Fish Population Dynamics Lab

Practical: Fish Population Dynamics Lab
1. a. Define fish population dynamics.
b. What is stock? Construct a table comparing the different stock abundance assessment
processes/methods.
2. What is gonosomatic index (GSI)? How does we estimate time of spawning using GSI? From
the data given below, estimate the spawning time of seabass (use graph paper).
Month Oct Nov Dec Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec
Gonad weight (g) 5 6 5.5 5 6.1 7 8 10 20 16 28 30 40 7 8
Total weight (g) 80 85 81 79 85 90 100 100 120 118 160 161 162 129 140
3. Determination of hepatosomatic index of given fish.
4. Determination of fecundity.
5. a. To find out growth pattern of fish by determining length-weight relationship.
b. “Weight = 0.05*Length2.5
” – What does the equation express?
c. Calculate length-weight relationship from the following data given for a fish population
(use graph paper).
Total length (cm) 10.5 12.0 14.0 15.0 16.0 18.0 19.0 20.0 21.0 22.0
Mean weight (kg) 1.00 1.39 2.47 3.17 3.93 4.54 6.14 6.80 7.00 10.65
6. To calculate the population of a fish pond by Peterson’s method taking glass beads as fish. If
total population = 1000, unmarked population = 900, marked population = 100, calculate
population of fish and per cent error.
Unmarked fish captured 50 32 20 20 13 10 12 10 8 6
Marked fish captured 9 4 0 1 2 3 0 1 1 0
7. What do you understand by depletion method. Calculate the stock size using efforts (in line-
hour) and catch (number) data for the bluefin tuna, Thunnus thynnus, of the Bay of Bengal
given below:
Effort (line-hour) 170.6 453.8 513.4 714.4 679.1 419.9 470.3 318.4 136.8 177.6
Catch (number) 60 274 240 244 301 151 127 90 31 7
8. Determination of fish age from hard parts.

a. Age determination from scales
b. Age determination from otoliths
9. Mention a list of basic fish growth parameters? Compare the Ford-Walford and von-
Bertalanffy plots for growth estimation.
10. Write the formula of von Bertalanffy growth equation. Calculate the value of K and L∞ based
on the data given below:
Length in one year, Lt 17 24 29 33
Length in one year later, Lt+1 24 29 33 35
11. What is surplus production model? Estimate MSY and FMSY using Schaefer model and Fox
model.
Catch
(t)
382 431.3 656 432 1054 820 745 531.7 764.1 856.1 607 632.1 592.8 533.9 505.4 507.8 593.8
Effort
(hmnd)
17300 21000 22800 15700 72000 95900 100700 71400 66900 95400 85500 71400 66300 45000 41400 34900 31300

Question no; 01: Define Fish Population Dynamics.
Fish population dynamics may be defined as the study of the rate of changes in number of fishes
in the population and the factors influencing these changes including the rate of loss and
replacement of individuals and any other regulatory process tending to keep the population number
steady or at last to prevent any change.
Fish population dynamics is a branch of fisheries science dealing with the fluctuation of fish
parameters such as growth, reproduction, recruitment, mortality, survival, yield, abundance,
migration etc.
Question no; 02: What is stock? Construct a table comparing the different
stock abundance assessment process.
Stock is a part of population which is manageable or which we like to manage.
A stock is the part of a fish population which is under consideration from the point of view of
actual or potential utilization. A group of a fish population which shares common ecological and
genetic features. In terms of stock assessment, stock is designated as a subset of species. For fishery
management purposes, stock is a sub group of species.
The estimation of stock abundance is important in determining the effects of fishing and
environmental disturbances as well as in estimating parameters such as mortality. Although
estimates of absolute abundance (the total number of individuals) are sometimes required, it is
often sufficient to obtain estimates of relative abundance – the number of individuals in one area
in relation to the numbers present in another area, or in the same area at another time. estimating
total stock size include sampling surveys, mark–recapture, depletion and swept area methods. The
comparison among the different stock abundance assessment process is given below:
Topics Mark –
recapture
method
Swept area
method
Depletion
method
Sampling
surveys
method

