26The rate at which a species responds to natural selection is a central predictor of the species' ability to 27 adapt to environmental change. It is well-known that spatially-structured environments slow the rate of 28 adaptation due to increased intra-genotype competition. Here, we show that this effect magnifies over 29 time as a species becomes better adapted and grows faster. Using a reaction-diffusion model, we 30 demonstrate that growth rates are inextricably coupled with effective spatial scales, such that higher 31 growth rates cause more localized competition. This has two effects: selection requires more 32 generations for beneficial mutations to fix, and spatially-caused genetic drift increases. Together, these 33 effects diminish the value of additional growth rate mutations in structured environments. 34
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Author Summary 36What determines how quickly a beneficial mutation will spread through a population? The intuitive 37 answer is that mutations that confer faster growth rates will spread at a rate that is relative to the size of 38 the growth-rate benefit. Indeed, this is true in a well-mixed environment where all genotypes compete 39 globally. But most organisms don't live in a simple well-mixed environment. Many organisms, like 40 bacteria, live in a structured environment, such as on the surface of a solid substrate. Does life on a 41 surface change the expectation about the spread of faster-growing mutants? We developed a 42mathematical model to answer this question, and found that on a surface, the actual growth rates-not 43 just the relative growth rates-were critical to determining how fast a faster-growing mutant spread 44 through a population. When the simulated organisms grew slowly, competition was basically global 45 and a faster-growing mutant could pre-empt resources from far-away competitors. In contrast, when 46 organisms grew more quickly, competition became much more localized, and the faster-growing 47 mutant could only steal resources from neighboring competitors. This result means that there are 48 diminishing returns to series of mutations which confer growth-rate benefits. This idea will help us 49 predict and understand future and past evolutionary trajectories. 50