Decades of both theoretical and empirical research based on the polygyny threshold model have suggested that polygyny should be more common and more pronounced in populations in which males differ substantially in resource control. In humans, this will be in socio-cultural contexts where wealth is held predominately by men, and where there is high inequality in its distribution. Historical and cross-cultural records, however, suggest that polygyny became less common as relatively egalitarian horticultural production systems transitioned into agricultural production systems, in spite of the fact that agriculture is characterized by both a greater importance of material wealth in the production process and greater levels of material wealth inequality than horticulture. This is the polygyny paradox. Existing hypotheses for the rise of monogamy with historic agricultural populations invoke the increasing importance of rival1 material wealth among agriculturalists, inheritance rules in conjunction with paternity certainty, male power relations, declines in female contributions to production, pathogen risk and punishment and cultural group selection via the imposition of norms. Since human behavioural variation is often determined by many underlying factors, there are likely to be complementary effects among the potential causes identified in these hypotheses. Specifically, there should be coevolutionary interactions between the individual-level, economic- and fitness-based explanations for the rise of monogamy advanced here,macetas para viveros and the cultural evolutionary explanations provided by Henrich et al. and Bauch & McElreath. Our results show how individual fitness maximization can explain the de novo origins of predominant monogamy within highly unequal populations. Should monogamy have group-level fitness benefits as suggested by Henrich et al., its emergence in specific groups via the mechanism we propose would provide the source populations for cultural group selection dynamics to propagate monogamy to other populations.

Explanations for the rise of monogamy in agricultural societies in the spirit of Alexander and Henrich et al. develop the idea that powerful leaders might have imposed monogamy on the masses because such a marriage norm leads to greater in-group male–male cooperation, improving the success of the group in inter-group contests. The economically grounded explanation for the rise of monogamy that we present here is not necessarily in competition with such theories. Our model, however, establishes that basic changes in the structuring of wealth inequality coinciding with the rise of class-based societies would have made monogamy adaptive at the individual level in a large fraction of the population—greatly increasing the scope for hypotheses advancing hierarchical imposition or even frequency dependent social transmission of norms for monogamy. The present analysis builds on work recognizing the importance of inherited wealth in structuring family relationships. To this existing literature, we introduce a new individual-level, cross-cultural dataset of wealth, marriage and reproductive outcomes, numbering 11 813 records from 29 human populations, including hunter –gathers, horticulturalists, agropastoralists and agriculturalists. Our dataset is unusual in both its scope and in the availability of individual-level information, rather than qualitative societal summaries. While not without its limitations—discussed in more detail throughout—it captures the core features of the polygyny paradox. Following Oh et al.,we develop a model of the equilibrium fraction of women married polygynously in a population where the extent of polygyny is determined by the fitness maximizing choices of both men and women. In contrast to the standard polygyny threshold model, which is a one-sided mate choice model that allows only for female choice, we develop a mutual or two-sided model. In this model, male choice refers not to selecting particular females on the basis of their quality , but rather to the male’s choice of the number of wives that will maximize his fitness.

A male’s demand for wives depends on his level of wealth and the costs of mating investment, and can be more than, less than or equal to the total number of women who would choose to marry him. Mutual mate choice is rare in nature, but the conditions for it are met in species in which biparental care is important for the survival of offspring, as is typically true of humans. From our theoretical model, we identify two conditions that jointly can lead to a decrease in the population-level frequency of polygyny in highly unequal agricultural populations: in these highly stratified economies, the fraction of men with sufficient wealth to make polygynous marriage an attractive option for them and their potential partners is low relative to other subsistence systems, and decreasing marginal fitness returns to increasing number of wives above and beyond the fitness costs of sharing a husband’s wealth sharply limit the number of wives acquired by exceptionally wealthy individuals. We use our empirical data to demonstrate that the transition to agriculture is associated with both of these factors identified as drivers of monogamy.The Standard Cross-Cultural Sample illustrates that the frequency of polygyny is relatively high in horticultural and pastoral populations, and low in agricultural populations.The third panel presents our estimates of the extent of material wealth inequality among males in the four production systems. Theoretical models of mating systems predict that polygyny should be positively associated with inequality in male resources, and more specifically with what Murdock [32, pp. 206 –207] terms ‘movable property or wealth which can be accumulated in quantity by men’. These forms of rival material wealth are, as we have just seen, more unequally held in horticultural economies than among foragers, which is consistent with the greater extent of polygyny in the former.Oh et al. show that inequality in reproductively important, non-rival forms of wealth—network ties, genes conferring adaptive phenotypes or acquired knowledge, for example— can also be a strong driver of polygyny, contributing to the explanation of substantial levels of polygyny in some societies with little rival wealth inequality.

