Mathematica Probes Decline in Sea Lion Population

Since 1975 the Stellar sea lion population has been decreasing in Western Alaska along the Aleutian chain. Anne York, of the National Marine Mammal Laboratory, has used Mathematica for statistical analysis and population modeling to find out why.

Using Mathematica to look at factors such as survival and reproductive rates, as well as age at first reproduction, York has been able to determine that the change in sea lion population is due to a lower survival rate of juvenile sea lions.

"Mathematica helped me quickly set up a population model for the sea lion population. Using data we had on the change in age-structure and the rate of decline of the population, I was able to solve some fairly complex equations and pinpoint a decrease in juvenile survival as the likely reason for the population decline," York said. "That steered the biologists I work with to further study the feeding and diving habits of young animals. From that we learned that young sea lions do not dive as deeply as adult animals. They dive at a maximum of about 50 meters as opposed to the over 200 meter depths that adult sea lions dive."

The biologists are still not sure how the decline in survival relates to the diving ability of young animals. It may be that oceanic conditions have changed in recent years and prey for sea lions has moved deeper and is therefore less available to juveniles. Another factor that York notes is that sea lions are also competing with the largest U.S. based fishery for pollock.

Key features of Mathematica used: Numeric--integration, differentiation, equation solving Symbolic--integration, differentiation, equation solving, symbolic matrix calculation Graphic--contour plotting