Fig 1. Population model.

A) General model: individuals can adopt N different phenotypes with probabilities α_j (j = 1, ⋯, N) and experience M different environmental conditions with probabilities p_i (i = 1, ⋯, M). The fitness of an individual with phenotype j in an environment i is given by s_ij. B) Two-phenotypes model: Individuals can adopt either a “risky” or a “safe” phenotype with probabilities α, and 1 − α respectively. The safe phenotype is characterized by an environment-independent growth rate s_s. The growth rate of the risky phenotype is s_a or s_b, depending on whether the current environment is “adverse” (a) or “favorable” (b). C) and D) Sketch of range expansion in a population having 0 ≤ α ≤ 1 for temporally varying C) and spatially varying D) environments, respectively.