stock_assessment_How to determine available stock in a fish pond.pdf

Fish population dynamics

1. Fish Population Dynamics

2. •Fish stock assessment
•This involves both a biological interpretation and the use of various
statistical and mathematical calculations to make quantitative predictions
about the reactions of fish populations to alternative management choices.
•The basic purpose of fish stock assessment is to provide advice on the
optimum exploitation of aquatic living resources such as fish and shrimp.
•Living resources are limited but renewable
•fish stock assessment may be described as the search for the exploitation level which
in the long run gives the maximum yield in weight from the fishery.

3. •The fishing effort level which in the long
term gives the highest yield is indicated
by F
MSY
•The corresponding yield is indicated by
"MSY", which stands for "Maximum
Sustainable Yield".
•"in the long term" is used because one
may achieve a high yield in one year by
suddenly increasing the effort, but then
meageryears will follow, because the
resource has been fished down.
•Normally, we are not aiming at such
single years with maximum yield, but at a
fishing strategy which gives the highest
steady yield year after year.

4. •The main objective of fish stock assessment is to give an assessment
of the state of the stock (size, composition, regeneration rate,
exploitation level, and fishing pattern) in order to assure, in the long
run, the self-sustainability of the stock under exploitation.
•Through stock assessment biological and economic reference points
which are useful guidelines for the rational management of the
fishery are provided.

5. •From simple application of a general biological model, stock
assessment has also includes a computer simulation of the specific
fishery and the resource.
•The resource part of the simulation is a quantitative model of the
dynamics of the fish population, while the fishery part, aims at
representing the harvesting process.
•Through the interaction of these two components, predictions about
properties of the resources under different scenarios and under
different assumptions that quantify the total catch or catch by size
category are produced.

6. Components of stock assessment
•Structure for most models in stock assessment is revolved around
three main components of a fishery and these are:
1.The input which represent the fishing effort as define in relation to fishing
gears and amount of time spent fishing
2.The output which stands for the amount of fish landed as a part of the
biological production.
3.The processes that describe and link the input and output (the biological
processes and fishing operations).
•Where input and output are normally based on observations (e.g.
catch and effort statistics) and one or several mathematical model(s)
represents the processes.

7. •Fish stock assessment aims at describing those processes, the link
between input and output and the tools used for that are called
"models".
•A model is a simplified description of the links between input data
and output data.
•It consists of a series of instructions on how to perform calculations
and it is constructed on the basis of what we can observe or measure,
such as for example fishing effort and landings

10. •There are two main groups of fish stock assessment models:
1.The so-called holistic, or biomass dynamic models,
•building on the overall stock (population) as the basic unit where individually based
processes such as growth and reproduction are inherently encapsulated in the stock model.
•The starting point of these models is population abundance indices generated from catch and
effort data or fishery independent biomass surveys (swept area method or acoustic surveys).
These models have their origin from Verhulst(1838), Graham (1935), and Schaefer (1954).
2.Analytical or so-called dynamic pool models
•building on individual fish as the basic unit and where dynamic processes such as age,
growth, mortality, and maturity are each represented by a sub-model.
•These models are age-or length structured and deal with a partial or the entire demographic
structure of the population.
•They have their origin from Baranov (1918), Thompson and Bell (1934) and Bevertonand Holt
(1957).

11. StockConcept
•When the dynamics of an exploited aquatic resource are described and
quantified, a fundamental concept is that of the “stock”.
•For fishery purposes the main criteria for such a concept is to identify and
operate with a group of organisms that fulfil the underlying assumptions of the
population models.
•A stock is normally a subset of one particular species having the same
demographic parameters (growth, natality, and mortality) and inhabiting a
defined geographical area.
•A unit stock is an arbitrary definition of a fish population that is large enough to
be essentially self-reproducing, where abundance changes are not dominated by
immigration or emigration, and where members of the population show similar
patterns of growth, mortality, migration and dispersal..
•

12. •A stock is a sub-set of a "species", which is generally considered as the
basic taxonomic unit.
•A prerequisite for the identification of stocks is the ability to
distinguish between different species.
•Because of the great number of different, but often similar, species
observed in tropical fisheries their identification can be problematic.
•The fishery scientist, however, must master the techniques of species
identification if any meaningful fish stock assessment is to come out
of the data collected

