@article{282, abstract = {Adaptive introgression is common in nature and can be driven by selection acting on multiple, linked genes. We explore the effects of polygenic selection on introgression under the infinitesimal model with linkage. This model assumes that the introgressing block has an effectively infinite number of genes, each with an infinitesimal effect on the trait under selection. The block is assumed to introgress under directional selection within a native population that is genetically homogeneous. We use individual-based simulations and a branching process approximation to compute various statistics of the introgressing block, and explore how these depend on parameters such as the map length and initial trait value associated with the introgressing block, the genetic variability along the block, and the strength of selection. Our results show that the introgression dynamics of a block under infinitesimal selection is qualitatively different from the dynamics of neutral introgression. We also find that in the long run, surviving descendant blocks are likely to have intermediate lengths, and clarify how the length is shaped by the interplay between linkage and infinitesimal selection. Our results suggest that it may be difficult to distinguish introgression of single loci from that of genomic blocks with multiple, tightly linked and weakly selected loci.}, author = {Sachdeva, Himani and Barton, Nicholas H}, journal = {Genetics}, number = {4}, pages = {1279 -- 1303}, publisher = {Genetics Society of America}, title = {{Introgression of a block of genome under infinitesimal selection}}, doi = {10.1534/genetics.118.301018}, volume = {209}, 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 = {00166731}, 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{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 = {00278424}, 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{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 = {1365294X}, 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{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 }, title = {{The spread of an inversion with migration and selection}}, doi = {10.1534/genetics.117.300426}, volume = {208}, 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}, } @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{139, abstract = {Genome-scale diversity data are increasingly available in a variety of biological systems, and can be used to reconstruct the past evolutionary history of species divergence. However, extracting the full demographic information from these data is not trivial, and requires inferential methods that account for the diversity of coalescent histories throughout the genome. Here, we evaluate the potential and limitations of one such approach. We reexamine a well-known system of mussel sister species, using the joint site frequency spectrum (jSFS) of synonymousmutations computed either fromexome capture or RNA-seq, in an Approximate Bayesian Computation (ABC) framework. We first assess the best sampling strategy (number of: individuals, loci, and bins in the jSFS), and show that model selection is robust to variation in the number of individuals and loci. In contrast, different binning choices when summarizing the jSFS, strongly affect the results: including classes of low and high frequency shared polymorphisms can more effectively reveal recent migration events. We then take advantage of the flexibility of ABC to compare more realistic models of speciation, including variation in migration rates through time (i.e., periodic connectivity) and across genes (i.e., genome-wide heterogeneity in migration rates). We show that these models were consistently selected as the most probable, suggesting that mussels have experienced a complex history of gene flow during divergence and that the species boundary is semi-permeable. Our work provides a comprehensive evaluation of ABC demographic inference in mussels based on the coding jSFS, and supplies guidelines for employing different sequencing techniques and sampling strategies. We emphasize, perhaps surprisingly, that inferences are less limited by the volume of data, than by the way in which they are analyzed.}, author = {Fraisse, Christelle and Roux, Camille and Gagnaire, Pierre and Romiguier, Jonathan and Faivre, Nicolas and Welch, John and Bierne, Nicolas}, journal = {PeerJ}, number = {7}, publisher = {PeerJ}, title = {{The divergence history of European blue mussel species reconstructed from Approximate Bayesian Computation: The effects of sequencing techniques and sampling strategies}}, doi = {10.7717/peerj.5198}, volume = {2018}, 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{286, abstract = {Pedigree and sibship reconstruction are important methods in quantifying relationships and fitness of individuals in natural populations. Current methods employ a Markov chain-based algorithm to explore plausible possible pedigrees iteratively. This provides accurate results, but is time-consuming. Here, we develop a method to infer sibship and paternity relationships from half-sibling arrays of known maternity using hierarchical clustering. Given 50 or more unlinked SNP markers and empirically derived error rates, the method performs as well as the widely used package Colony, but is faster by two orders of magnitude. Using simulations, we show that the method performs well across contrasting mating scenarios, even when