How the tortoise beats the hare: Slow and steady adaptation in structured populations suggests a rugged fitness landscape in bacteria

Joshua R. Nahum, Peter Godfrey-Smith, Brittany N. Harding, Joseph H. Marcus, Jared Carlson-Stevermer, Benjamin Kerr

In the context of Wright’s adaptive landscape, genetic epistasis can yield a multi-peaked or “rugged” topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to rapidly fix on one, which may not be the highest peak. Contrarily, beneficial mutations in a population with spatially restricted migration take longer to fix, allowing distant parts of the population to explore the landscape semi-independently. Such a population can simultaneous discover multiple peaks and the genotype at the highest discovered peak is expected to fix eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the Tortoise-Hare fable, the structured population (Tortoise) starts relatively slow, but eventually surpasses the unstructured population (Hare) in average fitness. In contrast, on single-peak landscapes (e.g., systems lacking epistasis), all uphill paths converge. Given such “smooth” topography, breadth of search is devalued, and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the Tortoise-Hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we then explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a Tortoise-Hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright’s Shifting Balance Process.

The largest strongly connected component in Wakeley et al’s cyclical pedigree model
Jochen Blath, Stephan Kadow, Marcel Ortgiese
Comments: 21 pages, 2 figures
Subjects: Probability (math.PR); Populations and Evolution (q-bio.PE)

We establish a link between Wakeley et al’s (2012) cyclical pedigree model from population genetics and a randomized directed configuration model (DCM) considered by Cooper and Frieze (2004). We then exploit this link in combination with asymptotic results for the in-degree distribution of the corresponding DCM to compute the asymptotic size of the largest strongly connected component $S^N$ (where $N$ is the population size) of the DCM resp. the pedigree. The size of the giant component can be characterized explicitly (amounting to approximately $80 \%$ of the total populations size) and thus contributes to a reduced `pedigree effective population size’. In addition, the second largest strongly connected component is only of size $O(\log N)$. Moreover, we describe the size and structure of the `domain of attraction’ of $S^N$. In particular, we show that with high probability for any individual the shortest ancestral line reaches $S^N$ after $O(\log \log N)$ generations, while almost all other ancestral lines take at most $O(\log N)$ generations.

Tractable stochastic models of evolution for loosely linked loci
Paul A. Jenkins, Paul Fearnhead, Yun S. Song
Comments: 32 pages, 1 figure
Subjects: Probability (math.PR); Populations and Evolution (q-bio.PE)

Of fundamental importance in statistical genetics is to compute the sampling distribution, or likelihood, for a sample of genetic data from some stochastic evolutionary model. For DNA sequence data with inter-locus recombination, standard models include the Wright-Fisher diffusion with recombination and its dual genealogical process, the ancestral recombination graph. However, under neither of these models is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new stochastic population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. In the former case, we show that the sampling distribution is available in closed form. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the two models agree with the standard ones up to the first two orders.

Dynamics of a combined medea-underdominant population transformation system
Chaitanya Gokhale, Richard Guy Reeves, Floyd A Reed

Transgenic constructs intended to be stably established at high frequencies in wild popu- lations have been demonstrated to “drive” from low frequencies in experimental insect populations. Link- ing such population transformation constructs to genes which render them unable to transmit pathogens could eventually be used to stop the spread of vector-borne diseases like malaria and dengue. Generally, population transformation constructs with only a single transgenic drive mechanism have been envisioned. Using a theoretical modelling approach we describe the predicted properties of a construct combining autosomal Medea and underdominant population transformation systems. We show that when combined they can exhibit synergistic properties which in broad circumstances surpass those of the single systems. With combined systems, intentional population transformation and its reversal can be achieved readily. Combined constructs also enhance the capacity to geographically restrict transgenic constructs to targeted populations. It is anticipated that these properties are likely to be of particular value in attracting regulatory approval and public acceptance of this novel technology.

Sperm should evolve to make female meiosis fair.
Yaniv Brandvain, Graham Coop

Genomic conflicts arise when an allele gains an evolutionary advantage at a cost to organismal fitness. Oogenesis is inherently susceptible to such conflicts because alleles compete to be the product of female meiosis transmitted to the egg. Alleles that distort meiosis in their favor (i.e. meiotic drivers) often decrease organismal fitness, and therefore indirectly favor the evolution of mechanisms to suppress meiotic drive. In this light, many facets of oogenesis and gametogenesis have been interpreted as mechanisms of protection against genomic outlaws. Why then is female meiosis often left uncompleted until after fertilization in many animals — potentially providing an opportunity for sperm alleles to meddle with its outcome and help like-alleles drive in heterozygous females? The population genetic theory presented herein suggests that sperm nearly always evolve to increase the fairness of female meiosis in the face of genomic conflicts. These results are consistent with current knowledge of sperm-dependent meiotic drivers (loci whose distortion of female meiosis depends on sperm genotype), and suggest that the requirement of fertilization for the completion of female meiosis potentially represents a mechanism employed by females to ensure a fair meiosis.

