Multifactorial inheritance with cultural transmission and assortative mating. III. Family structure and the analysis of separation experiments.

Demographic data about family composition or structure in the United States is reviewed. About 25% of white children and a majority of black children are reared in either broken or extended families, and this must be taken into consideration for valid studies of cultural inheritance. Atypical family structures are described including those in which parents include: biological parents, stepparents, grandparents, uncles, aunts, sibs, foster parents, and their spouses. General formulae for a wide variety of kinship correlations are derived using path analysis. The multifactorial model presented allows for cultural inheritance, polygenic inheritance, correlated sibling environments, and phenotypic assortative mating (as previously described for intact families) plus extensions necessary for the analysis of separation experiments. These extensions allow for variable family structure and differences in parental influence due to separation, age or stage of development of the child, birth order, or type of relationship. Family structure is observed to have a marked effect on familial resemblance. Computer simulation studies demonstrate marked heterogeneity among phenotypic correlations for kinships of the same degree of genetic relationship arising in different family structures. Analyses of multiple types of sibs and other relatives in variable family structures offer great promise for the study of cultural inheritance.     

Multifactorial inheritance with cultural transmission and assortative mating. II. a general model of combined polygenic and cultural inheritance.

A general linear model of combined polygenic-cultural inheritance is described. The model allows for phenotypic assortative mating, common environment, maternal and paternal effects, and genic-cultural correlation. General formulae for phenotypic correlation between family members in extended pedigrees are given for both primary and secondary assortative mating. A FORTRAN program BETA, available upon request, is used to provide maximum likelihood estimates of the parameters from reported correlations. American data about IQ and Burks' culture index are analyzed. Both cultural and genetic components of phenotypic variance are observed to make significant and substantial contributions to familial resemblance in IQ. The correlation between the environments of DZ twins is found to equal that of singleton sibs, not that of MZ twins. Burks' culture index is found to be an imperfect measure of midparent IQ rather than an index of home environment as previously assumed. Conditions under which the parameters of the model may be uniquely and precisely estimated are discussed. Interpretation of variance components in the presence of assortative mating and genic-cultural covariance is reviewed. A conservative, but robust, approach to the use of environmental indices is described.     

A family study of anthropometric traits in a Punjabi community: II. An investigation of familial transmission

Path analysis is used to characterize family resemblance for anthropometrics in twins and nuclear families from the Punjabi population of India. Significant positive assortative mating exists with respect to many body measurements, but not for cranial or facial variables. Evidence of a maternal effect for five measurements of bone diameter is reported. Twin resemblance is increased by a component not found in other pairs of relatives for all variables except nasal height, facial length, ear length, and head breadth. Although all variables have significant transmissible components, many have parameter estimates which are not consistent with strictly polygenic inheritance. Some form of cultural transmission is implicated for such variables, especially for those related to fatness levels.     

Consanguineous marriages in Italy: A Note

Abstract

A general multifactorial model is given for the inheritance of traits that exhibit a sexual dimorphism. The model allows for polygenic inheritance, cultural transmission, phenotypic assortative mating, and a common environment of rearing. Several cultural mechanisms are described for which transmission from parent to offspring is sex‐dependent and for which many different patterns of sex‐specific correlations can result. A special case of the general model is described in which phenotypic differences between males and females are due only to differences in nontransmissible environmental factors and/or genetic factors that do not contribute to variability within a sex. Application of these models to human spatial visualizing ability, using data reported by others, gives an estimate of 45 per cent for the proportion of the variance that is accounted for by transmissible factors. Neither an X‐linked hypothesis nor a sex‐specific cultural mechanism is required to explain the transmission of spatial ability.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

The effect of cultural transmission on continuous variation.

Cultural transmission may depend on the non-genetic transfer of information from parent to offspring. The consequences of such cultural transmission for continuous variation are investigated theoretically for randomly mating populations. Cultural inheritance may act on genetical and environmental differences between individuals. The consequences for cultural inheritance of polygenic variation and variation due to chance environmental factors are considered. An equilibrium may occur in which the population variance and the covariances between relatives can be expressed as functions of estimable parameters of genetical and environmental variation. Whatever the ultimate origin of culturally inherited differences they are expected to lead to environmental differences between families ("E2" variation). In addition, if cultural transmission maintains differences due ultimately to segregation at many gene loci we may find genotype-environmental covariation is generated.     

