Browsing by Subject "Rosenzweig-MacArthur"

Predator—prey models can be studied from several perspectives each telling its own story about real-life phenomena. For this thesis the perspective chosen, is to include prey—rescue to the standoff between the predator and the prey. Prey--rescue is seen in the nature for many species, but to point one occurrence out, the standoff between a hyena and a lion. When a lion attacks a hyena, the herd of the hyena try to frighten the lion away. The rescue attempt can either be successful or a failure. In this thesis the prey-rescue model is derived for an individual rescuer and for a group of prey. For both cases, the aim is to derive the functional and numerical responses of the predator, but the focus is on the deriving and studying of the functional responses. First, a brief background to motivate the study of this thesis is given. The indroduction goes through the most important aspects of predator—prey modelling and gives an example of a simple, but broadly known Lotka—Volterra predator-prey model. The study begins with the simplest case of prey-rescue, the individual prey—rescue. First, the individual level states, their processes and all the assumptions of the model are introduced. Then, the model is derived and reduced with timescale separation to achieve more interpretable results. The functional response is formed after solving the quasi-equilibrium of the model. It was found that this way of constructing the model gives the popular Holling Type II functional response. Then, it is examined what follows when more and more prey get involved to the standoff trying to rescue the individual being attacked by. This is studied in three different time-scales: ultra—fast, intermediate, and slow timescales. The process of deriving the model and the functional response is like in the simple case of individual prey rescue, but the calculations get more intense. The functional response was found to be uninteresting. In conclusion, the model was adjusted. One of the timescales is left out from the studies in hopes for more interesting results. The derivation came out similar as in the third chapter, but with more advanced calculations and different results of quasi-equilibrium and functional response. The functional response obtained, was found to be worth of studying in a detailed fashion. This detailed study of the functional response obtained, is done last. It was found that different parameter choices affect the shape of the functional response. The parameters were chosen to be biologically relevant. Assuming that the rescue is certain for the group size n = 2, it was found that the functional response took a humpback form for some choices of the other parameters. The parameter ranges, for which the functional response had a humpback shape, were found.