SYSTEMS OF MATING. I. THE BIOMETRIC RELATIONS BETWEEN PARENT AND OFFSPRING

Quantitative genetic analysis of longitudinal trends in height: preliminary results from the Louisville Twin Study

A preliminary series of quantitative genetic models was applied to a subset of longitudinal height data, spanning birth to maturity, gathered from twin families in the Louisville Twin Study. Descriptive Cholesky factor parameterization was found to give more satisfactory results than did a system of constraints based on a model of developmental transmission of a time-constant and time-specific factors. The results from application of two autosomal sex-limitation models are contrasted with those from a model specifying both autosomal and sex-chromosomal patterns of inheritance. The latter model was more conducive to parameter reduction. Although these models do not constitute conclusive tests of autosomal sex-limitation versus sex-linkage, the more parsimonious model is consistent with previous research suggesting a stature locus on the long arm of the Y chromosome. Heritability of height is estimated at about 90% or greater from 6 years of age on. Substantial and fairly constant longitudinal genetic correlations are found from 3 years of age on. Shared environmental effects unrelated to parental height were seen for birth length, corrected for gestational age, to height at 3 years of age, but these are not satisfactorily differentiated from possible twin effects in the present sample. The genetic consequences of assortative mating are emphasized since failure to take assortment into account can lead to overestimation of shared environmental effects and under-estimation of genetic effects. The results indicate that about 20% of within-gender variability for mature height can be attributed to the genetic consequences of assortment, even though the phenotypic marital correlation of 0.22 is quite modest. The importance of testing the assumption of multivariate normality underlying the application of the method of maximum-likelihood is also highlighted.

Sewall Wright (1889-1988)

The genetic contributions of Sewall Wright is briefly reviewed with special reference to J.B.S. Haldane's work. These include his work in population genetics, statistics, and animal breeding.

Five landmarks in inbreeding studies

A short review is made on papers by Mendel, Wright, Haldane and Moshinsky, Cotterman, Malécot, Morton et al., and Khoury et al. The accompanying paper applies the two epidemiological approaches of this paper to the Brazilian populations.

Embryonic mortality attributed to inherited deficiency of uridine monophosphate synthase

The deficiency of uridine-5'-monophosphate synthase is inherited as an autosomal recessive trait in Holstein-Friesian cattle. Heterozygotes are characterized by half normal activity of uridine monophosphate synthase, as measured in erythrocytes. Matings between heterozygotes for the deficiency have produced 31 pregnancies lasting at least one month, but only 23 full-term calves, including 9 homozygous normal and 14 heterozygotes. That the eight embryos were not carried to term is consistent with the probability of a homozygous-deficient genotype and are lost around 40 d of gestation. Although the homozygous deficiency of uridine monophosphate synthase is lethal embryonically in cattle, homozygotes for the analogous human condition have been born alive.

Variation in outcrossing rate and population genetic structure of Clarkia tembloriensis (Onagraceae)

Outcrossing rate estimates for eight accessions of Clarkia tembloriensis indicate that this annual plant species has a wide interpopulational range of outcrossing rate ([Formula: see text]). Populations' t estimates were significantly correlated with observed heterozygosity and mean number of alleles per locus. Estimated fixation indices, [Formula: see text], for most populations were very close to their expected values, Feq, for a given [Formula: see text] Nei's gene diversity statistics showed that the group of outcrossing populations have more total genetic variation and less differentiation among populations than does the group of selfing populations. These results indicate that the breeding system of C. tembloriensis has had a strong influence on the amount and distribution of genetic variation within and among its populations.

Quantitative genetic analysis of longitudinal trends in adoption designs with application to IQ in the Colorado Adoption Project

A factor model is presented that provides for either multivariate or developmental specification of longitudinal genetic and environmental effects in the presence of assortative mating and cultural transmission. Delta path methods are employed for the treatment of assortative mating and selective placement effects. The proportions of genetic and environmental variance and covariance attributable to assortative mating and cultural transmission are modeled explicitly. The model was applied to cognitive ability data on 493 families in the Colorado Adoption Project by means of maximum-likelihood pedigree analysis. A test of the assumption of multivariate normality of error provided an additional model criterion beyond the log-likelihood ratio statistic. No significant effects were found for cultural transmission, genetic-environmental covariance, or selective placement. The results suggest that the phenotypic stability of IQ during early childhood is largely, if not entirely, genetic in origin and that these longitudinal genetic effects can be represented most parsimoniously in the form of developmental transmission.

