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.