A theory of evolutionary dynamics on any complex spatial structure

Abstract

Understanding how the spatial arrangement of a population shapes its evolutionary dynamics has been of long-standing interest in population genetics. Most previous studies assume a small number of demes connected by migration corridors, symmetrical structures that most often act as well-mixed populations. Other studies use networks to model the more complex topologies of natural populations and to study the structures that suppress or amplify selection. However, they usually assume very small, regular networks, with strong constraints on the strength of selection considered. Here we build network generation algorithms, evolutionary simulations and derive general analytic approximations for probabilities of fixation in populations with complex spatial structure. By tuning network parameters and properties independent of each other, we systematically span across network families and show that both a network's degree distribution, as well as its node mixing pattern shape the evolutionary dynamics of new mutations. We analytically write the relevant selective parameter, predictive of evolutionary dynamics, as a combination of network statistics. As one application, we use recent imaging datasets and build the cellular spatial networks of the stem cell niches of the bone marrow. Across a wide variety of parameters and regardless of the birth-death process used, we find these networks to be strong suppressors of selection, delaying mutation accumulation in this tissue. We also find that decreases in stem cell population size decrease the suppression strength of the tissue spatial structure, hinting at a potential diminishing spatial suppression in the bone marrow tissue as individuals age.

Do amplifiers of selection maximise average fitness?

“…The prospects of engineering a population structure that can optimise the chances to evolve certain mutations or to observe evolved population structures that minimise the evolution of mutations seem exciting, but these applications call for an extension of the field of Evolutionary graph theory: Most applications implicitly assume that each node is a small population and not all results carry over from graphs of individuals to graphs of sub-populations [34][35][36][37]. In addition, the field has focussed so far on fixation probability and fixation time [38][39][40][41][42][43].…”

“…More than a decade ago, a framework known as Evolutionary graph theory has been introduced [1]. The primary quantity of interest has been the fixation probability of a mutant on graphs, which is the probability that a mutant with given fitness takes over the rest of the wild-type population [2][3][4][5][6].…”

Categorising update mechanisms for graph-structured metapopulations

“…For small populations under the update mechanism Bd , most small structures are amplifiers of selection, and only a minimal fraction of structures suppress selection [5]. In larger populations, in the weak selection regime, there are quite a lot of graphs that suppress selection [27]. Furthermore, some structures have the same fixation probability as the complete graph.…”

Fixation probabilities in network structured meta-populations

“…This approach can be motivated by several biological systems, from the spread of cancerous mutations through colonic crypts to the invasion of ecosystems structured by rivers. One of the major goals of evolutionary graph theory 1 is to assess the effect of underlying population structure on the fixation probability (the probability of ultimate fixation of a mutant) [2][3][4][5][6] and the fixation time [7][8][9][10] . An important aim is to find an optimized structure to speed up or slow down the spread of a newly arising mutant [11][12][13] .…”