Related Experiment Video
Updated: May 19, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
Published on: July 30, 2019
Derivation of stochastic partial differential equations for size- and age-structured populations
1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA. edward.allen@ttu.edu
Abstract:
Stochastic partial differential equations (SPDEs) for size-structured and age- and size-structured populations are derived from basic principles, i.e. from the changes that occur in a small time interval. Discrete stochastic models of size-structured and age-structured populations are constructed, carefully taking into account the inherent randomness in births, deaths, and size changes. As the time interval decreases, the discrete stochastic models lead to systems of Itô stochastic differential equations. As the size and age intervals decrease, SPDEs are derived for size-structured and age- and size-structured populations. Comparisons between numerical solutions of the SPDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations.
Related Concept Videos
Modeling with Differential Equations
Exponential Equations for Modeling Growth
Population Growth
Growth Models with Integration: Problem Solving
Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