13. •Gulland(1983) proposed an operational definition for management
purposes:
•a sub group of species can be treated as a stock if possible differences within
the group and interchange with other groups can be ignored without making
invalid the conclusions reached in the course of an assessment.
•Consequently, if it becomes clear that growth and mortality parameters differ
significantly in various part of the area of distribution of the species, then it
will be necessary to assess the species on an area by area basis.
•Fish stock assessment should ideally be made for each stock separately.
•The results may (or may not) be subsequently pooled in a multi-species
fishery.
•Therefore, the data must be available for each stock of each species
considered

14. •There are at least three main reasons for failing to work properly with the stock
unit.
•
•1) The full distribution area of the stock is not covered by the data collected, so
that only part of the stock is considered. This is a typical example where several
independent fisheries are exploiting the same stock.
•2) Several independent stocks are lumped together, for example, because their
areas of distribution overlap.
•3) Continuous immigration and emigration of the components of one or more
stocks from the fishing ground. Taking into account that most of the exploited
marine resources undertake migration, an essential element to perform stock
assessment is an understanding and knowledge of migration routes.
•

15. •The relationship between fishing effort and yield is based on the following established
proposition:
1.In the absence of fishing effort, there will be no catch.
2.Most stocks are part of a food chain, or food web, either feeding on or giving food to other
stocks, such that fishing is not the only exploiter of the system.
3.At low levels of effort the potential yield, or surplus production, of the resource is normally
under-utilized.
4.At high levels of fishing effort the stock will be fished so hard that the removal of fish exceeds
the regenerative capacity and the yields will start to decline.
•In the extreme, such a situation will eventually lead to a complete collapse of the stock and even eradication.
5.The maximum average yield, corresponding with maximum regenerative capacity of the stock, is
therefore somewhere in between no effort and very high effort.
•Furthermore, this maximum average yield must be shared between man and other predators in a multi-species
system.
6.As different stocks have different regenerative capacity rates and different size structures, the
overall effort level and fishing pattern in a multi-species fishery is therefore a very complicated
issue.

16. •Any stock assessment process implies at least three components.
1.A good overview of the fishery harvesting process and the data generated.
2.Choosing or developing a model according to knowledge, assumptions and
available input parameters.
3.Sound criteria to judge the goodness of fit to the data of any particular
model, the biological realism, and the output parameter estimates
•Once the stock assessment is complete, technical and political choices
remain.
•There is a distinction between assessment of biological potential and
the political/social decision on how to manage the stock

17. Biostatistics in stock assessment
•Essential part in stock assessment, is knowledge of basic statistics to be
able to plan, conduct and analyseexperiments and surveys in a satisfactory
manner
•Statistical sampling theory
•Population: A finite number of separate objects defined in space and time.
•The sample population consists of the objects that have an equal probability of being
selected.
•Population list: The table of the objects in a population.
•Variable: A property measured or recorded which has one and only one
value for each object in the population e.glength
•Samples, which are not random samples, are called biased samples.

18. •Frequency table
•Sometimes, for a continuous variable such as length, it is very convenient, for
treatment purposes, to arrange the sample in a table that is called a
“frequency table”, by dividing the length range into a number of length
intervals.
•Statistics, such as mean, variance, etc. can be calculated the standard way by
using the midpoints to represent the interval, but the precision of the
calculated values will decrease with increasing intervals

19. •Measures of dispersion and confidence intervals
•The mean value is often called a statistic of location or a measure of central tendency
•it is a representative value which describes the position along a given axis by which the variable is
characterised.
•However, the mean says nothing about how the individual observations are distributed, e.g., the width
of the frequency distribution.
•Therefore the range and the variance are needed as measures of dispersion (precision).
•When parameters are estimated, inclusion of estimates of dispersion is essential, since even if an
estimate of the mean may be very accurate (i.e. unbiased), it can remain highly imprecise due to an
extensive dispersion of the observations
•Hence, some estimate of dispersion is needed to determine how closely our sample mean estimates the
true parametric mean.
•The range is a poor expression, since it is highly sensitive to single extreme values
and should therefore be used with caution.
•The standard deviation, i.e. the square root of the variance, is preferable to the
range and can often be used to estimate the so-called confidence intervals to the
mean value.

20. •Inverse regression
•One of the assumptions behind linear regression analysis is that the
independent variable (x)cannot be random.
•It is therefore a question if it could be possible to obtain similar results of the
regression if the parameters are exchanged. This in the case both parameters
are measured under the same units and with the same accuracy.
•In this case, the result is an “inverse regression“.

