Extensions of models for the estimation of mating systems using n independent loci

Inferences about plant mating systems increasingly use highly informative genetic markers, and investigate finer facets of the mating system. Here, four extensions of models for the estimation mating systems are described. (1) Multiallelic probabilities for the mixed selfing-random mating model are given; these are especially suitable for microsatellites; a generalized Kronecker operator is basis of this formula. (2) Multilocus probabilities for the "correlated-matings model" are given; interestingly, comparisons between single- vs multilocus estimates of correlated-paternity can provide a new measure of population substructure. (3) A measure of biparental inbreeding, the "correlation of selfing among loci", is shown to approximate the fraction of selfing due to uniparental (as opposed to biparental) inbreeding; also joint estimation of 1- 2- and 3-locus selfing rates allow separation, under a simple model, of the frequency vs the magnitude of biparental inbreeding. (4) Method-of-moments estimators for individual outcrossing rates are given. Formulae are given for both gymnosperms and angiosperms, and the computer program "MLTR" implements these methods.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mammalian mating systems

Male mammals show a diverse array of mating bonds, including obligate monogamy, unimale and group polygyny and promiscuity. These are associated with a wide variety of different forms of mate guarding, including the defence of feeding and mating territories, the defence of female groups and the defence of individual receptive females. Female mating bonds include long-term monogamy, serial monogamy, polyandry and promiscuity. Both male and female mating behaviour varies widely within species. Variation in male mating behaviour is related to the effect of male assistance in rearing young and to the defensibility of females by males. The latter is, in turn, related to female ranging behaviour and to the size and stability of female groups. Much of the variation in mammalian mating bonds and systems of mate guarding can be attributed to differences in these three variables.     

Three mating type-like loci in Candida glabrata

Candida glabrata, the second most prevalent Candida species colonizing humans, possesses three mating type-like (MTL) loci (MTL1, MTL2, and MTL3). These loci contain pairs of MTL genes with their respective coding regions on complementary Crick and Watson DNA strands. Each pair of genes is separated by a shared intergenic promoter region, the same configuration found at the mating type loci of Saccharomyces cerevisiae. Two of the MTL loci, MTL1 and MTL2, contain either the MTLa1/MTLa2 configuration or the MTLalpha1/MTLalpha2 configuration in different strains. All but one of the 38 tested C. glabrata strains were either aaalpha or aalphaalpha. One test strain was alphaalphaalpha. Based on the mating type genotype, the MTL genes at the MTL1 or MTL2 loci, and the size of the XbaI fragment harboring MTL1 or MTL2, four classes of C. glabrata strains (I, II, III, and IV) were distinguished. Northern analysis revealed that strains were either a-expressors or alpha-expressors and that expression always reflected the genotype of either the MTL1 or MTL2 locus, depending on the class. The expression pattern in each class, therefore, is similar to that observed in S. cerevisiae, which harbors two silent cassette loci, HMR and HML, and the expression locus MAT. High-frequency phenotypic switching between core phenotypes in an alpha-expressing, but not in an a-expressing, strain modulated the level of MTL expression, suggesting a possible relationship between core phenotypic switching and mating.     

The structure of transposable yeast mating type loci

A recombinant plasmid containing a MAT alpha mating type locus of Saccharomyces cerevisiae has been isolated by its ability to complement a sterile mat alpha mutation. The plasmid hybridizes to restriction fragments containing both active mating type loci (MATa and MAT alpha) and both silent mating type loci (HMRa and HML alpha). All loci therefore have common sequences. Recombinant lambda clones of the locihave been isolated by plaque hybridization and their structures have been compared by a heteroduplex analysis. At its center, each locus contains one of two apparently nonhomologous sequences. Loci concerned with the alpha phenotype (MAT alpha and HML alpha) contain and 850 bp alpha-specific sequence, whereas loci concerned with the a phenotype (MATa and HMRa) contain a 700 bp a-specific sequence. The a- or alpha-specific sequences are surrounded by DNA sequences that are common to all loci. These homologous sequences extend for 230 bp on the left and 700 bp on the right. They appear to be unrelated to each other. Surprisingly, HML alpha and HMRa differ in their extent of homology to MATa and MAT alpha outside the above regions. HMRa lacks an extensive (700 bp) DNA sequence to the right of the large right-hand homologous region, and possibly also a small (90 bp) sequence to the left of the small left-hand homologous region, both of which are present at HML alpha, MATa and MAT alpha. Hybridization studies have shown that the 700 bp sequence is present at HMLa but absent at HMR alpha alleles. It is therefore characteristic of HML, irrespective of whether it contains a- or alpha-specific sequences. The results imply that mating type interconversion is effected by transposition of DNA sequences from HML or HMR to MAT, as predicted by the controlling element model of Oshima and Takano (1971) and the Cassette model of Hicks, Strathern and Herskowitz (1977).     

