The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation (SSWM) regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and how it affects the form of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the form of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the functional form of the fitness trajectory, while an enhancement of the beneficial mutation rate does the opposite of slowing down the form of the dynamics. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs. change in fraction of beneficial mutations).

Intra-Population Competition during Adaptation to Increased Temperature in an RNA Bacteriophage

Evolution of RNA bacteriophages of the family Leviviridae is governed by the high error rates of their RNA-dependent RNA polymerases. This fact, together with their large population sizes, leads to the generation of highly heterogeneous populations that adapt rapidly to most changes in the environment. Throughout adaptation, the different mutants that make up a viral population compete with each other in a non-trivial process in which their selective values change over time due to the generation of new mutations. In this work we have characterised the intra-population dynamics of a well-studied levivirus, Qβ, when it is propagated at a higher-than-optimal temperature. Our results show that adapting populations experienced rapid changes that involved the ascent of particular genotypes and the loss of some beneficial mutations of early generation. Artificially reconstructed populations, containing a fraction of the diversity present in actual populations, fixed mutations more rapidly, illustrating how population bottlenecks may guide the adaptive pathways. The conclusion is that, when the availability of beneficial mutations under a particular selective condition is elevated, the final outcome of adaptation depends more on the occasional occurrence of population bottlenecks and how mutations combine in genomes than on the selective value of particular mutations.

Dynamic Analysis of a Population Competition Model with Disease in One Species and Group Defense in Another Species

In this paper, we study the dynamics of an ecoepidemic competition system where the individuals of one population gather together in herds with a defensive strategy, showing social behavior, while another predator population is subject to a transmissible disease and behaves individually. By analyzing the existence and stability of the equilibria of the system, we find that the relatively isolated population can be eradicated, or the population with group defense can live alone eventually under some constraints. Infected individuals end up in two possible situations. In the first case, the disease is eventually eliminated, meaning that only healthy and group-defense individuals in the system can survive. In the other case, the spread of the disease is controlled and eventually all three individuals can coexist. We also conduct a correlation analysis using competition parameter and recovery rate of disease as birfurcation parameters in order to study the transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. The long-term dynamics of the boundary and interior equilibria are demonstrated by numerical simulations.

A Stackelberg-population competition model via variational inequalities and fixed points

In this paper, we introduce and study a new Stackelberg-population competition model which captures the desired features of both population games and Stackelberg competition model within the same framework. We obtain some characterization results for the Stackelberg-population equilibrium response set and the Stackelberg-population equilibrium leader set by using the variational inequality technique and Brouwer’s fixed point theorem. We also show an existence theorem of Nash equilibrium for Stackelbergpopulation competition model under some mild conditions. Finally, we give an example to illustrate our main results.