Substitution Processes in Molecular Evolution. III. Deleterious Alleles

The substitution processes for various models of deleterious alleles are examined using computer simulations and mathematical analyses. Most of the work focuses on the house-of-cards model, which is a popular model of deleterious allele evolution. The rate of substitution is shown to be a concave function of the strength of selection as measured by α = 2Nσ, where N is the population size and σ is the standard deviation of fitness. For α<1, the house-of-cards model is essentially a neutral model; for α>4, the model ceases to evolve. The stagnation for large α may be understood by appealing to the theory of records. The house-of-cards model evolves to a state where the vast majority of all mutations are deleterious, but precisely one-half of those mutations that fix are deleterious (the other half are advantageous). Thus, the model is not a model of exclusively deleterious evolution as is frequently claimed. It is argued that there are no biologically reasonable models of molecular evolution where the vast majority of all substitutions are deleterious. Other models examined include the exponential and gamma shift models, the Hartl-Dykhuizen-Dean (HDD) model, and the optimum model. Of all those examined, only the optimum and HDD models appear to be reasonable candidates for silent evolution. None of the models are viewed as good candidates for protein evolution, as none are both biologically reasonable and exhibit the variability in substitutions commonly observed in protein sequence data.     

Recessive Alleles Found at R and C Loci in Maize Stocks Showing Aberrant Ratio at the A Locus

Corn stocks showing virus-induced aberrant ratio (AR) at the "A" locus were found to have recessive alleles at the R and/or C loci. Since by the known pedigree these loci should be homozygous dominant, the results suggest an inactivation of maize genes by a mechanism as yet unknown. The presence of recessive alleles at these additional loci can explain the segregation ratios obtained in these particular stocks.     

Counting Alleles with Rarefaction: Private Alleles and Hierarchical Sampling Designs

The number of alleles (allelic richness) in a population is a fundamental measure of genetic variation, and a useful statistic for identifying populations for conservation. Estimating allelic richness is complicated by the effects of sample size: large samples are expected to have more alleles. Rarefaction solves this problem. This communication extends the rarefaction procedure to count private alleles and to accommodate hierarchical sampling designs.     

The Frequencies of Alleles of Single Nucleotide Substitutions in the CCK and CCK2R Genes in Some Russian Cattle Breeds

Russian Journal of Genetics - Allele frequencies of three substitutions in the CCK (rs42891945 and rs42891946) and CCKBR (rs42670352) genes were identified in three Russian cattle breeds: Holstein...     

Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.     

Evolutionary Dynamics of Sporophytic Self-Incompatibility Alleles in Plants

The stationary frequency distribution and allelic dynamics in finite populations are analyzed through stochastic simulations in three models of single-locus, multi-allelic sporophytic self-incompatibility. The models differ in the dominance relationships among alleles. In one model, alleles act codominantly in both pollen and style (SSIcod), in the second, alleles form a dominance hierarchy in pollen and style (SSIdom). In the third model, alleles interact codominantly in the style and form a dominance hierarchy in the pollen (SSIdomcod). The SSIcod model behaves similarly to the model of gametophytic self-incompatibility, but the selection intensity is stronger. With dominance, dominant alleles invade the population more easily than recessive alleles and have a lower frequency at equilibrium. In the SSIdom model, recessive alleles have both a higher allele frequency and higher expected life span. In the SSIdomcod model, however, loss due to drift occurs more easily for pollen-recessive than for pollen-dominant alleles, and therefore, dominant alleles have a higher expected life span than the more recessive alleles. The process of allelic turnover in the SSIdomcod and SSIdom models is closely approximated by a random walk on a dominance ladder. Implications of the results for experimental studies of sporophytic self-incompatibility in natural populations are discussed.