A reduced-parameter predator–prey model of soil formation from bedrock and biomass

Abstract

Soil–bedrock interaction on hillslopes is not well-studied, though it's affected by many physical and chemical factors. The aim of the present mathematical modelling study is to construct a model for soil formation utilising ordinary differential equations, all while reducing the number of required parameters. Parameters known from previous studies include, but not limited to, precipitation, temperature, soil properties, slope angle, soil depth, bedrock properties, topography and earthquakes. Due to correlations among the parameters, it is possible to consider all of them using three independent parameters: growth rate of soil (s ₁(t)), increasing rate of soil due to interaction (s ₂(t)) and decay rate of soil due to erosion (s ₃(t)). One population increases by destroying another, which is most common in predator–prey dynamics. By comparing the bedrock to prey and the soil to predators, we can create a mathematical model that accurately captures this complex interaction. Previous data sets suggest periodic, linear, exponentially decreasing or constant for different domains of study. The predator–prey model has been solved numerically using fifth-order Runge–Kutta in MATLAB. The actual and calculated soil volume differs by 0.00121 m³, while the biomass content difference is 2.28%, resulting in about 97% accuracy.