# Genetic variability under the seed bank coalescent

Genetic variability under the seed bank coalescent
Jochen Blath , Bjarki Eldon , Adrian Casanova , Noemi Kurt , Maite Wilke-Berenguer
doi: http://dx.doi.org/10.1101/017244

We analyse patterns of genetic variability of populations in the presence of a large seed bank with the help of a new coalescent structure called the seed bank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seed banks, if the seed bank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson processes on the active lineages, and potentially at reduced rate also on the dormant lineages. The presence of `dormant’ lineages leads to qualitatively altered times to the most recent common ancestor and non-classical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with seed bank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seed bank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seed bank, are compared. The effect of a seed bank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seed bank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect the presence of a large seed bank in genetic data.

# Analysis of adaptive walks on NK fitness landscapes with different interaction schemes

Analysis of adaptive walks on NK fitness landscapes with different interaction schemes
Stefan Nowak, Joachim Krug
Subjects: Populations and Evolution (q-bio.PE); Disordered Systems and Neural Networks (cond-mat.dis-nn)

Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and terminates at a local fitness maximum. We use three different types of walks and investigate how their length (the number of steps required to reach a local peak) and height (the fitness at the endpoint of the walk) depend on the dimensionality and structure of the landscape. We find that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern. Most quantities that we measure are simply correlated to the rank of the scheme, which is equal to the number of nonzero coefficients in the expansion of the fitness landscape in terms of Walsh functions.

# Selective strolls: fixation and extinction in diploids are slower for weakly selected mutations than for neutral ones

Selective strolls: fixation and extinction in diploids are slower for weakly selected mutations than for neutral ones

fabrizio mafessoni , Michael Lachmann
doi: http://dx.doi.org/10.1101/016881

In finite populations, an allele disappears or reaches fixation due to two main forces, selection and drift. Selec- tion is generally thought to accelerate the process: a selected mutation will reach fixation faster than a neutral one, and a disadvantageous one will quickly disappear from the population. We show that even in simple diploid populations, this is often not true. Dominance and recessivity unexpectedly slow down the evolutionary process for weakly selected alleles. In particular, slightly advantageous dominant and mildly deleterious recessive mu- tations reach fixation more slowly than neutral ones. This phenomenon determines genetic signatures opposite to those expected under strong selection, such as increased instead of decreased genetic diversity around the selected site. Furthermore, we characterize a new phenomenon: mildly deleterious recessive alleles, thought to represent the vast majority of newly arising mutations, survive in a population longer than neutral ones, before getting lost. Hence, natural selection is less effective than previously thought in getting rid rapidly of slightly negative mutations, contributing their observed persistence in present populations. Consequently, low frequency slightly deleterious mutations are on average older than neutral ones.

# The fate of a mutation in a fluctuating environment

The fate of a mutation in a fluctuating environment

Ivana Cvijovic , Benjamin H. Good , Elizabeth R. Jerison , Michael M. Desai
doi: http://dx.doi.org/10.1101/016709

Natural environments are never truly constant, but the evolutionary implications of temporally varying selection pressures remain poorly understood. Here we investigate how the fate of a new mutation in a variable environment depends on the dynamics of environmental fluctuations and on the selective pressures in each condition. We find that even when a mutation experiences many environmental epochs before fixing or going extinct, its fate is not necessarily determined by its time-averaged selective effect. Instead, environmental variability reduces the efficiency of selection across a broad parameter regime, rendering selection unable to distinguish between mutations that are substantially beneficial and substantially deleterious on average. Temporal fluctuations can also dramatically increase fixation probabilities, often making the details of these fluctuations more important than the average selection pressures acting on each new mutation. For example, mutations that result in a tradeoff between conditions but are strongly deleterious on average can nevertheless be more likely to fix than mutations that are always neutral or beneficial. These effects can have important implications for patterns of molecular evolution in variable environments, and they suggest that it may often be difficult for populations to maintain specialist traits, even when their loss leads to a decline in time-averaged fitness.