Bayesian mapping of quantitative trait loci under complicated mating designs

Quantitative trait loci (QTL) are easily studied in a biallelic system. Such a system requires the cross of two inbred lines presumably fixed for alternative alleles of the QTL. However, development of inbred lines can be time consuming and cost ineffective for species with long generation intervals and severe inbreeding depression. In addition, restriction of the investigation to a biallelic system can sometimes be misleading because many potentially important allelic interactions do not have a chance to express and thus fail to be detected. A complicated mating design involving multiple alleles mimics the actual breeding system. However, it is difficult to develop the statistical model and algorithm using the classical maximum-likelihood method. In this study, we investigate the application of a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to QTL mapping under arbitrarily complicated mating designs. We develop the method under a mixed-model framework where the genetic values of founder alleles are treated as random and the nongenetic effects are treated as fixed. With the MCMC algorithm, we first draw the gene flows from the founders to the descendants for each QTL and then draw samples of the genetic parameters. Finally, we are able to simultaneously infer the posterior distribution of the number, the additive and dominance variances, and the chromosomal locations of all identified QTL.     

The coupled variability of quantitative and qualitative traits: a single-locus 3-allele model

Statistics for estimation of additive and non-additive effects of marker gene on quantitative trait are developed from the mad-model of a quantitative trait for three-allelic codominant marker locus. All they may be obtained directly from population data, without any hybridological experiments.     

Gamete frequencies at two sex-linked loci in random mating age-structured populations

A study is made of the change with time of frequencies of gametic types with one or two sex-linked loci in an infinite random mating age-structured population. Recurrence equations for these gamete frequencies are derived under the assumptions that all matings of adults are equally fertile and the number of matings at any time is proportional to the number of mature females at that time. These generalize others in the literature. It is shown that gamete frequencies approach their limiting values at geometric rates in the long run. This implies that the asymptotic behavior of the gamete frequencies is like what it is in populations with discrete generations if the unit of time is replaced by an appropriately chosen generation interval. With either one locus or two loci, the generation interval is bounded below by an analogous measure from standard demographic theory. This result also holds when there are two autosomal loci. In numerical examples from both this paper and a previous one by Pollak and Callanan, the lower bound is a good estimate of the generation interval.     

Some multiallele partial assortative mating systems for a polygamous species

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA 74, 3476–3479), Wilbur et al. (1978, Evolution 32, 264–270), and Singh and Zouros (1978, Evolution 32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

Genetic and strategic models for the evolution of mating systems

Male and female fitnesses in the Shaw-Mohler equation are partitioned into components which putatively determine mating systems. The resultant genetic models provide criteria for evolutionary stable population states and yield strategic models based on maximization principles and fitness sets.     

Tests for association of gene frequencies at several loci in random mating diploid populations.

Methods are outlined for analyzing data on genotype frequencies at several codominant loci in random mating diploid populations. Maximum likelihood (ML) methods are given for estimating chromosomal frequencies. Using these, a succession of models of assumed independence of gene frequency are fitted. These are based on those used in multi-dimensional contigency tables, and tests for association (linkage disequilibrium), made using likelihood ratios. The methods are illustrated with an example.     

An implication about human mating systems.

Parent-offspring conflict, as put forth by R. L. Trivers, should be amended to exclude sequentially born offspring whose future siblings are expected to be full-sibs. The cost/benefit parameters set forth by Trivers for full-sibs should instead be applied to half-sibs. Accordingly, one should suspect that a diploid species which gives evidence of parent-offspring conflict does not have a mating system that insures a high probability of full-sibship among the offspring of the parent in question.