Comparing the biological and cultural inheritance of personality and social attitudes in the Virginia 30,000 study of twins and their relatives.

Measures of four dimensions of personality (Psychoticism, Extraversion, Neuroticism, and Lie scores) and six aspects of social attitudes (to sex, taxation, militarism, politics, religion and a general conservatism scale) were obtained by mailed questionnaire from 29,691 US subjects including adult twins (n = 14,761) their parents (n = 2360), their spouses (n = 4391), siblings (n = 3184) and adult children (n = 4800). After correction for the average effects of age, sex and source of sample, familial correlations were computed for 80 distinct biological and social relationships. The data allow for the estimation of the additive and non-additive effects of genes, assortative mating, vertical cultural inheritance and other non-parental effects of the shared environment on differences in personality and social attitudes. The interaction of genetic and environmental effects with sex may also be analyzed. Model-fitting analyses show that personality and social attitude measures differ markedly in major features of family resemblance. Additive and dominant genetic effects contribute to differences in both personality and attitudes, but the effects of the family environment, including vertical cultural transmission from parent to child, are much more marked for social attitudes than for personality. There is substantial assortative mating for social attitudes and almost none for personality. The causes of family resemblance depend significantly on sex for almost every variable studied. These findings clarify and extend the more tentative findings derived from previous twin, family and adoption studies.     

Family resemblance for components of craniofacial size and shape

Path analysis is used to analyze family resemblance for eight principal components extracted from 30 anthropometric measurements of the craniofacial complex. Based on likelihood ratio tests, the null hypothesis of no assortative mating is rejected for the nasal height component. The null hypothesis of no common sibling environmental effect is rejected for the cranial size, craniofacial breadth, and nasal height components. Finally, the hypothesis that transmission from both mother and father is equal to 1/2, consistent with simple autosomal polygenic inheritance, is rejected for components corresponding to craniofacial breadth and upper facial height, thus implicating some effect of familial environment. Transmissibility is higher for components related to cranial size and facial height than for those related to facial breadth or ear dimensions.     

Aspects of variance and covariance analysis with cultural inheritance

Linear Gaussian models of genotypic, phenotypic, and environmental transmission are studied. The nature of equilibrium assumptions under various modes of assortative mating are discussed with particular emphasis on expected correlations between relatives. Assorting models based only on phenotype, or only on environment, are compared with those in which the mating correlation structure is more complex. Explicit values in terms of transmission parameters and within individual covariances are given for the usual correlations between relatives. The possibility of decomposing these in terms of correlations involving adoptive families is indicated.     

Transfer systems and covariance under assortative mating

Summary This paper introduces the concept of a transfer system of random variables and uses it ot study various types of assortative mating. The standard correlation structure between relatives under phenotypic and genetic assortative mating are obtained easily and these results are then extended to multiple characters by means of multivariate transfer systems. Equilibrium values for the parameters are found and index assortative mating is considered with specific applications.     

Assortative mating and offspring well-being: theory and empirical findings from a native Amazonian society in Bolivia

Mate choice matters for inclusive fitness, household economic efficiency, assimilation, stratification, and economic inequalities in society. In positive assortative mating, people pair with someone who resembles them along a trait, whereas in negative assortative mating, people pair with someone who differs from them along a trait. In industrial nations, people tend to follow positive assortative mating for fundamental demographic dimensions (e.g., age, schooling) and might practice negative assortative mating for economic outcomes (e.g., earnings). Research on assortative mating has focused on industrial nations, generally compared only one trait between couples, and paid scant attention to the effects of assortative mating for offspring well-being. If assortative mating enhances inclusive fitness, it might also enhance offspring well-being. Drawing on data from a farming–foraging society in the Bolivian Amazon (Tsimane') that practices preferential cross-cousin marriage, we (a) identify six parental traits (age, knowledge, wealth, schooling, height, and smiles) for which Tsimane' might practice assortative mating and (b) test the hypothesis that assortative mating enhances offspring well-being. Proxies for offspring well-being include height and school attainment. Tsimane' resemble people of industrial nations in practicing mostly positive assortative mating. Pairwise, mother–father and Pearson correlations of age, schooling, and earnings among Tsimane' resemble correlations of industrial nations. Correlation coefficients for the six parental traits were far higher than correlations that might happened just by chance. We found weak support for the hypothesis that assortative mating improves offspring well-being.     