Definition Mark recapture
method is a
method commonly
used in ecology to
estimate an animal
population size
where a portion of
the population is
captured, marked,
and released and
then another
portion will be
captured and the
number of marked
individuals within
the sample is
counted.
Trawl net sweeps a
wide area of water
body to catch
(either in weight or
in numbers) put
unit of effort or per
unit of area is an
index of the stock
abundance to
convert absolute
measure of
biomass called
swept area method.
Population size
can be estimated
by the sum of
sequential catches
required to remove
all fish from the
population which
effect of fish
remaining in the
population are
called depletion
method.
Sampling survey
is a method of
examining the
distribution of
organisms by
taking samples
within squares of
known size where
the mean number
in each series of
quadrates can be
compared.
Other’s name Capture –
recapture method,
capture – mark –
recapture method,
sight– resight
method, mark –
release – recapture
method, Peterson
method, the
Lincoln method.
Effective path
swept method
Removal method Quadrat sampling
method
Inventor C.G Johannes
Peterson
Hilborn and
Walters
R. Pound and F.E
Clements
Estimating
equation
N =TC/R
Where, N= stock
size
T= tagged fish
C= total catch
R= recaptured
tagged fish
a= W×TV×D
where, a= swept
area
W= effective
width of the trawl
TV= towing
velocity
D= duration of the
tow
B=Cw/V×(A/a
Where, B=
biomass
Cw= mean catch
weight per tow
Nt=N∞ -∑Ct ∙∙1
Where,
Nt=numbers at
particular time
N∞=original stock
size
∑Ct=cumulative
catch
Nt=CPUEt/q∙∙…2
Where, q=
catchability
coefficient
1 and 2 →
N=A/a×∑x /n
Where,
A=total area
a=quadrant area
∑x/n= x
̄ = mean
number of
samples per
quadrate

V= vulnerability of
the fish
A= the total area
a= swept area
B= CPUE×A/a
Where,
B=Biomass
A= total area of
stock
a=circular area of
the traps influence
CPUEt = qN∞ -
q∑Ct
Advantage High accuracy Less time
consuming
Almost perfect
result can be
found
Low cost method
Limitation 1. Tagging
organisms may not
be distributed
themselves
randomly into the
population and
remain as a
separate shoal.
2. The tags have to
be retrieved. If
they are not easily
identified, they
won’t return.
1. Vulnerability is
difficult to
estimate by
conventional
means.
2. Expensive, trawl
net is not
applicable at any
place
3.Time consuming
and large area is
not possible
1.Either the
available fishing
effort was too
small or the
experimental area
was too large to
produce a
reduction in CPUE
over a short time,
depletion have
failed.
1.There exists
biasness in favor
of slow-moving
fish.
Mostly
applied area
Mostly in ponds River River Large area like
Bay of Bengal.
Outcomes Estimate the
individual numbers
in a particular area
Estimate the stock
biomass, not the
number of
individuals
Estimate the total
stock
Estimate the
individual
numbers
Others Anchor tag, PIT
tags are used to tag
in fishes
Trawl net is used Leslie plot, Delury
model, k-pass
processes are used
Standard
deviation process
is used
Question no;03: “Weight =0.05*Length2.5
” – What does the equation express?