Interactive influence of infectious disease and genetic diversity in natural populations

The importance of infectious disease in the survival and adaptation of animal populations is rapidly becoming apparent. Throughout evolution, animal species have been continually afflicted with devastating disease outbreaks which have influenced the demographic and genetic status of the populations. Some general population consequences of such epidemics include selection for disease resistance, the occasional alteration of host gene frequencies by a genetic 'founder effect' after an outbreak, and genetic adaptation of parasites to abrogate host defense mechanisms. A wide variety of host cellular genes which are polymorphic within species and which confer a regulatory effect on the outcome of infectious diseases has recently been discovered. The critical importance of maintaining genetic diversity with respect to disease defense genes in natural populations is indicated by certain populations which have reduced genetic variability and apparent increased vulnerability to infectious disease.

Regular systems of inbreeding with mutation

Probability of identity by type is studied for regular systems of inbreeding in the presence of mutation. Analytic results are presented for half-sib mating, first cousin mating, and half nth cousin mating under both infinite allele and two allele (back mutation) models. Reasonable rates of mutation do not provide significantly different results from probability of identity by descent in the absence of mutation. Homozygosity is higher under half-sib mating than under first cousin mating, but the expected number of copies of a gene in the population is higher under first cousin mating than under half-sib mating.

Pseudo-random mating populations. In celebration of the 80th anniversary of the Hardy-Weinberg law

That random mating leads to Hardy-Weinberg distribution of genotypes is well known. This report is to show that, if the deviations from random mating are of a certain pattern, the offspring generation will also be in Hardy-Weinberg proportions. This brings out the fact that random mating is a sufficient condition, not a necessary one, for the attainment of the Hardy-Weinberg proportions. Such nonrandom-mating populations are tentatively said to be pseudo-random mating. Pseudo-random-mating populations exist for both autosomal and sex-linked systems with two or multiple alleles. This report covers the basic case of a two-allele autosomal locus in detail, but the possible extension to two loci and cytonuclear systems have also been mentioned in discussion.

Regular systems of inbreeding

Regular systems of inbreeding with discrete, nonoverlapping generations and the same number of individuals and mating pattern in every generation are studied. The matrix Q that specifies the recursion relations satisfied by the probabilities of identity is expressed in terms of the matrix M that describes the mating system. Necessary and sufficient conditions for convergence to genetic uniformity are given, and it is determined which probabilities of identity approach one. If the mating system has certain symmetries and these are imposed initially, then a matrix R, of lower dimension than Q, specifies the recursion relations. For such a mating system, for generic initial conditions, the condensed matrix R suffices for determining whether convergence to uniformity occurs and which probabilities of identity approach one. If Q is irreducible, the maximal eigenvalue of R is the same as that of Q. If Q is also aperiodic, this implies that the asymptotic rate of convergence to homogeneity of the condensed system is the same as that of the complete one. The above results apply to autosomal loci in monoecious (with or without selfing) and dioecious populations and to X-linked loci. As an example, all the eigenvalues and right and left eigenvectors of Q for circular mating are found.

Inbreeding under a cyclical mating system

General recursion formulae for the coefficient of inbreeding under a cyclical mating system were derived in which one male and one female are selected from each of the n families per generation (population size N = 2 n). Each male is given the family number of his sire in each generation, while his mate comes from another family, varying systematically in different generations. Males of the r-th family in generations 1, 2, 3,..., t' = n-1 within each cycle mate with females from families r+1, r+2, r+3,..., r+t' to produce generations 2, 3, 4,..., t'+1=1, respectively. The change in heterozygosity shows a cyclical pattern of rises and falls, repeating in cycles of n-1 generations. The rate of inbreeding oscillates between <-3% to >6% in different generations within each cycle, irrespective of the population size. The average rate of inbreeding per generation is approximately 1/[4 N-(Log2N+1)], which is the rate for the maximum avoidance of inbreeding. The average inbreeding effective population size is approximately 2 N-2.