Deleterious passengers in adapting populations
Benjamin H Good, Michael M Desai
Subjects: Populations and Evolution (q-bio.PE)

Most new mutations are deleterious and are eventually eliminated by natural selection. But in an adapting population, the rapid amplification of beneficial mutations can hinder the removal of deleterious variants in nearby regions of the genome, altering the patterns of sequence evolution. Here, we analyze the interactions between beneficial “driver” mutations and linked deleterious “passengers” during the course of adaptation. We derive analytical expressions for the substitution rate of a deleterious mutation as a function of its fitness cost, as well as the reduction in the beneficial substitution rate due to the genetic load of the passengers. We find that the fate of each deleterious mutation varies dramatically with the rate and spectrum of beneficial mutations, with a non-monotonic dependence on both the population size and the rate of adaptation. By quantifying this dependence, our results allow us to estimate which deleterious mutations will be likely to fix, and how many of these mutations must arise before the progress of adaptation is significantly reduced.

Properties of selected mutations and genotypic landscapes under Fisher’s Geometric Model

François Blanquart, Guillaume Achaz, Thomas Bataillon, Olivier Tenaillon
(Submitted on 14 May 2014)

The fitness landscape – the mapping between genotypes and fitness – determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher’s geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected or co-selected in an adaptive walk. Using simulations, we show that genetic landscapes built from FGMA are very close to an additive landscape when the ancestral strain is far from the optimum. However, when close to the optimum, a large diversity of landscape with substantial ruggedness and sign epistasis emerged. Strikingly, landscapes built from different realizations of stochastic adaptive walks in the same exact conditions were highly variable, suggesting that several realizations of small genetic landscapes are needed to gain information about the underlying architecture of the global adaptive landscape.

Quadri-allele frequency spectrum in a coalescent topology for mutations in non-constant population size

Arka Bhattacharya
(Submitted on 11 May 2014)

The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for analyzing quadri-allele frequency spectrum, where the ancestral population diverged into three populations at a certain divergence time and the resulting mutations on the branches of the coalescent tree gave rise to three different derived alleles, which could be observed in the present generation along with the ancestral allele. The model has been analyzed for non-constant population size, assuming we had a certain number of extant lineages at the divergence time and no migration occurs between the populations.

Detection and Polarization of Introgression in a Five-taxon Phylogeny
James B Pease, Matthew W. Hahn

In clades of closely related taxa, discordant genealogies due to incomplete lineage sorting (ILS) can complicate the detection of introgression. The D-statistic (a.k.a. the ABBA/BABA test) was proposed to infer introgression in the presence of ILS for a four-taxon clade. However, the original D-statistic cannot be directly applied to a symmetric five-taxon phylogeny, and the direction of introgression cannot be inferred for any tree topology. Here we explore the issues associated with previous methods for adapting the D-statistic to a larger tree topology, and propose new “DFOIL” tests to infer both the taxa involved in and the direction of introgressions for a symmetric five-taxon phylogeny. Using theory and simulations, we find that previous modifications of the D-statistic to five-taxon phylogenies incorrectly identify both the pairs of taxa exchanging migrants as well as the direction of introgression. The DFOIL statistics are shown to overcome this deficiency and to correctly determine the direction of introgressions. The DFOIL tests are relatively simple and computationally inexpensive to calculate, and can be easily applied to various phylogenomic datasets. In addition, our general approach to the problem of introgression detection could be adapted to larger tree topologies and other models of sequence evolution.

The evolution of genetic diversity in changing environments

Oana Carja, Uri Liberman, Marcus W. Feldman

The production and maintenance of genetic and phenotypic diversity under temporally fluctuating selection and the signatures of environmental and selective volatility in the patterns of genetic and phenotypic variation have been important areas of focus in population genetics. On one hand, stretches of constant selection pull the genetic makeup of populations towards local fitness optima. On the other, in order to cope with changes in the selection regime, populations may evolve mechanisms that create a diversity of genotypes. By tuning the rates at which variability is produced, such as the rates of recombination, mutation or migration, populations may increase their long-term adaptability. Here we use theoretical models to gain insight into how the rates of these three evolutionary forces are shaped by fluctuating selection. We compare and contrast the evolution of recombination, mutation and migration under similar patterns of environmental change and show that these three sources of phenotypic variation are surprisingly similar in their response to changing selection. We show that knowing the shape, size, variance and asymmetry of environmental runs is essential for accurate prediction of genetic evolutionary dynamics.