SEPARATING MIXTURES OF NORMAL DISTRIBUTIONS: BASIC PROGRAMS FOR BHATTACHARYA’S METHOD AND THEIR APPLICATIONS TO FISH POPULATION ANALYSIS

Manuals and Guides - BOBP/MAG/4

SEPARATING MIXTURES OF NORMAL DISTRIBUTIONS: BASIC PROGRAMS FOR BHATTACHARYA’S METHOD AND THEIR APPLICATIONS TO FISH POPULATION ANALYSIS

by
H. Goonetilleke
Computer Technician, BOBP

K. Sivasubramaniam
Senior Fisheries Biologist BOBP

Executing Agency: FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS

Funding Agency :UNITED NATIONS DEVELOPMENT PROGRAMME

Marine Fishery Resources Management in the Bay of Bengal. Colombo, Sri Lanka, November 1987.

Table of Contents


The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of the Food and Agriculture Organization of the United Nations concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries.

All rights reserved. Reproduction and dissemination of material in this information product for educational or other non-commercial purposes are authorized without any prior written permission from the copyright holders provided the source is fully acknowledged. Reproduction of material in this information product for resale or other commercial purposes is prohibited without written permission of the copyright holders. Applications for such permission should be addressed to the Chief, Publishing and Multimedia Service, Information Division, FAO, Viale delle Terme di Caracalla, 00100 Rome, Italy or by email to [email protected]

© FAO 2004

ABSTRACT

This manual describes computer programs written in Microsoft BASIC (version 2.20B) for use on an Apple Ile micro-computer (with CP/M operating system) and EPSON RX-80 F/T printer.

These programs include a modification of Bhattacharya’s method for identifying and separating normal distributions, in a mixture of distributions in length frequency data, and computation of Chi square statistics for testing goodness of fit, as described by Pauly and Caddy (1985). This package includes a program that plots the frequency distributions for several samples of data. It is useful for estimating growth parameters and calculates the catch at length for each of the mean length groups separated, and gives 95% and 99% confidence limits for each mean.

Growth parameters can also be estimated using length-at-age data by the Ford- Walford Plot and von Bertalanffy Plot programs. In cases where the ages of fish are not known and a series of sizes at relative ages is not available, growth parameters can still be estimated using data on length increase in time (such as also obtained from tagging-recapture data) by the Gulland and Holt Plot program. This package also includes Sparre’s, Jones’ and Van Zalinge’s method for estimating total mortality coefficients from length frequency data. A new method for estimating the asymptotic length and mortality coefficient as proposed by J.A. Wetherall is also presented. This manual and the programs have been prepared by the BOBP project “Marine Fishery Resources Management in the Bay of Bengal” (RAS/81/051). The project commenced January 1983 and terminated December 1986. It was funded by the UNDP.

This document and the programs have not been officially cleared by the governments concerned or by the FAO.


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TABLE OF CONTENTS


Manuals and Guides - BOBP/MAG/4pdf

1. INTRODUCTION

2. GETTING STARTED

3. BHATTACHARYA METHOD

4. CHI SQUARE STATISTICS FOR TESTING RESULTS

5. SOME APPLICATIONS OF BHATTACHARYA’S METHOD TO FISH POPULATION ANALYSIS

6. TOTAL MORTALITY ESTIMATION

7. REFERENCES CITED

APPENDICESpdf

1. DETAILED PROGRAM LISTING

2a. PERCENTAGE POINTS OF THE X2 DISTRIBUTION

2b. PERCENTAGE POINTS OF THE T DISTRIBUTION

3. BHATTACHARYA ANALYSIS

4. CHI SQUARE STATISTICS

5. PLOT OF PERCENTAGE FREQUENCIES

6. FORD-WALFORD PLOT

7. GULLAND & HOLT PLOT

8. VON BERTALANFFY PLOT

9. JONES AND VAN ZALINGE METHOD

10. SPARRE’S CATCH CURVE METHOD

11. WETHERALL ET AL. METHOD

PUBLICATIONS OF THE BAY OF BENGAL PROGRAMME (BOBP)pdf