Weight=0.05*length2.5
, this express the cubic relationship between length(L) and weight(w) which
can be represented by the cubic or power curve equation and the equation is W=aLb
.
Given equation, W=0.05*L2.5
Here,
W=weight of fish
L=length of fish
Catchability coefficient, a = 0.05 [which indicate that no matter how much we change the length,
the minimum weight will be increased at the rate of 0.05. It is a constant value.]
And Slope, b=2.5, which indicate negative allometry
We know that, b=3 is called isometric growth. b<3 fish become inadequate with increasing length
and growth will be negatively allometric. b>3 shows the positive allometric growth and reflecting
optimum condition for growth.
Since that's given here, b=2.5, which is less than 3. That means, the overall growth of the fish we
have taken as sample, are not well in that environment.
Question no;04: Mention a list of basic fish growth parameters? Compare the
Ford-Walford and von-Bertalanffy plots for growth estimation.
A list of basic growth parameters:
Growth may be described in terms of changes in length, width or any other linear dimension as
well as weight.
Growth parameters are used as input data in the estimation of mortality parameters and in
yield/recruit in fish stock assessment. Growth parameters differ from species to species, even
between the sexes and also differ from stock to stock of a species.
Growth parameters are:
• Growth coefficient or curvature parameter (K)
• Theoretical maximum length or asymptotic length (L∞)
• Age at zero length(t0)
Growth coefficient (k): K is a growth coefficient, which is a measure of the rate at which
maximum size is reached. This is a parameter of Von Bertalanffy growth function.

Theoretical maximum length (L∞): The length of the fish corresponding to zero increment
is called “length infinity” or asymptotic length. This is the theoretical maximum length that the
species would reach it lived indefinitely.
Age at zero length (t0): It is the initial condition parameter.t0 is the hypothetical age The fish
would have had at zero length, if they had always grown according to VBGF equation. t0 is also
called as ‘arbitrary origin of growth'.
The comparison between Ford-Walford and von-Bertalanffy plots for growth
estimation is given below:
Ford-Walford plots Von-Vertalanffy plots
The inventor of this plots is British editor
Edward Walford.
The inventor of this plots is Austrian biologist
Karl Ludwig von Bertalanffy
Equation of this plot model are
Lt = L∞(1 − exp[−Kt]) and
Lt+1 = L∞(1 − exp[−K]) + Lt exp[−K]
Equation of this plot’s models are
Lt = L∞ (1 − exp[−K(t − t0)]) and
Wt = W∞(1 − exp[−K(t − t0)])3
Parameters of this plot are maximum length,
length at age, growth coefficient and the
length at age one year later.
Parameters of this plot are maximum length,
length at age and growth coefficient.
This plot method for estimating maximum
length and growth coefficient from mean
length at age.
The function is commonly applied in ecology
to model fish growth.
Data is collected at specific times of the year. Data is collected at different times of the year
This plot model shows pseudo-cohort This plot models shows cohort.
It is simple method and growth of fish can
solve in short time.
It is a multiple method and growth of fish can
solved in lengthy time.
Question no;05: What is GSI? How does we estimate time of spawning using
GSI?
GSI: A gonad or gonosomatic index (GI or GSI) is often used to follow the reproductive cycle of
a species over the year at monthly intervals or less. This index, which assumes that an ovary
increases in size with increasing development, compares the mass of the gonad (GM) with the total
mass of the animal (TM). Gonosomatic indices vary greatly and range from less than 1% in many
fish to almost 47% in the European eel.
Gonadosomatic index calculation:

