Pseudo-random mating systems for 3-allele loci

A random mating population attains equilibrium by the Hardy-Weinberg law. By demonstrating some simple examples for 2-allele loci, Li (1988) showed that a nonrandom mating population of certain mating patterns may also attain equilibrium. He called such a type of population a pseudo-random mating population. Tai (1990), then, gave a generalized representation of these pseudo-random mating systems. In this paper the clear patterns of pseudo-random mating behavior for a 3-allele locus are derived. Both autosomal and sex-linked systems are discussed. The study of these mating patterns provides a way to understand the complicated mating system of a population, which usually is only with difficulty realized through sampled individuals from that population.     

A Two-Stage Test for Distinguishing Random,Pseudo-Random and Nonrandom Mating Populations

There is no such an implication that a population in Hardy-Weinberg equilibrium must have undergone random mating. Therefore, it is unequivocal that the usual tests for “Hardy-Weinberg equilibrium” are indeed tests for “random union of gametes” but not for “random mating”. In this paper, utilizing population characteristics expressed in equilibrium state (equilibrium or disequilibrium) and mating behavior (random or nonrandom), a two-stage testing procedure for distinguishing random, pseudo-random and nonrandom mating populations is proposed. At the first stage, a population is tested for Hardy-Weinberg equilibrium. If insignificant result (i.e., in equilibrium) is obtained, then to a second stage the population is further tested for mating behavior. Random mating-pairs data are needed here for analysis instead of random individuals for usual Hardy-Weinberg equilibrium tests. Since distinguishing the three types of mating populations depends on the combined results of two stages, the probability of correct determination of the two-stage tests is discussed by simulation studies.     

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.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.     

Divergent mating systems and parental conflict as a barrier to hybridization in flowering plants

Parental conflicts can lead to antagonistic coevolution of the sexes and of parental genomes. Within a population, the resulting antagonistic effects should balance, but crosses between populations can reveal conflict. Parental conflict is less intense in self-pollinating plants than in outcrossers because outcrossing plants are pollinated by multiple pollen donors unrelated to the seed parent, while a self-pollinating plant is primarily pollinated by one individual (itself). Therefore, in crosses between plants with differing mating systems, outcrossing parents are expected to "overpower" selfing parents. We call this the weak inbreeder/strong outbreeder (WISO) hypothesis. Prezygotically, such overpowering can alter pollination success, and we argue that our hypothesis explains a common pattern of unilateral incompatibility, in which pollen from self-incompatible populations fertilizes ovules of self-compatible individuals but the reciprocal cross fails. A postzygotic manifestation of overpowering is aberrant seed development due to parent-of-origin effects such as genomic imprinting. We evaluate evidence for the WISO hypothesis by reviewing published accounts of crosses between plants of different mating systems. Many, but not all, of such reports support our hypothesis. Since parental conflicts can perturb fertilization and development, such conflicts may strengthen reproductive barriers between populations, contributing to speciation.     

A clarification of the Hardy-Weinberg law

C. C. Li showed that Hardy-Weinberg proportions (HWP) can be maintained in a large population by nonrandom mating as well as random mating. In particular he gave the mating matrix for the symmetric case in the most general form possible. Thus Li showed that, once HWP are attained, the same proportions can be maintained by what he called pseudorandom mating. This article shows that, starting from any genotypic distribution at a single locus with two alleles, the same in each sex, HWP can be reached in one round of nonrandom mating with no change in allele frequency. In the model that demonstrates this fact, random mating is represented by a single point in a continuum of nonrandom possibilities.     

Covariance between relatives for X-chromosomal loci in a population in disequilibrium

Summary According to Hardy-Weinberg, for a single autosomal locus, a population achieves equilibrium in one generation of random mating if allelic frequency is the same in the sexes, or in two generations if the frequency is not. For a single X-chromosomal locus, however, the approach to equilibrium oscillates and is gradual. Covariances between relatives for autosomal and for X-chromosomal loci are in the literature for a random mating population in equilibrium. Although assumption of equilibrium is defensible for an autosomal locus, it is less defensible for an X-chromosomal locus. Covariances between collateral and between lineal relatives are derived for X-chromosomal loci in a random mating population not in equilibrium. Collateral relatives such as sibs are of the same generation, and lineal relatives such as parent-offspring are of different generations. Coefficient of co-ancestry between relatives, based on identity by descent, was used in this development. Results are applicable to crossbreeding in livestock and poultry, and also to haplo-diploid organisms, such as the honeybee, in which the entire genome is equivalent to being X-chromosomal.Supported in part by the Illinois Agricultural Experiment Station, Hatch Project 35-0367     

