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

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.