# Estimation of some parameters of large fish populations by capture-recapture experiments

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## Abstract

A certain number of tagged fish is liberated and assumed to be distributed randomly among a natural fish population. The fish are subjected to a number of fishing experiments within relatively short periods, and lie between equal intervening periods of duration The above equation contains

*T*. Untagged fish are retained, while tagged fish are released during the fishing experiments. Denoting the catchability of untagged fish by*q*_{ u }and that for tagged fish by*q*_{ t }, it is assumed that they are related by the equation “*q*_{ u }=*cq*_{ t }” where*c*is a constant. Denoting the survival rates of tagged fish and the effective fishing effort of commerical fisheries per unit time from the (*k*-1)^{th}to the*k*^{th}experiments by_{ t }*S*_{ k }and*f*_{ k }, respectively, it is assumed that they vary from period to period. Assuming that during the*k*^{th}experiment, the number of untagged fish captured and the experimental fishing rate of tagged fish are denoted by_{ u }*X*_{ k }and_{ t }*P*_{ k }, respectively, then$$\begin{array}{*{20}c} {\frac{{(_u X_k )^2 }}{{[_u X_{(k - 1)} ][_u X_{(k + 1)} ]}} = \frac{{_t S_k }}{{_t S_{(k + 1)} }} \cdot \frac{{e^{ - (1 - c)q_t f_{(k + 1)} T} }}{{e^{ - (1 - c)q_t f_k T} }} \cdot } \\ {\frac{{1 - c_t P_{(k - 1)} }}{{1 - c_t P_k }} \cdot \frac{{(_t P_k )^2 }}{{[_t P_{(k - 1)} ][_t P_{(k + 1)} ]}}.} \\ \end{array}$$

*c*as a single unknown, while all other terms are supplied by the capture-recapture experiments, except*f*_{ k }and*f*_{(k+1)}which may be obtained from fisheries statistics. A number of the above equations are obtained from several experiments and can be combined into a single equation to obtain an overall estimate for*c*which can be used to derive estimates for experimental fishing rates, abundance, and instantaneous natural and fishing mortality rates for natural fish populations. These estimates are free from type (A) tagging errors, and have the advantage of taking into consideration the probable different behaviour of tagged and untagged fish.## Keywords

Mortality Rate Survival Rate Fishing Single Equation Fish Population
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Literature cited

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© Springer-Verlag 1971