Testing the viviparity-driven-conflict hypothesis: parent-offspring conflict and the evolution of reproductive isolation in a poeciliid fish

The evolution of viviparity increases the potential for genomic conflicts between mothers and offspring over the level of maternal investment. The viviparity-driven-conflict hypothesis predicts that such conflicts will drive the evolution of asymmetrical reproductive isolation between populations with divergent mating systems. We tested this hypothesis using crosses between populations of a poeciliid fish that differ in their level of polyandry. Our results support the prediction of an asymmetry in the rate of spontaneous abortion in reciprocal crosses, with the highest rate occurring in crosses between females from a relatively monandrous population and males from a relatively polyandrous population. The patterns of offspring size were not consistent with the pattern predicted by the viviparity-driven-conflict hypothesis: crosses between a monandrous female and a polyandrous male did not produce larger offspring than the reciprocal cross. This discrepancy was due to the presence of an effect of the maternal population on offspring size: polyandrous females produced larger offspring than monandrous females. In addition, offspring size was positively correlated with maternal size in crosses involving a polyandrous male. We discuss these results in light of models for intra- and intergenomic epistasis and the rapid origin of asymmetric reproductive isolation in viviparous taxa.     

Incipient Reproductive Isolation between Geographic Populations of Ophryotrocha labronica (Polychaeta, Dorvilleidae)

Åkesson, B. (Department of Zoology, University of Gothenburg, Göteborg, Sweden.) Incipient reproductive isolation between geographic populations of Ophryotrocha labronica (Polychaeta, Dorvilleidae). Zocl. Scripta 1 (5): 207–210, 1972.–The mechanism of sex determination and the incipient reproductive isolation between geographic populations of Ophryotrocha labronica are studied in intra- and interpopulation crosses. Two populations from the Naples area and one from Leghorn are employed in the crosses. The considerable genetic difference between the Leghorn population and any of the Naples populations is reflected in some crossing combinations by changes in sex ratios, by occurrence of individuals with a reduced viability in the progeny, by a decreased mating propensity, and by discrimination of mates from alien populations. It is stated that the changes in sex ratios, the decreased mating propensity, the dwarfed individuals in the progeny, and the preferential mating all reflect the incompatibility of gene complexes. The differences between reciprocal crosses are not fully explained. The occurrence of extranuclear DNA, as well as the existence of a maternal heredity in intrapopulation crosses, indicate that cytoplasmic inheritance may be one of the factors behind these reciprocal differences.     

Modifiers of mutation rate: a general reduction principle

A deterministic two-locus population genetic model with random mating is studied. The first locus, with two alleles, is subject to mutation and arbitrary viability selection. The second locus, with an arbitrary number of alleles, controls the mutation at the first locus. A class of viability-analogous Hardy-Weinberg equilibria is analyzed in which the selected gene and the modifier locus are in linkage equilibrium. It is shown that at these equilibria a reduction principle for the success of new mutation-modifying alleles is valid. A new allele at the modifier locus succeeds if its marginal average mutation rate is less than the mean mutation rate of the resident modifier allele evaluated at the equilibrium. Internal stability properties of these equilibria are also described.     

Haplotype inference in crossbred populations without pedigree information

Background

Current methods for haplotype inference without pedigree information assume random mating populations. In animal and plant breeding, however, mating is often not random. A particular form of nonrandom mating occurs when parental individuals of opposite sex originate from distinct populations. In animal breeding this is called crossbreeding and hybridization in plant breeding. In these situations, association between marker and putative gene alleles might differ between the founding populations and origin of alleles should be accounted for in studies which estimate breeding values with marker data. The sequence of alleles from one parent constitutes one haplotype of an individual. Haplotypes thus reveal allele origin in data of crossbred individuals.

