Name: Henry F Mollet
Title: Ph.D.
University/Organization: Monterey Bay Aquarium
Mailing Address:
P.O. Box 51091, Pacific Grove CA 93950

Phone: 831 375 5076
Fax: 831 644 7597

Methodology for estimating length-at-maturity with application to elasmobranchs

It is difficult to determine the exact length-at-maturity of elasmobranch specimens. The corresponding length-frequency distribution is expected to follow a normal distribution function (ZDF) with parameters mean length-at-maturity and standard deviation sigma. Available maturity data of specimens of length L are binomial (immature = 0, mature = 1). The normal cumulative function Y = ZCF (a + bL) is the most appropriate model function for fitting such data. Two meaningful, not correlated parameters, namely mean TL-at-maturity (MTL = - a/b) and slope at MTL (S = b/sqr(2 pi) = b/2.51 = 1/sigma) can be expressed in terms of a and b as given. The logistical function Y = 1/(1 + exp-(a + bL)) is similar and the two meaningful, not correlated parameters are MTL = - a/b and S = b/4. Parameter estimates are easily obtained with the help of non-linear statistical packages, which eliminates the need of cumbersome probit or logit transformations/calculations. MTL and slope at MTL of selected sharks are calculated from available maturity data. The advantages of these methods over conventional reporting are outlined.

Keywords: length-at-maturity, normal cumulative distribution, logistical function, probit, logit, elasmobranchs, sharks