Abstract: Many species are distributed
in space with local subpopulations connected by migration. If environmental
conditions vary in space, such species experience spatially heterogeneous selection which often acts on multiple genes. Local
adaptation of a subpopulation to its environment may be
counteracted by maladaptive gene flow from other subpopulations that are
genetically different. Strong gene flow or small population size can lead to
loss of variation and to genetic homogeneity. Lack of genetic diversity may
hamper future adaptation to changing environmental conditions and endanger
population survival.
Of particular interest are quantitative insights into
the dependence of the degree of local adaptation and the degree of genetic
divergence among subpopulations on the pattern and rate of migration, the form
and intensity of selection, the genetic architecture of the traits under
selection, and on population size and random genetic drift. From a genomics or
data-oriented point of view, it is important to quantify the combined
consequences of selection and gene flow on neutral (marker) sites linked to the
selected loci.
Using mathematical models, we shall explore the
consequences of genetic architecture on the maintenance of genetic variation,
on the evolution of local adaptation, and on the advance of genetic divergence
(an important factor in speciation). In particular, we will examine the role of
linkage, of the relative magnitude of locus effects, and of epistatic
interactions between loci. Of equal interest, and intimately related, is the
study of the evolution of genetic architecture caused by divergent selection.
We shall investigate the evolution of recombination, of chromosomal inversions,
and of genetic incompatibilities between subpopulations. A proper mathematical
treatment is very challenging because it requires the analysis of genuine multilocus models, both in a deterministic and a stochastic
context. Mathematical analyses will be complemented by
extensive computer simulations.
One major line of research will focus on stochastic
models that describe evolution of a finite population inhabiting discrete
demes. For the scenarios outlined above, we will analyze the invasion and
sojourn properties of locally beneficial mutations in a genomic context and the
concomitant signatures induced at linked neutral sites. The corresponding tools
are provided by the theory of branching processes,
Markov chains, and diffusion processes. A second major line of research will
focus on (infinitely large) populations distributed continuously in space.
Their evolution is modeled by systems of semilinear parabolic differential equations. We strive to
establish general existence, convergence, and perturbation results for multilocus clines, i.e., of non-constant stationary
solutions that describe the distribution of genotype frequencies in space. We
shall study the invasion of locally advantageous alleles at linked loci and the
consequences of linkage for the existence and properties of clines.
Persons funded by this project:
·
Ada Akerman:
PhD student from 01.01.2013 – 31.10.2013
·
Simon Aeschbacher: Postdoc from 16.12.2012 – 31.12.2013
·
Linlin Su: Postdoc from 01.08.2013 – 15.08.2014
·
Sebastian Matuszewski: PhD student from 01.08.2014 – 31.12.2014;
Postdoc from 01.01.2015 – 31.01.2015
·
Ludwig Geroldinger: PhD student from 01.09.2014 – 31.12.2014, Postdoc
from 01.01.2015 – 31.03.2015
·
Martin Pontz: Master student,
Forschungsbeihilfe 01.07.2015 – 30.11.2015
·
Swati Patel, Postdoc from
19.09.2016 – 31.08.2017
Publications
(partially) funded by this project:
Aeschbacher
S, Bürger R: The effect of linkage on establishment and survival of locally
beneficial mutations. Genetics 197,
317-336 (2014)
Akerman
A, Bürger R: The consequences of gene flow for local adaptation and
differentiation: a two-locus two-deme model. J. Math. Biol. 68, 1135-1198 (2014)
Akerman
A, Bürger R: The consequences of dominance and gene flow for local adaptation
and differentiation at two linked loci. Theor. Popul. Biol. 94, 42-61 (2014)
Bürger R: A survey of migration-selection models in population genetics.
Discrete Cont. Dyn.
Syst. B 19, 883-959 (2014)
Bürger
R: Two-locus clines on the real line with a step environment. Theor. Popul. Biol. 117, 1-22
(2017)
Geroldinger
L, Bürger R: A two-locus model of spatially varying stabilizing or directional
selection on a quantitative trait. Theor. Popul. Biol. 94, 10-41 (2014)
Geroldinger
L, Bürger R: Clines in quantitative traits: The role of migration patterns and
selection scenarios. Theor. Popul. Biol.
99, 43-66 (2015)
Hofbauer
J, Su L: Global stability in diallelic
migration-selection models. J. Math.
Anal. Appl. 428, 677-695 (2015)
Hofbauer
J, Su L: Global stability of spatially homogeneous equilibria in
migration-selection models. SIAM J. Appl.
Math. 76, 578-597 (2016)
Jones AG, Bürger R, Arnold SJ: Epistasis and
natural selection shape the mutational architecture of complex traits. Nat. Commun. 5:3709 (2014)
Matuszewski S., J. Hermisson
and M. Kopp: Catch me if you can: Adaptation from
standing genetic variation to a moving phenotypic optimum. Genetics 200, 1255-1274 (2015)
Nagylaki
T, Su L, Alevy I, Dupont
TF: Clines with partial panmixia in an environmental
pocket. Theor. Popul. Biol. 95, 24–32 (2014)
Patel S, Bürger R: Eco-evolutionary feedbacks between predator’s linkage
disequilibrium and prey densities maintain diversity. bioRxiv doi:
Patel S, Schreiber S: Robust permanence for ecological equations with
internal and external feedbacks. J. Math.
Biol. 77, 79-105 (2018); doi: 10.1007/s00285-017-1187-5
Pontz M, Hofbauer J, Bürger R: Evolutionary dynamics in the
two-locus two-allele model with weak selection. J. Math. Biol. 76, 151–203
(2018); doi: 10.1007/s00285-017-1140-7
Servedio
M, Bürger R: The counterintuitive role of sexual selection in species
maintenance and speciation. Proc. Natl.
Acad. Sci. 111, 8113-8118 (2014)
Servedio M, Bürger R: The effects of sexual selection on trait divergence in a
peripheral population with gene flow. Evolution 69, 2648–2661 (2015)
Su L, Lam K-Y, Bürger R: Two-locus clines maintained by diffusion and
recombination in a heterogeneous environment. J. Differential Equations, online first (2018), https://doi.org/10.1016/j.jde.2018.12.022; see also https://arxiv.org/abs/1808.03665
Su L, Nagylaki T: Clines with directional
selection and partial panmixia in an unbounded
unidimensional habitat. Discrete Cont. Dyn. Syst. A 35, 1697-1741 (2015)
Yeaman S, Aeschbacher S, Bürger R. The evolution of
genomic islands by increased establishment probability of linked alleles. Molecular
Ecology 25, 2542–2558
(2016)