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.     

The use of twins in the analysis of assortative mating

The simulations illustrated show that a plausible model for mate selection can generate data on the similarity of twins and their spouses which are remarkably consistent with a transitive model for the effects of mate selection. This is, biological considerations impose constraints upon the relative values of correlations which are not foreseen, for example, by the some advocates of conventional path models although they might be predicted by common sense. In particular, the correlation between the spouses of twins is expected to be non-zero under a model of phenotypic assortment and turns out to be approximately equal to the product of the twin correlation and the square of the marital correlation. The relative magnitudes of the correlations derived from an empirical study of such relationships should enable models of phenotypic assortment to be tested more rigorously. Including both identical and non-identical twins in the sample studied should permit the inherited and cultural components of the mating system to be identified with more conviction. In the event of one sex playing a more significant role in mate selection for particular traits, such studies should reveal diagnostic patterns of familial correlations as long as male and female twins and their spouses are analysed separately. If the analysis is restricted to phenotypic correlations of the parents, the qualitative findings do not appear to be greatly affected by selection due to assortative mating although a reduction in variance is to be expected if a large proportion of individuals is unable to mate. In such cases twins will also be significantly concordant for mating. The consequences of such varied regimes of assortation for the population structure and the relationship between traits in subsequent generations remain the object of future inquiry.     

Direct and indirect assortative mating: a multivariate approach to plant flowering schedules

This paper develops methods to partition the phenotypic correlation between mates for a focal trait--the standard measure for assortative mating--into a direct component and additional indirect components. Indirect assortative mating occurs when a nonassorting trait is correlated within individuals to a directly assorting trait. Direct and indirect assortative mating is assessed for flowering phenology in Brassica rapa. The flowering time of pollen recipients (mothers) was strongly correlated (rho=0.67) to that of potential pollen donors (fathers). Similarly, recipients and donors were correlated for duration of their flowering periods (rho=0.32) and stem diameters (rho=0.52). A partitioning of between-mate correlations revealed direct assortative mating for flowering time and period duration. However, assortment for stem diameter is explained solely through its correlation to flowering time. Examination of standard quantitative genetic theory shows that indirect assortative mating inflates genetic variance in a focal trait and the genetic covariance between focal and phenotypically correlated traits.     

The Genetic Correlation between Height and IQ: Shared Genes or Assortative Mating?

Traits that are attractive to the opposite sex are often positively correlated when scaled such that scores increase with attractiveness, and this correlation typically has a genetic component. Such traits can be genetically correlated due to genes that affect both traits (“pleiotropy”) and/or because assortative mating causes statistical correlations to develop between selected alleles across the traits (“gametic phase disequilibrium”). In this study, we modeled the covariation between monozygotic and dizygotic twins, their siblings, and their parents (total N = 7,905) to elucidate the nature of the correlation between two potentially sexually selected traits in humans: height and IQ. Unlike previous designs used to investigate the nature of the height–IQ correlation, the present design accounts for the effects of assortative mating and provides much less biased estimates of additive genetic, non-additive genetic, and shared environmental influences. Both traits were highly heritable, although there was greater evidence for non-additive genetic effects in males. After accounting for assortative mating, the correlation between height and IQ was found to be almost entirely genetic in nature. Model fits indicate that both pleiotropy and assortative mating contribute significantly and about equally to this genetic correlation.     

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.     

PARTITIONING THE EFFECTS OF SPATIAL ISOLATION,NEST HABITAT,AND INDIVIDUAL DIET IN CAUSING ASSORTATIVE MATING WITHIN A POPULATION OF THREESPINE STICKLEBACK

Assortative mating is measured as a phenotypic or genotypic correlation between mates. Although biologists typically view assortative mating in terms of mate preference for similar partners, correlations between mates can also arise from phenotypic spatial structure arising from spatial isolation or habitat preferences. Here, we test whether diet‐assortative mating within an ecologically variable population of threespine stickleback results from small‐scale geographic isolation or microhabitat preference. We find evidence for assortative mating in the form of a positive correlation between mated pairs’ diets (measured using stable isotopes). Stable isotopes reveal diet differences between different nesting areas and among individuals using different nest habitat within a nesting area. This spatial segregation of diet types should generate some assortative mating, but is insufficient to explain the observed assortment strength. Significant male–female isotope correlations remain after controlling for spatial variables. We therefore conclude that sticklebacks’ diet‐assortative mating arises from additional behavioral preference. More generally, our results illustrate the point that spatial segregation can only drive appreciable levels of phenotypic assortative mating when environment‐phenotype correlations are parallel and strong in both sexes. Consequently, intraspecific assortative mating may typically entail mating preferences rather than just spatial cosegregation of phenotypes.     