Geographic distribution of consanguinity in Europe

Average consanguinity (alpha) of 20 large regional or national samples derived from Roman Catholic Dispensations or state archives shows a strong negative relationship with latitude (r = -0.738; P less than 0.001) which seems best explained by cultural-historical factors. Isolates show no such pattern and are more variable in their inbreeding levels. Two-way analysis of variance shows the sample division by population size to be significant, the division by geography to be not significant, with no significant interaction between the two factors. In a one-way analysis of variance only the mainstream samples showed significant geographic differences (P less than 0.001). There is no such geographic association in Japan which has greater cultural and historical homogeneity. The clinical patterning in average consanguinity may bias frequency estimates of rare alleles, including genetic disorders.

Effect of assortative mating on genetic change due to selection

Two mathematical models (A and B) were used to study joint effects of selection and assortative mating on genetic change. Computer simulation was used to verify and extend the results. In each model, the genotype was additive with equal effects at each of N loci and the environmental distribution was N(0, σ(2)). In Model A, each locus had two alleles; in Model B, allelic effects at each locus followed a normal distribution. Using Model A, genetic change with assortative or random mating of selected parents was evaluated for combinations of number of loci (N = 1, 2, 3), heritability in base population (H([0]) = 0.2, 0.5, 0.8), allelic frequency in base population (p = 0.1, 0.5), and proportion selected (α = 0.20, 0.85). Using Model B, genetic change with or without assortative mating was calculated for combinations of N (1, 2, 3, 5, 10, 100, H([0]) (0.2, 0.5, 0.8) and α (0.20, 0.85). Response to selection under both mating systems in a finite population was estimated using Model A from 200 replications of a computer simulation; this was done for all combinations of N (1,2, 3, 5, 10) and α(0.20, 0.85), with H([0]) = 0.5 and p = 0.1. Results obtained with both models indicate that the effect of assortative mating on genetic change increases with H([0]) and α, and decreases with p. With Model A, the relationship between N and the effect of assortative mating on genetic change was not clear; with Model B, however, the advantage of assortative over random mating increased with N, as expected. Simulation results were in agreement with theory of Model A. This study indicates that selection with assortative mating can have a sizable (10 to 20%) long-term advantage over selection with random mating of parents when H([0]) is high, p is low and α is large.

The effect of positive assortative mating on genetic parameters in a simulated beef cattle population

Two simulated data sets, representing random mating and positive assortative mating in a beef cattle population over 10 rounds of mating, were each composed of 100 replicates. Three correlated traits were considered; calving ease (CE), 200 day weight (WW) and postweaning gain (PG). All selection practiced in the simulation was random. Positive assortative mating, which was based on parental WW phenotypic records, increased the progeny additive genetic variance of WW. The absolute values of genetic covariances and correlations between WW with CE and PG were also increased by positive assortative mating. Variances or covariances did not reach their expected equilibrium values due to overlapping generations, low replacement rates and only 10 rounds of mating.

Transmissible and nontransmissible components of anthropometric variation in the Alexanderwohl Mennonites: II. Resolution by path analysis

A study of the intergenerational transmissibilities of 34 anthropometric measures from the Alexanderwohl Mennonite congregations of Kansas and Nebraska is presented. Results presented tend to confirm the suggestion made previously by us (Devor et al., 1985) that patterns of transmissibility conform to a concept of "functional multifactorial complexes" operating in the body in a way analogous to the "field" concept of dental morphology.

Demographic components of gene frequency change in free-ranging macaques on Cayo Santiago

Gene frequency profiles from January 1973 to January 1977 for three polymorphic loci were examined in Cayo Santiago rhesus social groups. The effects of demographic components (i.e., births, deaths, immigrations, emigrations, and group fission and fusion) on total change in gene frequencies are assessed. Allelic frequencies at the carbonic anhydrase II, 6-phosphogluconate dehydrogenase, and transferrin loci were analyzed in four social groups. In the two groups that underwent fission and fusion during the study period, the timing of these processes was related to the largest short-term changes in gene frequences. However, immigration and emigration had the greatest effect on total change in gene frequency in all groups during the study period. The relative importance of births and deaths in producing gene frequency change varied among the social groups. These results suggest that the relative importance of the demographic components of gene frequency change in primate populations is determined by behavioral patterns and ecological conditions specific to the population considered.

