How to Build Matrix Population Models from Process Components

 Literature Introduction of "Notes on Building Matrix Population Models: Insights From Combining Distinct Matrices for Survival, Reproduction, and Growth" (Matsuda H & Taper ML 2025, Population Ecology POPE70005, doi.org/10.1002/1438-390x.70005) (full manuscript) (See html for lecture pdf & video).

Abstract

We propose a unified method for formulating matrix population models in wildlife and fisheries management, adaptable to variations in population measurement timing and natural and human-induced mortality. For populations with a common and short breeding season, this approach applies to age-, size-, and stage-structured populations. The process is considered separately as three: survival, reproduction, and age increment or growth, with the respective matrices designated as S, B, and G. In the age-structured model, reproduction and age increment occurs simultaneously, and are expressed as a matrix model of S(BG) if the population census is taken immediately before the parturition, and (BG)S if it is taken immediately after the parturition. In the size- or stage-structured model, growth and survival proceed in parallel, and are expressed as a matrix model of (GS)B if the population census is taken just before the parturition, and B(GS) if it is taken just after the parturition. When the population census is taken at any other time, the survival rate from the parturition to the census and the survival rate from the census to the parturition can be considered separately. Furthermore, even when capture mortality is given as the number of individuals rather than a rate, a unified formulation by capture time is possible by expressing the number of captures as a vector.