A SIMPLIFICATION FOR THE STUDY OF 

 FISH POPULATIONS BY CAPTURE DATA 



Samir Z. Rafaii. 1 



ABSTRACT 



Expressions given by Rafaii for estimating catchability are modified here to eliminate iteration, 

 for better accuracy, and a large economy in calculations and time. The evaluation of catchability 

 allows the estimation of other important parameters with the useful assumption of their variabilities 

 according to seasons and recognized sections of a population. 



The evaluation of some parameters offish popula- 

 tions from capture data began at the start of the 

 century (Edser 1908; Heincke 1913; Baranov 

 1918). Beverton and Holt ( 1957) derived an equa- 

 tion in two forms (equations (14.19) and (14.86)) 

 for the estimation of catchability and natural 

 mortality from catch and effort data for a whole 

 series of years assuming identical survival rates 

 and catchabilities for all ages in a given year, 

 fishing effort varies from year to year, and neg- 

 ligible recruitment and migrations. 



Paloheimo ( 1961 ) modified the iteration method 

 by Beverton and Holt (1957) to a simpler one 

 without iteration using the relationship (1 — e l )/i 

 » e -o.5i where i is the instantaneous total mor- 

 tality. 



Allen (1966) described three methods for esti- 

 mating a population and one for recruitment by 

 using data on annual age composition, number 

 caught, effort to take a known part of the catch 

 assuming a constant recruitment rate all over a 

 year, equal catchability for the different age 

 groups, and available comparisons between ex- 

 ploited and unexploited populations with equal 

 natural mortality. Allen (1968) described a 

 simplification of his method for computing re- 

 cruitment rates. 



Among the investigators who studied the vari- 

 ability of parameters offish populations, Gulland 

 (1964) described variations in catchability as 

 cyclical, long-term trends due to amount of fishing 

 and changes in abundance, diurnal changes due 

 to feeding and light, temperature like severe 



'Ministry of Agriculture and National Resources, Port Har- 

 court, Nigeria; present address: College of Science and Technol- 

 ogy, P. M. B. 5080, Port Harcourt, Nigeria. 



winters, and sex. Paloheimo and Kohler (1968) 

 concluded from their analysis of a cod population 

 that catchability and natural mortality showed 

 variations associated with age and years. Walker 

 (1970) gave evidence of increased natural mortal- 

 ity with age due to senescence for cod. 



Rafaii (1974) recognized the probable great 

 variability of parameters offish populations and 

 derived expressions for the evaluation of catch- 

 ability, fishing mortality, natural mortality, and 

 recruitment assuming their variability from one 

 season to another and their constancy during the 

 seasons as well as their variation from a recog- 

 nized section of a population to another like age- 

 groups and different sexes. His equations for the 

 evaluation of catchability as the first parameter 

 to be estimated require a number of iterations 

 which may be relatively very large if recruit- 

 ments exceed the sum of natural and fishing mor- 

 talities. Therefore, a computer is needed for 

 accurate calculations and this is a disadvantage. 



The present treatment transforms the equa- 

 tions given by Rafaii (1974) to estimate catch- 

 ability into forms that dispense with iterations 

 and yield more accurate estimates. 



SAMPLING PROCEDURE 



A fish population with a certain initial size is 

 distributed on a constant area and subjected to 

 a sequence of sampling surveys which can be 

 grouped into a number of groups. Each group of 

 surveys must contain at least three sampling 

 surveys. The parameters of the population are 

 assumed to vary among the groups of surveys and 

 remain constant within each group which repre- 

 sents a season with constant properties. The 

 entire fishing fleet may be considered as sampling 



Manuscript accepted November 1976. 

 FISHERY BULLETIN: VOL. 75, NO. 3, 1977. 



561 



