@article{564,
  abstract     = {Maladapted individuals can only colonise a new habitat if they can evolve a
positive growth rate fast enough to avoid extinction, a process known as evolutionary
rescue. We treat log fitness at low density in the new habitat as a
single polygenic trait and thus use the infinitesimal model to follow the evolution
of the growth rate; this assumes that the trait values of offspring of a
sexual union are normally distributed around the mean of the parents’ trait
values, with variance that depends only on the parents’ relatedness. The
probability that a single migrant can establish depends on just two parameters:
the mean and genetic variance of the trait in the source population.
The chance of success becomes small if migrants come from a population
with mean growth rate in the new habitat more than a few standard deviations
below zero; this chance depends roughly equally on the probability
that the initial founder is unusually fit, and on the subsequent increase in
growth rate of its offspring as a result of selection. The loss of genetic variation
during the founding event is substantial, but highly variable. With
continued migration at rate M, establishment is inevitable; when migration
is rare, the expected time to establishment decreases inversely with M.
However, above a threshold migration rate, the population may be trapped
in a ‘sink’ state, in which adaptation is held back by gene flow; above this
threshold, the expected time to establishment increases exponentially with M. This threshold behaviour is captured by a deterministic approximation,
which assumes a Gaussian distribution of the trait in the founder population
with mean and variance evolving deterministically. By assuming a constant
genetic variance, we also develop a diffusion approximation for the joint distribution
of population size and trait mean, which extends to include stabilising
selection and density regulation. Divergence of the population from its
ancestors causes partial reproductive isolation, which we measure through
the reproductive value of migrants into the newly established population.},
  author       = {Barton, Nicholas H and Etheridge, Alison},
  journal      = {Theoretical Population Biology},
  number       = {7},
  pages        = {110--127},
  publisher    = {Academic Press},
  title        = {{Establishment in a new habitat by polygenic adaptation}},
  doi          = {10.1016/j.tpb.2017.11.007},
  volume       = {122},
  year         = {2018},
}

@article{565,
  abstract     = {We re-examine the model of Kirkpatrick and Barton for the spread of an inversion into a local population. This model assumes that local selection maintains alleles at two or more loci, despite immigration of alternative alleles at these loci from another population. We show that an inversion is favored because it prevents the breakdown of linkage disequilibrium generated by migration; the selective advantage of an inversion is proportional to the amount of recombination between the loci involved, as in other cases where inversions are selected for. We derive expressions for the rate of spread of an inversion; when the loci covered by the inversion are tightly linked, these conditions deviate substantially from those proposed previously, and imply that an inversion can then have only a small advantage. },
  author       = {Charlesworth, Brian and Barton, Nicholas H},
  journal      = {Genetics},
  number       = {1},
  pages        = {377 -- 382},
  publisher    = {Genetics Society of America},
  title        = {{The spread of an inversion with migration and selection}},
  doi          = {10.1534/genetics.117.300426},
  volume       = {208},
  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    = {Institute of Science and Technology Austria},
  title        = {{Supplementary Files for "Pleiotropy modulates the efficacy of selection in Drosophila melanogaster"}},
  doi          = {10.15479/at:ista:/5757},
  year         = {2018},
}

