How the tortoise beats the hare: Slow and steady adaptation in structured populations suggests a rugged fitness landscape in bacteria

How the tortoise beats the hare: Slow and steady adaptation in structured populations suggests a rugged fitness landscape in bacteria

Joshua R. Nahum, Peter Godfrey-Smith, Brittany N. Harding, Joseph H. Marcus, Jared Carlson-Stevermer, Benjamin Kerr

In the context of Wright’s adaptive landscape, genetic epistasis can yield a multi-peaked or “rugged” topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to rapidly fix on one, which may not be the highest peak. Contrarily, beneficial mutations in a population with spatially restricted migration take longer to fix, allowing distant parts of the population to explore the landscape semi-independently. Such a population can simultaneous discover multiple peaks and the genotype at the highest discovered peak is expected to fix eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the Tortoise-Hare fable, the structured population (Tortoise) starts relatively slow, but eventually surpasses the unstructured population (Hare) in average fitness. In contrast, on single-peak landscapes (e.g., systems lacking epistasis), all uphill paths converge. Given such “smooth” topography, breadth of search is devalued, and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the Tortoise-Hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we then explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a Tortoise-Hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright’s Shifting Balance Process.

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