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

• 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)

• 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?

Outline• Describe current explanations for prevalence of

monogamy. • Describe data and estimation methods.• Show results.• Explain.

Explanations for prevalence of monogamy.• Three Darwinian explanations for stable pair bond

1. Male controls resources needed for children2. Mate Guarding3. Extrinsic risk is low

• Non-Darwinian explanations4. Group selection5. Cultural diffusion6. Genomic differences

• Two other possibilities7. Collective action8. Female-Female aggression

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

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

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

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

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

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

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

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

Two other possibilities7. 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

Two other possibilities8. 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

Two other possibilities8. 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

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

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.

Diverse sample. For example, many subsistence types…

Description No. Societies Gathering 9 Hunting and/or Marine Animals 9 Fishing 12 Anadromous Fishing (spawning fish such as Salmon) 8 Mounted Hunting 5 Pastoralism 18 Shifting Cultivation, with digging sticks or wooden hoes 33 Shifting Cultivations, with metal hoes 19 Horticultural Gardens or Tree Fruits 18 Intensive Agriculture, with no plow 23 Intensive Agriculture, with plow 32

Description No. Societies Nomadic or fully migratory 26 Seminomadic 24 Semisedentary 13 Compact but impermanent settlements 3 Neighborhoods of dispersed family homesteads 20 Seperated hamlets, forming a single community 17 Compact and relatively permanent settlements 75 Complex settlements 8

…and, many settlement types:

SCCS: Africa

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.

% married women in monogamous marriages vs. political complexityIn 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.

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

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

Pct. women in monogamous marriages vs. female contribution to subsistenceY-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

Three methodological issues

1. Galton’s problem2. Missing data3. Creating “scales”

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.

Example language phylogeny: some Indo-European languages

Danish

Norwegian BokmaalSwedish English

Standard German

Armenian

Hindi

Dari

Spanish

Portuguese

French

Cajun French

Indo-European

Indo-Iranian

Germanic

Italic

10

5

23

5

61

2

5

West Germanic

Danish

Norwegian BokmaalSwedish English

Standard German

Armenian

Hindi

Dari

Spanish

Portuguese

French

Cajun French

Indo-European

Indo-Iranian

Germanic

Italic

10

5

23

5

61

2

5

West Germanic

Basis for religion proximities

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Mah

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Indigenous religion 1 1 1 1 1 1 1 1 1 1 Deep Islamization 1 4 2 3 2 2 1 1 1 1 Deep Christianization 1 2 4 2 3 2 1 1 1 1 Superficial Islamization 1 3 2 4 2 2 1 1 1 1 Superficial Christianization 1 2 3 2 4 2 1 1 1 1 Hebrews 1 2 2 2 2 4 1 1 1 1 Mahayana Buddhism 1 1 1 1 1 1 4 3 3 2 Hinayana Buddhism 1 1 1 1 1 1 3 4 3 2 Vajrayana Buddhism 1 1 1 1 1 1 3 3 4 2 Hinduism 1 1 1 1 1 1 2 2 2 4 Notes: The above scores are used to create weights wij=exp(scoreab) where society i has religion a and society j has religion b.

Galton’s problem example:

alcohol wivesEcuador 1 0Iran 0 2Ireland 1 0Morocco 0 3Spain 1 0Yemen 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

Correcting for Galton’s problemspatial lag model:

yWyWXy DDLL (1)

Where y is an nx1 vector representing our dependent variable, X is an nxk

matrix representing the independent variables, β is a kx1 vector of

coefficients, WL and WD are weight matrices, for language and distance

respectively, λL and λD are scalar coefficients, and ε is a vector of errors.

The scalars λL and λD are the spatial lag parameters, allowing an estimate

of the effects of common descent or cultural borrowing on y.

