Demographic analysis of sperm whales using matrix population models

Abstract

The focus of this study is to investigate the demographic and sensitivity/elasticity analysis of the endangered sperm whale population. First, a matrix population model corresponding to a general sperm whale life cycle is presented. The values of the parameters in the model are then estimated. The population's asymptotic growth rate λ, life expectancy and net reproduction number are calculated. Extinction time probability distribution is also studied. The results show that the sperm whale population grows slowly and is potentially very fragile. The asymptotic growth rate is most sensitive to the survivorship rates, especially to survivorship rate of mature females, and less so to maturity rates. Our results also indicate that these survivorship rates are very delicate, and a slight decrease could result in an asymptotic growth rate below one, i.e., a declining population, leading to extinction.