The Gonadosomatic Index (GSI) of fish was determined by using the formula:
GSI = 100∗GM/TW
where GSI = Gonadosomatic Index, GW = Gonad weight, TW = Total body weight
Most of the species, including 96% of all fish, are external fertilizers. The chances of sperm
meeting eggs, high larval mortality and vagaries of currents carrying larvae to suitable settling
areas all result in a very low chance of survival. The spawning event may extend over either a
short or long time period, and be at either regular or irregular intervals, but in many species, occurs
once every year. The stimulus (or combination of stimuli) which induces resting gonads to become
active may include endogenous factors (internal events related to growth and maturity), and
exogenous events in the surrounding environment. GSI is a good indicator of reproductive activity,
so the spawning season is determined by an association of the GSI and the frequency distribution
of the gonadal maturity stages.
Stages in ovary development: Often in fisheries work, only the female ovaries are studied,
as these are larger and more easily examined than male testes; it is also assumed that development
of both ovaries and testes are synchronous. Ovaries may be examined microscopically and
classified into various developmental stages. One such classification is shown in the following
table. The progress of ovarian maturation was classified into five stages
Stages Description
0 Ovary not evident, gut and muscles visible
at joint between cephalothoraxes and
abdomen.
1 Ovary milk-white, ovary not visible through
carapace, gut and muscles visible.
2 Ovary pale yellow, ovary not visible
through carapace, gut and muscle visible.
3 Ovary yellow, red chromatophores evident,
ovary visible through carapace, muscle
partially obscured.
4 Ovary orange, red chromatophores, ovary
lobes cover most internal organ, muscle
obscured.
Table 5.1: Stages of reproductive development showing the appearance of ovary and eggs.

Ovaries taken from samples of females collected at intervals throughout the year may be classified
into developmental stages, and the percentages of each can be plotted by month in a histogram.
Some percentages of penaeid prawn are given in this table.
Month stage 0 stage 1 stage 2 stage 3 stage 4
July
August 5%
September 8% 4% 2% 1%
October 7% 5% 10% 7%
November 4% 7% 14% 10%
December 5% 6% 12% 3%
January 7% 4% 13% 2%
February 9% 3% 7% 2%
March 1% 3% 3% 7%
April 5%
May
Jun
Table 5.2: Observation of ovary development stages of prawn
Figure 5.3: Percentage of female prawn in five different development stages
Ovary maturation stages based on macroscopic criteria for a penaeid prawn are shown in table 5.2,
with analyses summarized in the histogram in Fig. 5.3. Relatively large numbers of individuals
with highly developed ovaries in November and March suggest peaks in spawning activity during
these periods.

Estimation of the time of spawning using GSI: Gonadosomatic index which is an index
of gonad size relative to fish size is a good indicator of gonadal development in fish. The
percentage of body weight of fish that is used for production of eggs is determined by the
gonadosomatic index. The average GSI value of a fish at different month is given below:
Month GM TM GSI
October 5 80 6.25
November 6 85 7.05
December 5.5 81 6.7
January 5 79 6.3
February 6.1 85 7.1
March 7 90 7.7
April 8 100 8
May 10 100 10
Jun 20 120 16.66
July 16 118 13.55
August 28 160 17.5
September 30 161 18.63
October 40 162 24.69
November 7 129 5.42
December 8 140 5.7
Figure 5.4: Seasonal variation in GSI (% of body weight) at different months. This solid line
indicates the average GSI of the month.
3
0 Spawnin
g Time
2
5
2
0
1
5
1
0
5
0
O ND J F M A
M J
Mont
h
J A S 0 N D
Gonadosomatic
Index(GSI)
%

GSI was observed in October to March, ranging from 6.25 to 7.7 (% of body weight. From March
to June the GSI values showed a little bit forward trend. But the overall trend of GSI moved a little
bit downward from the month of July. The highest amount of GSI indicates that the breeding
season is very near, i.e., they may breed either at the end of September or anytime in October.
Relatively lower GSI was observed in November to December. Monthly observations of gonadal
development depicted the prolific breeding nature of fishes possessing all maturity stages
throughout the year but with a considerable seasonal variation.
Question no; 06: What is surplus production model? Explain one model to
estimate the MSY.
Surplus production models, sometimes called surplus yield models or biomass dynamic models
are basses on the assumption that a fish stock produces an excess or surplus abundance that can
harvested.
Surplus production models are used to assess stock status and exploitation in data-limited areas
where reliable information on age and length structure and natural mortality are not available. They
are applied not only to stocks with available commercial catch data and some index of exploitable
biomass, such as catch per unit of effort (CPUE) derived from scientific surveys, but also to
migratory stocks and crustaceans that are difficult to age. They assume that sustainable catch is a
simple function of population biomass, regardless of the size and age composition of that biomass.
The primary advantages of surplus production models are that:
(1) Model parameters can be estimated with simple statistics on aggregate abundance and
(2) the models provide a simple response between changes in abundance and changes in
productivity.
The primary disadvantages of such models are that:
(1) They lack biological realism (i.e., they require that fishing have an effect on the population
within 1 year)
(2) They cannot make use of age- or size-specific information available from many fisheries.
However, in some circumstances, surplus production models may provide better answers than age-
structured models.
Maximum sustainable yield (MSY) is a theoretical concept used extensively in fisheries science
and management. In fisheries, MSY is defined as the maximum catch (in numbers or mass) that
can be removed from a population over an indefinite period. The concept of MSY relies on the
surplus production generated by a population that is depleted below its environmental carrying
capacity. Despite many concerns about MSY, MSY remains a key paradigm in fisheries