Correcting for Galton’s problem (continued)

The spatial lags yL=WL y and yD=WD y are endogenous, since they will be correlated

with the error term ε. For small sample sizes, two-stage least squares remains the

simplest way to estimate this model (Dow 2007). In the first stage, estimate yL and

yD, using as instruments the spatial lag of the original independent variables (X) as

well as the spatial lag of any other exogenous variables (Z):

ˆˆˆ ZWXWy LLL (2a)

ˆˆˆ ZWXWy DDD (2b)

Then substitute these into equation 1:

DDLL yyXy ˆˆ (3)

Problem: The spatial weight matrices WR, WL and WD 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 Woptimal = d*WD + r*WR + l*WL , where d+r+l=1. Make all possible matrices Woptimal 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 R2. Retain the spatial weight matrix Woptimal which explains the highest variation of the dependent variable.

Correcting for Galton’s problem (continued)

Second problem: Missing DataSociety markin markout money commland sharefoodNama Hottentot NA NA 1 NA NAKung Bushmen 1 4 1 3 6Thonga 4 4 3 3 6Lozi 3 3 1 3 NAMbundu NA NA 4 NA NASuku 2 2 4 2 2

Two solutions: 1. Listwise deletion2. Multiple imputation

Listwise deletionSociety markin markout money commland sharefoodNama Hottentot NA NA 1 NA NAKung Bushmen 1 4 1 3 6Thonga 4 4 3 3 6Lozi 3 3 1 3 NAMbundu NA NA 4 NA NASuku 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.

Multiple imputationSociety markin markout money commland sharefoodNama Hottentot 3 4 1 2 3Kung Bushmen 1 4 1 3 6Thonga 4 4 3 3 6Lozi 3 3 1 3 6Mbundu 4 5 4 3 1Suku 2 2 4 2 2

Society markin markout money commland sharefoodNama Hottentot 2 3 1 1 2Kung Bushmen 1 4 1 3 6Thonga 4 4 3 3 6Lozi 3 3 1 3 4Mbundu 3 5 4 5 3Suku 2 2 4 2 2

Society markin markout money commland sharefoodNama Hottentot 3 5 1 2 3Kung Bushmen 1 4 1 3 6Thonga 4 4 3 3 6Lozi 3 3 1 3 5Mbundu 2 6 4 4 2Suku 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.

Multiple imputation (continued)

• Estimate model on each of the m imputed data sets

• Combine m estimates using Rubin’s formulas, to get final estimate

Combining similar variables into “scales”• A composite index is the weighted sum of the component

variables:θi = ∑r yriμr

• where the value of the index for society i (θi) is the sum of the component variable values (yri), each component value weighted by weight μr.

• Problem: wide variety of methods exist for specifying the weights μr; 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 θi are not dependent on yri, not on weights μr .

Example of two “scales”

variable Description N min max mean stdev Violence stress violstr Violence stress (LP scale) 186 1 12 7.7 2.190 v1665 Homicide 121 1 9 3.92 2.840 v1666 Assault 113 1 9 4.64 3.060 v1667 Theft 112 1 9 4.33 3.070 v1668 Individual aggression – trespass 54 1 9 3.63 2.960 v1669 Suicide 87 1 9 3.08 2.520 v1675 Social homicide 67 1 9 4.14 2.890 v1676 Social assault 46 1 7 3.66 2.350 v1677 Social theft 38 1 7 2.78 2.480 Pathogen stress path Pathogen stress (LP scale) 186 1 14 6.68 3.650 v1253 Leishmanias 186 1 3 1.55 0.780 v1254 Trypanosomes 186 1 3 1.35 0.620 v1255 Malaria 186 1 3 2.3 0.900 v1256 Schistosomes 186 1 3 1.53 0.830 v1257 Filariae 186 1 3 2.04 1.000 v1258 Spirochetes 186 1 3 1.94 0.870 v1259 Leprosy 186 1 3 1.86 0.770

Table 3: Results for 4 models

Table 4: Results for best model

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 1st 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.

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).