9781934874097-ch10

Pacific Salmon Environmental and Life History Models: Advancing Science for Sustainable Salmon in the Future

Generalizing the Multi-Stage Stock-Production Paradigm: a Flexible Architecture for Population Modeling

Peter Fritz Baker

doi: https://doi.org/10.47886/9781934874097.ch10

Abstract.—The basic idea of stock-production theory is to regard a cohort of organisms at some life stage as a function of a corresponding cohort at some earlier life stage (a “stock-production relationship”). Stock-production relations were originally introduced for theoretical purposes, to clarify the role of density-dependence in population dynamics, but have been found to be useful in the construction of concrete models for specific populations. This chapter discusses generalizations of the stock-production approach which greatly extend its range of applicability. First, it is observed that the appropriate language for describing life-histories is that of periodic directed acyclic graphs. In the present formulation, population dynamics are regarded as processes on such graphs. Second, whereas it is customary to represent a cohort at a life stage by a single number, such as the number of individuals or total biomass, it is often important to keep track of additional information, such as age structure or spatial distribution. This can be done by using objects of more complex mathematical type, such as vectors, sets, or statistical distributions, in place of simple numbers. Theoretical and practical issues involved in implementing models with this architecture, relationships with other approaches such as individual-based models (IBM), and opportunities this general framework presents for smoothly and flexibly integrating disparate methodologies, are discussed.