Provides information about Vitrual population analysis method.

1. Virtual Population Methods
Presented by,
Phibi Philip N
BFT1326

2. History:
 The method was first developed as a age-based method by
Derzhavin in 1922.
 Later, rediscovered by Fry in 1949.
 Subsequently modified by many authors including Gulland
(1965) & Pope in 1972 (modifications made by Pope is
referred to as “Pope’s cohort analysis”).
 A complete review of the development of VPA methods was
given by Megrey in 1989.

3. Contd..
 Practical reviews of VPA methods are given by Pauly &
Jones in 1984.
 Recently length based methods have became available,
which are of particular interest to tropical fisheries.
 Multispecies version of the method was developed by
Sparre in 1991.

4. Introduction:
 Reconstruct fish population structure by age or length.
 Analyse the effect that, a fishery has had on a particular
year class of a stock.
 i.e., this method uses historic data to analyse the past
population and hence named as Virtual Population
Analysis.
 This method also analyse a particular year class of a
stock (cohort) and thus also called as cohort analysis.

5. Contd..
 The “virtual population” is a population created by the
method, based on real catch data & assumptions of the level
of natural mortality & terminal fisheries mortality.
 Methods dealing with the future are called predictive
methods developed by Thompson & Bell.

6. Concept:
 Idea behind the method is to “analyse the catch
(measurable factor), in order to back calculate the
population that must have been in the water to produce the
catch”.
 The total landings (catch) from a cohort in its lifetime is the
first estimate of the number of recruits from that cohort.
 But it is however an under-estimate, because natural
mortality is not considered here.

7. Contd..
 If the total mortality (M) is known, then we can do a
backward calculation & find out how many fish belonging
to the cohort were alive year by year & ultimately how
many recruits were there.
 At the same time F (fishing mortality) value will be also
known as the number of living individuals and number of
individuals caught are already calculated.

9. Equation:
 Catch (Ci) from a population during a unit time period
(i), is equal to the product of the population size at the
beginning of the time period (Ni) times the fraction of
the deaths caused by fishing, times the fraction of total
death (Zi).
 The equation is represented mathematically:

10. Example -VPA, North Sea Whiting:
 Consider the 1974 cohort of whiting. The annotation used is as follows:
C(y, t, t+1) = number caught in year y of age between t & t+1 years (in
millions)
The number caught (millions) were:
C(1974,0,1) = 599, number caught between age 0 & age 1
C(1975,1,2) = 860, number caught between age 1 & age 2
C(1976,2,3) = 1071, number caught between age 2 & age 3
C(1977,3,4) = 269, number caught between age 3 & age 4
C(1978,4,5) = 69, number caught between age 4 & age 5
C(1979,5,6) = 25, number caught between age 1 & age 2
C(1980,6,7) = 8, number caught between age 1 & age 2

11. Contd..
 Consider the last catch group (between age 6 and 7).
C(1980,6,7) = 8 million fish
Let the natural mortality (M) be 0.2 for all age group. If fishing mortality for 6-7
age group is known, then how many fishes there must have been in the sea on
1st January 1980 i.e., N(1980,6) to account for a catch of 8 million whiting can be
calculated using catch equation:
C(1980,6,7) = [N(1980,6)]*[F/Z]*[1-exp{-Z*(7-6)}]
Let F(1980,6,7)=0.5, then Z=0.7 (0.5+0.2). Then the above equation become:
8 = [N(1980,6)]*[0.5/0.7] ]*[1-exp{-0.7*(7-6)}] = N(1980,6) *0.36
Thus, N(1980,6) = 8/0.36 = 22.2 million.

12. Contd..
Number of survivors on January 1st 1980 i.e., N(1980,6) , is equal to the number at the end
of 1979. Now it is possible to calculate how many whiting there must have been in the
sea on January 1979 to account for the catch C(1979,5,6) which is 25 million.
Now there is no need to guess the F value for 5-6 age group i.e., because it is possible to
calculate the F value by equating equations as follows:
C(1979,5,6) = [N(1979,5)]*[F/Z]*[1-exp(-Z)] → Equation - 1
and, N(1980,6) = [N(1979,5)]*[exp(-Z)]
rearranging, [N(1979,5)] = [N(1980,6)]*[exp(Z)] → Equation – 2
Inserting the value of N(1980,6) = 22.2 million, equation 2 becomes:
N(1979,5) = 22.2*exp(Z)

13. Contd..
Inserting C(1979,5,6) =25 million into equation 1 gives:
25 = [22.2]*[F/Z]*[1-exp(-Z)]
after multiplication & rearranging:
[25/22.2] = [F/Z]*[exp(Z)-1]
Putting M=0.2, then Z=0.2+F gives:
1.126 = [F/(F+0.2)]*[exp(F+0.2)-1]
Now in the above equation has only F as unknown variable. By further equating. F = 0.696.
In this way of back calculation it is possible to estimate number of survivors & fishing
mortality for each age group.

14. Contd..
 From all the previous workouts two VPA equations are derived out:
[C (y,t,t+1) / N (y,t,t+1)] = {[F (y,t,t+1)] / [M+F (y,t,t+1)]}*{exp[F (y,t,t+1)+M]-1}
&
N (y,t,) = [N (y+1,t+1) * exp {F (y,t,t+1) + M}]

15. Contd..

16. Basic features of VPA:
 Better method to find out Natural Mortality.
 But when the caught stock is low, the total stock in the sea
becomes more uncertain. Thus higher the fishing mortality
more dependable is the VPA.