Estimating the juvenile survival rate of male Northern Fur (Сallorhinus ursinus): mathematical modelling and data analysis

For the sustainable use of the northern fur seal stocks, estimation and prediction of the number of the main age groups of males is very important. The data of direct observations make it possible to estimate only the size of the offspring (the number of pups) and the total number of bulls; and the age composition of the animals killed by the harvest is also known. It is necessary to be able to calculate the survival rates of individual age groups of fur seals to predict population dynamics using these data. This paper discusses and modernizes the previously proposed methods for estimating the survival rates of males. To narrow the calculated intervals of juvenile survival we use additional information (in particular, the estimated survival of males at subsequent stages of the life cycle), as well as adjust the evaluation procedure. Two methods for calculating the survival rates of males at different stages of the life cycle are proposed: the iteration method and the method of determining the survival limits of all age groups from the dynamic equations. Both methods are based on available observational data and features of the life cycle of the species in question, they do not require fulfillment of any assumptions about the nature of the harvest strategy. We obtain, as a result, satisfactory estimates of the coefficients characterizing the main stages of the life cycle of fur seal males. Moreover, both methods give very similar regression estimates of the average bulls’ survival: they hardly differ in size and have similar statistical characteristics. Thus, the first method gives higher juvenile survival and low survival of bachelors; and the second method, on the contrary, overestimates the survival of bachelors and underestimates the juvenile survival rate. However, as the regression analysis showed, both sets of estimates are well compatible with observational data.