TY - JOUR
AB - 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.
AU - Barton, Nicholas H
AU - Etheridge, Alison
ID - 564
IS - 7
JF - Theoretical Population Biology
TI - Establishment in a new habitat by polygenic adaptation
VL - 122
ER -
TY - JOUR
AB - 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.
AU - Charlesworth, Brian
AU - Barton, Nicholas H
ID - 565
IS - 1
JF - Genetics
TI - The spread of an inversion with migration and selection
VL - 208
ER -
TY - DATA
AB - 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.
AU - Fraisse, Christelle
ID - 5757
KW - (mal)adaptation
KW - pleiotropy
KW - selective constraint
KW - evo-devo
KW - gene expression
KW - Drosophila melanogaster
TI - Supplementary Files for "Pleiotropy modulates the efficacy of selection in Drosophila melanogaster"
ER -
TY - JOUR
AB - 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.
AU - Bodova, Katarina
AU - Haskovec, Jan
AU - Markowich, Peter
ID - 607
JF - Physica D: Nonlinear Phenomena
TI - Well posedness and maximum entropy approximation for the dynamics of quantitative traits
VL - 376-377
ER -
TY - JOUR
AB - 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.
AU - Sachdeva, Himani
AU - Barton, Nicholas H
ID - 282
IS - 4
JF - Genetics
TI - Introgression of a block of genome under infinitesimal selection
VL - 209
ER -