Stochastic Lotka-Volterra food chains

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Deterministic Lotka-Volterra systems offer clear results on species persistence and extinction.
• Stochastic counterparts, incorporating environmental variability, have fewer established outcomes.
• Simple food chains with one prey and multiple predators are analyzed.

Purpose of the Study:

• To investigate species persistence and extinction in a stochastic Lotka-Volterra food chain model.
• To extend existing deterministic results to a stochastic setting.
• To classify species' fates based on system interaction coefficients.

Main Methods:

• Modeling a food chain with one prey and multiple predators using a Lotka-Volterra system with environmental stochasticity.
• Analyzing species interactions within a trophic chain where each species interacts with at most two others.
• Developing an explicit quantity based on interaction coefficients to predict species outcomes.

Main Results:

• Species extinction likelihood increases with environmental stochasticity.
• Persistence observed in deterministic systems is maintained in stochastic systems with small environmental fluctuations.
• The addition of an apex predator increases the proneness of species to extinction.
• The behavior of the system with degenerate noise, accounting for species-specific environmental correlations, is described.

Conclusions:

• Environmental stochasticity generally elevates extinction risk in food chains.
• The impact of environmental noise on species persistence depends on fluctuation magnitude.
• Food chain structure, particularly the presence of apex predators, significantly influences species survival.
• The study provides a framework for understanding complex ecological dynamics under environmental uncertainty.