1. When One Wife is Enough: The Determinants of Monogamy. Malcolm McLaren Dow, Professor Emeritus of Anthropology and Mathematical Methods in the Social Sciences, Northwestern University E. Anthon Eff, Associate Professor, Department of Economics and Finance, Middle Tennessee State University

2. Only 5% of mammals monogamous; 15% of primates. Human sexual dimorphism (males 10% taller and 30% heavier than females) typical of species with mild polygyny. Sexual dimorphism greater in our ancestor species → monogamy increasing Comparison of mitochondrial DNA with Y- chromosome DNA → monogamy increasing (mean beginning time 15,000 BP)

3. All known societies permit monogamy—about 82% permit polygyny, 1% permit polyandry. In about 76% of societies the majority of married women are in monogamous marriages. 17% permit only monogamy (“Socially Imposed Monogamy”), usually large states (beginning over 2,000 years ago) → monogamy increasing Question: Why the increasing prevalence of monogamy?

4. Outline Describe current explanations for prevalence of monogamy. Describe data and estimation methods. Show results. Explain.

5. Explanations for prevalence of monogamy. Three Darwinian explanations for stable pair bond 1.Male controls resources needed for children 2.Mate Guarding 3.Extrinsic risk is low Non-Darwinian explanations 4.Group selection 5.Cultural diffusion 6.Genomic differences Two other possibilities 7.Collective action 8.Female-Female aggression

6. Three Darwinian explanations for stable pair bond 1.Male controls resources needed for children. – “Polygyny threshold model” (better to have a half share in a rich man than a full share in a poor) Monogamy more likely where low variation in male resource endowments. But model ignores conflict of interest between first wife and candidate second wife. – “Ecologically imposed monogamy” (in harsh environments, no man has enough resources to support more than one wife) – Low variation in male resources  monogamy

7. Three Darwinian explanations for stable pair bond 1.(continued) Male controls resources needed for children. – Male resources “generalizable”: non-rivalrous public goods, such as defense from other males, would favor polygyny (no resource depletion when adding second wife) – Peaceful conditions  monogamy – If male resources rivalrous private goods (food, direct care of children): favors monogamy. – Males provide most subsistence  monogamy

8. Three Darwinian explanations for stable pair bond 2.“Mate Guarding”—male directly controls female, keeping her away from other males. – More difficult to guard two than one, hence when guarding is especially difficult (such as high sex ratios) may favor monogamy. – High male/female sex ratio  monogamy – Relaxed social control of relations between sexes  monogamy

9. Three Darwinian explanations for stable pair bond 2.“Mate Guarding” (continued)—male directly controls female, keeping her away from other males. – Females not likely to submit to mate guarding unless they get something from it—protection from other males (infanticide, food stealing) – Protection is non-rivalrous, and favors polygyny. – Peaceful conditions  monogamy

10. Three Darwinian explanations for stable pair bond 3.Extrinsic risk is low (risk that parental investment can’t do much about: pathogens, violence, famine, predators). – Choice between mating effort and parenting effort. When extrinsic risk is high, parenting effort doesn’t pay, switch to mating effort. Monogamy represents higher paternal investment per child than does polygyny, hence monogamy more likely when extrinsic risk is low. – Pathogens “most extrinsic” form of risk—selective advantage to females mating with healthiest males – Low pathogen stress  monogamy

11. Non-Darwinian explanations 4.Group selection – Socially Imposed Monogamy (SIM) reduces the size of kin lineages, makes state more stable, useful in time of war (Richard Alexander and co- authors) – Large-scale society  monogamy – SIM is a concession by elite to the masses when the masses are important—which is the case when masses have high levels of human capital (high economic specialization) (Laura Betzig) – Fine-grained division of labor  monogamy

12. Non-Darwinian explanations 5.Cultural transmission – Societies with high prevalence of monogamy descend from a common ancestor that practiced monogamy (vertical transmission) model with proximity in language phylogeny – Monogamy diffuses from source society to neighboring societies (horizontal transmission) model with physical proximity – Monogamy transmitted with religion—especially Christianity (horizontal transmission) model with proximity in religion phylogeny – Proximate societies monogamous  monogamy