Rules for assortative mating in relation to selection for linear merit functions

This study examined how assortative mating (without selection) based on linear combinations of two traits could be used to change genetic parameters so as to increase efficiency of selection. The efficiency of the Smith-Hazel index for improvement of multiple traits is a function of phenotypic and genetic variances and covariances, and of the relative economic values of the traits involved. Assortative mating is known to change genetic variances and covariances. Recursive formulae were derived to obtain these variances and covariances after t generations of assortative mating on linear combinations (mating rules) of phenotypic values for two traits, with a given correlation between mates. Selection efficiency after t generations of assortative mating without selection was expressed as a function of random mating genetic parameters, economic values, the mating rule, and the correlation between mates. Selection efficiency was maximized with respect to the coefficients in the mating rule. Because the objective function was nonlinear, a computer routine was used for maximizing it. Two cases were considered. When random mating heritabilities for the two traits were h X (2) =0.25 and h Y (2) =0.50, the genetic correlation rXY=-0.60, and the economic values were aX=3 and aY=1, continued assortative mating based on the optimal mating rule for 31 generations (with a correlation of 0.80 between mates) increased selection efficiency by 29%. Heritabilities changed to 0.38 and 0.66, respectively, and the genetic correlation became - 0.79. When h X (2) =0.60, h Y (2) =0.60, rXY=- 0.20, a1=1 and a2=1, 36 generations of continued assortative mating with the optimal mating rule increased the efficiency of selection by 17%, heritabilities became h X (2) = h Y (2) =0.71, and the genetic correlation changed to 0.25. Only three generations of assortative mating were required to change the sign of the genetic correlation.

Assortative mating among in-patients with primary affective disorder

Assortative mating among 56 married in-patients with primary affective disorders and their spouses was studied by determining the prevalence of psychiatric illness among the spouses by means of direct interviews and standardized diagnostic criteria. A high degree of assortative mating among both male and female patients was observed for total psychiatric illness, broad spectrum affective illness and major depression. A significantly higher prevalence of psychiatric and affective illness was found among the first-degree relatives of the ill spouses when compared with the first-degree relatives of the well spouses. There was a high degree of diagnostic concordance between the patients and spouses for both affective illness and alcoholism, with a higher degree of assortative mating among bipolar patients than among unipolar patients. The finding in this study of an increased prevalence of psychiatric disorder in the first-degree relatives of the ill spouses would support the hypothesis that there is a tendency for individuals with a predisposition to psychiatric illness to marry, rather than the existence of a marital interaction which causes an increased concordance for psychiatric illness.

Extensions to multivariate normal models for pedigree analysis

Lange, Westlake & Spence (1976) used the assumption of multivariate normality to apply a likelihood method to the analysis of quantitative traits measured over pedigrees. We now introduce a test of the assumption of multivariate normality and methods for the detection of outlying families and outlying individuals. We also introduce a method for the estimation of effects of measured genetic markers as variance components, a flexible parameterization to estimate effects of shared family environment, and a method to allow for the ascertainment of pedigrees through probands. These innovations have been applied using numerical methods for maximization of the likelihood. Simulation studies and available theory suggest that the likelihood ratio criterion used in significance testing follows the expected asymptotic distribution with sample sizes encountered in typical applications.

Assortative mating and the genetic correlation

The effect of assortative mating on the genetic correlation between traits X and Y is considered. Assortation on trait X changes the magnitude of the genetic correlation but not its sign. There are two situations depending on the signs of the correlation between mates (ρ) and of the random mating genetic correlation (θ): 1) if sign (θ) = sign (ρ), then θ >θ, where θ is the genetic correlation at equilibrium after continued assortation, and 2) if sign (θ) ≠ = sign (ρ), then θ < θ. However, negative assortative mating is virtually powerless to alter the magnitude of the genetic correlation. The consequences of a "mixed" assortation model, e.g., high milk production females mated to fast growing males and lesser productive females mated to slower growing sires, were also studied. "Mixed" positive assortation always increases the genetic correlation, but negative assortation decreases it. The implications of assortative mating on correlated responses to selection and on the equilibrium covariances between relatives for pairs of traits are discussed.

Prairie Dogs Avoid Extreme Inbreeding

Black-tailed prairie dogs (Rodentia: Sciuridae: Cynomys ludovicianus) live in colonies composed of contiguous but separate family groups called coteries. During the 6 years that individuals in a colony were observed, they almost nevermated with close genetic relatives. Inbreeding is avoided in four ways: (i) a young male usually leaves his natal coterie before breeding, but his female relatives remain; (ii) an adult male usually leaves his breeding coterie before his daughters mature; (iii) a young female is less likely to come into estrus if her father is in her coterie; and (iv) an estrous female behaviorally avoids mating with a father, son, or brother in her coterie.