Models of multifactorial inheritance: II, the covariance structure for a scalar phenotype under selective assortative mating and sex-dependent symmetric parental-transmission

This study concentrates on a scalar trait for a two-sex population entailing symmetric sex-dependent parent-offspring transmission, a nonlinear (selective) assortative mating pattern, and random perturbation factors. A number of qualitative and comparative properties of the equilibrium covariance structure are set forth. In particular, it is shown that the phenotype variance generally increases under attenuated assortative mating tendencies and for an increased level of parent-offspring transmission. Moreover, with more contrasting sex-dependent transmission the sibling covariances diverge from the parent-offspring covariance. Also, shared residual-environmental covariance enhances the sibling covariances. The absolute product moment of the deviation of a child phenotype from the separate parental phenotypes exhibits a minimum for a mixed assortative random mating scheme rather than under extreme assortative mating or pure random mating. We establish that the equilibrium variance of a married individual is reduced compared to the variance of the population at large. Interpretations and implications are discussed.     

Assortative mating for anthropometric traits in parents of Punjabi twins

The marital correlations between 97 pairs of parents of Punjabi twins reveal positive phenotypic assortative mating for body traits while almost random mating with respect to cranio-facial traits. There is no evidence of any significant negative assortative mating for any of the 50 traits. The results have been compared with those from other world populations. The data contradict the earlier reported hypothesis that assortative mating is associated with lowered fertility.     

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.     

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.     

The strength of assortative mating for flowering date and its basis in individual variation in flowering schedule

Although it has been widely asserted that plants mate assortatively by flowering time, there is virtually no published information on the strength or causes of phenological assortment in natural populations. When strong, assortative mating can accelerate the evolution of plant reproductive phenology through its inflationary effect on genetic variance. We estimated potential assortative mating for flowering date in 31 old‐field species in Ontario, Canada. For each species, we constructed a matrix of pairwise mating probabilities from the individual flowering schedules, that is the number of flower deployed on successive dates. The matrix was used to estimate the phenotypic correlation between mates, ρ, for flowering date. We also developed a measure of flowering synchrony within species, S, based upon the eigenstructure of the mating matrix. The mean correlation between pollen recipients and potential donors for flowering date was  = 0.31 (range: 0.05–0.63). A strong potential for assortative mating was found among species with high variance in flowering date, flowering schedules of short duration and skew towards early flower deployment. Flowering synchrony, S, was negatively correlated with potential assortment (r = ?0.49), but we go on to show that although low synchrony is a necessary condition for phenological assortative mating, it may not be sufficient to induce assortment for a given phenological trait. The potential correlation between mates showed no seasonal trend; thus, as climate change imposes selection on phenology through longer growing seasons, spring‐flowering species are no more likely to experience an accelerated evolutionary response than summer species.     

Variation in human mate choice: simultaneously investigating heritability, parental influence, sexual imprinting, and assortative mating

Human mate choice is central to individuals' lives and to the evolution of the species, but the basis of variation in mate choice is not well understood. Here we looked at a large community-based sample of twins and their partners and parents ([Formula: see text] individuals) to test for genetic and family environmental influences on mate choice, while controlling for and not controlling for the effects of assortative mating. Key traits were analyzed, including height, body mass index, age, education, income, personality, social attitudes, and religiosity. This revealed near-zero genetic influences on male and female mate choice over all traits and no significant genetic influences on mate choice for any specific trait. A significant family environmental influence was found for the age and income of females' mate choices, possibly reflecting parental influence over mating decisions. We also tested for evidence of sexual imprinting, where individuals acquire mate-choice criteria during development by using their opposite-sex parent as the template of a desirable mate; there was no such effect for any trait. The main discernible pattern of mate choice was assortative mating; we found that partner similarity was due to initial choice rather than convergence and also at least in part to phenotypic matching.     

