Code from: Geometric-mean fitness does not correspond to long-term survival probability
Abstract
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.
Dataset DOI: 10.5061/dryad.0k6djhbdq
Files and variables
We present the code snippets used for the study titled Geometric-mean Fitness Does Not Correspond to Long-term Survival Probability by Takuya Okabe, Jin Yoshimura, and Hiromu Ito. The survival probability is estimated using a Monte Carlo simulation in Mathematica. A population is initialized with 100 individuals. The size of this population is iteratively updated based on a NextSize function, which determines the next population size from the previous one. This simulation is repeated 10,000 times. We record the proportion of simulations resulting in extinction and calculate the survival probability as 111 minus this extinction proportion.
File: Code.nb
Description: The notebook simulates how a population grows or goes extinct when its environment randomly changes over time. Starting with a fixed number of individuals, each generation, the population experiences one of two environments, and individuals reproduce randomly depending on which environment occurs. This process is repeated many times to estimate how often the population survives versus goes extinct. The key point is that even if a population has good average growth (especially a high geometric-mean growth rate), random bad years and chance fluctuations can still drive it to extinction. So the simulations show that average fitness alone does not reliably predict long-term survival for real, finite populations.