The other parameter estimates are largely consistent with findings from other studies. The coefficient for age is positive, indicating that clusters with older respondents have a higher HIV prevalence (the association is curvilinear for men). HIV prevalence is generally higher in urban areas, and male circumcision has a protective effect. Although the percentage of Muslims tends to be negatively correlated with HIV prevalence, its coefficient is not significant after adjusting for other controls. A more thorough evaluation of religion would include a measure of religious involvement , but that is not available in the DHS. The coefficient for the measure of male mobility is not significant either. Late marriage is protective (particularly for women). Its coefficient, however, should be interpreted in conjunction with the parameter estimate for the duration between first sex and first marriage; this suggests that late marriage will only contain the spread of HIV if it is not accompanied by premarital sexual activity. As could be expected, the latter is positively correlated with HIV prevalence, as is the percentage of married men and women reporting an extramarital sex partner. STI symptoms are another important covariate of HIV prevalence, with parameter estimates that appear stronger for women than for men (this could be due to sex differences in the presence, or, the reporting of STI symptoms). Importantly, none of these controls eliminate the apparent protective effect of polygyny at the population (survey cluster) level.
We extended the analyses in two respects. First, we estimated the model with all statistical controls for each country and sex separately, and plotted the z-statistic for the coefficient of polygyny in these regressions in Fig. 3. Despite the relatively small number of clusters per country, seven of the parameter estimates are negative and significant at the 10% level (z-score ≤−1.64), and another seven are significant at the 5% level (z-score ≤−1.96). None of the parameter estimates are positive and statistically significant, further supporting the results from the pooled analysis. Second, we fitted models with self-reports of STI symptoms instead of HIV as the outcome (pooled analysis for all countries). In these models, the coefficient of polygyny is insignificant. It is probably worth revisiting the association between polygyny and STIs (other than HIV) with biomarker data as opposed to self reports.
Our analyses establish a negative ecological relationship between polygyny and HIV prevalence at two levels of aggregation. At the country level, the association is most obvious, but it is confirmed by analyses that exploit within-country variation only (Kuate et al.  report a similar result for Cameroon) and control for other factors that are suspected to affect the spread of HIV (e.g. the prevalence of STIs, male circumcision, and the length of the premarital sexually active period). These findings are perhaps unexpected, and it is worth reflecting on the conditions that would render them consistent with predictions of the concurrency model.
We begin by acknowledging that concurrency could be driving our results if survey clusters with lower levels of polygyny are characterized by higher levels of informal concurrency and vice versa. Whereas we included statistical controls for the prevalence of premarital and extramarital sex, we cannot rule out that these measures are affected by reporting bias. Prior analyses [33,34] of the relationship between polygyny and extramarital sex are not conclusive either. A more interesting point relates to the sexual network structure produced by polygyny. Polygyny implies disassortative mixing, whereby high-degree nodes (men who already have one or more partners) are paired with low-degree nodes (women). As Morris and Kretzschmar  have shown, disassortative mixing is likely to increase the final epidemic size compared with a random mixing model. This does not bring us closer to reconciling our findings with predictions from their concurrency model, were it not for another respect in which polygyny constitutes a special case. Barring extramarital relationships, polygyny produces a system of gender asymmetric disassortatie mixing; this implies that the size of the largest temporally connected sexual network component will not exceed the maximum number of wives of any of the individual men in the population (see also ). Thus polygyny, in effect, creates small isolates of concurrent partnerships in which the virus is trapped until one or more of the (infected) spouses start a new relationship (Fig. 4c). In contrast, gender symmetric concurrency produces larger temporally connected network components (Fig. 4b), thus facilitating a more rapid and pervasive spread of the virus.
The arguments presented so far imply that polygyny hinders epidemic growth as compared with the scenario of gender symmetric concurrency in the Morris–Kretzchmar models. It is unlikely, however, that the sexual network structure alone can fully account for the negative statistical relationship between polygyny and HIV observed in this study. For a number of plausible complementary effects, we refer to other analyses of individual-level data that suggest that there are two other features of polygyny that influence the spread of HIV over and above the structural network effect [33,38]. First, polygynous marriage systems are in large part sustained by the rapid remarriage of divorcees and widows (often as second or third wives of polygynous men, and sometimes via the practice of widow inheritance) [39,40]. Because higher marriage order and widowhood are positively correlated with HIV status [41–43], the addition of new wives is likely to introduce HIV into what might have been an HIV-free monogamous marriage. This would, of course, fuel the epidemic, were it not for a second, and counterbalancing characteristic of polygynous marriages that delays the spread of the virus. We conveniently label it a coital dilution effect [44,45]; compared with a monogamous man, a polygynous husband divides his time between two or more wives, which inevitably leads to a reduction in the coital frequency with each wife. Just as coital dilution is claimed to affect fertility in polygynous marriages [46–48], it could reduce HIV incidence in serodiscordant couples within a polygynous union. The reduction in coital frequency not only arises from the resource constraints on a polygynous husband's coital budget but it may also result from the relatively old age of husbands in polygynous unions, and, more interestingly perhaps, from a conscious decision to reduce the risk of transmitting HIV (e.g. the new husband of an inherited spouse may be aware of the cause of death of his wife's previous husband). Together, these two mechanisms produce a mixing pattern, whereby HIV-positive women are disproportionately recruited into polygynous marriages in which coital frequency is lower. As a result, seronegative individuals in polygynous marriages may face greater exposure to HIV than those in a monogamous marriage, but the population-level effects of polygyny on the spread of HIV are beneficial on average. The policy implications of this finding will depend on whether individuals or the population at large ought to be the primary beneficiaries of public health policy interventions.
