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Index
SL Name of Contents Page
1. Introduction 2
2. Population structure 2
3. Estimation of population structure 3
4. The Gordon-Schaefer model 4
5. Sex ratio 5
6. Age distribution 6
7. Age specific birth and death rates 6
8. Age-structured model 7
9. Age-dependent method 8
10. Length frequency relationship 9
11. Conclusion 10
12. Reference 10
2
Introduction
Estimation of fish population dynamics are often based on age structures. Understanding past
population structure is of interest to evolutionary biologists because it can reveal when migration
regimes changed in natural populations, thereby pointing to potential environmental factors such as
climate changes as driving evolutionary forces. Characterizing the structure of extent populations is also
key to conservation genetics as translocation or reintroduction decisions must preserve evolutionary
stable units. Finally, population structure has important biomedical consequences either when a number
of subpopulation groups is locally adapted to particular environmental conditions (and maladapted
when exposed to new environments) or represents a confounding factor in the study of the statistical
association between genetic variants and phenotypic traits.
Population structure
The total population or size of a community, defined geographically or administratively, is the number
of persons residing there. The term “population structure usually refers to the patterns in neutral genetic
variation that result from the past or present departure from panmixia of a population. For example,
suppose mean length of fish in standardized samples from a population is used as an index of population
structure; shifts to smaller mean lengths of sampled fish may indicate increasing exploitation. The
effectiveness of length-limit regulations are often evaluated relative to changes in proportional size
distribution
from a random sample of individual fish Indices of structure rely on
 estimates of length,
 weight,
 age.
Maturity status and sex identification allow the calculation of several useful indices. The juvenile-to-
adult ratio can indicate important aspects of the dynamics of a fish population
To obtain an accurate estimate of age structure, biologists must obtain a random sample of a population.
Aging techniques alos for many important sport fish in have been validated and it is important to use the
3
standard techniques. Determining age of fish takes considerably more effort than measuring and
weighing fish but is usually warranted during population assessments.
Figure: Fluctuations of fish populations and the magnifying effects of fishing
The concept of equilibrium in population structure is being viewed more and more as a simplification of
the effect of fishing on exploited populations. It is still difficult to account for rapid changes in species
composition in multispecies fisheries.
Estimation of population structure
Population structure are directly related to the weight, size, number, length, birth, recruitment, biomass
and death of individuals. An organism as a reacting chemical system by asserting that the processes of
anabolism and catabolism control the weight of an organism. Since the biomass of a fish stock is affected
by natural mortality, fishing mortality, recruitment and growth.
A simple yield equation,
S= R+ G-M-F
Where, S = population biomass,
R = recruitment,
G = growth,
4
M = losses due to natural mortality
And F = losses due to fishing mortality.
The Gordon-Schaefer model
Figure: The Gordon-Schaefer model
The Gordon-Schaefer model describe the population growth with the following equation,
dB/dt= {rB(t) (1- B(t)}/K
Where, r is the intrinsic rate of population growth,
B(t) = population biomass in time t
K= the carrying capacity of the environment
Population structure changes (Biomass) through time can be expressed as:
dB/dt= rB[1- B/K] –Y
Where, the catch rate =Y,
B(t) = population biomass in time t
5
K= the carrying capacity of the environment
When the population is at equilibrium, i.e., dB/dt=0, and thus losses by natural and fishing mortalities
are compensated by the population increase due to individual growth and recruitment.
Sex ratio
The proportional distribution of the sexes in a population aggregate, expressed as the number of males
per female. The sex ratio at birth is an important demographic indicator used for determining the sex
composition of a population.
In Monosex tilapia culture there have seen a great change in growth as the male tilapia convert their
reproductive energy to form their body mass and a big difference seen between normal and monosex
male tilapia pond.
Table: Month-wise distribution of male and female sex ration of R. Corsula from rajshahi, Bangladesh
Month Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Gran
d
total
Percent
age of
male
80.2
3
73.3
3
55.8
8
84.9
0
63.1
6
22.5
0
21.3
5
10.1
1
16.5
0
12.0
0
34.8
5
15.4
9
44.50
Percent
age of
female
19.7
7
26.6
7
44.1
2
15.1
0
36.8
4
77.5
0
78.6
5
89.8
9
83.5
0
88.0
0
65.1
5
84.5
1
55.50
Sex-
ration
1:0.
