Vurtual population analysis ( VPA)

 First developed as a age-based method by Derzhavinin, 1922.
 Later, rediscovered by Fry in 1949.
 Introduced in fish stock assessment by Gulland (1965) based on older work (e.g. Fry 1949).
 Subsequently modified by many authors including, 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.
 Practical reviews of VPA methods are given by Pauly & Jones in 1984.
 Multispecies version of the method was developed by Sparre in 1991.

The word “virtual”, introduced by Fry is based on the analogy with the “virtual
image”, known from physics.
A “virtual population” is not the real population.
It is virtual in the sense that the population size is not observed or measured
directly but is inferred or back calculated to have been a certain size in the
past.
A “virtual population” denotes the exploited population or catch.

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

 The virtual population analysis (VPA) is the most wide spread method to assess long-lived finfish
stocks in developed countries (Hilborn and Walters, 1992).
 In a VPA, the stock is considered to be composed of several annual cohorts.
In cephalopod stocks as species have a short life cycle (generally 1 or 2 years), the VPA is generally
implemented on a monthly basis and using micro - cohorts (Jouffre et al., 2002; Royer et al., 2002, 2006;
Thiaw et al., 2011).
Equivalent to VPA.
This is the more common term used in USA and Canada.

A cohort Modeling technique commonly used in fisheries science
for reconstructing the historical population structure of a fish
stock using information on the deaths of individuals in each year.
VPA, calculates the number of fish alive in each cohort for each
past year.
It is also called cohort analysis because
each cohort is analyzed separately.

Virtual population analysis is basically an analysis of the catches of
commercial fisheries, obtained through fishery statistics, combined
with detailed information on the contribution of each cohort to the
catch, which is usually obtained through sampling programmes and
age readings.
VPA or Cohort analysis was first developed as,
1. Age-based methods - Temperate regions
2. length-based methods - Tropical regions.

Number
alive at
beginning
of this year
Number alive at
beginning of
next year
Catch of
year
Natural
mortality of
this year
“ The total landings from a cohort in its lifetime is
the first estimate of the numbers of recruits from
that cohort.”

Where,
C (y, t, t+1) = number caught between age ‘t’ and age ‘t+1’ in ‘y’ year
N (y, t) = No. of survivors in the sea with ‘t’ age in starting of ‘y’ year
N (y+1, t+1) = No. of survivors in the sea with ‘t+1’ age in starting of ‘y+1’ year
F = Fishing mortality coefficient
M = Natural mortality coefficient

 The calculation can be started from the bottom i. e. year of oldest age group
for VPA analysis (for example, if VPA analysis is carried out for the time
period from 1978 to 1980, the starting of VPA analysis can be begun from
the year 1980) using equation-1.1.
 At first step, the fishing mortality can be chosen on the basis of guess.
 Second step onward, fishing mortality cannot be taken simply on the basis
of guess, but it can be calculated with help of equation-1.2 by some trial and
error method.
 Once, fishing mortality has been estimated, the number of fish in the sea for
preceding year can be calculated by using equation-1.3.

Mensil (1988) presents a package of microcomputer programs,
1. ‘ANACO’ (Analysis of Cohort) which can perform the VPA
calculations.
2.‘COMPLEAT ELEFAN’ package (Gayanilo, Soriano and Pauly,
1988)
3. FiSAT contain also routines for VPA analysis.

 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 (in unit of millions) were:
1. C(1974,0,1) = 599, number caught between age 0 & age 1
We start our calculation from bottom, i.e. with the number caught between age 6 & 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 1
st 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.
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
Contd..

Inserting the value of N(1980,6) = 22.2 million, equation 2 becomes:
N(1979,5) = 22.2*exp(Z)
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]
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}]
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

Age group(t) Year (y) No. caught during year y
C (y, t, t+1)
Fishing mortality
during year y
F (y, t, t+1)
No. surviving on 1
jan, year y
N(y,t)
0 1974 599 t t
1 1975 860
t t2 1976 1071
3 1977 269
4 1978 69 t t
5 1979 25 0.70 54.4
6 1980 8 0.50 *) 22.2
The results of the calculations made so far may be summarized as follows:

 VPA methods require age-structured data.
 In general, VPA-type methods are always preferable when age-structured data are available.
 Natural mortality is only rarely estimated using VPA.
 Estimation of population parameter & used to determine the optimum fishing strategy .
 Useful information on natural mortality can be obtained through the Multispecies VPA technique
(Sparre 1991, Magnusson 1995, Section 4.8).

Better method to find out Natural Mortality.
 Natural mortality of cohort at age ‘t’ (M) is constant.
 It deals with the population dynamics of single species, whereas natural fish populations almost
always interact among themselves and with others.
 Calculation - very difficult

 Gulland, J. A. 1983. Fish Stock Assessment: A manual of basic
methods: Chichester, U.K. Wiley Interscience, FAO/Wiley Series of Food
and Agriculture Vol. 1, 223 pp.
 Sparre, P. and Venema, S. C. 1992. Introduction to Tropical Fish Stock
Assessment. Part I. Manual. FAO Fisheries Technical paper, No. 306.1.
Rev1. Rome. FAO. 376 pp.
 Hans Lassen & Paul Medley, 2001, Virtual population analysis - a
practical manual for stock assessment, FAO, 1 to 6.
 Vivekanand Bharti. Virtual population analysis, Fishery Resources
Assessment Division ICAR-Central Marine Fisheries Research Institute,
Chapter no. 20, pg. no. 232.
 Wikkipedia
 Google

Vurtual population analysis ( VPA)

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