  In ecology, species can mitigate their extinction risks in uncertain
environments by diversifying individual phenotypes. This observation is
quantified by the theory of bet-hedging, which provides a reason for the degree
of phenotypic diversity observed even in clonal populations. The theory of
bet-hedging in well-mixed populations is rather well developed. However, many
species underwent range expansions during their evolutionary history, and the
importance of phenotypic diversity in such scenarios still needs to be
understood. In this paper, we develop a theory of bet-hedging for populations
colonizing new, unknown environments that fluctuate either in space or time. In
this case, we find that bet-hedging is a more favorable strategy than in
well-mixed populations. For slow rates of variation, temporal and spatial
fluctuations lead to different outcomes. In spatially fluctuating environments,
bet-hedging is favored compared to temporally fluctuating environments. In the
limit of frequent environmental variation, no opportunity for bet-hedging
exists, regardless of the nature of the environmental fluctuations. For the
same model, bet-hedging is never an advantageous strategy in the well-mixed
case, supporting the view that range expansions strongly promote
diversification. These conclusions are robust against stochasticity induced by
finite population sizes. Our findings shed light on the importance of
phenotypic heterogeneity in range expansions, paving the way to novel
approaches to understand how biodiversity emerges and is maintained.
