Biology subjects

Nick H Barton

Publications and source records attributed to Nick H Barton.

2 recordsLinked to original sources

bioRxiv2016

The infinitesimal model

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 as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. We first review the long history of the infinitesimal model in quantitative genetics. Then we provide a definition of 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. In each case, by conditioning on the pedigree relating individuals in the population, we incorporate arbitrary selection and population structure. We suppose that we can observe the pedigree up to the present generation, together with all the ancestral traits, and we show, in particular, that 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 [Formula]. Simulations suggest that in particular cases the convergence may be as fast as 1/M.

Evolutionary Biology↗

bioRxiv2015

Efficient strategies for calculating blockwise likelihoods under the coalescent

The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proven difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of genealogies can be used to analytically compute likelihoods of demographic models from configurations of mutations in short sequence blocks (Lohse et al., 2011). Although the GF has a simple, recursive form, the size of such likelihood computations explodes quickly with the number of individuals and applications of this framework have so far been limited to small samples (pairs and triplets) for which the GF can be written down by hand. Here we investigate several strategies for exploiting the inherent symmetries of the coalescent. In particular, we show that the GF of genealogies can be decomposed into a set of equivalence classes which allows likelihood calculations from non-trivial samples. Using this strategy, we used Mathematica to automate block-wise likelihood calculations based on the GF for a very general set of demographic scenarios that may involve population size changes, continuous migration, discrete divergence and admixture between multiple populations. To give a concrete example, we calculate the likelihood for a model of isolation with migration (IM), assuming two diploid samples without phase and outgroup information, and compare the power of our approach to that of minimal pairwise samples. We demonstrate the new inference scheme with an analysis of two individual butterfly genomes from the sister species Heliconius melpomene rosina and Heliconius cyndo.

Genetics↗