Geometric-Mean Fitness Does Not Correspond to Long-Term Survival Probability

Unpredictable randomness plays a crucial role in 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 like geometric-mean fitness, or geometric mean of stochastic growth rates. However, 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.