The identifiability of piecewise demographic models from the sample frequency spectrum
Anand Bhaskar, Yun S. Song
(Submitted on 19 Sep 2013)

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different demographic models can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this non-identifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant and piecewise-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the “folded” SFS, which is often used when there is ambiguity as to which allelic type is ancestral.

Universality and predictability in the evolution of molecular quantitative traits
Armita Nourmohammad, Torsten Held, Michael Lässig
(Submitted on 12 Sep 2013)

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. Here we discuss recent developments in the evolutionary theory of quantitative traits that reach beyond classical quantitative genetics. We focus on universal evolutionary characteristics: these are largely independent of a trait’s genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology.

A Survey on Migration-Selection Models in Population Genetics
Reinhard Bürger
(Submitted on 10 Sep 2013)

This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to the scale at which the environment changes, or if the habitat is fragmented. The general goal of such models is to study the influence of population subdivision and gene flow among subpopulations on the amount and pattern of genetic variation maintained. Only deterministic models are treated. Because space is discrete, they are formulated in terms of systems of nonlinear difference or differential equations. A central topic is the exploration of the equilibrium and stability structure under various assumptions on the patterns of selection and migration. Another important, closely related topic concerns conditions (necessary or sufficient) for fully polymorphic (internal) equilibria. First, the theory of one-locus models with two or multiple alleles is laid out. Then, mostly very recent, developments about multilocus models are presented. Finally, as an application, analysis and results of an explicit two-locus model emerging from speciation theory are highlighted.

The inevitability of unconditionally deleterious substitutions during adaptation
David M. McCandlish, Charles L. Epstein, Joshua B. Plotkin
(Submitted on 4 Sep 2013)

Studies on the genetics of adaptation typically neglect the possibility that a deleterious mutation might fix. Nonetheless, here we show that, in many regimes, the first substitution is most often deleterious, even when fitness is expected to increase in the long term. In particular, we prove that this phenomenon occurs under weak mutation for any house-of-cards model with an equilibrium distribution. We find that the same qualitative results hold under Fisher’s geometric model. We also provide a simple intuition for the surprising prevalence of unconditionally deleterious substitutions during early adaptation. Importantly, the phenomenon we describe occurs on fitness landscapes without any local maxima and is therefore distinct from “valley-crossing”. Our results imply that the common practice of ignoring deleterious substitutions leads to qualitatively incorrect predictions in many regimes. Our results also have implications for the substitution process at equilibrium and for the response to a sudden decrease in population size.

Evolutionary consequences of assortativeness in haploid genotypes
David M. Schneider, Ayana B. Martins, Eduardo do Carmo, Marcus A.M. de Aguiar
(Submitted on 3 Sep 2013)

We study the evolution of allele frequencies in a large population where random mating is violated in a particular way that is related to recent works on speciation. Specifically, we consider non-random encounters in haploid organisms described by biallelic genes at two loci and assume that individuals whose alleles differ at both loci are incompatible. We show that evolution under these conditions leads to the disappearance of one of the alleles and substantially reduces the diversity of the population. The allele that disappears, and the other allele frequencies at equilibrium, depend only on their initial values, and so does the time to equilibration. However, certain combinations of allele frequencies remain constant during the process, revealing the emergence of strong correlation between the two loci promoted by the epistatic mechanism of incompatibility. We determine the geometrical structure of the haplotype frequency space and solve the dynamical equations, obtaining a simple rule to determine equilibrium solution from the initial conditions. We show that our results are equivalent to selection against double heterozigotes for a population of diploid individuals and discuss the relevance of our findings to speciation.

On the sympatric evolution of coexistence by relative nonlinearity of competition
Florian Hartig, Tamara Münkemüller, Karin Johst, Ulf Dieckmann
(Submitted on 14 Aug 2013)

If two species show different nonlinear responses to a single shared resource, and if each species modifies resource dynamics such that it favors its competitor, they may stably coexist. While the mechanism behind this phenomenon, known as relative nonlinearity of competition, is well understood, less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using the adaptive dynamics framework as well as individual-based simulations to compare dynamic and evolutionary stability of communities coexisting through relative nonlinearity. Evolution operates on the species’ density compensation strategies, and a trade-off between growth at high versus low resource availability (population density) is assumed. We confirm previous findings that, irrespective of the particular model of density-dependence, there are usually broad ranges of coexistence between overcompensating and undercompensating density-compensation strategies. We show that most of these strategies, however, are not evolutionarily stable and will be outcompeted by a single compensatory strategy. Only very specific evolutionary trade-offs allow evolutionary stability of strategies that coexist through relative nonlinearity. As we find no reason why these particular trade-offs should be abundant in nature, we conclude that sympatric evolution of relative nonlinearity seems possible, but rather unlikely. We speculate that this may explain why relative nonlinearity has seldom been observed, although we note that a low probability of sympatric evolution does not exclude the possibility that this mechanism of coexistence might still frequently occur when species with different evolutionary histories meet in the same community. Our results highlight the need for combining ecological and evolutionary perspectives for understanding community assembly and biogeographical patterns.

How Population Growth Affects Linkage Disequilibrium
Alan R. Rogers
(Submitted on 8 Aug 2013)

Linkage disequilibrium (LD) is often summarized using the “LD curve,” which relates the LD between pairs of sites to the distance that separates them along the chromosome. This paper shows how the LD curve responds to changes in population size. An expansion of population size generates an LD curve that declines steeply, especially if that expansion has followed a bottleneck. A reduction in size generates an LD curve that is high but relatively flat. In European data, the curve is steep, suggesting a history of population expansion.
These conclusions emerge from the study of $\sigma_d^2$, a measure of LD that has never played a central role. It has been seen merely as an approximation to another measure, $r^2$. Yet $\sigma_d^2$ has different dynamical behavior and provides deeper time depth. Furthermore, it is easily estimated from data and can be predicted from population history using a fast, deterministic algorithm.

Effect of linkage on the equilibrium frequency of deleterious mutations
Sona John, Kavita Jain
(Submitted on 5 Aug 2013)

We study the evolution of an asexual population of binary sequences of finite length in which both deleterious and reverse mutations can occur. Such a model has been used to understand the prevalence of preferred codons due to selection, mutation and drift, and proposed as a possible mechanism for halting the irreversible degeneration of asexual population due to Muller’s ratchet. Using an analytical argument and numerical simulations, we study the dependence of the equilibrium fraction of deleterious mutations on various population genetic parameters. In contrast to the one-locus theory, where the fraction of disadvantageous mutations decreases exponentially fast with increasing population size, we find that in the multilocus model, it decreases to zero exponentially for very large populations but approaches a constant for smaller populations logarithmically. The weak dependence on the population size may explain the similar levels of codon bias seen in populations of different sizes.

Population subdivision with migration can facilitate evolution on rugged fitness landscapes
Anne-Florence Bitbol, David J. Schwab
(Submitted on 1 Aug 2013)

We show that subdivision of an asexual population into demes connected by migration significantly accelerates the crossing of fitness valleys and plateaus over a wide parameter range, both with respect to the non-subdivided population and with respect to a single deme. We predict the existence of a parameter range where valley or plateau crossing by the metapopulation is as fast as that of the fastest deme, and we verify this prediction using stochastic simulations. Finally, we extend our work to the case of a large population connected by migration to one or several smaller islands.