25
1:0.
36
1:0.
79
1:0.
18
1:0.
58
1:3.
44
1:3.
38
1:8.
88
1:5.
06
1:7.
30
1:1.
87
1:5.
45
1:1.1
25
The relative condition factor (kn) was calculated for both sexes individually and combined. The kn values
range from 0.9478 to 1.2709 in male, 0.6188 to 1.2007 female and 0.1061 to 1.2084 in combined sexes.
Monthly and yearly percentage of male and female showed that the females dominated the natural
6
population over the year. Out of 1200 fishes, 534 were male and 666 were females. The total sex ratio
was found to be 1:1.247.
Calculation:
Sex ratio =(Number of Resident Male Live Births/ Number of Resident Female Live Births) x 100.
Age distribution
In population studies, the proportionate numbers of persons in successive age categories in a given
population or the total population in each age group or as the percent of total population in the age
groups. . In other way we can define the age distribution, the composition of a population in terms of
the proportions of individuals of different ages; represented as a bar graph with younger ages at the
bottom and males and females on either side.
Age at maturity can be determined during a population assessment. Selection pressure (e.g., harvest
aimed at larger, older individuals) at the population level could lead to maturity at a younger average
age.
Age specific birth and death rates
AGE-SPECIFIC DEATH RATE is the total number of deaths to residents of a specified age or age group in
a specified geographic area (country, state, county, etc.) divided by the population of the same age or
age group in the same geographic area (for a specified time period, usually a calendar year) and
multiplied by 100,000 natural mortality-at-age does not arise from a fish's age itself but rather from
factors such as predation. As fish get older, the suite of predators shifts both in terms of abundance and
the species involved, and the impact declines with age. One assumption that addresses this is that the
mortality rate decline is fixed over age.
Calculation:
(Total Deaths in Specified Age Group/ Total Population in the Same Specified Age Group) x 1,00,000
in mortality estimation with relation to age relation there are different type of methd,
7
 INDIRECT METHODS
 Age-independent methods
 Age-dependent methods
 DIRECT METHODS
 Requirements
 Catch curves
 Tagging
 Telemetry
 Cohort analysis
The first choice that a researcher needs to make is whether to use a direct or an indirect method to
estimate mortality. Early in the assessment of a population indirect methods are used as they can
provide quick and easy results, especially for inclusion in a model. When indirect methods are used for
input into a model it is prudent to construct multiple models that use as many of the indirect estimates
as possible.
Age-structured model
A Beverton–Holt stock–recruitment relationship was assumed:
R=0.8R0hS/[0.2S0(1−h)+(h−0.2)S]
Where, spawning–stock biomass S and S0 were computed from the weight-at-age and maturity
schedules. A steepness of h = 0.9 was assigned. While steepness is notoriously difficult to estimate, the
value of 0.9 is commonly used.
8
Age-dependent method
Estimation of natural mortality that varies with age using dry weight as a scaling factor. Using particle-
size theory and data from the pelagic ecosystem (including fish larvae, adult fish and chaetognaths) .the
natural mortality for a given weight organism (Mw) is
Mw = 1.92w-0.25
Where w is the dry weight of an organism. To make this estimate of natural mortality age-specific,
weight-at-age data is required. This is normally obtained from a length-weight relationship and length-
at-age data from a von Bertalanffy growth function. Such an approach yields wet weight. One criticism
of this method has been that it was developed for smaller pelagic organisms. However, McGurck (1986)
showed that it accurately predicted natural mortality rates over 16 orders of magnitude.
Chen and Watanabe (1989) recognized that natural mortality in fish populations, like most animal
populations, should have a U-shaped curve when plotted against age (they referred to it as a bathtub
curve).
To model this curve, they used two functions,
1. one describing the falling mortality rate early in life and
2. a second describing the increasing mortality towards the end of life. To scale the values of
mortality by age (M(t)), used the k and t0 parameters of the von Bertalanffy growth function.
