Modelling Walleye Population and Its Cannibalism Effect

Walleye is a very common recreational fish in Canada with a strong cannibalism tendency, such that walleyes with larger sizes will consume their smaller counterparts when food sources are limited or a surplus of adults is present. Cannibalism may be a factor promoting population oscillation. As fish reach a certain age or biological stage (i.e. biological maturity), the number of fish achieving that stage is known as fish recruitment. The objective of this thesis is to model the walleye population with its recruitment and cannibalism e↵ect. A matrix population model has been introduced to characterize the walleye population into three di↵erent groups: newborns, juveniles, and adults. A delay di↵erential equation (DDE) model has also been introduced to characterize walleyes into two groups including juveniles and adults. Local and global stabilities of equilibria have been discussed in both models. Furthermore, numerical simulations are present to visualize the e↵ects of both models.