management. However, MSY has evolved from a fisheries management target to a limit on fishing
mortality and biomass depletion.
MSY (also called maximum surplus production, maximum equilibrium catch, maximum constant
yield, maximum sustained yield, sustainable catch) is the highest theoretical equilibrium yield that
can be continuously taken from a stock under existing (average) environmental conditions. It is
the highest catch that still allows the population to sustain itself indefinitely through somatic
growth, spawning, and recruitment.
There are 2 models, by which we can estimate the MSY.
1) The Schaefer model
2) Fox model.
To estimate the MSY, one model is explained below:
The concept of maximum sustainable yield (MSY), the largest annual catch or yield that may be
taken from a stock continuously without affecting the catch of future years has had a fluctuating
history of favor and scorn in fisheries management.
The first model that is most associated with MSY is the surplus production model of Schaefer.
In the Schaefer model, the growth of a population or stock is assumed to increase with time in the
manner of a logistic or S- shaped
The model equation is ;
Bt+1=Bt +rBt(1-Bt/B∞)-Ct
That means the following years biomass ( Bt+1) will equal the present year biomass (Bt) plus the
surplus production minus the catch Ct.. r is the intrinsic rate of increase and B∞ is the unfished
equilibrium stock biomass.
Again
CPUE∞ is the catch per unit effort at the maximum biomass,B∞, of the stock.so that,
CPUE=CPUE∞-(CPUE∞q/r)f
[CPUE∞=a, (-CPUE∞q/r) =b, f=X, CPUE=Y]

Which is the straight line of the form:
CPUE=a+bf
As we know the CPUE = C/f so we can express it as,
C=af +bf2
,which is the equation for the symmetrical parabola in Schaefer’s model.
Maximum effort fMSY= -a/2b
And the Maximum sustainable yield or MSY = -a2/4b.
Now we are giving here an example:
Catch(t) Effort CPUE
382 17300 22.08
431.3 21000 20.54
656.0 22800 28.77
432.0 15700 27.52
1054.0 72000 14.64
820.0 95900 8.55
745.0 100700 7.40
531.0 71400 7.45
764.0 66900 11.42
856.1 95400 8.97
607.0 85500 7.10
632.1 71400 8.85
592.8 66300 8.94
533.9 45000 11.86
505.4 41400 12.21
507.8 34900 14.55
593.8 31300 18.97
We know that,
Y=a+bx { here,Y=CPUE,, x=effort}
So regression coefficient b= -0.0002
And a= 25.341116
So fishing effort at which yield maximized,
FMSY= -a/2b
=-25.341116/ 2×(-0.0002)
=63352.79

And MSY=-a2
/4b
=-(25.341116)2
/4×(-0.0002)
=802716.59
The MSY we counted here is 802716.59.we can collect maximum 802716.59 from the stock that
does not hamper in stock.
Figure.6.1: MSY is taken at half the maximum biomass

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