MATHEMATICAL MODELLING OF POPULATION DYNAMICS IN THEORETICAL ECOLOGY

MATHEMATICAL MODELLING OF POPULATION DYNAMICS IN THEORETICAL ECOLOGY Department of HARRY GREEN Supervisors: DR. CRISTIANA SEBU, PROF. KHALED HAYATLEH, DR. TIM SHREEVE Mechanical Engineering and Mathematical Sciences For predation terms, we use the ‘Holling Type II functional response’ given by To model single isolated populations in the absence of predation or competition we use a logistic growth curve given by Modelling Human population growth with the logistic curve (1). Data from UN estimates A strange chaotic attractor plotted from a tritrophic food chain model. The attractor demonstrates a sensitivity to initial conditions, and a small change in parameter values changes the shape unpredictably Modelling Human population growth with the logistic curve (1). Data from UN estimates The models given here are only a small and simple subset of the ODE based models used in theoretical ecology. Real world species display a much broader range of behaviour than simple Holling Type II predation. Using non-autonomous systems of ODEs we can account for seasonal variation in the system’s dynamics. It is also frequently seen to combine the predator-prey models with epidemiological models designed to model the spreading of disease to investigate the effect of an epidemic disease on a multiple-species ecosystem.