Cortes (1999) used this method to estimate the survival of sandbar sharks (Carcharhinus plumbeus) by
age-class. He demonstrated no increasing mortality in older age classes due to senescence. The survival
values that Cortes (1999) estimated using this method were similar to those for the Peterson and
Wroblewski (1984), Hoenig (1983) and Pauly (1980) methods.
9
Unlike the Peterson and Wroblewski (1984) method the Chen and Watanabe (1989) method
onlyrequires von Bertalannfy parameters, but the mathematics are more involved
Length frequency relationship
In this section we discuss a probability model for the length of fish. For a historical review of the model,
(1975). Assume that there are k age classes in a fish population, and that p, is the proportion of the
population of age i. Let the lengths .v of fish of age i be distributed normally with mean n, and variance
o,-2. The probability density function/(.x: 0}of .x for the population can be written as
f( 𝑥: ⦵ = ∑ Pi N(x: ϴi)
𝑘
𝑖=1
Where, ⦵= < 𝜭1, 𝜭2,….𝜭k, P1, P2, ……Pk>.
𝜭i= < µi, бi2 >,
N ( x: 𝜭i) = density function of a normal distribution with mean µi and variance бi 2 ,
10
Pi = proportion of the population of age I,
K= number of age classes in the population which is generally assumed to be known.
The parameter vector 0 is related to some well-known fishery statistics. For example, the catch curve*
can be represented by the plot of logefi. against age i, and the plot of u,- against age i is the growth
curve.
If the variances of the individual normal distributions are small, then the length frequency plot will have
k well-defined modes at / i j , P j , ..., M*- If there are differential growth rates for various year classes,
the modes may not be well defined. To estimate modes from the length frequency data for fast-growing
pike iEsocidae), and he was able to identify five separate age classes. For these data, the average distance
between the mean lengths for successive age classes was 100 mm. Separations this distinct would not
be expected for most smaller or slower-growing fish.
Conclusion
The incorporation of socioeconomic variables with sustainable management including the analysis of
fishing trends introduces complexities that require more and more basic data. If fish are aged correctly,
then estimates of population dynamics will be correct and should lead to wise management and resource
allocation decisions. As the population structure are directly related to the age, length, and growth, it
need to be concerned as a exigent.
Reference
Kevin L. Pope, Steve E. Lochmann, and Michael K. Young, “Methods for Assessing Fish Populations”,
Chapter-11.
11
Fredric M. Serchuk, (March 30, 1978) “POPULATION ESTIMATION”, AN INTRODUCTION TO STOCK
ASSESSMENT TECHNIQUES, Laboratory Reference No. 78-28 National Marine Fisheries Service Northeast
Fisheries Center Woods Hole Laboratory Woods Hole, Massachusetts 02543
Colin A. Simpfendorfera, Ramón Bonfilb and Robert J. Latourc, ” Mortality estimation”, aCenter for Shark
Research, Mote Marine Laboratory 1600 Ken Thompson Parkway Sarasota, Florida, 34236, USA
K. Deva Kumar and S. Marshall Adams, “Estimation of Age Structure of Fish Populations from Length-
Frequency Data”, Environmental Sciences Division Oak Ridge National Laboratory Oak Ridge, Tennessee
G.W. Ssentongo, “POPULATION STRUCTURE AND DYNAMICS STRUCTURE ET DYNAMIQUE DES
POPULATIONS”, chapter-17.
Tito de Morais, L. 2002.” Fish Population Structure and its Relation to Fisheries Yield in Small Reservoirs
in Côte d’Ivoire”. In Management and Ecology of Lake and Reservoir Fisheries. Edited by I.G. Cowx.
Blackwell Publishing Ltd. pp. 112–122.
S.M. NURUL AMIN, M.A. RAHMAN, G.C. HALDAR, M.A. MAZID and D. MILTON, (2002), “Population
Dynamics and Stock Assessment of Hilsa Shad, Tenualosa ilisha in Bangladesh”, Bangladesh Fisheries
Research Institute Riverine Station, Chandpur-3602 Bangladesh
D. Pauly, (1984), “Fish Population Dynamics in Tropical Waters: A Manual for Use with Programmable
Calculators”, INTERNATIONAL CENTER FOR LIVING AQUATIC RESOURCES MANAGEMENT MANILA,
PHILIPPINES.

