Increasing growth rate slows adaptation when genotypes compete for diffusing resources

Abstract

The rate at which a species responds to natural selection is a central predictor of the species ability to adapt to environmental change. It is well-known that spatially-structured environments slow the rate of adaptation due to increased intra-genotype competition. Here, we show that this effect magnifies over time as a species becomes better adapted and grows faster. Using a reaction-diffusion model, we demonstrate that growth rates are inextricably coupled with effective spatial scales, such that higher growth rates cause more localized competition. This has two effects: selection requires more generations for beneficial mutations to fix, and spatially-caused genetic drift increases. Together, these effects diminish the value of additional growth rate mutations in structured environments.\n\nAuthor SummaryWhat determines how quickly a beneficial mutation will spread through a population? The intuitive answer is that mutations that confer faster growth rates will spread at a rate that is relative to the size of the growth-rate benefit. Indeed, this is true in a well-mixed environment where all genotypes compete globally. But most organisms dont live in a simple well-mixed environment. Many organisms, like bacteria, live in a structured environment, such as on the surface of a solid substrate. Does life on a surface change the expectation about the spread of faster-growing mutants? We developed a mathematical model to answer this question, and found that on a surface, the actual growth rates--not just the relative growth rates--were critical to determining how fast a faster-growing mutant spread through a population. When the simulated organisms grew slowly, competition was basically global and a faster-growing mutant could pre-empt resources from far-away competitors. In contrast, when organisms grew more quickly, competition became much more localized, and the faster-growing mutant could only steal resources from neighboring competitors. This result means that there are diminishing returns to series of mutations which confer growth-rate benefits. This idea will help us predict and understand future and past evolutionary trajectories.