@article{607,
abstract = {We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain's boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker-Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.},
author = {Bodova, Katarina and Haskovec, Jan and Markowich, Peter},
journal = {Physica D: Nonlinear Phenomena},
pages = {108--120},
publisher = {Elsevier},
title = {{Well posedness and maximum entropy approximation for the dynamics of quantitative traits}},
doi = {10.1016/j.physd.2017.10.015},
volume = {376-377},
year = {2018},
}
@misc{5757,
abstract = {File S1. Variant Calling Format file of the ingroup: 197 haploid sequences of D. melanogaster from Zambia (Africa) aligned to the D. melanogaster 5.57 reference genome.
File S2. Variant Calling Format file of the outgroup: 1 haploid sequence of D. simulans aligned to the D. melanogaster 5.57 reference genome.
File S3. Annotations of each transcript in coding regions with SNPeff: Ps (# of synonymous polymorphic sites); Pn (# of non-synonymous polymorphic sites); Ds (# of synonymous divergent sites); Dn (# of non-synonymous divergent sites); DoS; ⍺ MK . All variants were included.
File S4. Annotations of each transcript in non-coding regions with SNPeff: Ps (# of synonymous polymorphic sites); Pu (# of UTR polymorphic sites); Ds (# of synonymous divergent sites); Du (# of UTR divergent sites); DoS; ⍺ MK . All variants were included.
File S5. Annotations of each transcript in coding regions with SNPGenie: Ps (# of synonymous polymorphic sites); πs (synonymous diversity); Ss_p (total # of synonymous sites in the polymorphism data); Pn (# of non-synonymous polymorphic sites); πn (non-synonymous diversity); Sn_p (total # of non-synonymous sites in the polymorphism data); Ds (# of synonymous divergent sites); ks (synonymous evolutionary rate); Ss_d (total # of synonymous sites in the divergence data); Dn (# of non-synonymous divergent sites); kn (non-synonymous evolutionary rate); Sn_d (total # of non-
synonymous sites in the divergence data); DoS; ⍺ MK . All variants were included.
File S6. Gene expression values (RPKM summed over all transcripts) for each sample. Values were quantile-normalized across all samples.
File S7. Final dataset with all covariates, ⍺ MK , ωA MK and DoS for coding sites, excluding variants below 5% frequency.
File S8. Final dataset with all covariates, ⍺ MK , ωA MK and DoS for non-coding sites, excluding variants below 5%
frequency.
File S9. Final dataset with all covariates, ⍺ EWK , ωA EWK and deleterious SFS for coding sites obtained with the Eyre-Walker and Keightley method on binned data and using all variants.},
author = {Fraisse, Christelle},
keywords = {(mal)adaptation, pleiotropy, selective constraint, evo-devo, gene expression, Drosophila melanogaster},
publisher = {IST Austria},
title = {{Supplementary Files for "Pleiotropy modulates the efficacy of selection in Drosophila melanogaster"}},
doi = {10.15479/at:ista:/5757},
year = {2018},
}
@article{723,
abstract = {Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The (1+1) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the (1+1) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.},
author = {Oliveto, Pietro and Paixao, Tiago and Pérez Heredia, Jorge and Sudholt, Dirk and Trubenova, Barbora},
journal = {Algorithmica},
number = {5},
pages = {1604 -- 1633},
publisher = {Springer},
title = {{How to escape local optima in black box optimisation when non elitism outperforms elitism}},
doi = {10.1007/s00453-017-0369-2},
volume = {80},
year = {2018},
}
@article{1063,
abstract = {Severe environmental change can drive a population extinct unless the population adapts in time to the new conditions (“evolutionary rescue”). How does biparental sexual reproduction influence the chances of population persistence compared to clonal reproduction or selfing? In this article, we set up a one‐locus two‐allele model for adaptation in diploid species, where rescue is contingent on the establishment of the mutant homozygote. Reproduction can occur by random mating, selfing, or clonally. Random mating generates and destroys the rescue mutant; selfing is efficient at generating it but at the same time depletes the heterozygote, which can lead to a low mutant frequency in the standing genetic variation. Due to these (and other) antagonistic effects, we find a nontrivial dependence of population survival on the rate of sex/selfing, which is strongly influenced by the dominance coefficient of the mutation before and after the environmental change. Importantly, since mating with the wild‐type breaks the mutant homozygote up, a slow decay of the wild‐type population size can impede rescue in randomly mating populations.},
author = {Uecker, Hildegard},
issn = {00143820},
journal = {Evolution},
number = {4},
pages = {845 -- 858},
publisher = {Wiley-Blackwell},
title = {{Evolutionary rescue in randomly mating, selfing, and clonal populations}},
doi = {10.1111/evo.13191},
volume = {71},
year = {2017},
}
@article{1077,
abstract = {Viral capsids are structurally constrained by interactions among the amino acids (AAs) of their constituent proteins. Therefore, epistasis is expected to evolve among physically interacting sites and to influence the rates of substitution. To study the evolution of epistasis, we focused on the major structural protein of the fX174 phage family by first reconstructing the ancestral protein sequences of 18 species using a Bayesian statistical framework. The inferred ancestral reconstruction differed at eight AAs, for a total of 256 possible ancestral haplotypes. For each ancestral haplotype and the extant species, we estimated, in silico, the distribution of free energies and epistasis of the capsid structure. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that higher-order epistasis sometimes compensates pairwise interactions making the free energy seem additive. The dN/dS ratio is low, suggesting strong purifying selection, and that structure is under stabilizing selection. We synthesized phages carrying ancestral haplotypes of the coat protein gene and measured their fitness experimentally. Our findings indicate that stabilizing mutations can have higher fitness, and that fitness optima do not necessarily coincide with energy minima.},
author = {Fernandes Redondo, Rodrigo A and Vladar, Harold and Włodarski, Tomasz and Bollback, Jonathan P},
issn = {17425689},
journal = {Journal of the Royal Society Interface},
number = {126},
publisher = {Royal Society of London},
title = {{Evolutionary interplay between structure, energy and epistasis in the coat protein of the fX174 phage family}},
doi = {10.1098/rsif.2016.0139},
volume = {14},
year = {2017},
}
@article{1111,
abstract = {Adaptation depends critically on the effects of new mutations and their dependency on the genetic background in which they occur. These two factors can be summarized by the fitness landscape. However, it would require testing all mutations in all backgrounds, making the definition and analysis of fitness landscapes mostly inaccessible. Instead of postulating a particular fitness landscape, we address this problem by considering general classes of landscapes and calculating an upper limit for the time it takes for a population to reach a fitness peak, circumventing the need to have full knowledge about the fitness landscape. We analyze populations in the weak-mutation regime and characterize the conditions that enable them to quickly reach the fitness peak as a function of the number of sites under selection. We show that for additive landscapes there is a critical selection strength enabling populations to reach high-fitness genotypes, regardless of the distribution of effects. This threshold scales with the number of sites under selection, effectively setting a limit to adaptation, and results from the inevitable increase in deleterious mutational pressure as the population adapts in a space of discrete genotypes. Furthermore, we show that for the class of all unimodal landscapes this condition is sufficient but not necessary for rapid adaptation, as in some highly epistatic landscapes the critical strength does not depend on the number of sites under selection; effectively removing this barrier to adaptation.},
author = {Heredia, Jorge and Trubenova, Barbora and Sudholt, Dirk and Paixao, Tiago},
issn = {00166731},
journal = {Genetics},
number = {2},
pages = {803 -- 825},
publisher = {Genetics Society of America},
title = {{Selection limits to adaptive walks on correlated landscapes}},
doi = {10.1534/genetics.116.189340},
volume = {205},
year = {2017},
}
@inproceedings{1112,
abstract = {There has been renewed interest in modelling the behaviour of evolutionary algorithms by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogs of the additive and multiplicative drift theorems for SDEs. We exemplify the use of these methods for two model algorithms ((1+1) EA and RLS) on two canonical problems(OneMax and LeadingOnes).},
author = {Paixao, Tiago and Pérez Heredia, Jorge},
booktitle = {Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms},
isbn = {978-145034651-1},
location = {Copenhagen, Denmark},
pages = {3 -- 11},
publisher = {ACM},
title = {{An application of stochastic differential equations to evolutionary algorithms}},
doi = {10.1145/3040718.3040729},
year = {2017},
}
@article{1169,
abstract = {Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being “pulled” to being “pushed” wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies.},
author = {Novak, Sebastian and Kollár, Richard},
issn = {00166731},
journal = {Genetics},
number = {1},
pages = {367 -- 374},
publisher = {Genetics Society of America},
title = {{Spatial gene frequency waves under genotype dependent dispersal}},
doi = {10.1534/genetics.116.193946},
volume = {205},
year = {2017},
}
@article{1199,
abstract = {Much of quantitative genetics is based on the ‘infinitesimal model’, under which selection has a negligible effect on the genetic variance. This is typically justified by assuming a very large number of loci with additive effects. However, it applies even when genes interact, provided that the number of loci is large enough that selection on each of them is weak relative to random drift. In the long term, directional selection will change allele frequencies, but even then, the effects of epistasis on the ultimate change in trait mean due to selection may be modest. Stabilising selection can maintain many traits close to their optima, even when the underlying alleles are weakly selected. However, the number of traits that can be optimised is apparently limited to ~4Ne by the ‘drift load’, and this is hard to reconcile with the apparent complexity of many organisms. Just as for the mutation load, this limit can be evaded by a particular form of negative epistasis. A more robust limit is set by the variance in reproductive success. This suggests that selection accumulates information most efficiently in the infinitesimal regime, when selection on individual alleles is weak, and comparable with random drift. A review of evidence on selection strength suggests that although most variance in fitness may be because of alleles with large Nes, substantial amounts of adaptation may be because of alleles in the infinitesimal regime, in which epistasis has modest effects.},
author = {Barton, Nicholas H},
journal = {Heredity},
pages = {96 -- 109},
publisher = {Nature Publishing Group},
title = {{How does epistasis influence the response to selection?}},
doi = {10.1038/hdy.2016.109},
volume = {118},
year = {2017},
}
@article{1191,
abstract = {Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher–Kolmogorov–Petrovskii–Piskunov (F–KPP) equation. This generalized F–KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F–KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth–decay rate in the generalized F–KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.},
author = {Kollár, Richard and Novak, Sebastian},
journal = {Bulletin of Mathematical Biology},
number = {3},
pages = {525--559},
publisher = {Springer},
title = {{Existence of traveling waves for the generalized F–KPP equation}},
doi = {10.1007/s11538-016-0244-3},
volume = {79},
year = {2017},
}