# ESTIMATING TOTAL MORTALITY RATE FROM LONGEVITY DATA (FISH, MOLLUSKS, CETACEANS)

#### Abstract

Methods of estimating the total mortality rate have been developed by examining the relationship between the mortality rate and the maximum ages in a sample. A plot of the logarithm of the total mortality rate against the logarithm of the maximum reported age for a wide variety of fish, mollusks and cetaceans produced a strongly linear relationship with a coefficient of determination (r('2)) of 0.82. The total mortality rate can thus be estimated from the maximum age using the following regression equation: ln(Z) = 1.44 - 0.982 x ln(t(,max)). The procedure does not take the sample size into consideration and therefore cannot be used in critical comparisons. In order to take sample size into consideration, the oldest ages in a sample were considered as order statistics from an exponential population. The expected values of the reciprocals of the order statistics are linear functions of the mortality rate Z. An unbiased estimator of the mortality rate was derived by minimizing the variance of a linear combination of the reciprocals of the order statistics while constraining the expected value to be equal to the mortality rate. Estimates are easily computed with the aid of supplied tables. These techniques should find greatest use in situations where age determinations are tedious and must be kept to a minimum.^

#### Subject Area

Biology, Biostatistics|Biology, Oceanography|Agriculture, Fisheries and Aquaculture

#### Recommended Citation

JOHN MAURICE HOENIG,
"ESTIMATING TOTAL MORTALITY RATE FROM LONGEVITY DATA (FISH, MOLLUSKS, CETACEANS)"
(1983).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI8401408.

http://digitalcommons.uri.edu/dissertations/AAI8401408