Fluctuating Environments Favor Extreme Dormancy Strategies and Penalize Intermediate Ones

TL;DR

The study investigates how dormancy duration $\alpha$ interacts with temporally correlated environmental variability to shape fitness. Using a minimal delayed-logistic model with a colored birth-rate noise and a demographic delay, the authors uncover a non-monotonic fitness landscape featuring three regimes: rapid growth at small $\alpha$ but high extinction risk, strong buffering and persistence at large $\alpha$ with slower growth, and a broad maladaptive middle region where timing mismatches the environment. An analytical approximation alongside an agent-based evolutionary model reveals bistability between short- and long-dormancy strategies, with intermediate delays consistently disfavored. These results imply that dormancy timing is an adaptive trait tuned to environmental timescales and offer a general mechanism by which delays under correlated noise select for extreme strategies, with implications for seed banks, persisters, and cancer dynamics.

Abstract

Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy interacts with environmental correlation times using a delayed-logistic model in which dormant individuals reactivate after a fixed lag while birth rates fluctuate under temporally correlated stochasticity. Numerical simulations and analytical calculations show that the combination of demographic memory and colored multiplicative noise generates a strongly non-monotonic dependence of fitness on dormancy duration, with three distinct performance regimes. Very short dormancy maximizes linear growth but amplifies fluctuations and extinction risk. Very long dormancy buffers environmental variability, greatly increasing mean extinction times despite slower growth. Strikingly, we find a broad band of intermediate dormancy durations that is maladaptive, simultaneously reducing both growth and persistence due to a mismatch between delay times and environmental autocorrelation. An evolutionary agent-based model confirms bistability between short- and long-dormancy strategies, which avoid intermediate lag times and evolve toward stable extremes. These results show that dormancy duration is not merely a life-history parameter but an adaptive mechanism tuned to environmental timescales, and that intermediate "dangerous middle" strategies can be inherently disfavored. More broadly, this work identifies a generic mechanism by which demographic delays interacting with correlated environmental variability produce a non-monotonic fitness landscape that selects for extreme timing strategies.

Figures (11)

• Figure 1: Population life cycle with dormancy in a stochastic environment. Individuals reproduce to produce dormant propagules (e.g., seeds, spores, persister cells) at time $t - \alpha$, which remain in a quiescent state for a delay $\alpha$ before activating into reproductive, mortal individuals at time $t$. Active individuals experience alternating good and bad environmental conditions, represented as temporal fluctuations in the birth rate with mean $b$, variance $\sigma$, and correlation time $\tau$.We then use this life–cycle framework to investigate (left) ecological competition among species that differ in dormancy and activation, and (right) evolutionary change in dormancy duration via single mutations that shift the delay from $\alpha$ to $\alpha' = \alpha + \delta\alpha$. In both cases, extreme strategies with either very long or very short delays gain a competitive advantage, whereas intermediate dormancy strategies are maladaptive and are progressively replaced by fitter ones.
• Figure 2: Time series of the population density $x(t)$ for different values of the dormancy $\alpha$, illustrating the effect of delayed reproduction under environmental noise. The inset shows the corresponding stationary probability density functions (PDFs) of $x(t)$, highlighting qualitative changes in population variability across dormancy regimes. Parameters: $b = 1.05$, $\tau = 1$, $\sigma = 0.5$, $d = 1$, $K=1$.
• Figure 3: Mean population density $x^*$ as a function of dormancy $\alpha$ and noise amplitude $\sigma$. Upper panel: heat map of $x^*$ in the $(\alpha,\sigma)$ plane. Lower panel: the same data shown as $x^*$ versus $\alpha$ for different fixed values of $\sigma$, highlighting its non-monotonic behavior. To calculate $x^\ast$, we numerically integrate Eq. \ref{['eq:model']} up to a burn-in time $T_{\min}$ to remove transients, compute the time average over the window $[T_{\min},\,T_{\max}]$, and then average over independent noise realizations. Intermediate dormancy combined with strong noise leads to a marked decrease in population size, reflecting poor timing strategies. Parameters: $d = 1$, $b = 1.25$, $\tau = 1$, $K = 1$, $T_{\min} = T_{\max}/2$, $T_{\max} = 10^4$, averages over $10^3$ realizations.
• Figure 4: Mean linear growth rate $G$ as a function of dormancy $\alpha$, for different values of the noise amplitude $\sigma$ (main panel) and correlation time $\tau$ (inset), in the linearized model (numerical results from simulations). While $G$ is maximal at $\alpha = 0$ for all cases, increasing $\sigma$ or $\tau$ leads to the emergence of a local minimum at intermediate delays. Parameters: $d = 1$, $b = 1.25$, $T_{\max}=10^3$, averages over $10^4$ independent realizations.
• Figure 5: Noise-induced correction to the mean linear growth rate as a function of dormancy $\alpha$, rescaled by the factor $\tau \sigma^2$. Solid lines correspond to the approximation given in Eq. \ref{['eq:G-formula']}, while points denote numerical simulation results. Top panel: fixed correlation time $\tau = 1$ and varying noise amplitude $\sigma$. Bottom panel: fixed $\sigma = 1$ and varying $\tau$. Insets show the same data (in absolute value) on log-log scale, highlighting the asymptotic decay at large values of $\alpha$. Parameters: $d = 1$, $b = 1.25$.