Search strategies that find generalists in time varying environments

Many evolutionary and ecological processes can be seen as a search process for fitter genotypes or spatial regions with more resources. Time varying environments are often thought to naturally bias such search processes towards generalists, i.e., regions with relatively smaller changes in fitness or resources over time. But it is not clear what underlying characteristics of a search process lead to this effect.

Here we consider several search processes in biology such as foraging in real space, growth of microtubules towards chromosomes, and evolution towards fitter genotypes in sequence space. We find that a class of biased random walks that we call `directed’ are naturally driven towards generalists by time varying environments at intermediate timescales; this class includes classic E. coli chemotaxis with run times modulated by food availability and constant tumble times. However, closely related `undirected’ biased walks are not driven towards generalists, such as chemotaxis with constant run times but modulated tumble times. The distinction between directed and undirected walks corresponds to the Ito and Stratonovich ambiguity in stochastic calculus. Our work provides examples where the microscopic details of biological search have macroscopic consequences.