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fish population dynamics, Population structure

  • 1. 1 Index SL Name of Contents Page 1. Introduction 2 2. Population structure 2 3. Estimation of population structure 3 4. The Gordon-Schaefer model 4 5. Sex ratio 5 6. Age distribution 6 7. Age specific birth and death rates 6 8. Age-structured model 7 9. Age-dependent method 8 10. Length frequency relationship 9 11. Conclusion 10 12. Reference 10
  • 2. 2 Introduction Estimation of fish population dynamics are often based on age structures. Understanding past population structure is of interest to evolutionary biologists because it can reveal when migration regimes changed in natural populations, thereby pointing to potential environmental factors such as climate changes as driving evolutionary forces. Characterizing the structure of extent populations is also key to conservation genetics as translocation or reintroduction decisions must preserve evolutionary stable units. Finally, population structure has important biomedical consequences either when a number of subpopulation groups is locally adapted to particular environmental conditions (and maladapted when exposed to new environments) or represents a confounding factor in the study of the statistical association between genetic variants and phenotypic traits. Population structure The total population or size of a community, defined geographically or administratively, is the number of persons residing there. The term “population structure usually refers to the patterns in neutral genetic variation that result from the past or present departure from panmixia of a population. For example, suppose mean length of fish in standardized samples from a population is used as an index of population structure; shifts to smaller mean lengths of sampled fish may indicate increasing exploitation. The effectiveness of length-limit regulations are often evaluated relative to changes in proportional size distribution from a random sample of individual fish Indices of structure rely on  estimates of length,  weight,  age. Maturity status and sex identification allow the calculation of several useful indices. The juvenile-to- adult ratio can indicate important aspects of the dynamics of a fish population To obtain an accurate estimate of age structure, biologists must obtain a random sample of a population. Aging techniques alos for many important sport fish in have been validated and it is important to use the
  • 3. 3 standard techniques. Determining age of fish takes considerably more effort than measuring and weighing fish but is usually warranted during population assessments. Figure: Fluctuations of fish populations and the magnifying effects of fishing The concept of equilibrium in population structure is being viewed more and more as a simplification of the effect of fishing on exploited populations. It is still difficult to account for rapid changes in species composition in multispecies fisheries. Estimation of population structure Population structure are directly related to the weight, size, number, length, birth, recruitment, biomass and death of individuals. An organism as a reacting chemical system by asserting that the processes of anabolism and catabolism control the weight of an organism. Since the biomass of a fish stock is affected by natural mortality, fishing mortality, recruitment and growth. A simple yield equation, S= R+ G-M-F Where, S = population biomass, R = recruitment, G = growth,
  • 4. 4 M = losses due to natural mortality And F = losses due to fishing mortality. The Gordon-Schaefer model Figure: The Gordon-Schaefer model The Gordon-Schaefer model describe the population growth with the following equation, dB/dt= {rB(t) (1- B(t)}/K Where, r is the intrinsic rate of population growth, B(t) = population biomass in time t K= the carrying capacity of the environment Population structure changes (Biomass) through time can be expressed as: dB/dt= rB[1- B/K] –Y Where, the catch rate =Y, B(t) = population biomass in time t
  • 5. 5 K= the carrying capacity of the environment When the population is at equilibrium, i.e., dB/dt=0, and thus losses by natural and fishing mortalities are compensated by the population increase due to individual growth and recruitment. Sex ratio The proportional distribution of the sexes in a population aggregate, expressed as the number of males per female. The sex ratio at birth is an important demographic indicator used for determining the sex composition of a population. In Monosex tilapia culture there have seen a great change in growth as the male tilapia convert their reproductive energy to form their body mass and a big difference seen between normal and monosex male tilapia pond. Table: Month-wise distribution of male and female sex ration of R. Corsula from rajshahi, Bangladesh Month Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Gran d total Percent age of male 80.2 3 73.3 3 55.8 8 84.9 0 63.1 6 22.5 0 21.3 5 10.1 1 16.5 0 12.0 0 34.8 5 15.4 9 44.50 Percent age of female 19.7 7 26.6 7 44.1 2 15.1 0 36.8 4 77.5 0 78.6 5 89.8 9 83.5 0 88.0 0 65.1 5 84.5 1 55.50 Sex- ration 1:0. 25 1:0. 36 1:0. 79 1:0. 18 1:0. 58 1:3. 44 1:3. 38 1:8. 88 1:5. 06 1:7. 30 1:1. 87 1:5. 45 1:1.1 25 The relative condition factor (kn) was calculated for both sexes individually and combined. The kn values range from 0.9478 to 1.2709 in male, 0.6188 to 1.2007 female and 0.1061 to 1.2084 in combined sexes. Monthly and yearly percentage of male and female showed that the females dominated the natural