A rapid generalized least squares model for a genome-wide quantitative trait association analysis in families

Genome-wide association studies (GWAS) using family data involve association analyses between hundreds of thousands of markers and a trait for a large number of related individuals. The correlations among relatives bring statistical and computational challenges when performing these large-scale association analyses. Recently, several rapid methods accounting for both within- and between-family variation have been proposed. However, these techniques mostly model the phenotypic similarities in terms of genetic relatedness. The familial resemblances in many family-based studies such as twin studies are not only due to the genetic relatedness, but also derive from shared environmental effects and assortative mating. In this paper, we propose 2 generalized least squares (GLS) models for rapid association analysis of family-based GWAS, which accommodate both genetic and environmental contributions to familial resemblance. In our first model, we estimated the joint genetic and environmental variations. In our second model, we estimated the genetic and environmental components separately. Through simulation studies, we demonstrated that our proposed approaches are more powerful and computationally efficient than a number of existing methods are. We show that estimating the residual variance-covariance matrix in the GLS models without SNP effects does not lead to an appreciable bias in the p values as long as the SNP effect is small (i.e. accounting for no more than 1% of trait variance).     

Familial Clustering of Abdominal Visceral Fat and Total Fat Mass: The Québec Family Study

The evidence for common familial factors underlying total fat mass (estimated from underwater weighing) and abdominal visceral fat (assessed from CT scan) was examined in families participating in phase 2 of the Québec Family Study (QFS) using a bivariate familial correlation model. Previous QFS investigations suggest that both genetic (major and polygenic) and familial environmental factors influence each phenotype, accounting for between 55% to 71% of the phenotypic variance in fat mass, and between 55% to 72% for abdominal visceral fat The current study suggests that the bivariate familial effect ranges from 29% to 50%. This pattern suggests that there may be common familial determinants for abdominal visceral fat and total fat mass, as well as additional familial factors which are specific to each. The relatively high spouse cross-trait correlations usually suggest that a large percent of the bivariate familial effect may be environmental in origin. However, if mating is not random, then the spouse resemblance may reflect either genetic or environmental causes, depending on the source [i.e., through similar genes or cohabitation (environmental) effects]. Finally, there are significant sex differences in the magnitude of the familial cross-trait correlations involving parents, but not offspring, suggesting complex generation (i.e., age) and sex effects. For example, genes may turn on or off as a function of age and sex, and/or there may be an accumulation over time of effects due to the environment which may vary by sex. Whether the common familial factors are genetic (major and/or polygenic), environmental, or some combination of both, and whether the familial expression depends on sex and/or age warrants further investigation using more complex models.     

Heterogeneity in the biological and cultural determinants of high-density lipoprotein cholesterol in five North American populations: the Lipid Research Clinics Family Study

Heterogeneity in the source of familial resemblance for high-density lipoprotein (HDL) cholesterol in 5 different Lipid Research Clinics (Cincinnati, Iowa, Minnesota, Oklahoma and Stanford) was assessed using a general linear model for cultural and biological inheritance. No evidence of heterogeneity was found in any of the parameters of the model. Under the most parsimonious hypothesis, using data pooled over all clinics, genetic and cultural heritability were both significant and were estimated to be 0.52 +/- 0.04 and 0.09 +/- 0.02, respectively; there was cultural transmission but no maternal effects; marital and nontransmitted sibship environmental resemblance were significant.     

NMπ—improved re‐implementation of NM+, a software for estimating gene dispersal and mating patterns

This study introduces the NMπ computer program designed for estimation of plant mating system and seed and pollen dispersal kernels. NMπ is a re‐implementation of the NM+ program and provides new features such as support for multicore processors, explicit treatment of dioecy, the possibility of incorporating uniparentally cytoplasmic markers, the possibility of assessing assortative mating due to phenotypic similarity and inference about offspring genealogies. The probability model of parentage (the neighbourhood model) accounts for missing data and genotyping errors, which can be estimated along with regular parameters of the mating system. The program has virtually no restrictions with respect to a number of individuals, markers or phenotypic characters. A console version of NMπ can be run under a wide variety of operating systems, including Windows, Linux or Mac OS. For Windows users, a graphical user interface is provided to facilitate operating the software. The program, user manual and example data are available on http://www.ukw.edu.pl/pracownicy/plik/igor_chybicki/3694/ .     