21. •Functional regression analysis
•One way to circumvent the problem of choosing the independent variable
when both variables are random is by using the so-called functional
regression analysis.
•This method estimates a slope b’ by the expressions
•b’=sy/sxif r>0
•b’=-sx/syif r<0
•and the intercept a' = y − b'⋅x
•Functional regression may be considered as a compromise between
ordinary regression and inverse regression.
•In all cases, it may be seen that for all three types, the lines will pass
through the mean x and mean y.

22. •Linear regression with two variables
•Sometimes, there is more than one variable connected to the
measurements of y.
•If, for example, x and z are used to explain how y changes (often used
in biomass dynamic models),
•it is possible to use the model: yi= α + βxi + γzi+ ε
•where ε again denotes the measurement error in yi.

23. •Multi-dimensional regression
•All the above examples can be extended in such a way that the
models can contain as many variables as needed.
•This is normally done by using matrixes.
•It is assumed that a given y-measurement is connected to many (e.g.
m ) x-values thus:
•yi= α + β x i+ β x i+ β x i+ +βm xmi+ εiwhere i= n 1 1 2 2 2 3 ....
1,2,....

24. •Non-Linear Regression
•Many common models are such that they are not linear in the parameters.
•Ricker Stock-recruitment model is non-linear in α and β.
•Although it is possible to linearly transform the Ricker model by modelling not R
and B, but ln (R/B) and B, it is obvious that if recruitment is completely random,
this transformation will indicate a relationship that does not exist.
•In this instance, there is reason to try to estimate parameters in a non-linear
model.
•In general, measurements are made on variables y and x, and some function
connects the measurements but the function contains unknown parameters: yi=
f (xi ,β) + ε
•The parameters in β may of course be as many as required but the quality of the
data will determine what can be estimated with any amount of accuracy.

25. •Sample must reflect -
Randomisation: = each object in the population has the same chance of being
sampled (avoiding bias = accuracy)
Replication: = sampling size, measure of variability or dispersion (SD, SE,CL)
(large sample = precision)
•Sampling design is to secure randomisationand plan replication (for
the desired level of precision)

26. •Randomisationin fisheries is in practisevery difficult due to:
•Selectivity of sampling gear
•Unknown spatial and temporal distribution of population
•Sampling artifacts as when catches are sorted or discarded at sea
•Replication is a matter of capacity and costs

27. •Sampling designs
•Simple random sampling (distribution homogeneous or uniform:
variance ≤ mean)
•Stratified random sampling (distribution contagious, patched with
known external factors, e.g. depth: variance > mean)
•Systematic sampling (distribution heterogeneous without periodicity
or due to unknown factors)
•Multiple step sampling (in the case of large variation in objects, e.g.
trawl catches)

28. •Sampling gear
•The choice of the sampling gear and methodology depends on the
objectives of the investigation:
•Which objects are to be examined and what are their characteristics and relevant
properties?
•Which level of precision is desired/necessary?
•Qualitative work like determining the number of species in an area requires very different
data from quantitative work such as abundance estimation of a few selected species.
•A very high level of precision is most often associated with high costs because a very intensive
sampling programme(replications) is required. A high precision is not always appropriate.
•If, for example, the applied methodology does not give a representative picture of the
situation; the sampling is biased, then a high precision is of minor value and can even give the
misleading impression of a highly accurate result.
•Every sampling gear is developed and designed for specific tasks and for
specific conditions and all have inherent biases and sources of error.

29. •When choosing a sampling gear, one should carefully consider the
attributes and limitations of the individual gear in relation to one’s
objectives:
•What are the selective properties of the gear, i.e., does the gear sample the objects
in the volume covered quantitatively?
•Where can it be used and how precise can it be positioned?
•The following practical aspects should be considered at an early stage of
the work in selecting gear:
How does the gear function technically and how is it operated?
Is the gear really available at the times and places required?
What are the costs of regular operation?
Where can the gear be repaired and what are the costs and time required?

