Biology subjects

Khatri, B. S.

Publications and source records attributed to Khatri, B. S..

3 recordsLinked to original sources

bioRxiv2018

Survival of the frequent at finite population size and mutation rate: filing the gap between quasispecies and monomorphic regimes

In recent years, there has been increased attention on the non-trivial role that genotype-phenotype maps play in the course of evolution, where natural selection acts on phenotypes, but variation arises at the level of mutations. Understanding such mappings is arguably the next missing piece in a fully predictive theory of evolution. Although there are theoretical descriptions of such mappings for the monomorphic (N << 1) and deterministic or very strong mutation (N [>>>] 1) limit, given by developments of Iwasas free fitness and quasispecies theories, respectively, there is no general description for the intermediate regime where N ~ 1. In this paper, we address this by transforming Wrights well-known stationary distribution of genotypes under selection and mutation to give the probability distribution of phenotypes, assuming a general genotype-phenotype map. The resultant distribution shows that the degeneracies of each phenotype appear by weighting the mutation term; this gives rise to a bias towards phenotypes of larger degeneracy analogous to quasispecies theory, but at finite population size. On the other hand we show that as population size is decreased, again phenotypes of higher degeneracy are favoured, which is a finite mutation description of the effect of sequence entropy in the monomorphic limit. We also for the first time (to the authors knowledge) provide an explicit derivation of Wrights stationary distribution of the frequencies of multiple alleles.

evolutionary biology↗

bioRxiv2017

Rate Of Fixation Of Rare Variants In A Population

The process of molecular evolution has been dominated by the Kimura paradigm for nearly 60 years; mutations arise at a certain rate in the population and they go to fixation with a probability given by Kimuras classic formula, which assumes there are no further mutations that interfere with the fixation process. An alternative view is that rare variants exist in the population in a mutation-drift-selection balance and rise to fixation through a combination of chance (genetic drift), selection and mutation. When mutations increase in strength, but still in the weak regime, we would expect the Kimura rate approximation to be an overestimate, as a rare variant which grows in frequency will suffer a greater backward flux of mutations, slowing progress to fixation. However, to date calculating important quantities for a general model of selection and mutation, like the rate of fixation of these rare variants has not been tractable in the conventional diffusion approximation of population genetics. Here, we use Fishers angular transformation to convert the frequency-dependent diffusion inherent in population genetics to simple diffusion in an effective potential, which describes the forces of selection, drift and mutation. Once this potential is defined it is simple to show that the mean first passage time is given by a double integral which relate to populations at the barrier. Exact numerical integration shows excellent agreement with discrete Wright-Fisher simulations, which do show a slowing down of the fixation of mutants at higher mutation rates and for strong positive selection, compared to the Kimura prediction. We then seek a closed-form analytical expression for the rate of fixation of mutants, by adapting Kramers approximation for the mean first passage time. This overall gives an accurate approximation, but however, does not improve on the Kimura rate.

evolutionary biology↗

bioRxiv2017

Pairwise Hybrid Incompatibilities Dominate During Allopatric Speciation For A Simple Genotype-Phenotype Map Of Embryonic Spatial Patterning

Developmental system drift is a likely mechanism for the origin of hybrid incompatibilities between closely related species. We examine here the detailed mechanistic basis of hybrid incompatibilities for a genotype-phenotype map for developmental system drift under stabilising selection, where the organismal phenotype is conserved, but the underlying molecular phenotypes and genotype can drift. This leads to number of emergent phenomenon not obtainable by modelling genotype or phenotype alone. Our results show that: 1) speciation is more rapid at smaller population sizes with a characteristic, Orr-like, power law, but at large population sizes slow, characterised by a sub-diffusive growth law; 2) the molecular phenotypes under weakest selection contribute to the earliest incompatibilities; and 3) pairwise incompatibilities dominate over higher order, contrary to previous predictions that the latter should dominate. Our results indicate that biophysics and population size provide a much stronger constraint to speciation than suggested by previous models.

evolutionary biology↗