When is selection effective?

When is selection effective?
Simon Gravel
doi: http://dx.doi.org/10.1101/010934

Deleterious alleles are more likely to reach high frequency in small populations because of chance fluctuations in allele frequency. This may lead, over time, to reduced average fitness in the population. In that sense, selection is more `effective’ in larger populations. Many recent studies have considered whether the different demographic histories across human populations have resulted in differences in the number, distribution, and severity of deleterious variants, leading to an animated debate. This article seeks to clarify some terms of the debate by identifying differences in definitions and assumptions used in these studies and providing an intuitive explanation for the observed similarity in genetic load among populations. The intuition is verified through analytical and numerical calculations. First, even though rare variants contribute to load, they contribute little to load differences across populations. Second, the accumulation of non-recessive load after a bottleneck is slow for the weakly deleterious variants that contribute much of the long-term variation among populations. Whereas a bottleneck increases drift instantly, it affects selection only indirectly, so that fitness differences can keep accumulating long after a bottleneck is over. Third, drift and selection tend to have opposite effects on load differentiation under dominance models. Because of this competition, load differences across populations depend sensitively and intricately on past demographic events and on the distribution of fitness effects. A given bottleneck can lead to increased or decreased load for variants with identical fitness effects, depending on the subsequent population history. Because of this sensitivity, both classical population genetic intuition and detailed simulations are required to understand differences in load across populations.

Multicellularity makes cellular differentiation evolutionarily stable

Multicellularity makes cellular differentiation evolutionarily stable
Mary Elizabeth Wahl, Andrew Wood Murray
doi: http://dx.doi.org/10.1101/010728

Multicellularity and cellular differentiation, two traits shared by all developing organisms, have evolved independently in many taxa and are often found together in extant species. Differentiation, which we define as a permanent and heritable change in gene expression, produces somatic cells from a totipotent germ line. Though somatic cells may divide indefinitely, they cannot reproduce the complete organism and are thus effectively sterile on long timescales. How has differentiation evolved, repeatedly, despite the fitness costs of producing non-reproductive cells? The absence of extant unicellular differentiating species, as well as the persistence of undifferentiated multicellular groups among the volvocine algae and cyanobacteria, have fueled speculation that multicellularity must arise before differentiation can evolve. We propose that unicellular differentiating populations are intrinsically susceptible to invasion by non-differentiating mutants (“cheats”), whose spread eventually drives differentiating lineages extinct. To directly compare organisms which differ only in the presence or absence of these traits, we engineered both multicellularity and cellular differentiation in budding yeast, including such essential features as irreversible conversion, reproductive division of labor, and clonal multicellularity. We find that non-differentiating mutants overtake unicellular populations but are outcompeted effectively by multicellular differentiating strains, suggesting that multicellularity evolved before differentiation.

On the role of epistasis in adaptation

On the role of epistasis in adaptation
David M. McCandlish, Jakub Otwinowski, Joshua B. Plotkin
Subjects: Populations and Evolution (q-bio.PE)

Although the role of epistasis in evolution has received considerable attention from experimentalists and theorists alike, it is unknown which aspects of adaptation are in fact sensitive to epistasis. Here, we address this question by comparing the evolutionary dynamics on all finite epistatic landscapes versus all finite non-epistatic landscapes, under weak mutation. We first analyze the fitness trajectory — that is, the time course of the expected fitness of a population. We show that for any epistatic fitness landscape and choice of starting genotype, there always exists a non-epistatic fitness landscape and starting genotype that produces the exact same fitness trajectory. Thus, surprisingly, the presence or absence of epistasis is irrelevant to the first-order dynamics of adaptation. On the other hand, we show that the time evolution of the variance in fitness across replicate populations can be sensitive to epistasis: some epistatic fitness landscapes produce variance trajectories that cannot be produced by any non-epistatic landscape. Likewise, the mean substitution trajectory — that is, the expected number of mutations that fix over time — is also sensitive to epistasis. These results on identifiability have direct implications for efforts to infer epistasis from the types of data often measured in experimental populations.

