Mathematical modeling of plankton patchiness

In natural systems, it has been observed that plankton exist in patches rather than in an even distribution across a body of water. However, the mechanisms behind this patchiness are not fully understood. Several previous modeling studies have examined the effects of abiotic and biotic factors on patch structure. Yet these models ignore a key point: zooplankton often undergo diel vertical migration. I have formulated a model that incorporates vertical movement into the Rosezweig-MacArthur (R-M) predator-prey model. The R-M model is stable only at a carrying capacity below a critical value. I found that adding vertical movement stabilizes the system even at a high carrying capacity. By analyzing temporal stability and spatial structure, my results show that vertical movement interacts with carrying capacity to determine patch structure.