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[Q.sub.ST] measures the differentiation of quantitative traits between populations. It is often compared to [F.sub.ST], which measures population differentiation at neutral marker loci due to drift, migration, and mutation. When [Qsub.ST] is different from [F.sub.ST], it is usually taken as evidence that selection has either restrained or accelerated the differentiation of the quantitative trait relative to neutral markers. However; a number of other factors such as inbreeding, dominance, and epistasis may also affect the [Q.sub.ST] - [F.sub.ST] contrast. In this study, we examine the effects of dominance, selection, and inbreeding on [Q.sub.ST] - [F.sub.ST]. We compare [Q.sub.ST] with [F.sub.ST] at selected and neutral loci for populations at equilibrium between selection, drift, mutation, and migration using both analytic and simulation approaches. Interestingly, when divergent selection is acting on a locus, inbreeding and dominance generally inflate [Q.sub.ST] relative to [F.sub.ST] when they are both measured at the quantitative locus at equilibrium. As a consequence, dominance is unlikely to hide the signature of divergent selection on the [Q.sub.ST] - [F.sub.ST] contrast. However, although in theory dominance and inbreeding affect the expectation for [Q.sub.ST] - [F.sub.ST], of most concern is the very large variance in both [Q.sub.ST] and [F.sub.ST], suggesting that we should be cautious in attributing small differences between [Q.sub.ST] and [F.sub.ST] to selection.

A variety of estimators have been developed to use genetic marker information in inferring the admixture proportions (parental contributions) of a hybrid population. The majority of these estimators used allele frequency data, ignored molecular information that is available in markers such as microsatellites and DNA sequences, and assumed that mutations are absent since the admixture event. As a result, these estimators may fail to deliver an estimate or give rather poor estimates when admixture is ancient and thus mutations are not negligible. A previous molecular estimator based its inference of admixture proportions on the average coalescent times between pairs of genes taken from within and between populations. In this article I propose an estimator that considers the entire genealogy of all of the sampled genes and infers admixture proportions from the numbers of segregating sites in DNA sequence samples. By considering the genealogy of all sequences rather than pairs of sequences, this new estimator also allows the joint estimation of other interesting parameters in the admixture model, such as admixture time, divergence time, population size, and mutation rate. Comparative analyses of simulated data indicate that the new coalescent estimator generally yields better estimates of admixture proportions than the previous molecular estimator, especially when the parental populations are not highly differentiated. It also gives reasonably accurate estimates of other admixture parameters. A human mtDNA sequence data set was analyzed to demonstrate the method, and the analysis results are discussed and compared with those from previous studies.

Although the distribution of frequencies of genes influencing quantitative traits is important to our understanding of their genetic basis and their evolution, direct information from laboratory experiments is very limited. In theory, different models of selection and mutation generate different predictions of frequency distributions. When a large population at mutation-selection balance passes through a rapid bottleneck in size, the frequency distribution of genes is dramatically altered, causing changes in observable quantities such as the mean and variance of quantitative traits. We investigate the gene frequency distribution of a population at mutation-selection balance under a joint-effect model of real stabilizing and pleiotropic selection and its redistribution and thus changes of the genetic properties of metric and fitness traits after the population passes a rapid bottleneck and expands in size. If all genes that affect the trait are neutral with respect to fitness, the additive genetic variance (V.sub.A) is always reduced by a bottleneck in population size, regardless of their degree of dominance. For genes that have been under selection, [V.sub.A] increases following a bottleneck if they are (partially) recessive, while the dominance variance increases substantially for any degree of dominance. With typical estimates of mutation parameters, the joint-effect model can explain data from laboratory experiments on the effect of bottlenecking on fitness and morphological traits, providing further support for it as a plausible mechanism for maintenance of quantitative genetic variation.

Likelihood methods have been developed to partition individuals in a sample into full-sib and half-sib families using genetic marker data without parental information. They invariably make the critical assumption that marker data are free of genotyping errors and mutations and are thus completely reliable in inferring sibships. Unfortunately, however, this assumption is rarely tenable for virtually all kinds of genetic markers in practical use and, if violated, can severely bias sibship estimates as shown by simulations in this article. I propose a new likelihood method with simple and robust models of typing error incorporated into it. Simulations show that the new method can be used to infer full- and half-sibships accurately Iron marker data with a high error rate and to identify typing errors at each locus in each reconstructed sib family. The new method also improves previous ones by adopting a fresh iterative procedure for updating allele frequencies with reconstructed sibships taken into account, by allowing for the use of parental information, and by using efficient algorithms for calculating the likelihood function and searching for the maximum-likelihood configuration. It is tested extensively on simulated data with a varying number of marker loci, different rates of typing errors, and various sample sizes and family structures and applied to two empirical data sets to demonstrate its usefulness.