@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},
}

@phdthesis{200,
  abstract     = {This thesis is concerned with the inference of current population structure based on geo-referenced genetic data. The underlying idea is that population structure affects its spatial genetic structure. Therefore, genotype information can be utilized to estimate important demographic parameters such as migration rates. These indirect estimates of population structure have become very attractive, as genotype data is now widely available. However, there also has been much concern about these approaches. Importantly, genetic structure can be influenced by many complex patterns, which often cannot be disentangled. Moreover, many methods merely fit heuristic patterns of genetic structure, and do not build upon population genetics theory. Here, I describe two novel inference methods that address these shortcomings. In Chapter 2, I introduce an inference scheme based on a new type of signal, identity by descent (IBD) blocks. Recently, it has become feasible to detect such long blocks of genome shared between pairs of samples. These blocks are direct traces of recent coalescence events. As such, they contain ample signal for inferring recent demography. I examine sharing of IBD blocks in two-dimensional populations with local migration. Using a diffusion approximation, I derive formulas for an isolation by distance pattern of long IBD blocks and show that sharing of long IBD blocks approaches rapid exponential decay for growing sample distance. I describe an inference scheme based on these results. It can robustly estimate the dispersal rate and population density, which is demonstrated on simulated data. I also show an application to estimate mean migration and the rate of recent population growth within Eastern Europe. Chapter 3 is about a novel method to estimate barriers to gene flow in a two dimensional population. This inference scheme utilizes geographically localized allele frequency fluctuations - a classical isolation by distance signal. The strength of these local fluctuations increases on average next to a barrier, and there is less correlation across it. I again use a framework of diffusion of ancestral lineages to model this effect, and provide an efficient numerical implementation to fit the results to geo-referenced biallelic SNP data. This inference scheme is able to robustly estimate strong barriers to gene flow, as tests on simulated data confirm.},
  author       = {Ringbauer, Harald},
  issn         = {2663-337X},
  pages        = {146},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Inferring recent demography from spatial genetic structure}},
  doi          = {10.15479/AT:ISTA:th_963},
  year         = {2018},
}

@article{315,
  abstract     = {More than 100 years after Grigg’s influential analysis of species’ borders, the causes of limits to species’ ranges still represent a puzzle that has never been understood with clarity. The topic has become especially important recently as many scientists have become interested in the potential for species’ ranges to shift in response to climate change—and yet nearly all of those studies fail to recognise or incorporate evolutionary genetics in a way that relates to theoretical developments. I show that range margins can be understood based on just two measurable parameters: (i) the fitness cost of dispersal—a measure of environmental heterogeneity—and (ii) the strength of genetic drift, which reduces genetic diversity. Together, these two parameters define an ‘expansion threshold’: adaptation fails when genetic drift reduces genetic diversity below that required for adaptation to a heterogeneous environment. When the key parameters drop below this expansion threshold locally, a sharp range margin forms. When they drop below this threshold throughout the species’ range, adaptation collapses everywhere, resulting in either extinction or formation of a fragmented metapopulation. Because the effects of dispersal differ fundamentally with dimension, the second parameter—the strength of genetic drift—is qualitatively different compared to a linear habitat. In two-dimensional habitats, genetic drift becomes effectively independent of selection. It decreases with ‘neighbourhood size’—the number of individuals accessible by dispersal within one generation. Moreover, in contrast to earlier predictions, which neglected evolution of genetic variance and/or stochasticity in two dimensions, dispersal into small marginal populations aids adaptation. This is because the reduction of both genetic and demographic stochasticity has a stronger effect than the cost of dispersal through increased maladaptation. The expansion threshold thus provides a novel, theoretically justified, and testable prediction for formation of the range margin and collapse of the species’ range.},
  author       = {Polechova, Jitka},
  issn         = {1544-9173},
  journal      = {PLoS Biology},
  number       = {6},
  publisher    = {Public Library of Science},
  title        = {{Is the sky the limit? On the expansion threshold of a species’ range}},
  doi          = {10.1371/journal.pbio.2005372},
  volume       = {16},
  year         = {2018},
}

@article{316,
  abstract     = {Self-incompatibility (SI) is a genetically based recognition system that functions to prevent self-fertilization and mating among related plants. An enduring puzzle in SI is how the high diversity observed in nature arises and is maintained. Based on the underlying recognition mechanism, SI can be classified into two main groups: self- and non-self recognition. Most work has focused on diversification within self-recognition systems despite expected differences between the two groups in the evolutionary pathways and outcomes of diversification. Here, we use a deterministic population genetic model and stochastic simulations to investigate how novel S-haplotypes evolve in a gametophytic non-self recognition (SRNase/S Locus F-box (SLF)) SI system. For this model the pathways for diversification involve either the maintenance or breakdown of SI and can vary in the order of mutations of the female (SRNase) and male (SLF) components. We show analytically that diversification can occur with high inbreeding depression and self-pollination, but this varies with evolutionary pathway and level of completeness (which determines the number of potential mating partners in the population), and in general is more likely for lower haplotype number. The conditions for diversification are broader in stochastic simulations of finite population size. However, the number of haplotypes observed under high inbreeding and moderate to high self-pollination is less than that commonly observed in nature. Diversification was observed through pathways that maintain SI as well as through self-compatible intermediates. Yet the lifespan of diversified haplotypes was sensitive to their level of completeness. By examining diversification in a non-self recognition SI system, this model extends our understanding of the evolution and maintenance of haplotype diversity observed in a self recognition system common in flowering plants.},
  author       = {Bodova, Katarina and Priklopil, Tadeas and Field, David and Barton, Nicholas H and Pickup, Melinda},
  journal      = {Genetics},
  number       = {3},
  pages        = {861--883},
  publisher    = {Genetics Society of America},
  title        = {{Evolutionary pathways for the generation of new self-incompatibility haplotypes in a non-self recognition system}},
  doi          = {10.1534/genetics.118.300748},
  volume       = {209},
  year         = {2018},
}