Results

We introduce a new method for haplotype inference without pedigree that allows nonrandom mating and that can use genotype data of the parental populations and of a crossbred population. The aim of the method is to estimate line origin of alleles. The method has a Bayesian set up with a Dirichlet Process as prior for the haplotypes in the two parental populations. The basic idea is that only a subset of the complete set of possible haplotypes is present in the population.

Conclusion

Line origin of approximately 95% of the alleles at heterozygous sites was assessed correctly in both simulated and real data. Comparing accuracy of haplotype frequencies inferred with the new algorithm to the accuracy of haplotype frequencies inferred with PHASE, an existing algorithm for haplotype inference, showed that the DP algorithm outperformed PHASE in situations of crossbreeding and that PHASE performed better in situations of random mating.     

4-way bred rats as experimental animals

The present study is an attempt to utilize hybrids among several inbred strains of rats as useful animals for the studies of effectiveness and toxicology on drugs., Four-way crosses were made among the LEW, WM, F344 and DRY strains of rats, and their characteristics were examined. From the breeding data of diallel crosses among these four strains and reciprocal crosses among their F1 hybrids, the mating type indicating the highest reproductivity was (LEW X WM) F1 X (F344 X DRY) F1. These four-way crosses were designated as LWFD. The reproductivity of this mating type was exceedingly higher than those of four strains. In order to examine the susceptibility to thiamine hydrochloride, the acute toxicity test was practiced in inbred strains, F1 hybrids and four-way crosses. As a result, in spite of highly heterogeneous population, the LWFD did not show a peculiar response in comparison with four strains and their F1 hybrids. Furthermore, hematological and clinico-biochemical values of the LWFD did not show a large variability as presumed. From these results, it is suggested that hybrids such as four-way crosses among inbred strains can be used as useful animals for the studies of effectiveness and toxicology on drugs.     

MATING PATTERN AND FITNESS-COMPONENT ANALYSIS ASSOCIATED WITH INVERSION POLYMORPHISM IN A NATURAL POPULATION OF DROSOPHILA BUZZATII

Direct studies of mating success or mating pattern associated with Mendelian factors rarely have been carried out in nature. From the samples taken for the standard analyses of selection components, it is not usually possible to obtain the mating table, and only directional selection for male mating success can be detected. Both processes, mating pattern and differential mating probability, together with other fitness components, have been investigated for the inversion polymorphism of a natural population of the cactophilic species Drosophila buzzatii. Two independent samples of adult flies were collected: nonmating or single individuals (base population) and mating pairs (mating population). All individuals were karyotyped for the second and fourth chromosomes. A sequence of models with increasing simplicity was fitted to the data to test null hypotheses of no selection and random union of gametes and karyotypes. The main results were (1) no deviations from random mating were found; (2) differential mating probability was nonsignificant in both sexes; (3) inversion and karyotypic frequencies did not differ between sexes; and (4) karyotypic frequencies did not depart from Hardy-Weinberg expectations. These results are discussed in light of complementary evidence showing the need for interpreting with caution no-effect hypotheses such as the ones tested here. The use of complementary selective tests in these studies is suggested.     

Natural Selection and Age-Structured Populations

This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reproductive potential. This result is an information theoretic analog of Fisher''s fundamental theorem of natural selection.     

A new test for detecting ongoing selection

Much effort has been made to search for signatures of past natural selection in DNA sequences. However, currently acting selection is rarely detected in natural populations because of its rarity, low detection power of available methods, or both. Here, we develop a new test to detect viability selection over a single generation. In this test, one specific type of chromosomes is chosen as a reference, while all other chromosomes are designated as "focal". The test compares measures of variation between two groups of "focal" chromosomes: those found in reference/focal heterozygous individuals and those found in focal/focal homozygous individuals. In the absence of selection, we do not expect differences between these two groups as long as mating is random. On the other hand, currently acting selection can cause differences in some measures of variation. We applied this test to typing data for In(2L)t inversion polymorphism in a Drosophila melanogaster population, using "standard" (non-inverted) chromosomes as the focal class. Although the frequencies of In(2L)t and standard chromosomes did not deviate from the Hardy-Weinberg equilibrium, we found differences in allele frequency and the number of haplotypes between the two groups of standard chromosomes. This new test, in conjunction with the Hardy-Weinberg test, may shed light on how often strong selection is operating in extant populations.     

