Limits to adaptation along environmental gradients

Limits to adaptation along environmental gradients
Jitka Polechová, Nick Barton
doi: http://dx.doi.org/10.1101/012690

Why do species not adapt to ever-wider ranges of conditions, gradually expanding their ecological niche? Theories of niche evolution typically omit spatial context, yet all species experience spatially variable conditions. Gene flow across environments has two conflicting effects on adaptation: while it increases genetic variation, which is a prerequisite for adaptation, gene flow may swamp adaptation to local conditions. We show that genetic drift can generate a sharp margin to a species’ range, by reducing genetic variance below the level needed for adaptation to spatially variable conditions. Dimensional arguments and separation of ecological and evolutionary time scales reveal a simple threshold that predicts when adaptation at the range margin fails. Two observable parameters describe the threshold: i) the effective environmental gradient, which can be measured by the loss of fitness due to dispersal to a different environment, and ii) the efficacy of selection relative to genetic drift. The theory predicts sharp range margins even in the absence of abrupt changes in the environment. Furthermore, it implies that gradual worsening of conditions across a species’ habitat may suddenly lead to range fragmentation – as adaptation to a wide span of conditions within a single species becomes impossible.

The competition between simple and complex evolutionary trajectories in asexual populations


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

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

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

Recombination and peak jumping

Kristina Crona
(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

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 [4] for the karyotic
pedigree. When r = 0, our model is equivalent to Kingman’s discrete coalescent
model [16] 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 [4]. 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 [12] and Griffiths [9].

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.