30. •It is most important at the collection stage in the field to ensure that
the planned sampling design is followed in order to obtain the
optimal amount of data
•What to be recorded during
A.Basic data
B.Catch composition
C.Individual species data

31. Basic data
•Information on who took the samples and when, where and how the
survey/sampling was conducted.
•This is important in all investigations and must be properly described
in detail.
•Furthermore additional environmental information should preferably
always be included to the extent possible:
•Bottom topography and depths
•Temperatures, salinities and oxygen
•Meteorological observations
•These variables are now routinely recorded in most fishery surveys

32. Catch composition
•List of species and numbers and/or weight caught.
•Be sure to identify the species correctly and unambiguously
(Taxonomic literature, FAO identification sheets).
•If in doubt, a sample of specimens should be preserved for later taxonomic
studies.
•If the catches are big, one might decide to examine only a random
representative sub-sample but always record the total weight and numbers.
•Due to size and morphometric differences, the individual fish are
rarely randomly distributed within the catch

33. Individual species data
•length
•weight or volume
•sex and stage of maturity
•Age
•These data alone provide variables which form the cornerstones of present
fishery research, assessment and management
•The numbers and sizes of available fish in a population (stock) determine
the potentials for exploitation
•Information on maturity gives important understanding about biology and
reproduction for initial management and enables separation of estimates
of abundance into values representing the immature and mature
populations

34. •Supplementary data include:
•fecundity
•stomach contents
•parasitism
•genetics
•biochemical composition (lipids, proteins etc.)
•occurrence of pollutants

35. •Kind of variables recorded
•continuous variables (can have any value within an interval, e.g. length and
weight)
•discrete variables (also called discontinuous or meristic, i.e. counted values in
whole numbers (integers) e.g. number of eggs, fin rays, vertebrae etc.).
•ranked variables (e.g. stomach fullness)
•character variables (for attributes e.g. colour, taste, smell, visually determined
maturity stages etc.)

36. •How should the data be recorded and at which level of precision?
•All units in the International System of Units (SI).
•Level of precision, units (kg or grams, cm or mm etc) must be decided upon.
•Measurements are always connected with some errors: e.g. weight
measurements are influenced by wind, motion, water, accuracy of the
weighing device, changes of the fish by death or preservation.
•How are the data to be treated/processed?
•Manually.
•Computerisedprocessing (this requires an unambiguous coding system for
recording the data in a fashion immediately readable for the computer).

37. •Which statistical methods to employ.
•It is always wise to design the data sheets and recording routines to suit
subsequent computerisedprocessing.
•design a sheet that is simple to fill out and that does need rewriting or
transformation before logging into a database.
•prepare and insert codes in the sheets. Make sure that all the codes are
unambiguous.
•Data that are not recorded in digital units can be treated as character
variables and assigned letters or numbers.
•never introduce new codes if others are already established.
•always store data in a database at the lowest level of the treatment, i.e. no
transformations, aggregations, averaging, summing, etc

38. Methodology-
Length measurements
•Why length measurements?
•length frequency distributions provide information on the demographic
structure of the populations sampled.
•measuring the rate of change in length of individuals or populations are
approaches to estimating growth processes.
•length is often better than age as an indicator of recruitment, maturity, and
fecundity.
•in many fisheries, length is used to define legal size for harvest.
•length-measurements are easy to make but require many observations (big
sample size).
•Therefore it must be well defined and standardized and made in accordance
with previous investigations or recommendations.

39. •There are (at least) three common standards:
•Total length (TL). (used for species with rounded or truncate tails)
•Fork length (FL). (for species with forked tails)
•Standard length (SL). (mostly used for larvae and in taxonomic studies)
•There are also three different ways of measuring:
•to the nearest unit below
•to the nearest unit above
•to the nearest whole unit

40. •The International Council for the Exploration of the Sea (ICES)
recommends the first, but in all reports, it should be clearly stated
which method and which measurement practice were applied.
•Conversion factors can be established for transforming the data from
one standard to another.
•Length is easily measured with a measuring board or callipers.
•Automatic measuring boards with direct logging capabilities through
connection to a computer are available.
•It is important to establish a standardized, simple but functional
system for recording the observations

41. •Causes of bias and errors:
•Live fish: Muscle: contractions/relaxation
•Dead fish: Rigor mortis
•Shrinkage from preservation.
•Variation in measurement techniques:
•Spreading/folding of tail
•Pressing of the nose into the headboard
•Individual tendency to prefer certain numbers or approximations.

