@article{15358, abstract = {We consider how a population of N haploid individuals responds to directional selection on standing variation, with no new variation from recombination or mutation. Individuals have trait values z1,…,zN, which are drawn from a distribution ψ; the fitness of individual i is proportional to [Formula: see text] . For illustration, we consider the Laplace and Gaussian distributions, which are parametrised only by the variance V0, and show that for large N, there is a scaling limit which depends on a single parameter NV0. When selection is weak relative to drift (NV0≪1), the variance decreases exponentially at rate 1/N, and the expected ultimate gain in log fitness (scaled by V0), is just NV0, which is the same as Robertson's (1960) prediction for a sexual population. In contrast, when selection is strong relative to drift (NV0≫1), the ultimate gain can be found by approximating the establishment of alleles by a branching process in which each allele competes independently with the population mean and the fittest allele to establish is certain to fix. Then, if the probability of survival to time t∼1/V0 of an allele with value z is P(z), with mean P¯, the winning allele is the fittest of NP¯ survivors drawn from a distribution ψP/P¯. The expected ultimate change is ∼2log(1.15NV0) for a Gaussian distribution, and ∼-12log0.36NV0-log-log0.36NV0 for a Laplace distribution. This approach also predicts the variability of the process, and its dynamics; we show that in the strong selection regime, the expected genetic variance decreases as ∼t-3 at large times. We discuss how these results may be related to selection on standing variation that is spread along a linear chromosome.}, author = {Barton, Nicholas H and Sachdeva, Himani}, issn = {1096-0325}, journal = {Theoretical Population Biology}, pages = {129--137}, publisher = {Elsevier}, title = {{Limits to selection on standing variation in an asexual population}}, doi = {10.1016/j.tpb.2024.04.001}, volume = {157}, year = {2024}, } @article{3610, abstract = {For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111–2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.}, author = {Hill, William and Barton, Nicholas H and Turelli, Michael}, issn = {1096-0325}, journal = {Theoretical Population Biology}, number = {1}, pages = {56 -- 62}, publisher = {Academic Press}, title = {{Prediction of effects of genetic drift on variance components under a general model of epistasis}}, doi = {10.1016/j.tpb.2005.10.001}, volume = {70}, year = {2006}, } @article{3657, abstract = {Shifts between adaptive peaks, caused by sampling drift, are involved in both speciation and adaptation via Wright's “shiftingbalance.” We use techniques from statistical mechanics to calculate the rate of such transitions for apopulation in a single panmictic deme and for apopulation which is continuously distributed over one- and two-dimensional regions. This calculation applies in the limit where transitions are rare. Our results indicate that stochastic divergence is feasible despite free gene flow, provided that neighbourhood size is low enough. In two dimensions, the rate of transition depends primarily on neighbourhood size N and only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined by the local population structure, in contrast with the exponential dependence on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(− cNs)). Our calculations agree with simulations of a single deme and a one-dimensional population.}, author = {Rouhani, Shahin and Barton, Nicholas H}, issn = {1096-0325}, journal = {Theoretical Population Biology}, number = {3}, pages = {465 -- 492}, publisher = {Elsevier}, title = {{Speciation and the "shifting balance" in a continuous population}}, doi = {10.1016/0040-5809(87)90016-5}, volume = {31}, year = {1987}, } @article{3662, abstract = {The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the “homogeneous” approximation to this “exact” model, end effects are disregarded; in the “exchangeable” approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that (i) the exchangeable and homogeneous models are both qualitatively correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative conclusions, and (iii) the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.}, author = {Nagylaki, Thomas and Barton, Nicholas H}, issn = {1096-0325}, journal = {Theoretical Population Biology}, number = {3}, pages = {407 -- 437}, publisher = {Academic Press}, title = {{Intrachromosomal gene conversion, linkage, and the evolution of multigene families}}, doi = {10.1016/0040-5809(86)90017-1}, volume = {29}, year = {1986}, }