The evolution of fitness during range expansions in different dimensions

ABSTRACT We develop a set of programs – the range expansions simulation kit (RESK) – to efficiently simulate range expansions of populations on a square lattice in 1D, 2D (on a strip, and on a disk) and 3D (in a cylinder, and in a sphere). In this study, we present the simulation kit to the public and present some results of using it to simulate a population of diploid individuals with finite genome regions, each containing infinite sites. Specifically, using the programs, we calculate and analyse the temporal evolution of population fitness, as well as fitness on the expansion front, in 3D for the first time. We explore the model over different conditions, compare normalisation methods for fitness, and explore the case of radial (sphere) and axial (cylinder) expansions in 3D, which might apply in the analysis of the different real-life populations, such as viruses/bacteria inside a host, marine species in ocean environments, and potentially in future space colonization planning. In 3D expansions, we find complex spatial fluctuations in deme-average fitness values, different from those in radial 2D expansions. In axial 3D (cylinder) expansions, we determine that the highest-valued deme-average fitness lies along the axis of the expansion. We also find the fluctuation patterns of fitness in 3D cylinder expansions, similar to those previously seen in radial expansions in 2D. In radial 2D (disk) expansions, we find that the fitness of a population undergoing multiple mutations shows a smooth combination of binary segregation pictures against each of those mutations. We confirm the accumulation of deleterious mutations -- a phenomenon known as expansion load -- in all scenarios above. We present the software used in the above to the public as a Julia repository, ready to use with different functions for simulating range expansions with minimal syntax.