Idealized Migrations and Compartmental Modeling

Compartmental modeling is both important and increasing in importance in biology, medicine, pharmacology, and a number of the other life sciences often as a pathway into systems biology.  However, the mathematics associated with these applications is not always student friendly, especially when the models meet the need for meaningful quantitative applications.

Fortunately, there are linear compartmental that are analogous to the biological context of migratory models are not only important in the biosciences, but are also mathematically accessible.  In this website, we focus on several models related to the annual juvenile salmon migrations toward the oceans. These juvenile salmon are known as smolts, and correspondingly, these migrations are called smolt migrations.

These annual migrations have been compromised, often severely, by the construction of dams and other man-made features, thus greatly adding to the naturally large mortality rates of the smolt populations.  These models are highly idealized and simple in nature, but still they can serve as both contexts for introducing mathematical and statistical ideas and concept tools for increasing our understanding of complex biological systems.