@inbook{3675,
  abstract     = {Sex and recombination have long been seen as adaptations that facilitate natural selection by generating favorable variations. If recombination is to aid selection, there must be negative linkage disequilibria—favorable alleles must be found together less often than expected by chance. These negative linkage disequilibria can be generated directly by selection, but this must involve negative epistasis of just the right strength, which is not expected, from either experiment or theory. Random drift provides a more general source of negative associations: Favorable mutations almost always arise on different genomes, and negative associations tend to persist, precisely because they shield variation from selection.

We can understand how recombination aids adaptation by determining the maximum possible rate of adaptation. With unlinked loci, this rate increases only logarithmically with the influx of favorable mutations. With a linear genome, a scaling argument shows that in a large population, the rate of adaptive substitution depends only on the expected rate in the absence of interference, divided by the total rate of recombination. A two-locus approximation predicts an upper bound on the rate of substitution, proportional to recombination rate.

If associations between linked loci do impede adaptation, there can be substantial selection for modifiers that increase recombination. Whether this can account for the maintenance of high rates of sex and recombination depends on the extent of selection. It is clear that the rate of species-wide substitutions is typically far too low to generate appreciable selection for recombination. However, local sweeps within a subdivided population may be effective.},
  author       = {Barton, Nicholas H},
  booktitle    = {Cold Spring Harbor Symposia on Quantitative Biology},
  pages        = {187 -- 195},
  publisher    = {Cold Spring Harbor Laboratory Press},
  title        = {{Why sex and recombination?}},
  doi          = {10.1101/sqb.2009.74.030},
  volume       = {74},
  year         = {2009},
}

@article{3775,
  abstract     = {There is a close analogy between statistical thermodynamics and the evolution of allele frequencies under mutation, selection and random drift. Wright's formula for the stationary distribution of allele frequencies is analogous to the Boltzmann distribution in statistical physics. Population size, 2N, plays the role of the inverse temperature, 1/kT, and determines the magnitude of random fluctuations. Log mean fitness, View the MathML source, tends to increase under selection, and is analogous to a (negative) energy; a potential function, U, increases under mutation in a similar way. An entropy, SH, can be defined which measures the deviation from the distribution of allele frequencies expected under random drift alone; the sum View the MathML source gives a free fitness that increases as the population evolves towards its stationary distribution. Usually, we observe the distribution of a few quantitative traits that depend on the frequencies of very many alleles. The mean and variance of such traits are analogous to observable quantities in statistical thermodynamics. Thus, we can define an entropy, SΩ, which measures the volume of allele frequency space that is consistent with the observed trait distribution. The stationary distribution of the traits is View the MathML source; this applies with arbitrary epistasis and dominance. The entropies SΩ, SH are distinct, but converge when there are so many alleles that traits fluctuate close to their expectations. Populations tend to evolve towards states that can be realised in many ways (i.e., large SΩ), which may lead to a substantial drop below the adaptive peak; we illustrate this point with a simple model of genetic redundancy. This analogy with statistical thermodynamics brings together previous ideas in a general framework, and justifies a maximum entropy approximation to the dynamics of quantitative traits.},
  author       = {Barton, Nicholas H and Coe, Jason},
  journal      = {Journal of Theoretical Biology},
  number       = {2},
  pages        = {317 -- 324},
  publisher    = {Elsevier},
  title        = {{On the application of statistical physics to evolutionary biology}},
  doi          = {10.1016/j.jtbi.2009.03.019},
  volume       = {259},
  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{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{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{4242,
  abstract     = {Felsenstein distinguished two ways by which selection can directly strengthen isolation. First, a modifier that strengthens prezygotic isolation can be favored everywhere. This fits with the traditional view of reinforcement as an adaptation to reduce deleterious hybridization by strengthening assortative mating. Second, selection can favor association between different incompatibilities, despite recombination. We generalize this “two allele” model to follow associations among any number of incompatibilities, which may include both assortment and hybrid inviability. Our key argument is that this process, of coupling between incompatibilities, may be quite different from the usual view of reinforcement: strong isolation can evolve through the coupling of any kind of incompatibility, whether prezygotic or postzygotic. Single locus incompatibilities become coupled because associations between them increase the variance in compatibility, which in turn increases mean fitness if there is positive epistasis. Multiple incompatibilities, each maintained by epistasis, can become coupled in the same way. In contrast, a single-locus incompatibility can become coupled with loci that reduce the viability of haploid hybrids because this reduces harmful recombination. We obtain simple approximations for the limits of tight linkage, and strong assortment, and show how assortment alleles can invade through associations with other components of reproductive isolation.},
  author       = {Barton, Nicholas H and De Cara, Maria},
  journal      = {Evolution; International Journal of Organic Evolution},
  number       = {5},
  pages        = {1171 -- 1190},
  publisher    = {Wiley},
  title        = {{The evolution of strong reproductive isolation}},
  doi          = {10.1111/j.1558-5646.2009.00622.x},
  volume       = {63},
  year         = {2009},
}

@article{517,
  author       = {Barton, Nicholas H},
  journal      = {Genetics 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},
}