@article{33,
  abstract     = {Secondary contact is the reestablishment of gene flow between sister populations that have diverged. For instance, at the end of the Quaternary glaciations in Europe, secondary contact occurred during the northward expansion of the populations which had found refugia in the southern peninsulas. With the advent of multi-locus markers, secondary contact can be investigated using various molecular signatures including gradients of allele frequency, admixture clines, and local increase of genetic differentiation. We use coalescent simulations to investigate if molecular data provide enough information to distinguish between secondary contact following range expansion and an alternative evolutionary scenario consisting of a barrier to gene flow in an isolation-by-distance model. We find that an excess of linkage disequilibrium and of genetic diversity at the suture zone is a unique signature of secondary contact. We also find that the directionality index ψ, which was proposed to study range expansion, is informative to distinguish between the two hypotheses. However, although evidence for secondary contact is usually conveyed by statistics related to admixture coefficients, we find that they can be confounded by isolation-by-distance. We recommend to account for the spatial repartition of individuals when investigating secondary contact in order to better reflect the complex spatio-temporal evolution of populations and species.},
  author       = {Bertl, Johanna and Ringbauer, Harald and Blum, Michaël},
  journal      = {PeerJ},
  number       = {10},
  publisher    = {PeerJ},
  title        = {{Can secondary contact following range expansion be distinguished from barriers to gene flow?}},
  doi          = {10.7717/peerj.5325},
  volume       = {2018},
  year         = {2018},
}

@article{38,
  abstract     = {Genomes of closely-related species or populations often display localized regions of enhanced relative sequence divergence, termed genomic islands. It has been proposed that these islands arise through selective sweeps and/or barriers to gene flow. Here, we genetically dissect a genomic island that controls flower color pattern differences between two subspecies of Antirrhinum majus, A.m.striatum and A.m.pseudomajus, and relate it to clinal variation across a natural hybrid zone. We show that selective sweeps likely raised relative divergence at two tightly-linked MYB-like transcription factors, leading to distinct flower patterns in the two subspecies. The two patterns provide alternate floral guides and create a strong barrier to gene flow where populations come into contact. This barrier affects the selected flower color genes and tightlylinked loci, but does not extend outside of this domain, allowing gene flow to lower relative divergence for the rest of the chromosome. Thus, both selective sweeps and barriers to gene flow play a role in shaping genomic islands: sweeps cause elevation in relative divergence, while heterogeneous gene flow flattens the surrounding "sea," making the island of divergence stand out. By showing how selective sweeps establish alternative adaptive phenotypes that lead to barriers to gene flow, our study sheds light on possible mechanisms leading to reproductive isolation and speciation.},
  author       = {Tavares, Hugo and Whitley, Annabel and Field, David and Bradley, Desmond and Couchman, Matthew and Copsey, Lucy and Elleouet, Joane and Burrus, Monique and Andalo, Christophe and Li, Miaomiao and Li, Qun and Xue, Yongbiao and Rebocho, Alexandra B and Barton, Nicholas H and Coen, Enrico},
  issn         = {0027-8424},
  journal      = {PNAS},
  number       = {43},
  pages        = {11006 -- 11011},
  publisher    = {National Academy of Sciences},
  title        = {{Selection and gene flow shape genomic islands that control floral guides}},
  doi          = {10.1073/pnas.1801832115},
  volume       = {115},
  year         = {2018},
}