Other avenues through which polygyny may affect the spread of HIV deserve more careful consideration than we have been able to provide. Polygynous marriage systems may, for example, exert greater control over female sexuality or restrict younger men's access to women, and, as a result, not only reduce the coital frequency in conjugal dyads of polygynous marriages but also among those who are single. Since the polygyny effect persists after accounting for the duration of the premarital sexual interval and the prevalence of extramarital sex, this mechanism is, however, unlikely to fully account for the polygyny effect observed in this study. We also recognize that polygyny could have a different effect at different stages of the epidemic, just as it has been demonstrated that disassortative mixing on the number of existing partners can have different effects on the takeoff and the leveling of a simulated epidemic . Similarly, we have not explored whether the mediating effect of polygyny is dependent on the distribution of wives per polygynous husband (i.e., whether it is also dependent on the intensity of polygyny).
Because of the cross-sectional nature of the DHS and AIS, we are limited to a contemporaneous measure of polygyny (and most other control variables), whereas prevalent HIV infection is the cumulative result of past exposure. We tested the hypothesis that the prevalence of polygyny has changed over time such that the association between polygyny and HIV prevalence would have reversed entirely by analyzing the correlation between changes in the practice of polygyny and HIV prevalence. Of the countries with more than one DHS, the proportion of married women in polygynous marriages declined in all but one (Eritrea). The proportion of men in polygynous unions increased only in Guinea. The annual rate of change in the prevalence of polygyny between the first and the last DHS with information on polygyny is, however, not significantly correlated with HIV prevalence: r = 0.09 (P = 0.85) and r = 0.26 (P = 0.21) for men and women, respectively.
Despite these open questions and limitations, it is clear from the rather benign relationship between polygyny and HIV that refinements to the description of concurrency effects on the spread of HIV are in order, particularly in settings in which a substantial proportion of concurrent partnerships are polygynous marriages. Polygyny produces a specific pattern of sexual mixing with outcomes that are not accommodated by existing models. We believe that future models of concurrency need to incorporate (a) variability in sexual mixing patterns and how these correlate with concurrency and HIV status and (b) the heterogeneity across union types in coital frequency. More realistic models of concurrency need to account for the variable infectiousness by duration since infection as well. Such models might also help us understand whether, and if so why, the relationship between polygyny and HIV differs from its relationship with other STIs.
We have described polygyny as a special type of concurrency but it is not an uncommon form of concurrency in SSA. Public health policies that target concurrency in a generic fashion are likely to be as culturally insensitive as early missionary efforts to ban polygyny. In addition, the negative association identified in this study suggests that they may have counterproductive public health implications. We conclude by invoking the practice of widow inheritance as a concrete illustration. Whereas the re-entry of widows into the marriage or partnership market implies a nonnegligible risk of transmitting HIV, an important social function of widow inheritance is to provide a safety net for the surviving spouse, who may or may not have been previously infected . Women in populations in which the practice is common are embedded in the lineage of their husband and their livelihood is, at least in principle, independent of their husband's survival. If a widow remarries her former husband's relative, she is likely to become a second or third wife in a polygynous marriage, which, as we have argued above, implies a reduction in her sexual activity level. In the absence of widow inheritance (and adult male children), a widow may need to seek an alliance with another man to secure her own and possibly her children's livelihoods. That process may induce an even greater risk of transmitting HIV if she has indeed been infected by her deceased spouse.
We thank Measure DHS for granting us access to the data. We wish to thank Jimi Adams, Ron Brookmeyer, Jeffrey Eaton, Stephane Helleringer, Jenny Higgins, Matthew Salganik Rania Tfaily, Erik Vickstrom, and several other colleagues for useful comments and suggestions.
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