A Stage-structured population demographic model for organismal development

Olwa Bathlomeo Onyango; Michael Woyengo; George Simmons

doi:10.51867/asarev.maths.3.1.23

Authors

Olwa Bathlomeo Onyango Department of Pure and Applied Mathematics, Maseno University, Kenya Author https://orcid.org/0009-0006-3734-6541
Michael Woyengo Department of Pure and Applied Mathematics, Maseno University, Kenya Author
George Simmons IDEMS International CIC, United Kingdom Author https://orcid.org/0000-0002-9076-4973

DOI:

https://doi.org/10.51867/asarev.maths.3.1.23

Keywords:

Distributed Delay Model, Fall Armyworm, Kolmogorov Forward Equation, Physiological Age, Stage-Structured Population Dynamics

Abstract

Developmental variability shapes population dynamics, generational turnover, and the timing of
ecological processes in stage-structured populations. Distributed Delay Models are the standard
tool to capture this variability through compartmental developmental chains, but the intermediate
compartments carry no direct biological meaning and their connection to continuous physiological
age dynamics is rarely made explicit. We develop a stage-coupled Kolmogorov Forward Equation
framework in which developmental progression is a continuous stochastic process in physiological
age space: advection describes deterministic advancement, diffusion accounts for individual variability,
and boundary flux conditions couple successive developmental stages. We show that Distributed
Delay Models arise as finite-dimensional approximations of this continuous equation, and derive
a moment-based parametrization linking the model coefficients to observed means and variances
of developmental duration. Applied to Fall Armyworm (Spodoptera frugiperda) as a case study,
the two formulations are compared on their predictions of developmental timing and population
peaks to justify the Kolmogorov-based framework as a viable, biologically-motivated alternative to
Distributed Delay Models for capturing stage-structured population dynamics.

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