@article{39,
  abstract     = {We study how a block of genome with a large number of weakly selected loci introgresses under directional selection into a genetically homogeneous population. We derive exact expressions for the expected rate of growth of any fragment of the introduced block during the initial phase of introgression, and show that the growth rate of a single-locus variant is largely insensitive to its own additive effect, but depends instead on the combined effect of all loci within a characteristic linkage scale. The expected growth rate of a fragment is highly correlated with its long-term introgression probability in populations of moderate size, and can hence identify variants that are likely to introgress across replicate populations. We clarify how the introgression probability of an individual variant is determined by the interplay between hitchhiking with relatively large fragments during the early phase of introgression and selection on fine-scale variation within these, which at longer times results in differential introgression probabilities for beneficial and deleterious loci within successful fragments. By simulating individuals, we also investigate how introgression probabilities at individual loci depend on the variance of fitness effects, the net fitness of the introduced block, and the size of the recipient population, and how this shapes the net advance under selection. Our work suggests that even highly replicable substitutions may be associated with a range of selective effects, which makes it challenging to fine map the causal loci that underlie polygenic adaptation.},
  author       = {Sachdeva, Himani and Barton, Nicholas H},
  issn         = {0016-6731},
  journal      = {Genetics},
  number       = {4},
  pages        = {1411--1427},
  publisher    = {Genetics Society of America},
  title        = {{Replicability of introgression under linked, polygenic selection}},
  doi          = {10.1534/genetics.118.301429},
  volume       = {210},
  year         = {2018},
}

@article{40,
  abstract     = {Hanemaaijer et al. (Molecular Ecology, 27, 2018) describe the genetic consequences of the introgression of an insecticide resistance allele into a mosquito population. Linked alleles initially increased, but many of these later declined. It is hard to determine whether this decline was due to counter‐selection, rather than simply to chance.},
  author       = {Barton, Nicholas H},
  issn         = {1365-294X},
  journal      = {Molecular Ecology},
  number       = {24},
  pages        = {4973--4975},
  publisher    = {Wiley},
  title        = {{The consequences of an introgression event}},
  doi          = {10.1111/mec.14950},
  volume       = {27},
  year         = {2018},
}

@article{423,
  abstract     = {Herd immunity, a process in which resistant individuals limit the spread of a pathogen among susceptible hosts has been extensively studied in eukaryotes. Even though bacteria have evolved multiple immune systems against their phage pathogens, herd immunity in bacteria remains unexplored. Here we experimentally demonstrate that herd immunity arises during phage epidemics in structured and unstructured Escherichia coli populations consisting of differing frequencies of susceptible and resistant cells harboring CRISPR immunity. In addition, we develop a mathematical model that quantifies how herd immunity is affected by spatial population structure, bacterial growth rate, and phage replication rate. Using our model we infer a general epidemiological rule describing the relative speed of an epidemic in partially resistant spatially structured populations. Our experimental and theoretical findings indicate that herd immunity may be important in bacterial communities, allowing for stable coexistence of bacteria and their phages and the maintenance of polymorphism in bacterial immunity.},
  author       = {Payne, Pavel and Geyrhofer, Lukas and Barton, Nicholas H and Bollback, Jonathan P},
  journal      = {eLife},
  publisher    = {eLife Sciences Publications},
  title        = {{CRISPR-based herd immunity can limit phage epidemics in bacterial populations}},
  doi          = {10.7554/eLife.32035},
  volume       = {7},
  year         = {2018},
}

@article{430,
  abstract     = {In this issue of GENETICS, a new method for detecting natural selection on polygenic traits is developed and applied to sev- eral human examples ( Racimo et al. 2018 ). By de fi nition, many loci contribute to variation in polygenic traits, and a challenge for evolutionary ge neticists has been that these traits can evolve by small, nearly undetectable shifts in allele frequencies across each of many, typically unknown, loci. Recently, a helpful remedy has arisen. Genome-wide associ- ation studies (GWAS) have been illuminating sets of loci that can be interrogated jointly for c hanges in allele frequencies. By aggregating small signal s of change across many such loci, directional natural selection is now in principle detect- able using genetic data, even for highly polygenic traits. This is an exciting arena of progress – with these methods, tests can be made for selection associated with traits, and we can now study selection in what may be its most prevalent mode. The continuing fast pace of GWAS publications suggest there will be many more polygenic tests of selection in the near future, as every new GWAS is an opportunity for an accom- panying test of polygenic selection. However, it is important to be aware of complications th at arise in interpretation, especially given that these studies may easily be misinter- preted both in and outside the evolutionary genetics commu- nity. Here, we provide context for understanding polygenic tests and urge caution regarding how these results are inter- preted and reported upon more broadly.},
  author       = {Novembre, John and Barton, Nicholas H},
  journal      = {Genetics},
  number       = {4},
  pages        = {1351 -- 1355},
  publisher    = {Genetics Society of America},
  title        = {{Tread lightly interpreting polygenic tests of selection}},
  doi          = {10.1534/genetics.118.300786},
  volume       = {208},
  year         = {2018},
}

