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About the marine mammal calculations

Thursday - 7/3/2014, 1:29pm  ET

MIKE SCHNEIDER
Associated Press

ORLANDO, Fla. (AP) -- The Associated Press calculated annual survival rates and life expectancy averages for four species of marine mammals at more than 170 parks and aquariums in the United States. The species -- killer whales, bottlenose dolphins, California sea lions and beluga whales -- are among the most popular marine mammals kept in captivity at U.S facilities.

The source of the data was the Marine Mammals Inventory Report (MMIR), which is maintained by the National Marine Fisheries Service. U.S. parks and aquariums that hold marine mammals are required by law to report any deaths, transfers or acquisitions to the federal agency. The MMIR also includes data from non-U.S. parks that hold animals that once were at U.S. facilities.

The AP discarded data points where there was incomplete information on the birth date, death date or date the animals were taken into custody. The AP eliminated data from non-U.S. facilities since reporting by those institutions is not legally mandatory and is therefore less reliable. The AP also eliminated animals less than a year old given the difficulties of making comparisons at that age with animals in the wild and also to eliminate bias from stillborn births, which are common both in captivity and the wild.

Some critics say the MMIR data is incomplete since it depends on the parks and aquariums to self-report, although a 1993 academic study concluded the MMIR data was highly accurate. Critics also argue that animals at international facilities should be included in any analysis about marine mammals in captivity, and that animals under a year should be included since they reflect birth-related deaths.

The annual survival rate represents the estimated proportion of animals at a facility that will be alive a year later. It is calculated by taking the daily survival rate and raising it to the 365.25 power, or (daily survival rate) 365.25. That creates a figure ranging from 0 to 1.

The daily survival rate is calculated by dividing the number of deaths at a facility by the number of days the facility's animals were kept alive. That number is then subtracted from 1 to create a number that ranges from 0 to 1. Mathematically, it can be represented as 1 - (# of animal deaths/ # of animal days).

Life expectancy averages are calculated from annual survival rates, and they estimate the average age an animal in the population can be expected to reach. They are calculated by dividing -1 by the natural log of the annual survival rate. Mathematically, that would be -1/ ln(annual survival rate).

Confidence intervals also were calculated for the survival rates and life expectancy estimates. Confidence intervals give a range of values in which the estimates are likely to fall within 95 percent certainty. They were calculated by taking standard errors and multiplying them by 1.96. Those figures were then added and subtracted to the daily survival rates to create confidence interval ranges. High and low ranges for the annual survival rates and life expectancy averages were then calculated.

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