Fish Population Dynamic and Stock Assessment (2+1)

Problem

Estimate of gear selection ogive for Nemipterus japonicus from a covered codend experiment (from Jones, 1976)

A	B	C	D	E	F	G	H
Length interval L1-L2	Number in codend	Number in cover	Total number	Fraction retained SL obs	Ln (1/SL-1) (Y)	Midlength (L1+L2)/2 (X)	Fraction retained SLest
9-10	0	1	-1	0	-	-	-
10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19	1 2 2 7 30 61 27 7 4	6 7 4 5 13 8 3 0 1	7 9 6 12 43 69 30 7 5	0.14 0.22 0.33	1.82 1.27 0.71	10.5 11.5 12.5	0.13 0.23 0.38

Step 1: Column A

Length interval of total length of fishes caught.

Step 2: Column B

Number of fishes retained in codend of trawl net.

Step 3: Column C

Number of fishes caught in the small meshed cover

Step 4: Column D

Total number of fishes caught trawl net is entered in the column D (Cover + codend)

Step 5: Column E

The fraction of the total catch which was retained in the codend is calculated. It is presented as fraction and entered in the column ‘E’.

Fraction retained (SL obs) =          No. of fishes in the codend

                                  --------------------------------------------------------------

                                Total number of fish caught both in cover & codend

SL obs for the length group 10-11 is calculated = 1/7 = 0.14

SL obs for the length group 11-12 is calculated = 2/9 = 0.22

Similarly calculate Fraction retained SL obs for other length group When fraction retained is plotted against the mid length of the corresponding length group it appears that the points are following a sigmoid curve, which reaches 1.00 (100% retention) at a certain length and which approaches 0.00 (0% retention) at a certain small length. The sigmoid curve is called as “gear selection ogive”.

Step 6:

Another easy way to describe gear selection ogive is the “logistic curve”. The mathematical expression is as follows

                      1

 SL =   ---------------------------

           1 + exp (S1 – S2 x L)

Where,

SL = No. of fish of length L ¢ in the codend

------------------------------------------------------------

No. of fish of length L ¢ in the codend and in the cover

L is midpoint of length interval

S1 and S2 are constants

The above equation can be rewritten as follows

Ln (1/SL-1) = S1 – S2 x L

This equation represent a straight line where

S1 = a

S2 = b

So the observation of the fraction retained (Column E) can be used to determine the logistic curve

Step 7: Column F:

Ln (1/SL-1) is calculated for each length interval and filled in the column F which is treated as ‘Y’ axis

Ln(1/SL-1) for the length interval 10 – 11 is calculated as follows

= Ln (1/0.14 – 1)

= Ln (7.1428 – 1)

= Ln 6.1428 = 1.82

Similarly fill the column ‘F’ by calculating Ln (1/SL-1) for other groups

Step 8: Column G:

Midlength of length interval is presented in the column G(L1+L2)/2

(Eg) For the length group 10-11, the mid length is 10+11/2 = 10.5

Similarly fill the midlength for other length groups and treat this column as ‘X’ axis

Step 9:

Calculate ‘a’ and ‘b’ values by using column ‘F’ (‘Y’ axis) and column ‘G’ (X axis)

Intercept a = S1 = 9.4875

Slope b = S2 = 0.7193

Step 10:

Now calculate by using the following formula for each length group

SL_est = 1/(1+exp(9.4875 – 0.7193 x L)

(Eg) SL_est for the length interval 10 – 11 is calculated as follows

                                1                                        1            1

SL_est= -------------------------------------       = ----------- =   --------- = 0.13

          (1 + exp(9.4875 – 0.7193 x 10.5)    1 + 6.923      7.923

Similarly calculated SL_est for other length interval and fill it in the column ‘H’

Step 11:

L 25%, L50% and L75% are the lengths at which 25%, 50%, and 75% of the fish are retained in the codend. The length range from L25% to L75% is symmetrical around L50% and is called as ‘Selection Range’. The following are the formula for calculating L25%, L50% and L75%

L25% = (S1 - Ln3) / S2

L50% = S1 / S2

L75% = (S1 + Ln3) / S2

Calculate L25%, L50% and L75% by using the above formula

Step 12:

L50 values for various meshes sizes of codend are calculated as follows

L50% = SF x meshsize

Where SF is ‘Selection Factor’. This cn be calculated from the table or from the graph.

SF L50% / meshsize = 13.2 / 4 = 3.3

Selection Factor is 3.3 for 4cm mesh sized codend.

Selection factor can now be used to determine L50% for different meshsizes, for example, L50% when using meshsizes of 3 cm could be,

L50% = 3.3 x 3 = 9.9cm

Similarly calculate L25%, L50% and L75% values for various mesh sizes and analyse the results.