TY - JOUR
AB - All species are restricted in their distribution. Currently, ecological models can only explain such limits if patches vary in quality, leading to asymmetrical dispersal, or if genetic variation is too low at the margins for adaptation. However, population genetic models suggest that the increase in genetic variance resulting from dispersal should allow adaptation to almost any ecological gradient. Clearly therefore, these models miss something that prevents evolution in natural populations. We developed an individual-based simulation to explore stochastic effects in these models. At high carrying capacities, our simulations largely agree with deterministic predictions. However, when carrying capacity is low, the population fails to establish for a wide range of parameter values where adaptation was expected from previous models. Stochastic or transient effects appear critical around the boundaries in parameter space between simulation behaviours. Dispersal, gradient steepness, and population density emerge as key factors determining adaptation on an ecological gradient.
AU - Bridle, Jon
AU - Polechova, Jitka
AU - Kawata, Masakado
AU - Butlin, Roger
ID - 4134
IS - 4
JF - Ecology Letters
TI - Why is adaptation prevented at ecological margins? New insights from individual-based simulations
VL - 13
ER -
TY - JOUR
AB - We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large scale extinction-recolonisation events. The lineages ancestral to a sample from a population evolving according to this model can be described in terms of a spatial version of the Lambda-coalescent. Using a technique of Evans (1997), we prove existence and uniqueness in law for the model. We then investigate the asymptotic behaviour of the genealogy of a finite number of individuals sampled uniformly at random (or more generally `far enough apart') from a two-dimensional torus of sidelength L as L tends to infinity. Under appropriate conditions (and on a suitable timescale) we can obtain as limiting genealogical processes a Kingman coalescent, a more general Lambda-coalescent or a system of coalescing Brownian motions (with a non-local coalescence mechanism).
AU - Barton, Nicholas H
AU - Etheridge, Alison
AU - Véber, Amandine
ID - 4243
IS - 7
JF - Electronic Journal of Probability
TI - A new model for evolution in a spatial continuum
VL - 15
ER -
TY - JOUR
AB - Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneficial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a “fitness valley” to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest fitness valley, in which an adaptation requires one mutation at each of two loci to provide a fitness benefit. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We find that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when the recombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valley-crossing time by up to several orders of magnitude relative to that in an asexual population.
AU - Weissman, Daniel
AU - Feldman, Marcus
AU - Fisher, Daniel
ID - 3303
IS - 4
JF - Genetics
TI - The rate of fitness-valley crossing in sexual populations
VL - 186
ER -
TY - JOUR
AB - We investigated temporal changes in hybridization and introgression between native red deer (Cervus elaphus) and invasive Japanese sika (Cervus nippon) on the Kintyre Peninsula, Scotland, over 15 years, through analysis of 1513 samples of deer at 20 microsatellite loci and a mtDNA marker. We found no evidence that either the proportion of recent hybrids, or the levels of introgression had changed over the study period. Nevertheless, in one population where the two species have been in contact since ∼1970, 44% of individuals sampled during the study were hybrids. This suggests that hybridization between these species can proceed fairly rapidly. By analysing the number of alleles that have introgressed from polymorphic red deer into the genetically homogenous sika population, we reconstructed the haplotypes of red deer alleles introduced by backcrossing. Five separate hybridization events could account for all the recently hybridized sika-like individuals found across a large section of the Peninsula. Although we demonstrate that low rates of F1 hybridization can lead to substantial introgression, the progress of hybridization and introgression appears to be unpredictable over the short timescales.
AU - Senn, Helen
AU - Goodman, Simon
AU - Swanson, Graeme
AU - Barton, Nicholas H
AU - Pemberton, Josephine
ID - 3604
IS - 5
JF - Molecular Ecology
TI - Investigating temporal changes in hybridisation and introgression between invasive sika (Cervus nippon) and native red deer (Cervus elaphus) on the Kintyre Peninsula, Scotland
VL - 19
ER -
TY - JOUR
AB - 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.
AU - Barton, Nicholas H
AU - Coe, Jason
ID - 3775
IS - 2
JF - Journal of Theoretical Biology
TI - On the application of statistical physics to evolutionary biology
VL - 259
ER -
TY - JOUR
AB - 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.
AU - Davison, Angus
AU - Barton, Nicholas H
AU - Clarke, Bryan
ID - 3780
IS - 8
JF - Journal of Evolutionary Biology
TI - 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
VL - 22
ER -
TY - JOUR
AB - 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.
AU - Polechova, Jitka
AU - Barton, Nicholas H
AU - Marion, Glenn
ID - 4136
IS - 5
JF - American Naturalist
TI - Species' range: Adaptation in space and time
VL - 174
ER -
TY - JOUR
AB - 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.
AU - Barton, Nicholas H
AU - De Vladar, Harold
ID - 4231
IS - 3
JF - Genetics
TI - Statistical mechanics and the evolution of polygenic quantitative traits
VL - 181
ER -
TY - JOUR
AB - 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.
AU - Barton, Nicholas H
AU - De Cara, Maria
ID - 4242
IS - 5
JF - Evolution; International Journal of Organic Evolution
TI - The evolution of strong reproductive isolation
VL - 63
ER -
TY - CHAP
AB - 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.
AU - Barton, Nicholas H
ID - 3675
T2 - Cold Spring Harbor Symposia on Quantitative Biology
TI - Why sex and recombination?
VL - 74
ER -
TY - JOUR
AU - Barton, Nicholas H
ID - 517
IS - 5-6
JF - Genetical Research
TI - Identity and coalescence in structured populations: A commentary on 'Inbreeding coefficients and coalescence times' by Montgomery Slatkin
VL - 89
ER -