MULTIFAN a Likelihood-Based Method for Estimating Growth Parameters and Age Composition from Multiple Length Frequency Data Sets Illustrated using Data for Southern Bluefin Tuna (Thunnus maccoyii)

Abstract

We present a method for simultaneously analyzing multiple length frequency data sets. The method utilizes a robust likelihood-based estimation procedure that provides an objective criterion for hypothesis testing. The method is applied to length frequency data from southern bluefin tuna (Thunnus maccoyii) for which independent estimates of growth parameters based on tag return data are available. The estimates of the growth parameters from the new method were found to be in substantial agreement with the values previously obtained for these parameters. The strength of the likelihood approach is demonstrated by discriminating between alternative structural hypotheses for describing the data. The ability to simultaneously analyze multiple samples permits the method to exploit the extra information not available when analyzing samples one by one. The computer program maintains a database of fits to the data which enable the user to organize the results of the analysis. Graphical displays permit the user to view any of the fits, and an interactive graphics routine aids the user to find good initial parameter estimates.

Incorporating uncertainty into the estimation of biological reference points for a spiny lobster(Panulirus penicillatus)fishery

“…The mean length-at-age values and their associated uncertainty were estimated based on multiple length frequency analyses (MULTIFAN;Fournier et al 1990). Eight modes in length distribution were separated, and the estimates of CL^ and K tended to be more biologically realistic when the sampling duration was 15 months.…”

Growth rates of five species of surf clams on a southern North Island beach, New Zealand

“…Von Bertalanffy growth curves were fitted to length-frequency distributions for each species using the computer program MULTIFAN version 3.2 (Fournier et al 1990). MULTIFAN makes three assumptions: (1) that the lengths of the shellfish in each age class are normally distributed around their mean length; (2) that the mean lengths at age lie on (or near) a von Bertalanffy curve; (3) that the standard deviation of the actual lengths about the mean length at age is a simple function of the mean length at age.…”

“…Standard errors estimated by a covariance matrix in MULTIFAN are presented for the von Bertalanffy growth parameters L m k, and t 0 . These errors are probably underestimated (see Fournier et al 1990).…”

“…The improvement of fit caused by addition of age classes within models was tested for significance at the level of 0.10 (Type 2 errors are more serious than Type 1 errors in estimating k (Fournier et al 1990)). The improvement of fit between models was tested for significance at the 0.05 level.…”

“…We estimated growth in the same five species of surf clam on a Kapiti Coast beach using the same methods as Cranfield et al (1996), so growth data would be available to estimate sustainable yields of surf clams in the North Island. Growth was estimated from analysis of sequential length-frequency samples using the computer program MULTIFAN (Fournier et al 1990) and the analysis of incremental growth of marked surf clams using the computer program GROTAG (Francis 1988a).…”