Code from: Geometric-mean fitness does not correspond to long-term survival probability

Unpredictable randomness plays a crucial role in the long-term sustainability of biological systems. The population growth of a species in variable environments is typically described in terms of a long-term measure, such as geometric mean fitness or the geometric mean of stochastic growth rates. However, a quantitative understanding of the relationship between these fitness measures and long-term survival probability remains a critical, and often overlooked, aspect of ecological modeling. Here, we investigate this relationship using large-scale numerical simulations, focusing on the implications for bet-hedging strategies. To this end, we develop two individual-based growth models incorporating randomly varying growth rates. Our simulations reveal that a one-to-one correspondence, or monotonic relationship, does not exist between geometric-mean fitness and survival probability. Specifically, higher geometric-mean fitness does not necessarily correlate with increased survival probability. These findings challenge the assumption of a universal, time-independent measure of long-term fitness, and suggest that the ”optimal” survival strategy is likely contingent on the timescale of observation.