Theoretical population genetics

Most of evolutionary theory considers neutral models of evolution, or selection acting on one, two, or maybe a few sites at a time. Most populations, however, are polymorphic at a large number of sites and a fraction of these sites is under selection. Furthermore, fitness might depend on particular combinations of alleles, i.e. alleles might interact and their effect is dependent on the genetic background. The large number of possible genotypes and the constant reshuffling of alleles make multi-locus evolution a challenging subject. Statistical physics, however, provides many examples how complex systems with many degrees of freedom give rise to simple macroscopic behavior. We want to explore how methods from statistical physics can help to develop a general understanding of multi-locus evolution.

Individual Projects

Coalescent processes and genealogies in rapidly adapting populations. 

The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies that emerge from models of continual adaptation. We show that lineages trace back to a small pool of highly fit ancestors, in which simultaneous coalescence of more than two lineages frequently occurs. While such multiple mergers are unlikely under the neutral coalescent, they create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is non-monotonic and has a peak at high frequencies, whereas Tajima's D becomes more and more negative with increasing sample size. Since multiple merger coalescents emerge in various evolutionary scenarios characterized by sustained selection pressures, we argue that they should be considered as null-models for adapting populations.

Opens external link in new windowGenealogies of rapidly adapting populations. R.A. Neher and O. Hallatschek.

Source code of the simulations and analysis scripts.

see also the Opens external link in new windowarticle by M.M. Desai, A. Walczak, and D.S. Fisher who come to very similar conclusions.


Recombination and Epistasis

Recombination and re-assortment of chromosomes continuously reshuffle genomes in the population allowing selection to act directly on alleles and eliminate the less fit variants. Yet recombination can also be detrimental to fitness because it breaks up the combinations of alleles that interact synergistically with each other.

In the presence of genetic interaction, selection and recombination therefore act as opposing forces, the former trying to enrich favorable combinations, the latter breaking them apart and producing novel variants. We study a model of natural selection in a recombining population. We find, that depending on the relative strength of epistasis and recombination, two distinct  "phases" of selection appear. In one regime, recombination wins over selection and decouples the loci along the genome, such that selection
operates on individual loci. In the other regime, selection is sufficiently strong to overcome recombination and amplifies fit genotypes, which then enter a competition between clonal subpopulations.

Opens external link in new windowCompetition between recombination and epistasis can cause a transition from allele to genotype selection
R.A. Neher and B.I. Shraiman, Proc. Natl. Acad. Sci, vol. 106 pp. 6866-6871, (2009)

Opens external link in new windowStatistical Genetics and Evolution of Quantitative Traits.
R.A. Neher, B.I. Shraiman, Rev. Mod. Phys (2011), Vol 83(4), pp. 1283.


Adaptation in sexual populations

Adaptation to novel environments often requires the acquisition of a large number of alterations in the genome which arise as mutations in single individuals. In asexual populations, mutations can fix only when they arise in the common ancestor of the future population, while in a population where genetic information is exchanged between individuals, beneficial mutations can
arise in different individuals and still be combined later. We calculated the rate of adaptation in a sexual population where individuals outcross and reassort their genes with rate r. We show that the rate of adaptation increases only logarithmically with the population size and the mutation rate when populations are large. Furthermore, the rate of adaptation increases with the
outcrossing rate r as  ~r2, which implies a strong evolutionary benefit of sex.

Opens external link in new windowRate of Adaptation in Large Sexual Populations.
R.A. Neher, B. I. Shraiman and D. S. Fisher. Genetics (2010) vol. 184 pp. 467-481

Opens external link in new windowGenetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations.
R.A. Neher, B.I. Shraiman, Genetics (2011)


Population genetic inference

In most cases, evolution is too slow to be observed directly (HIV intra-patient evolution being a prominent exception). In such cases, parameters have to be inferred by comparing patterns of genetic diversity to expectations generated by simple models. We have developed methods to use patterns of rare variation to estimate selection coefficients of beneficial variants. We have also looked at patterns of correlated substitutions to estimate the prevalence of compensatory evolution in adaptation.

Opens external link in new windowEstimating the Strength of Selective Sweeps from Deep Population Diversity Data.
P.W. Messer and R.A. Neher. Genetics (2012), accepted.

Opens external link in new windowCorrelated Evolution of Nearby Residues in Drosophilid Proteins.
B. Callahan, R.A. Neher, D. Bachtrog, P. Andolfatto, B.I. Shraiman, PLoS Genet (2011) vol. 7 (2) pp. e1001315


Deleterious Mutations and Muller's ratchet

The majority of mutations are deleterious and the importance of deleterious mutations for the evolutionary process and their contribution to intra-species diversity have long been debated. The term "Muller's Ratchet" has been coined to describe the phenomenon of almost irreversible (other than exact back mutation) accumulation of deleterious mutations in asexual populations. Muller's ratchet has mostly been studied in a very simple model introduced by Haigh, which despite its simplicity has resisted a satisfactory solution. We have recently made two contributions that (i) calculate the rate of Muller's ratchet in a consistent manner, and (ii) determine how large a beneficial mutation rate is necessary to offset the ratchet.

Opens external link in new windowFluctuations of fitness distributions and the rate of Muller's ratchet. R.A. Neher and B.I. Shraiman.

 Opens external link in new windowRare beneficial mutation can halt Muller's ratchet. Sidhartha Goyal, Daniel J. Balick, Elizabeth R. Jerison, Richard A. Neher, Boris I. Shraiman, Michael M. Desai.