Incorporating environmental stochasticity within a biological population model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Population dynamics are influenced by birth and death rates, which can vary with population size and environmental conditions.
• Understanding these influences is crucial for ecological modeling and conservation efforts.
• Previous models often simplify environmental interactions or population size dependencies.

Purpose of the Study:

• To develop and analyze mathematical models for population dynamics where birth and death rates are functions of population size and environmental conditions.
• To explore theoretical results and analytical techniques applicable to such models.
• To apply these methods to specific case studies involving environmental factors.

Main Methods:

• Modeling birth and death transition rates as functions of population size and environmental variables.
• Utilizing theoretical results and analytical techniques for population behavior analysis.
• Applying models to two distinct case studies: a population with linear environmental dependence and a population affected by interdependent environmental factors.

Main Results:

• Analysis of a population exhibiting a stable equilibrium, with per capita rates linearly dependent on an Ornstein-Uhlenbeck process environmental condition.
• Investigation of a population influenced by two interdependent environmental factors, demonstrating complex dynamics.
• Demonstration of the utility of the presented theoretical results and techniques in analyzing these specific population models.

Conclusions:

• The study provides a framework for analyzing population dynamics under size- and environment-dependent rates.
• The applied methods offer insights into population stability and responses to environmental fluctuations.
• The findings are applicable to ecological scenarios with varying environmental complexities.