@misc{9813,
  abstract     = {File S1 contains figures that clarify the following features: (i) effect of population size on the average number/frequency of SI classes, (ii) changes in the minimal completeness deficit in time for a single class, and (iii) diversification diagrams for all studied pathways, including the summary figure for k = 8. File S2 contains the code required for a stochastic simulation of the SLF system with an example. This file also includes the output in the form of figures and tables.},
  author       = {Bod'ová, Katarína and Priklopil, Tadeas and Field, David and Barton, Nicholas H and Pickup, Melinda},
  publisher    = {Genetics Society of America},
  title        = {{Supplemental material for Bodova et al., 2018}},
  doi          = {10.25386/genetics.6148304.v1},
  year         = {2018},
}

@misc{9837,
  abstract     = {Both classical and recent studies suggest that chromosomal inversion polymorphisms are important in adaptation and speciation. However, biases in discovery and reporting of inversions make it difficult to assess their prevalence and biological importance. Here, we use an approach based on linkage disequilibrium among markers genotyped for samples collected across a transect between contrasting habitats to detect chromosomal rearrangements de novo. We report 17 polymorphic rearrangements in a single locality for the coastal marine snail, Littorina saxatilis. Patterns of diversity in the field and of recombination in controlled crosses provide strong evidence that at least the majority of these rearrangements are inversions. Most show clinal changes in frequency between habitats, suggestive of divergent selection, but only one appears to be fixed for different arrangements in the two habitats. Consistent with widespread evidence for balancing selection on inversion polymorphisms, we argue that a combination of heterosis and divergent selection can explain the observed patterns and should be considered in other systems spanning environmental gradients.},
  author       = {Faria, Rui and Chaube, Pragya and Morales, Hernán E. and Larsson, Tomas and Lemmon, Alan R. and Lemmon, Emily M. and Rafajlović, Marina and Panova, Marina and Ravinet, Mark and Johannesson, Kerstin and Westram, Anja M and Butlin, Roger K.},
  publisher    = {Dryad},
  title        = {{Data from: Multiple chromosomal rearrangements in a hybrid zone between Littorina saxatilis ecotypes}},
  doi          = {10.5061/dryad.72cg113},
  year         = {2018},
}

@misc{9840,
  abstract     = {Herd immunity, a process in which resistant individuals limit the spread of a pathogen among susceptible hosts has been extensively studied in eukaryotes. Even though bacteria have evolved multiple immune systems against their phage pathogens, herd immunity in bacteria remains unexplored. Here we experimentally demonstrate that herd immunity arises during phage epidemics in structured and unstructured Escherichia coli populations consisting of differing frequencies of susceptible and resistant cells harboring CRISPR immunity. In addition, we develop a mathematical model that quantifies how herd immunity is affected by spatial population structure, bacterial growth rate, and phage replication rate. Using our model we infer a general epidemiological rule describing the relative speed of an epidemic in partially resistant spatially structured populations. Our experimental and theoretical findings indicate that herd immunity may be important in bacterial communities, allowing for stable coexistence of bacteria and their phages and the maintenance of polymorphism in bacterial immunity.},
  author       = {Payne, Pavel and Geyrhofer, Lukas and Barton, Nicholas H and Bollback, Jonathan P},
  publisher    = {Dryad},
  title        = {{Data from: CRISPR-based herd immunity limits phage epidemics in bacterial populations}},
  doi          = {10.5061/dryad.42n44},
  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{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         = {0016-6731},
  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         = {0016-6731},
  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},
}