Estimating Survival Rate (S) - Powell Method

There are a number of methods to estimate survival rate (S) of a fish population, such as CPUE, Heincke (1913), Jackson (1939), Beverton-Holt (1956) and Ricker (1975). Powell (1979) wrote this method in case that there are no biological data anything but lengths exist.

From a Beverton-Holt equation L_inf = - a/b and Z/K = -(1+b)/b, where a is y intercept, b is slope, Z is instantaneous coefficient of total mortality, K is growth coefficient. Lengths on the table (left) are mean lengths. a = 11.906 and b - - 0.2349 (R square = 1.0) after regression on SPSS. Thereby, L_inf = 50.69 cm, Z/K = 3.26, and if K value is known, S can be calculated by equation S = exp (-Z).












revised on Apr. 3 2007
by Yeongha Jung

von Bertalanffy Growth Model example 1

I used age, length and weight data of Pacific Ocean perch, Sebates alutus from Zhang (1981) to extract a growth model. Coefficients L_inf and K are estimated 357.7 mm and 0.1625 for Walford method, and 371 mm and 0.1298 for von Bertalanffy method, respectively.
This picture on the right shows the growth model by von Bertalanffy method. The advantage of this method is that t_0 can be obtained simultaneously and utilize all raw data without weighting from the sample size. However, the calculation take longer time than the other method. Microsoft Excel is used.

















revised 0n Apr.2 2007
by Yeongha Jung

Beverton-Holt yield-per-recruit example 1

This is an example of Beverton and Holt (1964) yield-per-recruit (YPR) analysis. The species used for this model is an Asian Navodon modestus from Park (1985). The isopleth diagram (up, x-axis is F, y-axis is tc) and 3D graph (down) on the right show the relationship between YPR, F and tc.

The lines and the surface on the pictures present the values of YPR. If the present tc is 1.77, the optimal YPR meets at F is 0.72. If the strength of fishing at this point goes higher (F value goes higher), YPR decreases, and if wants to increase YPR at the same F, the best age of catch (tc) is around 3.

The diagrams are produced by Mathematica.


F : instantaneous rate of fishing mortality
tc : age of capture

M = 0.26 // instantaneous rate of natural mortality
tr = 0.38 // age of recruit
tL = 10.0 //maximum age in fishery
t0 = -2.262 // theoretical age of 0
Winf = 654.2 g // maximum weight


revised Apr.1 2007
by Yeongha Jung