Construction And Analysis Of Leslie Matrix Population Model For Amboseli Elephants

Abstract

In this study, construction of a density independent Leslie matrix used for projecting Amboseli elephant population is discussed, where the only factors that determine the population dynamics are survivorship and fertility rates. Only the female population is considered and elephant population are grouped into age classes comprising of individuals with similar characteristics. All elephants population in a certain age class move to the next age class during the next time step. Properties of the matrix relevant to population growth rate and stable population is highlighted and discussed.Transient and asymptotic population dynamics are analysed.Perturbation methods have also been discussed. It is noted that in the lower age classes, change in survival rates have more effect to the asymptotic growth rate than change in fertility rates while in the older population,change in fertility rates bring greater effect to the asymptotic growth rate than change in survivorship. The eigenvalues of the Leslie matrix are calculated and the dominant eigenvalue is found to represent the long run growth rate.Its corresponding right and left eigenvectors represent stable age structure and reproductive value respectively.Attempt to incorporate density dependence into the model is made with density as the total number of population. Model analysis shows that population increases in all the age classes.