@article{4231,
abstract = {The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.},
author = {Barton, Nicholas H and De Vladar, Harold},
journal = {Genetics},
number = {3},
pages = {997 -- 1011},
publisher = {Genetics Society of America},
title = {{Statistical mechanics and the evolution of polygenic quantitative traits}},
doi = {10.1534/genetics.108.099309},
volume = {181},
year = {2009},
}
@article{4136,
abstract = {Populations living in a spatially and temporally changing environment can adapt to the changing optimum and/or migrate toward favorable habitats. Here we extend previous analyses with a static optimum to allow the environment to vary in time as well as in space. The model follows both population dynamics and the trait mean under stabilizing selection, and the outcomes can be understood by comparing the loads due to genetic variance, dispersal, and temporal change. With fixed genetic variance, we obtain two regimes: (1) adaptation that is uniform along the environmental gradient and that responds to the moving optimum as expected for panmictic populations and when the spatial gradient is sufficiently steep, and (2) a population with limited range that adapts more slowly than the environmental optimum changes in both time and space; the population therefore becomes locally extinct and migrates toward suitable habitat. We also use a population‐genetic model with many loci to allow genetic variance to evolve, and we show that the only solution now has uniform adaptation.},
author = {Polechova, Jitka and Barton, Nicholas H and Marion, Glenn},
journal = {American Naturalist},
number = {5},
pages = {E186 -- E204},
publisher = {University of Chicago Press},
title = {{Species' range: Adaptation in space and time}},
doi = {10.1086/605958},
volume = {174},
year = {2009},
}
@article{3780,
abstract = {Why are sinistral snails so rare? Two main hypotheses are that selection acts against the establishment of new coiling morphs, because dextral and sinistral snails have trouble mating, or else a developmental constraint prevents the establishment of sinistrals. We therefore used an isolate of the snail Lymnaea stagnalis, in which sinistrals are rare, and populations of Partula suturalis, in which sinistrals are common, as well as a mathematical model, to understand the circumstances by which new morphs evolve. The main finding is that the sinistral genotype is associated with reduced egg viability in L. stagnalis, but in P. suturalis individuals of sinistral and dextral genotype appear equally fecund, implying a lack of a constraint. As positive frequency-dependent selection against the rare chiral morph in P. suturalis also operates over a narrow range (< 3%), the results suggest a model for chiral evolution in snails in which weak positive frequency-dependent selection may be overcome by a negative frequency-dependent selection, such as reproductive character displacement. In snails, there is not always a developmental constraint. As the direction of cleavage, and thus the directional asymmetry of the entire body, does not generally vary in other Spiralia (annelids, echiurans, vestimentiferans, sipunculids and nemerteans), it remains an open question as to whether this is because of a constraint and/or because most taxa do not have a conspicuous external asymmetry (like a shell) upon which selection can act.},
author = {Davison, Angus and Barton, Nicholas H and Clarke, Bryan},
journal = {Journal of Evolutionary Biology},
number = {8},
pages = {1624 -- 1635},
publisher = {Wiley},
title = {{The effect of chirality phenotype and genotype on the fecundity and viability of Partula suturalis and Lymnaea stagnalis: Implications for the evolution of sinistral snails}},
doi = {10.1111/j.1420-9101.2009.01770.x},
volume = {22},
year = {2009},
}
@article{517,
author = {Barton, Nicholas H},
journal = {Genetical Research},
number = {5-6},
pages = {475 -- 477},
publisher = {Cambridge University Press},
title = {{Identity and coalescence in structured populations: A commentary on 'Inbreeding coefficients and coalescence times' by Montgomery Slatkin}},
doi = {10.1017/S0016672308009683},
volume = {89},
year = {2008},
}