# Beyond 2/3 and 1/3: the complex signatures of sex-biased admixture on the X chromosome

Beyond 2/3 and 1/3: the complex signatures of sex-biased admixture on the X chromosome
Amy Goldberg , Noah A Rosenberg
doi: http://dx.doi.org/10.1101/016543

# The Spatial Mixing of Genomes in Secondary Contact Zones

The Spatial Mixing of Genomes in Secondary Contact Zones
Alisa Sedghifar , Yaniv Brandvain , Peter L. Ralph , Graham Coop
doi: http://dx.doi.org/10.1101/016337

Recent genomic studies have highlighted the important role of admixture in shaping genome-wide patterns of diversity. Past admixture leaves a population genomic signature of linkage disequilibrium (LD), reflecting the mixing of parental chromosomes by segregation and recombination. The extent of this LD can be used to infer the timing of admixture. However, the results of inference can depend strongly on the assumed demographic model. Here, we introduce a theoretical framework for modeling patterns of LD in a geographic contact zone where two differentiated populations are diffusing back together. We derive expressions for the expected LD and admixture tract lengths across geographic space as a function of the age of the contact zone and the dispersal distance of individuals. We develop an approach to infer age of contact zones using population genomic data from multiple spatially sampled populations by fitting our model to the decay of LD with recombination distance. We use our approach to explore the fit of a geographic contact zone model to three human population genomic datasets from populations along the Indonesian archipelago, populations in Central Asia and populations in India.

# Coalescent histories for lodgepole species trees

Coalescent histories for lodgepole species trees
Filippo Disanto, Noah A. Rosenberg
Subjects: Populations and Evolution (q-bio.PE); Combinatorics (math.CO)

Coalescent histories are combinatorial structures that describe for a given gene tree and species tree the possible lists of branches of the species tree on which the gene tree coalescences take place. Properties of the number of coalescent histories for gene trees and species trees affect a variety of probabilistic calculations in mathematical phylogenetics. Exact and asymptotic evaluations of the number of coalescent histories, however, are known only in a limited number of cases. Here we introduce a particular family of species trees, the \emph{lodgepole} species trees $(\lambda_n)_{n\geq 0}$, in which tree $\lambda_n$ has $m=2n+1$ taxa. We determine the number of coalescent histories for the lodgepole species trees, in the case that the gene tree matches the species tree, showing that this number grows with $m!!$ in the number of taxa $m$. This computation demonstrates the existence of tree families in which the growth in the number of coalescent histories is faster than exponential. Further, it provides a substantial improvement on the lower bound for the ratio of the largest number of matching coalescent histories to the smallest number of matching coalescent histories for trees with $m$ taxa, increasing a previous bound of $(\sqrt{\pi} / 32)[(5m-12)/(4m-6)] m \sqrt{m}$ to $[ \sqrt{m-1}/(4 \sqrt{e}) ]^{m}$. We discuss the implications of our enumerative results for phylogenetic computations.

# Catch me if you can: Adaptation from standing genetic variation to a moving phenotypic optimum

Catch me if you can: Adaptation from standing genetic variation to a moving phenotypic optimum

Sebastian Matuszewski , Joachim Hermisson , Michael Kopp
doi: http://dx.doi.org/10.1101/015685
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Abstract

# Partitioning, duality, and linkage disequilibria in the Moran model with recombination

Partitioning, duality, and linkage disequilibria in the Moran model with recombination
Mareike Esser, Sebastian Probst, Ellen Baake
The Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. There are $n$ sites (or loci), a finite number of letters (or alleles) at every site, and we do not make any scaling assumptions. In particular, we do not assume a diffusion limit. We consider the following marginal ancestral recombination process. Let $S = \{1,…c,n\}$ and $\mathcal A=\{A_1, …c, A_m\}$ be a partition of $S$. We concentrate on the joint probability of the letters at the sites in $A_1$ in individual $1$, $…c$, at the sites in $A_m$ in individual $m$, where the individuals are sampled from the current population without replacement. Following the ancestry of these sites backwards in time yields a process on the set of partitions of $S$, which, in the diffusion limit, turns into a marginalised version of the $n$-locus ancestral recombination graph. With the help of an inclusion-exclusion principle, we show that the type distribution corresponding to a given partition may be represented in a systematic way, with the help of so-called recombinators and sampling functions. The same is true of correlation functions (known as linkage disequilibria in genetics) of all orders.