Instant cost and delayed reward. Demographic eco-evolutionary game dynamics under the impact of the delay resulting from the offspring maturation time

TL;DR

This paper investigates how delays from juvenile maturation influence eco-evolutionary game dynamics, revealing that delays can destabilize equilibria, induce complex behaviors, and affect system resilience, with implications for understanding population stability.

Contribution

It introduces delay differential equations into demographic eco-evolutionary models, providing theoretical tools to assess critical delays and exploring their effects on stability and dynamics.

Findings

Delay causes loss of stability when critical thresholds are exceeded

Different suppression modes lead to diverse dynamic patterns, including chaos

Delay extends transient metastable states, affecting resilience

Abstract

In this paper, we extend the demographic eco-evolutionary game approach, based on explicit birth and death dynamics instead of abstract "fitness" interpreted as an abstract "Malthusian parameter", by the introduction of the delay resulting from the juvenile maturation time. This leads to the application of the Delay Differential Equations (DDE). We show that delay seriously affects the resulting dynamics and may lead to the loss of stability of equilibria when critical delay is exceeded. We provide theoretical tools for the assessment of the critical delays and the parameter values when this may happen. Our results emphasize the importance of the mechanisms of density dependence. We analyze the impact of three different suppression modes based on: adult mortality, juvenile recruitment survival after the maturation period (without delay), and juvenile recruitment at birth (with the delay). The last mode leads to extreme patterns such as bifurcations, complex cycles, and chaotic dynamics. However, surprisingly, this mode leads to extension of the duration of the temporary transient metastable states known as "ghost attractors". In addition, we also focus on the problem of resilience of the analyzed systems against external periodic perturbations and feedback-driven factors such as additional predator pressure.