Indeed, there is empirical evidence that non-rival forms of wealth are associated with polygynyous marriage in some foraging and horticultural populations. While the polygyny threshold model has been effective in predicting the distribution of polygynous males within populations , the reduced level of polygyny in agricultural populations typically characterized by greater inequality poses a serious challenge to existing models of mating and marriage.To address this challenge, we build a comparative database of individual-level wealth, marriage and reproductive success measures in 29 diverse populations distributed over a wide geographical range . Table 1 provides population-specific background data. In order to use all cohorts of the adult male populations, relevant measures—wives and wealth proxies—are age adjusted in a Bayesian framework to represent their predicted values at age 60. This method of age adjustment assumes that the additional acquisition of wives and wealth from the time of censor to the age of 60 are unmeasured positive random variables,pot growing supplies with mean values governed by the remaining time for acquisition and the age-specific acquisition rate trajectories inferred from the population cross sections . Our polygyny measures reflect the per cent of women who will ever be married to a man who marries more than once—in other words, in contrast to the data in figure 1a, we consider sequential marriage as a form of polygyny since the offspring of each mother are rival claimants to a father’s property. Our age adjustment delivers a measure that could be called ‘completed polygyny’ by analogy to ‘completed fertility’. The populations exhibiting surprisingly high levels of polygyny by our definition—e.g. the Ache´, Hadza, Maya, English and Krummho¨rn populations—reflect the prevalence of serial monogamy, not polygyny in the usual sense of multiple concurrent wives. Although most anthropological analyses of polygyny limit the definition of the term to two or more co-occuring wives of one man, we forego the sequential/concurrent distinction because a male’s wealth is generally shared to some degree across all wives and the children of each over the male’s lifetime and as we show later, the elasticities2 of fitness with respect to times married are reliably positive for almost all populations sampled here, even those in which serial monogamy is practised. This suggests that males do indeed increase fitness through marriage to multiple women, even in cases in which these marriages are sequential. Sequential marriage can be considered a form of polygyny insofar as men typically replace divorced wives with younger women, allowing a subset of males in the population to increase their lifetime reproductive success relative to less wealthy males in the population, as has been shown in many of the populations sampled here and elsewhere, both directly and indirectly. The essential puzzle to be explained with our model, however, is not the extent to which effective polygyny is driven by concurrent marriage versus sequential remarriage, but rather how effective polygyny can be attenuated by changes in the structuring of wealth inequality. As in the Standard Cross-Cultural Sample, there is no overall relationship between wealth inequality as measured by the Gini coefficient and per cent age-adjusted female polygyny in our sample . However, analysed by subsistence category, this relationship varies.

Foragers show little variation in wealth inequality, but high variation in polygyny. Agricultural populations show high variation in inequality, but low and relatively invariant levels of polygyny. Among horticultural—b ¼ 2.02 —and agropastoral—b ¼ 0.86 — populations, we find the expected positive associations between wealth inequality as measured by the Gini coefficient and per cent female polygyny. A possible concern related to the cross-cultural compatibility of our estimates is that our rival wealth proxies vary between populations and productions systems; in cross-cultural projects as wide-ranging as this one, however, there is rarely a single variable that can be compared directly across populations—instead, we have relied on ethnographic accounts to identify which sources of wealth are most relevant to production and reproduction in each society, and attempted to build a cross culturally comparable dataset by using the most locally relevant measures of wealth in each population .Following Oh et al., we consider a population of men with two types of fitness-relevant resources: non-rival wealth, denoted as g, and rival wealth, denoted as m. As a useful mnemonic, we can think of g as the value of a male’s genetic contribution to offspring production and survival, and m as the value of his material contributions, but the general definitions are considerably broader. Although we treat g and m as completely distinct stores of wealth in this mathematical model, we recognize that most empirical wealth variables will lie somewhere on a continuum of rivalness between non-rival resources, like genes, that can be provided to all offspring in equal measure, and rival resources, like land, which must be divided among offspring. For example, local ecological knowledge can be passed in equal measure to all offspring, but the time allocated to personal instruction may be rival. We represent the total mating investment devoted to acquiring a wife by a cost equal to c units of the rival resource per wife; this term includes classic costs, such as bride price, in addition to all other costs associated with courtship and marriage. For an explanation of these and all other variables and functions used in this paper, see table 2.The parameters g and m are constrained to the unit interval reflecting the assumption—strongly confirmed in our empirical estimates—that the marginal fitness effect of additional wealth of either type, while positive, is either constant or diminishing as wealth increases. Note that rival and non-rival wealth are modelled as complementary inputs using a fitness function analogous to the Cobb–Douglas function widely used in economics. This assumption formalizes the idea that having high non-rival wealth with limited material wealth will not contribute as much to fitness as having farming skill in the presence of substantial amounts of such material resources. In other words, the multiplicative nature of the fitness function means that the marginal fitness effect of each kind of wealth is greater as the amount of the other kind of wealth increases. The parameter d is key to our proposed resolution of the polygyny paradox. It controls the extent of diminishing returns to increasing number of wives for reasons unrelated to the need to share a male’s rival wealth among wives; a value of one indicates no such sources of diminishing returns and an increasing extent of such diminishing returns is indicated by values of d falling farther below one. In the model, as d decreases the effective number of wives falls further below the empirically observed number n, indicating that female reproduction is constrained in some way by a male’s additional marriages for reasons other than rival wealth sharing.