samples are large. We then apply the method to open-pollinated arrays of the snapdragon Antirrhinum majus and find evidence for a high degree of multiple mating. Although we focus on diploid SNP data, the method does not depend on marker type and as such has broad applications in nonmodel systems. }, author = {Ellis, Thomas and Field, David and Barton, Nicholas H}, journal = {Molecular Ecology Resources}, number = {5}, pages = {988 -- 999}, publisher = {Wiley}, title = {{Efficient inference of paternity and sibship inference given known maternity via hierarchical clustering}}, doi = {10.1111/1755-0998.12782}, volume = {18}, year = {2018}, } @misc{5583, abstract = {Data and scripts are provided in support of the manuscript "Efficient inference of paternity and sibship inference given known maternity via hierarchical clustering", and the associated Python package FAPS, available from www.github.com/ellisztamas/faps. Simulation scripts cover: 1. Performance under different mating scenarios. 2. Comparison with Colony2. 3. Effect of changing the number of Monte Carlo draws The final script covers the analysis of half-sib arrays from wild-pollinated seed in an Antirrhinum majus hybrid zone.}, author = {Ellis, Thomas}, publisher = {Institute of Science and Technology Austria}, title = {{Data and Python scripts supporting Python package FAPS}}, doi = {10.15479/AT:ISTA:95}, 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}, } @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{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}, } @article{570, abstract = {Most phenotypes are determined by molecular systems composed of specifically interacting molecules. However, unlike for individual components, little is known about the distributions of mutational effects of molecular systems as a whole. We ask how the distribution of mutational effects of a transcriptional regulatory system differs from the distributions of its components, by first independently, and then simultaneously, mutating a transcription factor and the associated promoter it represses. We find that the system distribution exhibits increased phenotypic variation compared to individual component distributions - an effect arising from intermolecular epistasis between the transcription factor and its DNA-binding site. In large part, this epistasis can be qualitatively attributed to the structure of the transcriptional regulatory system and could therefore be a common feature in prokaryotes. Counter-intuitively, intermolecular epistasis can alleviate the constraints of individual components, thereby increasing phenotypic variation that selection could act on and facilitating adaptive evolution. }, author = {Lagator, Mato and Sarikas, Srdjan and Acar, Hande and Bollback, Jonathan P and Guet, Calin C}, issn = {2050084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Regulatory network structure determines patterns of intermolecular epistasis}}, doi = {10.7554/eLife.28921}, volume = {6}, year = {2017}, } @article{611, abstract = {Small RNAs (sRNAs) regulate genes in plants and animals. Here, we show that population-wide differences in color patterns in snapdragon flowers are caused by an inverted duplication that generates sRNAs. The complexity and size of the transcripts indicate that the duplication represents an intermediate on the pathway to microRNA evolution. The sRNAs repress a pigment biosynthesis gene, creating a yellow highlight at the site of pollinator entry. The inverted duplication exhibits steep clines in allele frequency in a natural hybrid zone, showing that the allele is under selection. Thus, regulatory interactions of evolutionarily recent sRNAs can be acted upon by selection and contribute to the evolution of phenotypic diversity.}, author = {Bradley, Desmond and Xu, Ping and Mohorianu, Irina and Whibley, Annabel and Field, David and Tavares, Hugo and Couchman, Matthew and Copsey, Lucy and Carpenter, Rosemary and Li, Miaomiao and Li, Qun and Xue, Yongbiao and Dalmay, Tamas and Coen, Enrico}, issn = {00368075}, journal = {Science}, number = {6365}, pages = {925 -- 928}, publisher = {American Association for the Advancement of Science}, title = {{Evolution of flower color pattern through selection on regulatory small RNAs}}, doi = {10.1126/science.aao3526}, volume = {358}, year = {2017}, } @article{626, abstract = {Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence may be as fast as 1∕M.}, author = {Barton, Nicholas H and Etheridge, Alison and Véber, Amandine}, issn = {00405809}, journal = {Theoretical Population Biology}, pages = {50 -- 73}, publisher = {Academic Press}, title = {{The infinitesimal model: Definition derivation and implications}}, doi = {10.1016/j.tpb.2017.06.001}, volume = {118}, year = {2017}, } @misc{9849, abstract = {This text provides additional information about the model, a derivation of the analytic results in Eq (4), and details about simulations of an additional parameter set.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Modelling and simulation details}}, doi = {10.1371/journal.pcbi.1005609.s001}, year = {2017}, } @misc{9850, abstract = {In this text, we discuss how a cost of resistance and the possibility of lethal mutations impact our model.}, author = {Lukacisinova, Marta and Novak, Sebastian and Paixao, Tiago}, publisher = {Public Library of Science}, title = {{Extensions of the model}}, doi = {10.1371/journal.pcbi.1005609.s002}, year = {2017}, }