@article{3375,
abstract = {By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as five loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.},
author = {de Vladar, Harold and Barton, Nicholas H},
journal = {Journal of the Royal Society Interface},
number = {58},
pages = {720 -- 739},
publisher = {Royal Society of London},
title = {{The statistical mechanics of a polygenic character under stabilizing selection mutation and drift}},
doi = {10.1098/rsif.2010.0438},
volume = {8},
year = {2011},
}
@article{3380,
abstract = {Linkage between markers and genes that affect a phenotype of interest may be determined by examining differences in marker allele frequency in the extreme progeny of a cross between two inbred lines. This strategy is usually employed when pooling is used to reduce genotyping costs. When the cross progeny are asexual, the extreme progeny may be selected by multiple generations of asexual reproduction and selection. We analyse this method of measuring phenotype in asexual progeny and examine the changes in marker allele frequency due to selection over many generations. Stochasticity in marker frequency in the selected population arises due to the finite initial population size. We derive the distribution of marker frequency as a result of selection at a single major locus, and show that in order to avoid spurious changes in marker allele frequency in the selected population, the initial population size should be in the low to mid hundreds.},
author = {Logeswaran, Sayanthan and Barton, Nicholas H},
journal = {Genetical Research},
number = {3},
pages = {221 -- 232},
publisher = {Cambridge University Press},
title = {{Mapping Mendelian traits in asexual progeny using changes in marker allele frequency}},
doi = {10.1017/S0016672311000115},
volume = {93},
year = {2011},
}
@article{3390,
abstract = {What determines the genetic contribution that an individual makes to future generations? With biparental reproduction, each individual leaves a 'pedigree' of descendants, determined by the biparental relationships in the population. The pedigree of an individual constrains the lines of descent of each of its genes. An individual's reproductive value is the expected number of copies of each of its genes that is passed on to distant generations conditional on its pedigree. For the simplest model of biparental reproduction analogous to the Wright-Fisher model, an individual's reproductive value is determined within ~10 generations, independent of population size. Partial selfing and subdivision do not greatly slow this convergence. Our central result is that the probability that a gene will survive is proportional to the reproductive value of the individual that carries it, and that conditional on survival, after a few tens of generations, the distribution of the number of surviving copies is the same for all individuals, whatever their reproductive value. These results can be generalized to the joint distribution of surviving blocks of ancestral genome. Selection on unlinked loci in the genetic background may greatly increase the variance in reproductive value, but the above results nevertheless still hold. The almost linear relationship between survival probability and reproductive value also holds for weakly favored alleles. Thus, the influence of the complex pedigree of descendants on an individual's genetic contribution to the population can be summarized through a single number: its reproductive value.},
author = {Barton, Nicholas H and Etheridge, Alison},
journal = {Genetics},
number = {4},
pages = {953 -- 973},
publisher = {Genetics Society of America},
title = {{The relation between reproductive value and genetic contribution}},
doi = {10.1534/genetics.111.127555},
volume = {188},
year = {2011},
}
@article{3391,
abstract = {Evolutionary biology shares many concepts with statistical physics: both deal with populations, whether of molecules or organisms, and both seek to simplify evolution in very many dimensions. Often, methodologies have undergone parallel and independent development, as with stochastic methods in population genetics. Here, we discuss aspects of population genetics that have embraced methods from physics: non-equilibrium statistical mechanics, travelling waves and Monte-Carlo methods, among others, have been used to study polygenic evolution, rates of adaptation and range expansions. These applications indicate that evolutionary biology can further benefit from interactions with other areas of statistical physics; for example, by following the distribution of paths taken by a population through time},
author = {de Vladar, Harold and Barton, Nicholas H},
journal = {Trends in Ecology and Evolution},
number = {8},
pages = {424 -- 432},
publisher = {Cell Press},
title = {{The contribution of statistical physics to evolutionary biology}},
doi = {10.1016/j.tree.2011.04.002},
volume = {26},
year = {2011},
}
@article{3393,
abstract = {Unlike unconditionally advantageous “Fisherian” variants that tend to spread throughout a species range once introduced anywhere, “bistable” variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or “engineered underdominance” to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications.},
author = {Barton, Nicholas H and Turelli, Michael},
journal = {American Naturalist},
number = {3},
pages = {E48 -- E75},
publisher = {University of Chicago Press},
title = {{Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects}},
doi = {10.1086/661246},
volume = {178},
year = {2011},
}