The competition between simple and complex evolutionary trajectories in asexual populations
Ian E. Ochs, Michael M. Desai
Comments: 8 pages, 3 figures
Subjects: Populations and Evolution (q-bio.PE)
On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial “uphill” mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the evolutionary process determine the probability that evolution will take any specific path among a variety of competing possible trajectories. Understanding this evolutionary choice is essential if we are to understand the outcomes and predictability of adaptation on rugged landscapes. We present a simple model to analyze the probability that evolution will eschew immediately uphill paths in favor of crossing fitness valleys or plateaus that lead to higher fitness but less accessible genotypes. We calculate how this probability depends on the population size, mutation rates, and relevant selection pressures, and compare our analytical results to Wright-Fisher simulations. We find that the probability of valley crossing depends nonmonotonically on population size: intermediate size populations are most likely to follow a “greedy” strategy of acquiring immediately beneficial mutations even if they lead to evolutionary dead ends, while larger and smaller populations are more likely to cross fitness valleys to reach distant advantageous genotypes. We explicitly identify the boundaries between these different regimes in terms of the relevant evolutionary parameters. Above a certain threshold population size, we show that the degree of evolutionary “foresight” depends only on a single simple combination of the relevant parameters.
The seed-bank coalescent
Jochen Blath, Adrián González Casanova, Noemi Kurt, Maite Wilke-Berenguer
(Submitted on 18 Nov 2014)
We identify a new natural coalescent structure, the seed-bank coalescent, which describes the gene genealogy of populations under the influence of a strong seed-bank effect, where `dormant forms’ of individuals (such as seeds or spores) may jump a significant number of generations before joining the `active’ population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright-Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size N. This extends earlier results of Kaj, Krone and Lascaux (2001) who show that the genealogy of a Wright-Fisher model in the presence of a `weak’ seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent `does not come down from infinity’, and the time to the most recent common ancestor of a sample of size n grows like loglogn, which is the order also observed for the Bolthausen-Sznitman coalescent. This is in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.
A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments
Hannes Svardal, Claus Rueffler, Joachim Hermisson
Comments: Accepted for publication in Theoretical Population Biology
Subjects: Populations and Evolution (q-bio.PE)
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of invasion fitness and evolutionary branching, we derive a simple and transparent condition for the adaptive evolution and maintenance of genetic diversity. This condition relates the strength of selection within patches to expectations and variances in the environmental conditions across space and time. Our results unify, clarify, and extend a number of previous results on the evolution and maintenance of genetic variation under fluctuating selection. Individual-based simulations show that our results are independent of the details of the genetic architecture and on whether reproduction is clonal or sexual. The onset of increased genetic variance is predicted accurately also in small populations in which alleles can go extinct due to environmental stochasticity.
Recombination and peak jumping
(Submitted on 7 Nov 2014)
We find an advantage of recombination for a category of complex fitness landscapes. Recent studies of empirical fitness landscapes reveal complex gene interactions and multiple peaks, and recombination can be a powerful mechanism for escaping suboptimal peaks. However classical work on recombination largely ignores the effect of complex gene interactions. The advantage we find has no correspondence for 2-locus systems or for smooth landscapes. The effect is sometimes extreme, in the sense that shutting off recombination could result in that the organism fails to adapt. A standard question about recombination is if the mechanism tends to accelerate or decelerate adaptation. However, we argue that extreme effects may be more important than how the majority falls.
Ancestries of a Recombining Diploid Population,
R Sainudiin, B. Thatte and A. Veber, UCDMS Research Report 2014/3, 42 pages, 2014
We derive the exact one-step transition probabilities of the number of lineages
that are ancestral to a random sample from the current generation of a bi-parental
population that is evolving under the discrete Wright-Fisher model with n diploid
individuals. Our model allows for a per-generation recombination probability of
r. When r = 1, our model is equivalent to Chang’s model  for the karyotic
pedigree. When r = 0, our model is equivalent to Kingman’s discrete coalescent
model  for the cytoplasmic tree or sub-karyotic tree containing a DNA locus that
is free of intra-locus recombination. When 0 < r < 1 our model can be thought to
track a sub-karyotic ancestral graph containing a DNA sequence from an autosomal
chromosome that has an intra-locus recombination probability r. Thus, our family
of models indexed by r 2 [0; 1] connects Kingman's discrete coalescent to Chang's
pedigree in a continuous way as r goes from 0 to 1. For large populations, we
also study three properties of the r-specific ancestral process: the time Tn to a
most recent common ancestor (MRCA) of the population, the time Un at which all
individuals are either common ancestors to all present day individuals or ancestral
to none of them, and the fraction of individuals that are common ancestors at time
Un. These results generalize the three main results in . When we appropriately
rescale time and recombination probability by the population size, our model leads
to the continuous time Markov chain called the ancestral recombination graph of
Hudson  and Griffiths .
When is selection effective?
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
Mary Elizabeth Wahl, Andrew Wood Murray
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
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
Peter L. Ralph, Graham Coop
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
Jeffrey D. Jensen
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.