The role of standing variation in geographic convergent adaptation

The role of standing variation in geographic convergent adaptation
Peter L. Ralph, Graham Coop
doi: http://dx.doi.org/10.1101/009803

The extent to which populations experiencing shared selective pressures adapt through a shared genetic response is relevant to many questions in evolutionary biology. In a number of well studied traits and species, it appears that convergent evolution within species is common. In this paper, we explore how standing, deleterious genetic variation contributes to convergent genetic responses in a geographically spread population, extending our previous work on the topic. Geographically limited dispersal slows the spread of each selected allele, hence allowing other alleles — newly arisen mutants or present as standing variation — to spread before any one comes to dominate the population. When such alleles meet, their progress is substantially slowed — if the alleles are selectively equivalent, they mix slowly, dividing the species range into a random tessellation, which can be well understood by analogy to a Poisson process model of crystallization. In this framework, we derive the geographic scale over which a typical allele is expected to dominate, the time it takes the species to adapt as a whole, and the proportion of adaptive alleles that arise from standing variation. Finally, we explore how negative pleiotropic effects of alleles before an environment change can bias the subset of alleles that get to contribute to a species adaptive response. We apply the results to the many geographically localized G6PD deficiency alleles thought to confer resistance to malaria, whose large mutational target size and deleterious effects make them likely candidates to have been present as deleterious standing variation. We find the numbers and geographic spread of these alleles matches our predictions reasonably well, which suggest that these arose both from standing variation and new mutations since the advent of malaria. Our results suggest that much of adaptation may be geographically local even when selection pressures are wide-spread. We close by discussing the implications of these results for arguments of species coherence and the nature of divergence between species.

On the unfounded enthusiasm for soft selective sweeps

On the unfounded enthusiasm for soft selective sweeps
Jeffrey D. Jensen
doi: http://dx.doi.org/10.1101/009563

Underlying any understanding of the mode, tempo, and relative importance of the adaptive process in the evolution of natural populations is the notion of whether adaptation is mutation-limited. Two very different population genetic models have recently been proposed in which the rate of adaptation is not strongly limited by the rate at which newly arising beneficial mutations enter the population. This review discusses the theoretical underpinnings and requirements of these models, as well as the experimental insights on the parameters of relevance. Importantly, empirical and experimental evidence to date challenges the recent enthusiasm for invoking these models to explain observed patterns of variation in humans and Drosophila.

Biallelic Mutation-Drift Diffusion in the Limit of Small Scaled Mutation Rates

Biallelic Mutation-Drift Diffusion in the Limit of Small Scaled Mutation Rates

Claus Vogl
(Submitted on 8 Sep 2014)

The evolution of the allelic proportion x of a biallelic locus subject to the forces of mutation and drift is investigated in a diffusion model, assuming small scaled mutation rates. The overall scaled mutation rate is parametrized with θ=(μ1+μ0)N and the ratio of mutation rates with α=μ1/(μ1+μ0)=1−β. The equilibrium density of this process is beta with parameters αθ and βθ. Away from equilibrium, the transition density can be expanded into a series of modified Jacobi polynomials. If the scaled mutation rates are small, i.e., θ≪1, it may be assumed that polymorphism derives from mutations at the boundaries. A model, where the interior dynamics conform to the pure drift diffusion model and the mutations are entering from the boundaries is derived. In equilibrium, the density of the proportion of polymorphic alleles, \ie\ x within the polymorphic region [1/N,1−1/N], is αβθ(1x+11−x)=αβθx(1−x), while the mutation bias α influences the proportion of monomorphic alleles at 0 and 1. Analogous to the expansion with modified Jacobi polynomials, a series expansion of the transition density is derived, which is connected to Kimura’s well known solution of the pure drift model using Gegenbauer polynomials. Two temporal and two spatial regions are separated. The eigenvectors representing the spatial component within the polymorphic region depend neither on the on the scaled mutation rate θ nor on the mutation bias α. Therefore parameter changes, e.g., growing or shrinking populations or changes in the mutation bias, can be modeled relatively easily, without the change of the eigenfunctions necessary for the series expansion with Jacobi polynomials.

The general recombination equation in continuous time and its solution

The general recombination equation in continuous time and its solution

Ellen Baake, Michael Baake, Majid Salamat
(Submitted on 4 Sep 2014)

The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it to an equivalent finite-dimensional nonlinear problem, and solve the latter recursively for generic sets of parameters. We also briefly discuss the singular cases, and how to extend the solution to this situation.