42. Weight measurements
•Why weight measurements?
•The production of a population and of the individual organism in terms of somatic
growth and gonad growth is better reflected by weight changes than by information
of length alone.
•Weight changes may reflect changes of the nutritional condition of the fish.
•Total weight or weight per unit area or time is the statistics normally reported in
fisheries.
•Annual weight increments (growth) are significant for assessments of commercial
value.
•Weight is applied at different levels:
•the entire catch
•sub-units of the catch (e.g. by species)
•individual specimens

43. •The weighing of specimens is more difficult, more inaccurate and
more time consuming than length measurements.
•Weight can be replaced by volume (displacement volume) which is
especially useful with live fish. If the length-weight relationship is
known, then the individual weight can easily be estimated in
databases from length measurements.
•Weighing devices:
•hanging balances or platform scales
•spring balances
•electronic balances

44. •The choice depends on the size of the object(s), the desired precision
and on the working conditions.
•Only hanging balances are reasonably satisfactory when working at
sea in bad weather, but they are not sensitive enough for individual
measurements of small fish.
•Generally, scale sensitivity should be about 1% of fish weight. All
types of weighing devices should be calibrated periodically

45. •Causes of bias and error:
•external disturbance (wind, motion etc.)
•dryness or amount of water evaporated, i.e. the time the specimens have
been out of water.
•stomach contents
•relative weight of inner organs (liver, gonads etc.)
•Weight/length relations can be established by regression or non-linear fitting,
and are important when converting length at age into weight at age. This
requires a large range of data.
•The weight/length relations may vary seasonally and there are differences
between sexes.

46. •Sex and stage of maturity
•Information on sex and sexual maturity are used to:
•• determine current reproductive status.
•• during the spawning season, determine the location of spawning
grounds.
•• determine size and age at first spawning.
•• determine what proportion of the stock is reproductively mature/active.
•• describe the reproductive cycles of species and relate them to
environmental factors.
•• estimate the approximate birthday of a cohort when fitting growth
curves to length frequency samples.

47. •Sex-determinations: Very few fish have clear external sexual
dimorphism, especially in the younger stages. It is therefore necessary
to dissect the fish and examine the gonads. In adult females, the eggs
are readily seen in the ovaries. In adult males, the testes are typically
smooth, whitish and non-granular (be careful not to confuse fat
bodies with testes). In immature fish, the sex is usually not an
important observation, but if needed it will often be necessary to use
a dissecting microscope for determination. One should always build
up experience before making routine records. Also be aware of
problems with hermaphroditic species (e.g. many Labridae).

48. •Maturity: These examinations are aimed at determining whether each fish
is sexually immature, mature, ripe or spent. Usually a macroscopic scale is
used, requiring only trained visual inspection. The criteria are based on
size, location, colourand development of roe and the vascular system of
the gonads and the classification is done after a key (see e.g. Kesteven
1960, Nikolsky1963). Some experience is required and it is important that
consistency is retained if several workers are involved. For high precision or
resolution, a microscopic examination is employed requiring histological
preparation and perhaps staining. The classification is based on the state
and size of the gametes and follicles only, also using a key. This is
potentially less subjective, but of course, much more labourdemanding.
•

50. Morphometric and Meristic tools in stock
assessment
•Stock identification is an interdisciplinary field that involves the
recognition of self-sustaining components within natural populations.
•The concept of stock separates the population into groups with
different growth rates and reproductive dynamics, irrespective of
genetic similarities.
•Morphometric differences among stocks of a species are recognized
as important tool for evaluating the population structure and
identifying stocks

51. •Identification of stock helps to effectively:
•manage the stock separately.
•estimate stock-wise population abundance.
•retain the biologically sustainable productivity.
•determine how each stock respond to fisheries exploitation.
•fulfillthe purpose of fishery stock assessment by modeling

52. •Morphometrics may be defined as a more or less interwoven set of
largely statistical procedures for analyzingvariability in size and shape
of organs and organisms.
•Morphometric differences among stocks of a species are recognized
as important for evaluating the population structure and as a basis for
identifying stocks.
•Morphometric measurements are widely used to identify differences
between fish populations.

