A coarse-grained biophysical model of sequence evolution and the population size dependence of the speciation rate.
Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineages leads to incompatibilities. To develop a tractable analytical theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution that accounts for the fact that natural selection acts on phenotypes, but variation arises from mutations in sequences; the Smoluchowski equation includes selection due to both gradients in fitness and gradients in sequence entropy, which is the logarithm of the number of sequences that correspond to a particular binding energy. This simple consideration predicts that smaller populations develop incompatibilities more quickly in the weak mutation regime; this trend arises as sequence entropy poises smaller populations closer to incompatible regions of phenotype space. These results suggest a generic coarse-grained approach to evolutionary stochastic dynamics, allowing realistic modelling at the phenotypic level.
The Francis Crick Institute, Mill Hill Laboratory, The Ridgeway, London NW7 1AA, UK; Division of Infection & Immunity, University College London, London WC1E 6BT, UK. Electronic address: bhavin.khatri@physics.org.
Bhavin S
BS
Khatri
Division of Infection & Immunity, University College London, London WC1E 6BT, UK. Electronic address: r.goldstein@ucl.ac.uk.
Richard A
RA
Goldstein
D000818:Animals; D004268:DNA-Binding Proteins / Q000378:metabolism; D019143:Evolution, Molecular; D049810:Genetic Speciation; D008957:Models, Genetic; D011156:Population Density; D012641:Selection, Genetic; D013269:Stochastic Processes
D004268:DNA-Binding Proteins
Dobzhansky Muller incompatibilities; Evolution; Free fitness; Genotype phenotype map; Sequence entropy