Assortative mating and grandparental transmission facilitate the persistence of a sign language.

Conditions for the persistence (i.e., protection from loss) of a sign language are investigated assuming monogenic recessive inheritance of deafness, assortative mating for deafness or hearing, and cultural transmission of the sign language to deaf individuals from their deaf parents and deaf maternal grandparents. A new method is introduced to deal with the problem of grandparental transmission in which the basic variables are the frequencies of triplets comprising a mother, a father, and their daughter of permissible phenogenotypes. Usual stability analysis is then done on the system of linear recursions in the frequencies of these triplets, derived on the assumption that signers (users of the sign language) are rare. It is shown that assortative mating is the most important factor contributing to persistence, but that grandparental transmission can also have a significant effect when assortment is as strong as observed in England and the United States.     

Paternity cues and mating opportunities: what makes fathers good?

Human males provide facultative paternal investment to their offspring; that is, the male care is not necessary for the survival of his offspring. It is expected that the degree of male investment (1) increases with growing paternity certainty, (2) increases when investment increases the survival and later reproductive prospect of offspring and (3) declines when there are opportunities to mate with multiple females. Using a large sample of adult offspring and their fathers (n = 245), we first investigated the role of two factors possibly involved in the assessment of paternity and subsequently regulating the level of paternal investment: (a) father–child facial resemblance and (b) assortative mating for eye colour. Second, because mating opportunities are inversely related to paternal investment, we also investigated how male facial attractiveness (a cue of mate opportunities) correlates with paternal investment. In line with paternal investment theory, male investment positively correlated with offspring facial resemblance. However, paternal investment were neither higher among blue-eyed couples, nor there were preferences of blue-eyed men to marry with blue-eyed women. Moreover, father facial attractiveness was unrelated to paternal investment. These results indicate that resemblance between offspring and their fathers still plays an important role in paternal investment decision later in offspring’s life.     

CORRELATED INBREEDING AMONG RELATIVES: OCCURRENCE,MAGNITUDE, AND IMPLICATIONS

Understanding the magnitude and causes of genetic and phenotypic resemblance among relatives is key to understanding evolutionary processes. Contrary to basic expectation, individual coefficients of inbreeding ( f) were recently hypothesized to be intrinsically correlated across parents and offspring in structured populations, potentially creating an additional source of phenotypic resemblance in traits that show inbreeding depression. To test this hypothesis, we used individual‐based simulations to quantify the parent–offspring correlations in f arising under random mating in populations of different size, immigration rate, and mating system. Parent–offspring correlations in f were typically positive (median r≈ 0.2–0.4) in relatively small and isolated populations. Relatively inbred parents therefore produced relatively inbred offspring on average, although the magnitude of this effect varied considerably among replicate populations. Correlations were higher given more generations of random mating, greater variance in reproductive success, polygynous rather than monogamous mating, and for midparent–offspring rather than parent–offspring relationships. Furthermore, f was also positively correlated across half‐siblings, and closer relatives had more similar inbreeding coefficients across entire generations. Such intrinsic resemblance in f among relatives could provide an additional genetic benefit of mate choice and bias quantitative genetic analyses that do not account for correlated inbreeding depression.     

Host–parasite interactions and the evolution of nonrandom mating

Some species mate nonrandomly with respect to alleles underlying immunity. One hypothesis proposes that this is advantageous because nonrandom mating can lead to offspring with superior parasite resistance. We investigate this hypothesis, generalizing previous models in four ways: First, rather than only examining invasibility of modifiers of nonrandom mating, we identify evolutionarily stable strategies. Second, we study coevolution of both haploid and diploid hosts and parasites. Third, we allow for maternal parasite transmission. Fourth, we allow for many alleles at the interaction locus. We find that evolutionarily stable rates of assortative or disassortative mating are usually near zero or one. However, for one case, in which assumptions most closely match the major histocompatibility complex (MHC) system, intermediate rates of disassortative mating can evolve. Across all cases, with haploid hosts, evolution proceeds toward complete disassortative mating, whereas with diploid hosts either assortative or disassortative mating can evolve. Evolution of nonrandom mating is much less affected by the ploidy of parasites. For the MHC case, maternal transmission of parasites, because it creates an advantage to producing offspring that differ from their parents, leads to higher evolutionarily stable rates of disassortative mating. Lastly, with more alleles at the interaction locus, disassortative mating evolves to higher levels.