In models of maintenance of genetic variance ([V.sub.G]) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a joint-effect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium [V.sub.G]. Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher [V.sub.G] than does an additive model. Importantly, tier what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most [V.sub.G] comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations.

For an admixed population, an important question is how much genetic contribution comes from each parental population. Several methods have been developed to estimate such admixture proportions, using data on genetic markers sampled from parental and admixed populations. In this study, I propose a likelihood method to estimate jointly the admixture proportions, the genetic drift that occurred to the admixed population and each parental population during the period between the hybridization and sampling events, and the genetic drift in each ancestral population within the interval between their split and hybridization. The results from extensive simulations using various combinations of relevant parameter values show that in general much more accurate and precise estimates of admixture proportions are obtained from the likelihood method than from previous methods. The likelihood method also yields reasonable estimates of genetic drift that occurred to each population, which translate into relative effective sizes ([N.sub.e]) or absolute average [N.sub.e]'s if the times when the relevant events (such as population split, admixture, and sampling) occurred are known. The proposed likelihood method also has features such as relatively low computational requirement compared with previous ones, flexibility for admixture models, and marker types. In particular, it allows for missing data from a contributing parental population. The method is applied to a human data set and a wolflike canids data set, and the results obtained are discussed in comparison with those from other estimators and from previous studies.

In the past, moment and likelihood methods have been developed to estimate the effective population size ([N.sub.e]) on the basis of the observed changes of marker allele frequencies over time, and these have been applied to a large variety of species and populations. Such methods invariably make the critical assumption of a single isolated population receiving no immigrants over the study interval. For most populations in the real world, however, migration is not negligible and can substantially bias estimates of [N.sub.e] if it is not accounted for. Here we extend previous moment and maximum-likelihood methods to allow the joint estimation of [N.sub.e] and migration rate (m) using genetic samples over space and time. It is shown that, compared to genetic drift acting alone, migration results in changes in allele frequency that are greater in the short term and smaller in the long term, leading to under- and overestimation of [N.sub.e], respectively, if it is ignored. Extensive simulations are run to evaluate the newly developed moment and likelihood methods, which yield generally satisfactory estimates of both [N.sub.e] and m for populations with widely different effective sizes and migration rates and patterns, given a reasonably large sample size and number of markers.

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection ([V.sub.s]) and the genetic variance maintained in segregating populations ([V.sub.G]) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, [V.sub.G] increases to an asymptote as the population size increases. Both [V.sub.G] and [V.sub.s] are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher [V.sub.G] but also a high [V.sub.s] ([V.sub.s] in phenotypic standard deviation units, which is always larger than the ratio [V.sub.P]/[V.sub.m]), implying weak apparent stabilizing selection. If the mutational variance [V.sub.m] is ~[10.sup.-3] [V.sub.e] ([V.sub.e], environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/ or small sample sizes.

The phenomenon that the genetic variance of fitness components increase following a bottleneck or inbreeding is supported by a growing number of experiments and is explained theoretically by either dominance or epistasis. In this article, diffusion approximations under the infinite sites model are used to quantify the effect of dominance, using data on viability in Drosophila melanogaster. The model is based on mutation parameters from mutation accumulation experiments involving balancer chromosomes (set I) or inbred lines (set II). In essence, set I assumes many mutations of small effect, whereas set II assumes fewer mutations of large effect. Compared to empirical estimates from large outbred populations, set I predicts reasonable genetic variances but too low mean viability. In contrast, set II predicts a reasonable mean viability but a low genetic variance. Both sets of parameters predict the changes in mean viability (depression), additive variance, between-line variance and heritability following bottlenecks generally compatible with empirical results, and these changes are mainly caused by lethals and deleterious mutants of large effect. This article suggests that dominance is the main cause for increased genetic variances for fitness components and fitness-related traits after bottlenecks observed in various experiments.

For a dioecious diploid population subdivided into an arbitrary number of subpopulations, we have derived recurrence equations for the inbreeding coefficient and coancestries between individuals within and among subpopulations and formulas for effective size and F-statistics. Stable population size and structure, discrete generations, autosomal inheritance, and the island migration model are assumed, and arbitrary distributions of the numbers of male and female progeny per family, different numbers and variable migration rates of males and females are incorporated in our derivation. Some published equations for effective size and F-statistics for a subdivided population are shown to be incorrect because several incorrect probabilities are used in the derivation. A more general equation for effective size is obtained by finding eigenvalue solutions to the recurrence equations for inbreeding coefficient and coancestry in this article, which reduces to the simple and familiar expressions derived by previous authors for the special case of a single unsubdivided population. Our general expressions for F-statistics also reduce to the classical results of WRIGHT's infinite island model and its extensions. It is shown that population structure is important in determining effective size and F-statistics and should be recognized and incorporated into programs for genetic conservation and evolution.

Assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, we have derived recurrence equations for the inbreeding coefficient and coancestry between individuals within and among subpopulations for a subdivided monoecious population with arbitrary distributions of male and female gametes per family, variable pollen and seed migration rates, and partial selfing. From the equations, formulas for effective size and expressions for F-statistics are obtained. For the special case of a single unsubdivided population, our equations reduce to the simple expressions derived by previous authors. It is shown that population structure (subdivision and migration) is important in determining the inbreeding coefficient and effective size. Failure to recognize internal structures of populations may lead to considerable bias in predicting effective size. Inbreeding coefficient, coancestry between individuals within and among subpopulations accrue at different and variable rates over initial generations before they converge to the same asymptotic rate of increase. For a given population, the smaller the pollen and seed migration rates, the more generations are required to attain the asymptotic rate and the larger the asymptotic effective size. The equations presented herein can be used for the study of evolutionary biology and conservation genetics.

An approach to the optimal utilization of marker and pedigree information in minimizing the rates of inbreeding and genetic drift at the average locus of the genome (not just the marked loci) in a small diploid population is proposed, and its efficiency is investigated by stochastic simulations. The approach is based on estimating the expected pedigree of each chromosome by using marker and individual pedigree information and minimizing the average coancestry of selected chromosomes by quadratic integer programming. It is shown that the approach is much more effective and much less computer demanding in implementation than previous ones. For pigs with 10 offspring per mother genotyped for two markers (each with four alleles at equal initial frequency) per chromosome of 100 cM, the approach can increase the average effective size for the whole genome by ~40 and 55% if mating ratios (the number of females mated with a male) are 3 and 12, respectively, compared with the corresponding values obtained by optimizing between-family selection using pedigree information only. The efficiency of the marker-assisted selection method increases with increasing amount of marker information (number of markers per chromosome, heterozygosity per marker) and family size, but decreases with increasing genome size. For less prolific species, the approach is still effective if the mating ratio is large so that a high marker-assisted selection pressure on the rarer sex can be maintained.

Using both the genetic drift and inbreeding approaches, we derive more general equations for effective size ([N.sub.e]) of a diploid species under random mating. These equations show explicitly that inbreeding or genetic drift comes from two sources, the variation in the number of offspring from each parent and the variation in contribution between these parents' own paternally and maternally derived genes to their offspring. The first source can be easily and effectively controlled by choosing an equal number of offspring from each family, while the second can be manipulated by using information on genetic markers to reduce the variance due to Mendelian segregation. Marker-assisted selection (MAS) methods to increase [N.sub.e] for the whole genome with single or multiple marker loci per chromosome, different numbers of males, and females are developed and implemented in stochastic simulations. The analytical and simulation results show that, although in principle [N.sub.e] can be increased indefinitely, the efficiency of MAS is restricted in practice by the amount of marker information, the genome size, and the number of marker-genotyped offspring per family. The assumptions made in developing the theory and methods and the applications of MAS in conservation are discussed.

Transition matrices for selfing and full-sib mating were derived to investigate the effect of selection against deleterious mutations on the process of inbreeding at a linked neutral locus. Selection was allowed to act within lines only (selection type I) or equally within and between lines (type II). For selfing lines under selection type I, inbreeding is always retarded, the retardation being determined by the recombination fraction between the neutral and selected loci and the inbreeding depression from the selected locus, irrespective of the selection coefficient (s) and dominance coefficient (h) of the mutant allele. For selfing under selection type II or full-sib mating under both selection types, inbreeding is delayed by weak selection (small s and sh), due to the associative overdominance created at the neutral locus, and accelerated by strong selection, due to the elevated differential contributions between alternative alleles at the neutral locus within individuals and between lines (for selection type II). For multiple fitness loci under selection, stochastic simulations were run for populations with selfing, full-sib mating, and random mating, using empirical estimates of mutation parameters and inbreeding load in Drosophila. The simulations results are in general compatible with empirical observations.

In models of maintenance of genetic variance (VG) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a jointeffect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium VG. Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher VG than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most VG comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations. [ABSTRACT FROM AUTHOR]

Presents an exact recurrence mathematical model equation for inbreeding coefficient for a partially sib-mated population. Distribution of the family sizes; Stochastic simulations.