Forging links between population and quantitative genetics

An initially rare allele with a large effect on a quantitative character is expected to exhibit the following behaviour in artificial selection lines: 1. It should change in frequency, or be lost by chance, at rates predictable from the effects of the allele on the quantitative character and the selection regime imposed. 2. At the phenotypic level the behaviour of the allele should cause (a) asymmetrical responses to bidirectional selection, (b) variation among replicate lines in response to selection corresponding to the behaviour of the allele in individual lines, (c) changes in heritability in lines in which the allele increases in frequency and (d) selection response compatible with the effects of the allele. This paper reports an experimental evaluation of these predictions utilizing a rare allele of large effect (sm (lab) ) detected in a sample of the Canberra outbred population of Drosophila melanogaster at a frequency of 1/120. Homosygosity for this allele reduced abdominal bristle number by more than 50%, altered the abdominal bristle pattern and reversed the sexual dimorphism for abdominal bristle number. Experiments were done to characterise sm (lab) and all evidence indicates that it is a single allele with a very large effect.Bidirectional selection for abdominal bristle number was carried out in three high and three low lines from this sample of the Canberra population. The sm (lab) allele rose in frequency and went to fixation in two of the low lines (in 10 generations) but was lost from the third. These times to fixation were slower than the expectations derived from computer simulations of the behaviour of such an allele but this can be attributed to the lower fitness of sm (lab) homozygotes. The proportions of lines with the allele fixed or lost were compatible with expectations. At the phenotypic level, the behavior of sm (lab) had the expected consequences, namely, (i) asymmetrical responses to bidirectional selection, (ii) variation in response among replicate low lines corresponding to the behaviour of sm (lab) , (iii) changes in heritabilities in the lines in which sm (lab) went to fixation, and (iv) selection responses compatible with the effects of the allele.A test for rare alleles of large effect was proposed, based on the expected pattern of change in heritability under artificial selection. This test was applied to the high selection lines but no evidence was found for important effects due to rare alleles of large effect increasing abdominal bristle number, a conclusion consistent with other independent evidence.This work provides experimental corroboration of the links between population genetics and quantitative genetics.

Aanlysis of some regular systems of inbreeding

A probabilistic method is used to calculate the asymptotic rate of loss of genetic variability for half-sib and first-cousin mating of an infinite number of individuals. For both systems of inbreeding, all probabilities of nonidentity by descent converge to zero at ultimate rate proportional to t-1/2, where t is the time in generations. The rate of decay is faster for half-sibs than for first cousins, the respective asymptotic allozygosities being 4(pit)-1/2 and 8(pi t)-1/2.

Restriction and persistence of polymorphisms of HLA and other blood genetic traits in the Parakanã Indians of Brazil

Results concerning HLA types and 22 other blood genetic systems are reported for the Parakanã Indians of northern Brazil, a tribe that is notable for the light color and pilosity of some of its members. No clear evidence of Caucasoid admixture was found, but the Parakanã show unusual frequencies in the EsD1, PGM1(1) Gc2, CpB, Fya, Dia, and LM genetic markers. In addition, the very rare Rh allele ry is present, as well as what seems to be a new PGM2 variant. There is very limited heterogeneity in the HLA system. All these distinctive features may have arisen through a combination of founder effects and genetic drift. However, low FIS values, as well as higher mean ages in heterozygous as compared to homozygous persons, suggest that an heterotic effect is counteracting these dispersive forces.

New studies on the esterase D polymorphism in South American Indians

A total of 2,490 South American Indians affiliated with 10 tribes were studied for esterases A1, A2, A3, B, D, and carbonic anhydrases 1 and 2. Wide variation was observed in the prevalence of ESD1, the extreme values being 0.44, encountered among the Xikrin, and 0.95, found among the Cashinawa. Seven of the 10 frequencies fell within the interval of 0.66--0.87. These results were integrated with those of earlier surveys. In a general way we observe lower values in the eastern and Atlantic Coast groups, but this is mainly due to the low frequencies found among the Gê tribes and the Caingang, who speak a language which has many affinities with Gê. High prevalences were observed among the tropical forest tribes. A fair amount of intervillage, intratribal variation was found among the Ticuna and Caingang. No variability was detected in the A1, A2, A3, B esterases. In the carbonic anhydrases we confirmed the presence of a "private polymorphism" among the Baniwa.