Lotka-Volterra predator-prey model with periodically varying carrying capacity

Abstract

We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state.

Extracted equations

• dA/dt = -μA + λAB
• dB/dt = σB(1 - B/K(t)) - λAB
• K(t) = K_min + (K_max - K_min)/2 * (1 + sin(2πt/T))

Paper claims vs. our run

• Parameter region of predator-prey coexistence is enlarged relative to stationary case when carrying capacity varies periodically
  not-testable
  no fidelity score recorded
• Periodic carrying capacity switching prevents predator extinction in regimes where static carrying capacity would lead to extinction
  not-testable
  no fidelity score recorded
• Mean-field equations predict period-doubling scenarios that are washed out by stochastic noise in lattice model
  not-testable
  no fidelity score recorded
• Resonance effects cause prolonged persistent spatial correlations
  not-testable
  no fidelity score recorded
• Time delay observed in system response to sudden environmental changes
  not-testable
  no fidelity score recorded
• Fast-switching regime enables semi-quantitative description via effective static environment
  not-testable
  no fidelity score recorded

Parameters

Run notes

Stub simulator: Monte Carlo runner not yet wired