Browsing by Author "Suomenrinne-Nordvik, Anna"

Group defense against predator attacks are common for prey species. Some group defense mechanisms are more passive, like swarm confusion. In this thesis the focus is an active type of group defense where the prey fight back against the attacking predator as a group. The aim of this thesis is to formulate a model with active groups defense and to mechanistically derive and analyse the functional response arising from it. The motivation is to understand the impact of this special type of group defense on the functional response of the predator, and hence on the whole dynamics of the model. Some theory about prey-predator models, the functional response and tools for analysing dynamical systems are presented as background first. Following this, the model is formulated from the individual level processes and the functional response derived using the method of time-scale separation. Finally, two special cases of the model are analysed. In the model, the defense of the prey is modelled as a coagulation and fragmentation process, where the prey can join the fight to protect the individual that is being attacked. These fights become clusters where the attacking predator is the coagulation kernel. The clusters can grow or shrink by one prey joining or leaving at a time, or the cluster breaking up completely due to success of either the attack or the defense. This type of coagulation and fragmentation process can be seen as a generalization of the Becker-Döring equations, where the clusters are homogenous groups and the groups can also only grow and shrink by one individual at a time. The cluster dynamics truncated with a maximum size for the clusters was found to have a unique and stable equilibrium for arbitrarily large maximum cluster sizes in both special cases of the model. The stability analysis for cluster dynamics with no maximum cluster size was not successful, even though there is reason to believe the results for the truncated system is generalizable to that case. The functional response was found to take a dome-shaped form, decreasing to zero under certain circumstances, or the form of Holling type II functional response. The determining factor for which type of functional response the model gives rise to is whether the predator’s attack rate is dependent on the cluster size or not. The same dependence of the form of the functional response on the attack rate was found to hold in both special cases of the model.