular media’s interpretations of unbalanced sex ratios. Predictions derived from the socio-demographic approach [2], while intuitive, are largely unsupported empirically. While it is true that men are more likely to be both victims and perpetrators of violence, they also behave variably in response to partner availability. Here we show that men are more likely to marry, be part of a family, and commit to a single partner when women are rare. Although male aggression might be elevated under certain circumstances (e.g., when men are excluded from the mating market or have short-term mating goals), it appears that it is female-biased rather than male-biased sex ratios that have negative effects on relationship and family instability.