13. Non-Darwinian explanations 6.Genomic effects – Much human behavior heritable – Societies differ genetically – Paternal provisioning likely to be adaptive in some environments—mutations favoring paternal care would be adaptive—monogamy is a high-paternal care form of marriage – Channels of gene transmission same as culture transmission: societies will be similar if they have common ancestor or are physically proximate – Proximate societies monogamous  monogamy

14. Two other possibilities 7.Collective action – When female marries male A, other male B loses fitness =Prob(female would have married male B)*(number of offspring of female if had married B) – Collective action to enforce monogamy would give fitness gain to all unmarried males – Coalitions to reduce power of dominant males characteristic of humans and nearest relatives – But: free rider problem – And: benefits only unmarried males – Expectation: collective action to reduce number of wives (upper limit>1) but only in small groups

15. Two other possibilities 8.Female-Female aggression – Wives added sequentially – First wife will not want to share resources with a prospective second wife—first wife resistance enforces monogamy – Exception: if adding second wife actually increases resources available to first. Increased efficiency via within-household specialization Increased security via wider network of affinal kin Male resources mostly non-rivalrous

16. Two other possibilities 8.Female-Female aggression (continued) – Monogamy favored if adding second wife reduces resources available to first. No important efficiency advantages via within-household specialization – Fine-grained extra-household division of labor  monogamy No increased security via wider network of affinal kin – Peaceful conditions  monogamy Male resources mostly rivalrous – Males provide most subsistence  monogamy

17. Hypotheses Monogamy more likely where – there is a harsher environment – there is less variation in male resources – there is more male provisioning – there is less social control over male-female contact – there is a higher male/female sex ratio – there is less violence – there is less pathogen stress – there is less famine – there is a larger-scale society – there is a finer-grained societal division of labor – there is broader political participation – proximate societies are monogamous

18. Standard Cross-Cultural Sample World divided up into “culture regions,” one well-documented society picked from each of these, for total of 186 societies. Over 2,000 variables gradually added. Full range of human societies, so that any statement that claims to hold universally for humans can be tested.

19. Diverse sample. For example, many subsistence types…

20. …and, many settlement types:

21. SCCS: Africa

22. Pct Monogamy for SCCS societies (local Getis) Smaller lighter circles have higher percent married women in polygynous marriages; larger darker circles have higher percent married women in monogamous marriages. Spatially smoothed.

23. % married women in monogamous marriages vs. political complexity In a box and whisker plot, the median is indicated by a heavy line, the box encloses the second and third quartile, and the whiskers extend out to a distance of 1.5 times the box, unless the minimum or maximum are less than that amount, in which case they extend out to the minimum or maximum. The points beyond the whiskers are considered outliers.

24. % married women in monogamous marriages, by major language phylum and by religion

25. Pct. women in monogamous marriage vs. Pathogen Stress Y-axis: pct married women in monogamous marriages; x-axis: pathogen stress. Dotted red line is lowess smoother—high pathogen environments have less monogamy.

26. Pct. women in monogamous marriages vs. female contribution to subsistence Y-axis: pct married women in monogamous marriages; x-axis: female contribution to subsistence. Dotted red line is lowess smoother—societies in which females contribute heavily to subsistence have less monogamy

27. Three methodological issues 1.Galton’s problem 2.Missing data 3.Creating “scales”

28. First problem: Galton’s problem Observations not independent. Common descent (language phylogeny) Cultural borrowing (geographic distance, religion phylogeny) In regression context, Galton’s problem will cause biased coefficients and biased standard errors.

29. Example language phylogeny: some Indo- European languages

30. Basis for religion proximities

31. Galton’s problem example: alcohol wives Ecuador 1 0 Iran 0 2 Ireland 1 0 Morocco 0 3 Spain 1 0 Yemen 0 4 Pearson correlation= -0.9332565, p-value=0.0065 An observed correlation between a pair of cultural traits across cultures could be due to the borrowing of the traits, as a package, from a common source (“horizontal transmission”), or could be due to their transmission, as a package, from a common ancestor (“vertical transmission”), or could be due to a true functional relationship. Hypothesis: Drinking alcohol dampens the libido of religious specialists. Adapted from Victor de Munck and Andrey Korotayev. 2000. “Cultural Units in Cross-Cultural Research.“ Ethnology 39(4): 335-348