  • 6. 6 population over the year. Out of 1200 fishes, 534 were male and 666 were females. The total sex ratio was found to be 1:1.247. Calculation: Sex ratio =(Number of Resident Male Live Births/ Number of Resident Female Live Births) x 100. Age distribution In population studies, the proportionate numbers of persons in successive age categories in a given population or the total population in each age group or as the percent of total population in the age groups. . In other way we can define the age distribution, the composition of a population in terms of the proportions of individuals of different ages; represented as a bar graph with younger ages at the bottom and males and females on either side. Age at maturity can be determined during a population assessment. Selection pressure (e.g., harvest aimed at larger, older individuals) at the population level could lead to maturity at a younger average age. Age specific birth and death rates AGE-SPECIFIC DEATH RATE is the total number of deaths to residents of a specified age or age group in a specified geographic area (country, state, county, etc.) divided by the population of the same age or age group in the same geographic area (for a specified time period, usually a calendar year) and multiplied by 100,000 natural mortality-at-age does not arise from a fish's age itself but rather from factors such as predation. As fish get older, the suite of predators shifts both in terms of abundance and the species involved, and the impact declines with age. One assumption that addresses this is that the mortality rate decline is fixed over age. Calculation: (Total Deaths in Specified Age Group/ Total Population in the Same Specified Age Group) x 1,00,000 in mortality estimation with relation to age relation there are different type of methd,
  • 7. 7  INDIRECT METHODS  Age-independent methods  Age-dependent methods  DIRECT METHODS  Requirements  Catch curves  Tagging  Telemetry  Cohort analysis The first choice that a researcher needs to make is whether to use a direct or an indirect method to estimate mortality. Early in the assessment of a population indirect methods are used as they can provide quick and easy results, especially for inclusion in a model. When indirect methods are used for input into a model it is prudent to construct multiple models that use as many of the indirect estimates as possible. Age-structured model A Beverton–Holt stock–recruitment relationship was assumed: R=0.8R0hS/[0.2S0(1−h)+(h−0.2)S] Where, spawning–stock biomass S and S0 were computed from the weight-at-age and maturity schedules. A steepness of h = 0.9 was assigned. While steepness is notoriously difficult to estimate, the value of 0.9 is commonly used.
  • 8. 8 Age-dependent method Estimation of natural mortality that varies with age using dry weight as a scaling factor. Using particle- size theory and data from the pelagic ecosystem (including fish larvae, adult fish and chaetognaths) .the natural mortality for a given weight organism (Mw) is Mw = 1.92w-0.25 Where w is the dry weight of an organism. To make this estimate of natural mortality age-specific, weight-at-age data is required. This is normally obtained from a length-weight relationship and length- at-age data from a von Bertalanffy growth function. Such an approach yields wet weight. One criticism of this method has been that it was developed for smaller pelagic organisms. However, McGurck (1986) showed that it accurately predicted natural mortality rates over 16 orders of magnitude. Chen and Watanabe (1989) recognized that natural mortality in fish populations, like most animal populations, should have a U-shaped curve when plotted against age (they referred to it as a bathtub curve). To model this curve, they used two functions, 1. one describing the falling mortality rate early in life and 2. a second describing the increasing mortality towards the end of life. To scale the values of mortality by age (M(t)), used the k and t0 parameters of the von Bertalanffy growth function. Cortes (1999) used this method to estimate the survival of sandbar sharks (Carcharhinus plumbeus) by age-class. He demonstrated no increasing mortality in older age classes due to senescence. The survival values that Cortes (1999) estimated using this method were similar to those for the Peterson and Wroblewski (1984), Hoenig (1983) and Pauly (1980) methods.
