A numerical framework for genetic hitchhiking in populations of variable size

Natural selection on beneficial or deleterious alleles results in an increase or decrease, respectively, of its frequency within the population. Due to chromosomal linkage, the dynamics of the selected site affect the genetic variation at nearby neutral loci in a process commonly referred to as genetic hitchhiking. Changes in population size, however, can yield patterns in genomic data that mimic the effects of selection. Accurately modeling these dynamics is thus crucial to understanding how selection and past population size changes impact observed patterns of genetic variation. Here, we model the evolution of haplotype frequencies with the Wright-Fisher diffusion to study the impact of selection on linked neutral variation. Explicit solutions are not known for the dynamics of this diffusion when selection and recombination act simultaneously. Thus, we present a method for numerically evaluating the Wright-Fisher diffusion dynamics of two linked loci separated by a certain recombination distance when selection is acting. We can account for arbitrary population size histories explicitly using this approach. A key step in the method is to express the moments of the associated transition density, or sampling probabilities, as solutions to ordinary differential equations. Numerically solving these differential equations relies on a novel accurate and numerically efficient technique to estimate higher order moments from lower order moments. We demonstrate how this numerical framework can be used to quantify the reduction and recovery of genetic diversity around a selected locus over time and elucidate distortions in the site-frequency-spectra of neutral variation linked to loci under selection in various demographic settings. The method can be readily extended to more general modes of selection and applied in likelihood frameworks to detect loci under selection and infer the strength of the selective pressure.

A role for neutral variation in the evolution of C4 photosynthesis

Convergent trait evolution is a recurrent phenomenon in all domains of the tree of life. While some convergent traits are caused by simple sequence changes, many are associated with extensive changes to the sequence and regulation of large cohorts of genes. It is unknown how organisms traverse this expansive genotype space to assemble such complex convergent phenotypes. C4 photosynthesis is a paradigm of large-scale phenotypic convergence. Conceptual and mathematical models propose that C4 photosynthesis evolved from ancestral C3 photosynthesis through sequential adaptive changes. These adaptive changes could have been rapidly assembled if modifications to the activity and abundance of enzymes of the C4 cycle was neutral in C3 plants. This neutrality would enable populations of C3 plants to maintain genotypes with expression levels of C4 enzymes analogous to those in C4 species and thus enable rapid assembly of a functional C4 cycle from naturally occurring genotypes given shared environmental selection. Here we show that there is substantial natural variation in expression of genes encoding C4 cycle enzymes between natural accessions of the C3 plant Arabidopsis thaliana. We further show through targeted transgenic experiments in the C3 crop Oryza sativa, that high expression of the majority of C4 cycle enzymes in rice is neutral with respect to growth, development, biomass and photosynthesis. Thus, substantial variation in the abundance and activity of C4 cycle enzymes is permissible within the limits of operation of C3 photosynthesis and the emergence of component parts of this complex convergent trait can be facilitated by neutral variation.