Evolution of populations expanding on curved surfaces^(a)

¹ Department of Physics, University of California - Merced, CA, 95343, USA
² School of Engineering, Brown University - Providence, RI 02912, USA
³ Department of Applied Physics, Eindhoven University of Technology - P.O. Box 513, 5600 MB Eindhoven, The Netherlands
⁴ Laboratoire de Physique et Mécanique des Milieux Hétérogénes (PMMH), CNRS, ESPCI Paris PSL Research University, Sorbonne Université, Univ. Paris Diderot - Paris, 75005, France
⁵ Departamento de Matemática Aplicada, Universidade Estadual de Campinas - 13083-859, Campinas, SP, Brazil
⁶ Living Systems Institute, University of Exeter - Exeter, EX4 4QD, UK
⁷ Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter Exeter, EX4 4QL, UK

Received: 21 July 2018
Accepted: 4 September 2018

Abstract

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.