Predator-Prey dynamics is one of the simplest non-linear ecological systems. The Lotka-Volterra (LV) framework provides a minimal mathematical representation of these interactions. It expresses population change as a set of coupled differential equation.
The conceptual model defines the interacting variables and directional processes. The system is reduced to two populations: Prey (N), and Predator (P). Prey reproduce, predators consume prey, and predators experience mortality. This isolates the essential dynamics prior to the mathematical representation.
Figure 1: Structural representation of predator-prey interaction. source: Author.
The Lotka-Volterra equation describes the temporal dynamics of the system:
dN/dt = rN - aNP
dP/dt = bNP - mP
where:
- N: prey population
- P: predator population
- r: intrinsic growth rate of prey
- a: predation rate coefficient
- b: conversion efficiency of consumed prey into predator reproduction
- m: predator mortality rate
The coupled differential equations are Numerically integrated to observe the system dynamics over time.
Figure 2: Simulated Predator-prey osillations generated from the LV system.