  • 9. 9 Unlike the Peterson and Wroblewski (1984) method the Chen and Watanabe (1989) method onlyrequires von Bertalannfy parameters, but the mathematics are more involved Length frequency relationship In this section we discuss a probability model for the length of fish. For a historical review of the model, (1975). Assume that there are k age classes in a fish population, and that p, is the proportion of the population of age i. Let the lengths .v of fish of age i be distributed normally with mean n, and variance o,-2. The probability density function/(.x: 0}of .x for the population can be written as f( 𝑥: ⦵ = ∑ Pi N(x: ϴi) 𝑘 𝑖=1 Where, ⦵= < 𝜭1, 𝜭2,….𝜭k, P1, P2, ……Pk>. 𝜭i= < µi, бi2 >, N ( x: 𝜭i) = density function of a normal distribution with mean µi and variance бi 2 ,
  • 10. 10 Pi = proportion of the population of age I, K= number of age classes in the population which is generally assumed to be known. The parameter vector 0 is related to some well-known fishery statistics. For example, the catch curve* can be represented by the plot of logefi. against age i, and the plot of u,- against age i is the growth curve. If the variances of the individual normal distributions are small, then the length frequency plot will have k well-defined modes at / i j , P j , ..., M*- If there are differential growth rates for various year classes, the modes may not be well defined. To estimate modes from the length frequency data for fast-growing pike iEsocidae), and he was able to identify five separate age classes. For these data, the average distance between the mean lengths for successive age classes was 100 mm. Separations this distinct would not be expected for most smaller or slower-growing fish. Conclusion The incorporation of socioeconomic variables with sustainable management including the analysis of fishing trends introduces complexities that require more and more basic data. If fish are aged correctly, then estimates of population dynamics will be correct and should lead to wise management and resource allocation decisions. As the population structure are directly related to the age, length, and growth, it need to be concerned as a exigent. Reference Kevin L. Pope, Steve E. Lochmann, and Michael K. Young, “Methods for Assessing Fish Populations”, Chapter-11.
  • 11. 11 Fredric M. Serchuk, (March 30, 1978) “POPULATION ESTIMATION”, AN INTRODUCTION TO STOCK ASSESSMENT TECHNIQUES, Laboratory Reference No. 78-28 National Marine Fisheries Service Northeast Fisheries Center Woods Hole Laboratory Woods Hole, Massachusetts 02543 Colin A. Simpfendorfera, Ramón Bonfilb and Robert J. Latourc, ” Mortality estimation”, aCenter for Shark Research, Mote Marine Laboratory 1600 Ken Thompson Parkway Sarasota, Florida, 34236, USA K. Deva Kumar and S. Marshall Adams, “Estimation of Age Structure of Fish Populations from Length- Frequency Data”, Environmental Sciences Division Oak Ridge National Laboratory Oak Ridge, Tennessee G.W. Ssentongo, “POPULATION STRUCTURE AND DYNAMICS STRUCTURE ET DYNAMIQUE DES POPULATIONS”, chapter-17. Tito de Morais, L. 2002.” Fish Population Structure and its Relation to Fisheries Yield in Small Reservoirs in Côte d’Ivoire”. In Management and Ecology of Lake and Reservoir Fisheries. Edited by I.G. Cowx. Blackwell Publishing Ltd. pp. 112–122. S.M. NURUL AMIN, M.A. RAHMAN, G.C. HALDAR, M.A. MAZID and D. MILTON, (2002), “Population Dynamics and Stock Assessment of Hilsa Shad, Tenualosa ilisha in Bangladesh”, Bangladesh Fisheries Research Institute Riverine Station, Chandpur-3602 Bangladesh D. Pauly, (1984), “Fish Population Dynamics in Tropical Waters: A Manual for Use with Programmable Calculators”, INTERNATIONAL CENTER FOR LIVING AQUATIC RESOURCES MANAGEMENT MANILA, PHILIPPINES.