We also assume that females hold no wealth and are identical in their reproductive potential

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,container raspberries 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. 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 nonrival 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.

In order to produce analytically tractable results, we simplify by assuming throughout that there are only two types of males, rich and poor, with rich males being a fraction u of the population. All rich are identical, as are all poor. The rich males are indexed by r and the poor by p.We now demonstrate two theoretical results with the potential to resolve the polygyny paradox. First, diminishing returns to additional wives arising from causes other than necessity to share a husband’s rival material wealth will reduce the number of wives acquired by each rich male. Second, because of this fact, a highly unequal wealth distribution with few extraordinarily rich men may produce little polygyny, while a less unequal wealth distribution with a larger fraction of rich men may produce a greater extent of polygyny. Two rich men, for example,draining pots can be expected to have more wives in total than one very rich man whose wealth equals their combined wealth. For this same reason, the Gini coefficient—see table 2 for a definition—is not a sufficient statistic for the analysis of the relationship between polygyny and wealth inequality. We take up each of these results, in turn, before assessing if our empirical estimates are consistent with this explanation.To address prediction P1, we present empirical estimates of m and d. These values are estimated using a multi-level regression model fit to our individual level data; methodological details are provided in the electronic supplementary material. In all but four of the populations in our sample, the estimated d coefficient is reliably less than 1. This result provides cross-cultural empirical support for the first of the two conditions needed to generate a transition to a greater degree of monogamy with increasing wealth inequality. Note two further results also shown in figure 5. First, our estimates for m are quite low, particularly across the agricultural economies. Second, our estimates of d 2 m are positive in almost all populations, including those that are concurrently polygynous and those that are serially monogamous. The consistently small values of m across all of our samples, even the monogamous ones, was unexpected. However, these low values reflect changes in male fitness per wife. Because of biological limits to the rate of reproduction in human females, significant increases to wealth are constrained to have less than proportional effects on fitness per wife. The effects observed here are more likely to reflect the ability of males with more than a threshold level of resources per wife to minimize offspring mortality, rather than to significantly enhance their own fertility. Though not discussed in detail here, our data suggest that male wealth impacts male fitness primarily by increasing the rate of wife acquisition rather than by increasing reproductive success per wife . Our second point addresses the possible concern that our estimates of d may be low, in part, because we use times married as our measure of polygyny. While it is true that men can accumulate a greater maximal number of marriage years through concurrent polygyny than serial monogamy, figure 5a demonstrates that the use of times married is an appropriate measure of polygyny for our purposes.

Across almost all populations, the elasticity of fitness with respect to times married, d 2 m, is positive and reliably non-zero. Because these estimates measure the population-specific effects of cumulative number of wives on reproductive success, they demonstrate that an increased number of marriages leads to increased reproductive success in both types of marriage systems—concurrently polygynous and serially monogamous.We have established that there exists a strong cross-cultural pattern of decreasing—but reliably non-zero—fitness returns to increasing number of wives for reasons beyond rival wealth sharing. We now turn our attention to testing if the transition to agriculture is associated with a decreasing fraction of wealthy males. In our theoretical model, we assume a discrete two-class wealth distribution, but empirical wealth data typically have continuous distributions. To deal with this issue, we consider two proxy measures for per cent rich in our empirical data: the minimum percentage of men that account for a fraction f of the total wealth and the frequency of men with more than c wealth, where c is the empirical midpoint in each population between the average wealth of males with one wife and the average wealth of males with two wives. More details about these metrics are included in the electronic supplementary material. Table 3 provides population-level posterior estimates of the completed wealth and completed polygyny measures, with the mean estimates by subsistence type shown in the bottom panel. To address prediction P2, we calculate empirical estimates of the fraction of rich men by production system . We find that agricultural populations have a significantly reduced frequency of wealthy individuals relative to horticultural populations. All four panels show reliable differences in mean per cent rich between the horticultural and agricultural subsistence modes. This lesser fraction of wealthy individuals suggests a decreased number of men both able and willing to take second wives. This in turn leads to reduced levels of per cent female polygyny in contexts where large wealth differentials are not able to underwrite large differentials in wives due to the existence of diminishing fitness returns to such additional wives. A limitation of this last result is that it is based on data from only four agricultural populations, three of them concentrated in a restricted region and time period . Moreover, a more informative dataset would come not from agricultural populations in the time period between the 1700s and 2000s, but rather from the agricultural populations in which monogamy actually began to emerge denovo. In our main analysis, we use estimates derived from the individual-level records available in the populations shown in table 1; in the electronic supplementary material, we present comparable analyses that include 14 additional wealth distributions from historical agricultural populations. The results of this supplementary analysis are consistent with our arguments here—and in fact show stronger and more reliable effects in the direction predicted by P2. These supplementary data, however, are based on sometimes contested reconstructions of the historical wealth distributions pieced together by archaeologists and economic historians;they must be appreciated within the constraints associated with such forms of data.Using individual-level data from 29 populations, we show evidence of a general cross-cultural pattern of decreasing marginal fitness returns to increasing number of marriages. Further, using these same 29 datasets , we demonstrate the existence of an increasingly skewed distribution of material wealth in class-based agricultural societies . Both of these empirical findings are consistent with our model-based explanation for the decline of polygyny in societies engaged in agricultural production.We use cross-cultural data and a new mutual mate choice model to propose a resolution to the polygyny paradox. Following Oh et al., we extend the standard polygyny threshold model to a mutual mate choice model that accounts for both female supply to, and male demand for, polygynous matchings, in the light of the importance of, and inequality in, rival and non-rival forms of wealth.