Persistence of small populations under seasonal resource fluctuations

Populations that remain at critical low sizes are acutely sensitive to random fluctuations in birth–death processes and to the accumulation of mildly deleterious mutations. We begin with a deterministic consumer–resource model featuring seasonally forced inputs, and based on this framework, we develop an individual-based, discrete-generation stochastic simulation to capture demographic and mutational randomness. The phase diagram of the deterministic model reveals the existence of three distinct regimes: one in which the population goes extinct, a second regime in which the population remains at a finite size, and finally a third non-physical regime observed at low mortality rates. Our simulation outcomes address the second regime. Two easily measured statistics – the minimum influx smin and the fraction of each cycle spent below a critical threshold, τ/T – are predictors of extinction. We demonstrate that enhancing long-term population persistence by increasing the peak of resource influx, reducing oscillation amplitude, or phase-shifting multiple resources out of sync is possible.