Sam Karlin and multi-locus population genetics

Between 1967 and 1982, Sam Karlin made fundamental contributions to many areas of deterministic population genetic theory. This remembrance focuses on his work in multi-locus population genetics, primarily on the interaction between genotypic selection and the rate of recombination.     

Expectations of means and genetic variances in backcross populations

Summary The genetic variance among F₂-derived lines of backcrosses (BC_gF₂-derived lines) depends on the backcross generation (g), the number of F₁ plants crossed and selfed in generations 1 through g, and the number of BC_gF₂-derived lines evaluated. Additive genetic variance decreases linearly with backcrossing when one BCF₁ plant per generation is crossed and selfed. The relationship is curvilinear if more than one BCF₁ plant is used; as the number of BCF₁ plants increases, additive genetic variance among BC₁F₂-derived lines approaches that among BC₀F₂-derived lines. The effect of population size on genetic variance is due both to fixation of alleles in previous generations and to sampling of genotypes in the population being evaluated. Dominance and repulsion linkage can cause small increases in genetic variance from BC₀ to BC₁.Joint contribution of USDA-ARS and Journal Paper No. J-11095 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2471     

Diffusion approximations of the two-locus Wright-Fisher model

Diffusion approximations are established for the multiallelic, two-locus Wright-Fisher model for mutation, selection, and random genetic drift in a finite, panmictic, monoecious, diploid population. All four combinations of weak or strong selection and tight or loose linkage are treated, though the proof in the case of strong selection and loose linkage is incomplete. Under certain conditions, explicit formulas are obtained for the stationary distributions of the two diffusions with loose linkage.Supported in part by NSF Grant DMS-8704369Supported in part by NSF Grant BSR-8512844     

Strong evolutionary conservation of broadly expressed protein isoforms in the troponin I gene family and other vertebrate gene families

The sequences of the adenylate kinase gene (adk) and the RecA gene (recA) were determined from the same isolates ofNeisseria gonorrhoeae, N. meningitidis, N. lactamica, N. polysaccharea, N. cinerea, N. mucosa, N. pharyngis var.flava, N. flavescens, andN. animalis. The patterns of sequence divergence observed atadk andrecA were very different. Dendrograms constructed from therecA data using two different algorithms were statistically robust and were congruent with each other and with the relationships between the species previously proposed using other data. In contrast, the dendrograms derived from theadk data were noncongruent with each other, and with those from therecA data, and were statistically poorly supported. These results, along with the uniform distribution of pairwise sequence divergences between the species atadk, suggest there has been a history of interspecies recombination within theadk gene of the humanNeisseria species which has obscured the phylogenetic relationships between the species. This view was supported by Sawyer's runs test, and the Index of Association (I_A) between codons, which provided significant evidence for interspecies recombination between theadk genes from the humanNeisseria species, but no evidence of interspecies recombination between therecA sequences.