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Translation Series No.1211

Translation Series No.1211

Translation Series No.1211

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•<br />

- 1 98-<br />

the stock losses are composed of the waste by fishing, the natural mortal-<br />

ity and the losses caused by the spawning mration.<br />

7.2.1. Total mortality<br />

Beverton and Holt (1957) have, among other things, described<br />

the losses in a stock of fish with the aid of a differential equation.<br />

According to this the number of fish that is lost from the stock in the<br />

time t is proportional to the total mortality Z and the number N of the<br />

fish present.<br />

obtain<br />

dN =<br />

dt<br />

Through solving the differential quotient and integration we<br />

W<br />

- t<br />

W<br />

The mortality . thus follows the law of exponential dependence.<br />

N is proportional to t, when t increases arithmetically, N decreases geo-<br />

metrically. Z . is called the exponential coefficient of the total losses.<br />

Equation (1). thus gives the number of survivors at the time t.<br />

. The nuiber of the dead is then<br />

N o _ N t= N o _ oe -Zt<br />

.<br />

• N o -'r t D0 (1 e t)<br />

With the aid of - (1) and . the values available, one can now<br />

calculate the total mortality<br />

11- = 0. e<br />

ln 1.4 = Zt<br />

ln -D = Z:t N<br />

t<br />

(1 )<br />

(2)<br />

(3)<br />

[ p. 347]

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