CROSS ABILITY OF MIMULUS GUTTATUS IN RELATION TO COMPONENTS OF GENE FIXATION

The joint effects of parental gene fixation and consanguinity of mates upon the fitness of matings was examined in Mimulus guttatus. Plants from four populations were crossed at five levels of genetic relatedness, and five viability characters were scored in progeny. Parental gene fixation at 12 polymorphic allozyme loci was partitioned into local, subpopulation, and population components. A model is proposed wherein parental gene fixation influences distance-dependent crossing success. At a fixed locus, inbreeding is favored if natural selection caused allele fixation, or is disfavored if gene fixation was random. The distance between mates required to eliminate gene fixation depends upon patch size of fixation. When selective fixation and patch size differ among loci, an optimal crossing distance is possible. In M. guttatus, progeny viability generally decreased with greater relatedness between mates, but this decrease was often heterogeneous among populations. The highest pollen viability and the lowest seed set were found at an intermediate relatedness between mates. To determine whether parental gene fixation influences these crossing patterns, a type of mutational-load analysis was performed. Progeny fitness was regressed on parent F and fitness estimated at F = 1. This was done for each component of F, for a) crosses that maintain gene fixation and b) crosses that eliminate gene fixation. A multiplicative, composite measure of fitness indicates that, in M. guttatus, genes fixed during local or population differentiation favor outbreeding, while genes fixed during subpopulation differentiation favor inbreeding. This predicts that random mating within subpopulations confers highest progeny fitness, exclusive of between-population matings. However, predictions did not fit the observed patterns of crossing success very well, perhaps because gene fixation was relatively low or was not adequately measured at loci influencing fitness.     

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.     

Comparisons of positive assortative mating and sexual selection models

A series of theoretical models of positive assortative mating and sexual selection are contrasted. It is established that for a dominant trait partial positive assortative mating generally implies some fixation, whereas sexual selection exhibits a unique globally stable polymorphism exhibiting Hardy-Weinberg proportions. The effects of monogamy against polygamy do not qualitatively alter the equilibrium outcomes, although the rate of evolutionary change is generally slowed with monogamy vis-à-vis polygamy. For sexual selection the influence of timing of random mating as against preferential mating causes no change in the equilibrium states, although the rates of convergence can be slowed if sexual selection occurs late in the breeding season. Under assortative mating the timing can alter the equilibrium outcomes. The amount of heterozygosity is always deficient in cases of assortative mating, but always exhibits Hardy-Weinberg ratios under a sexual selection mechanism. This suggests that observations consistent with Hardy-Weinberg equilibrium states cannot preclude ipso facto certain forms of selection forces, including mating patterns and some natural selection structures.     

Correlated evolution in parental care in females but not males in response to selection on paternity assurance behaviour

According to classical parental care theory males are expected to provide less parental care when offspring in a brood are less likely to be their own, but empirical evidence in support of this relationship is equivocal. Recent work predicts that social interactions between the sexes can modify co‐evolution between traits involved in mating and parental care as a result of costs associated with these social interactions (i.e. sexual conflict). In burying beetles (Nicrophorus vespilloides), we use artificial selection on a paternity assurance trait, and crosses within and between selection lines, to show that selection acting on females, not males, can drive the co‐evolution of paternity assurance traits and parental care. Males do not care more in response to selection on mating rate. Instead, patterns of parental care change as an indirect response to costs of mating for females.     

Minimizing inbreeding by managing genetic contributions across generations

Here we present the strategy that achieves the lowest possible rate of inbreeding (DeltaF) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a DeltaF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and consequently DeltaF is minimized. Using the concept of long-term genetic contributions, the asymptotic DeltaF of the new strategy for random mating, M sires and d dams per sire, is phi/(12M), where phi = [1 + 2((1)/(4))(d)]. Predictions were validated using Monte Carlo simulations. The scheme was shown to achieve the lowest possible DeltaF using pedigree alone and showed that further reductions in DeltaF below that obtained from random mating arise from preferential mating of relatives and not from their avoidance.