32. Correcting for Galton’s problem

33. Correcting for Galton’s problem (continued)

34. Problem: The spatial weight matrices W R, W L and W D will be correlated with each other (societies with similar languages are usually physically proximate and have similar religions, as well), so that there is an identification problem with more than one spatial lag term. Solution: Create a new spatial matrix W optimal = d*W D + r*W R + l*W L, where d+r+l=1. Make all possible matrices W optimal using values (0,0.05,0.10,0.15,…, 0.85,0.90,0.95,1) for each of the weights (d,r,l). Estimate the model using each of the (211) weight matrices, recording the model R 2. Retain the spatial weight matrix W optimal which explains the highest variation of the dependent variable. Correcting for Galton’s problem (continued)

35. Second problem: Missing Data Society markin markout money commland sharefood Nama Hottentot NA NA 1 NA NA Kung Bushmen 1 4 1 3 6 Thonga 4 4 3 3 6 Lozi 3 3 1 3 NA Mbundu NA NA 4 NA NA Suku 2 2 4 2 2 Two solutions: 1.Listwise deletion 2.Multiple imputation

36. Listwise deletion Society markin markout money commland sharefood Nama Hottentot NA NA 1 NA NA Kung Bushmen 1 4 1 3 6 Thonga 4 4 3 3 6 Lozi 3 3 1 3 NA Mbundu NA NA 4 NA NA Suku 2 2 4 2 2 Lose three observations. Lose all of the information in the cells marked in red. Of 186 societies, 156 would have been dropped using listwise deletion. No longer testing against the full range of human societies. Losing the big advantage of the SCCS. Probable sample selection bias.

37. Multiple imputation Society markin markout money commland sharefood Nama Hottentot 3 4 1 2 3 Kung Bushmen 1 4 1 3 6 Thonga 4 4 3 3 6 Lozi 3 3 1 3 6 Mbundu 4 5 4 3 1 Suku 2 2 4 2 2 Society markin markout money commland sharefood Nama Hottentot 2 3 1 1 2 Kung Bushmen 1 4 1 3 6 Thonga 4 4 3 3 6 Lozi 3 3 1 3 4 Mbundu 3 5 4 5 3 Suku 2 2 4 2 2 Society markin markout money commland sharefood Nama Hottentot 3 5 1 2 3 Kung Bushmen 1 4 1 3 6 Thonga 4 4 3 3 6 Lozi 3 3 1 3 5 Mbundu 2 6 4 4 2 Suku 2 2 4 2 2 Replace missing values with imputed values, drawn from conditional distribution. Create several (5 to 10) new data sets with imputed values.

38. Multiple imputation (continued) Estimate model on each of the m imputed data sets Combine m estimates using Rubin’s formulas, to get final estimate

39. Combining similar variables into “scales” A composite index is the weighted sum of the component variables: θ i = ∑ r y ri μ r where the value of the index for society i ( θ i ) is the sum of the component variable values (y ri ), each component value weighted by weight μ r. Problem: wide variety of methods exist for specifying the weights μ r ; in most cases there is no a priori reason to choose one weighting scheme over another. The choice of weights can therefore often be criticized as arbitrary. Solution: method based on Tiered Data Envelopment Analysis, so that differences in θ i are not dependent on y ri, not on weights μ r.

41. Example of two “scales”

42. Table 3: Results for 4 models Table 4: Results for best model

43. Conclusion Modernization and religion are not effective channels for cultural transmission of monogamy, though distance and language are (suggests genomic effects?) Results consistent with ideas about “female-female aggression”– our hypothesis that polygyny accepted by 1 st wife only when large household confers fitness advantages. – Peaceful conditions lead to monogamy – Fine-grained extra-household division of labor leads to monogamy – Beneficent environment leads to monogamy Results consistent with female “gene-shopping” in environments with high pathogen stress.

44. Conclusion (continued) Male resource inequality, male contribution to subsistence, had little influence on monogamy. Sex ratio and strictness of social control of marriage had no effect on monogamy. Scale of society, and “elite concession” (signaled by broad political participation) were not associated with monogamy. In sum, can explain prevalence of monogamy as the result of two forces: – individual agents optimizing their own fitness—no need to invoke group selection. – cultural transmission (including genomic effects).