The evolutionary history of Drosophila buzzatii. XX. Positive phenotypic covariance between field adult fitness components and body size

In the cactophilic species Drosphila buzzatii, it is feasible to infer the action of natural selection by simultaneously sampling different life history stages in the field. During four years of research, samples of mating and non-mating adults and pupae were taken from a natural population. The main adult fitness components, i.e., mating success, longevity, and fecundity, were recorded in relation to body size, as measured by thorax length. The age of flies was estimated by observing the developmental stage of the reproductive system. Our data showed that larger flies can outlive and outmate small flies, and that mating success is related to age. An estimate of the fitness function showed a linear increase of mating success with increasing thorax length. There was no assortative mating for this trait. We advance the hypothesis that mating success is related to the rate of encounter and courtship time through general activity, which in turn may be related to body size. A positive phenotypic correlation between thorax length and ovariole number, which is related to fecundity, was found in females emerged from wild pupae. Neither the phenotypic nor the genetic (additive) correlations between these two traits were statistically different from zero in laboratory reared females. The genetic consequences of the observed phenotypic selection on body size are discussed.     

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.     

Genetic components of variation in Nemophila menziesii undergoing inbreeding: morphology and flowering time.

The standard approaches to estimation of quantitative genetic parameters and prediction of response to selection on quantitative traits are based on theory derived for populations undergoing random mating. Many studies demonstrate, however, that mating systems in natural populations often involve inbreeding in various degrees (i.e. , self matings and matings between relatives). Here we apply theory developed for estimating quantitative genetic parameters for partially inbreeding populations to a population of Nemophila menziesii recently obtained from nature and experimentally inbred. Two measures of overall plant size and two of floral size expressed highly significant inbreeding depression. Of three dominance components of phenotypic variance that are defined under partial inbreeding, one was found to contribute significantly to phenotypic variance in flower size and flowering time, while the remaining two components contributed only negligibly to variation in each of the five traits considered. Computer simulations investigating selection response under the more complete genetic model for populations undergoing mixed mating indicate that, for parameter values estimated in this study, selection response can be substantially slowed relative to predictions for a random mating population. Moreover, inbreeding depression alone does not generally account for the reduction in selection response.     

Assortative mating for a quantitative character

Phenotypic assortative mating is investigated for a character determined by additive loci without dominance and a stochastically independent environment. Conditional-expectation arguments are used to calculate the equilibrium values of the phenotypic variance and the correlation between sundry relatives. For the latter, it suffices to suppose that the regressions of an individual's genotype on his phenotype and of his phenotype on that of his mate are linear. For the former, linearity of the regression of the allelic effects on the phenotype is also posited. The biological implications of these assumptions are discussed.Supported by National Science Foundation Grant DEB81-03530     

Intermediate inheritance of Tourette syndrome, assuming assortative mating.

Segregation analysis incorporating assortative mating was used to test for major locus inheritance of Tourette syndrome in a single large pedigree containing 182 members. The analysis provided evidence of a major locus with an intermediate inheritance pattern for which the penetrance was estimated from the data as 28% in heterozygotes and 98%-99% in homozygotes. A significant assortative mating correlation was estimated from the data as 70%-79%. In contrast, when assortative mating was not included in the model, intermediate inheritance was not inferred. If, in addition, constancy of the allele frequencies across generations was not assumed, Mendelian transmission was rejected. Each subject, affected or unaffected, was assigned a score reflecting the presence and severity of symptoms. Higher means scores in affected homozygotes than in affected heterozygotes suggested greater severity in homozygotes: genotype information was obtained from genotype probabilities computed assuming intermediate inheritance.     

Genetic variation in flowering time induces phenological assortative mating: quantitative genetic methods applied to Brassica rapa

It has been argued from first principles that plants mate assortatively by flowering time. However, there have been very few studies of phenological assortative mating, perhaps because current methods to infer paternal phenotype are difficult to apply to natural populations. Two methods are presented to estimate the phenotypic correlation between mates-the quantitative genetic metric for assortative mating-for phenological traits. The first method uses individual flowering schedules to estimate mating probabilities for every potential pairing in a sample. These probabilities are then incorporated into a weighted phenotypic correlation between all potential mates and thus yield a prospective estimate based on mating opportunities. The correlation between mates can also be estimated retrospectively by comparing the regression of offspring phenotype over one parent, which is inflated by assortative mating, to the regression over mid-parent, which is not. In a demonstration experiment with Brassica rapa, the prospective correlation between flowering times (days from germination to anthesis) of pollen recipients and their potential donors was 0.58. The retrospective estimate of this correlation strongly agreed with the prospective estimate. The prospective method is easily employed in field studies that explore the effect of phenological assortative mating on selection response and population differentiation.