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Abstract The literature about mutant invasion and fixation typically assumes populations to exist in isolation from their ecosystem. Yet, populations are part of ecological communities, and enemy-victim (e.g. predator-prey or pathogen-host) interactions are particularly common. We use spatially explicit, computational pathogen-host models (with wild-type and mutant hosts) to re-visit the established theory about mutant fixation, where the pathogen equally attacks both wild-type and mutant individuals. Mutant fitness is assumed to be unrelated to infection. We find that pathogen presence substantially weakens selection, increasing the fixation probability of disadvantageous mutants and decreasing it for advantageous mutants. The magnitude of the effect rises with the infection rate. This occurs because infection induces spatial structures, where mutant and wild-type individuals are mostly spatially separated. Thus, instead of mutant and wild-type individuals competing with each other, it is mutant and wild-type “patches” that compete, resulting in smaller fitness differences and weakened selection. This implies that the deleterious mutant burden in natural populations might be higher than expected from traditional theory. 

Human immunodeficiency virus (HIV-1) replicates in the secondary lymphoid tissues, which are characterized by complex compartmental structures. While cytotoxic T lymphocytes (CTL) readily access infected cells in the extrafollicular compartments, they do not home to follicular compartments, which thus represent an immune-privileged site. Using mathematical models, previous work has shown that this compartmental tissue structure can delay the emergence of CTL escape mutants. Here, we show computationally that the compartmental structure can have an impact on the evolution of advantageous mutants that are not related to CTL recognition: (i) compartmental structure can influence the fixation probability of an advantageous mutant, with weakened selection occurring if CTL responses are of intermediate strength; (ii) compartmental structure is predicted to reduce the rate of mutant generation, which becomes more pronounced for stronger CTL responses; and (iii) compartmental structure is predicted to slow down the overall rate of mutant invasion, with the effect becoming more pronounced for stronger CTL responses. Altogether, this work shows thatin vivovirus evolution proceeds slower in models with compartmental structure compared with models that assume equivalent virus load in the absence of compartmental structure, especially for strong CTL-mediated virus control. This has implications for understanding the rate of disease progression. 

We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms.