The Symbiosis Project 

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.


URL Module Description
Migration Concept 7 Immigration into and Emigration out from a Habitat Zone
Leaving Zone 0 7 Smolt migration begins with the entire population in zone 0

Moving Through Zone 1

7 Smolts move out of zone 0 through zone 1 (the first lake)
Idealized Multizone Migration 7 Migration through a sequence of habitat zones
Multizone Migration with Mortality 7 A multi-zone migration incorporating mortality throughout
Mark-Recapture 7 Estimating the size of a population via mark/recapture
Compartmental Modeling Constructor 7 A tool for constructing simulations of compartmental models

Other Resources