53. •the morphology of fishes has been the primary source of information for
taxonomic and evolutionary studies.
•There are numerous characters viz. upper jaw length, slandered length,
body depth at dorsal fin origin, mandibular length, body depth at dorsal fin
origin, fleshy orbit head length, pre-dorsal length, pelvic fin length, pre-
anal length, pre-pelvic length, dorsal fin base, peduncle depth, anal fin
base, peduncle length, snout length, pre-maxillary teeth and head width
available for morphological study.
•Most of the measurements are parallel and horizontal along the vertebral
column of the fish.
•Many measurements have a common landmark i.e., the tip of snout.
•A major drawback of this morphometric system is their dependency on the
size of the fish and high correlation with total length of the fish

55. •Morphology, refers to the phenotype of an organism.
•It is a primary and direct means by which organisms interact with
environment. In population biology, it is useful to know whether two
populations of organisms have the same typical body form to indicate:
•size allometry
•shape changes accompanying size increase over the life span
•characterization of the difference between sexes
•responses to environmental variation.
•Morphometric, the study of geometrical form of organisms,
•indicate differences in growth and maturity patterns which are sensitive to
environmental fluctuations and show little variation in the gene pool

56. •Althoughgeneticdifferencesinapopulationisofutmostimportance,
phenotypicvariationsstillcontinuetohaveauniqueroleinstock
identificationamonggroupsoffish.
•Theusageofphenotypiccharactersisparticularlyimportantwherethe
differencesareattributedtoenvironmentalinfluencesratherthanto
geneticdifferentiationwhicheventuallydetermineshoweachstock
respondtoexploitation.
•Thetraditionalmorphometricinvestigationsconcentratethe
measurementsalongthespecificlocusofthefishi.e.,fromthehead/tipof
snouttoposteriorendofthevertebralcolumnthusuni-directionaland
non-uniformcoverageofthebodyform.
•AnalternativetothedrawbackoftraditionalmeasurementsistheTruss
NetworkSystem

57. Truss Network System
•Truss Network System is a landmark-based technique using geometric
morphometrics and imposes no restrictions on the direction of variation or
localization of shape changes.
•The truss network system is highly effective in capturing information about
the shape of an organism
•Truss network measurements are a series of distances calculated between
landmarks that form a regular pattern of connected quadrilaterals or cells
across the body form
•One major advantage of deriving morphometric data from digital images is
the ability to store the image and the potential for reprocessing each
individual to confirm anomalous measurements or derive alternative sets
of characteristics

58. •Truss network systems constructed with the help of landmark points are
powerful tools for stock identification of fish species
•Truss measurements are a powerful tool for the analysis of shape, and
generally are designed to cover all, or most, of the animal’s body
•the truss network is more useful and an effective strategy for the
descriptions of shape;
•it has better data collection and diversified analytical tools in comparison
to traditional morphometrics method.
•Thus it is able to discriminate phenotypic stock because the configuration
of the constructed landmarks covers the entire fish body with no loss of
information, and it is more sensitive to change

59. •Trust network measurement in fish involves anaesthetizing with
benzocaine (ethyl-p-amino-benzoate) before being weighed and measured
•The first step is to take and record the standard length (LS), post-orbital
length (LPO) and maximum body width of the fish.
•Standard length will be taken from the tip of the upper jaw to the base of
the caudal peduncle.
•Then a truss network is constructed between landmark points,
homologous throughout the population, chosen because they describe the
major features of the fish
•The landmarks were linked closely to the skeletal structure of fish and were
easily observed by eye.

60. The landmarks
•These are anatomical points on the body form of an organism .
•In truss system, Homologous landmarks on the boundary of the form
are divided into two tiers and paired.
•Homogeneity in landmarks helps to appropriately archive the body
form.
•The distances that connect these landmarks forms a series of
quadrilaterals each having internal diagonals.
•Each quadrilateral share one side with each succeeding and preceding
quadrilateral

61. •Landmarks should be anatomical points, representing the same
developmental feature among specimens, and should be easily
located.
•The most effective landmarks are those defined by the intersection of
different tissues, such as insertion points of fins and anal pores.
•The network should resemble the shape of the specimen from which
it is derived

63. •Legends: 1. Mouth tip to premaxilla (MTPM), 2. Mouth tip to dorsal
fin (MTDF), 3. Mouth tip to operculum top (MTOT), 4. Pre maxilla to
dorsal fin (PMDF), 5. Pre maxilla to operculum tip (PMOT), 6. Pre
maxilla to pectoral fin (PMPC), 7. Pre maxilla to pelvic fin (PMPV), 8.
Dorsal fin to operculum tip (DFOT), 9. Pectoral fin to operculum tip
(PCOT), 10. Pectoral fin to pelvic fin (PCPV), 11. Dorsal fin to pelvic fin
(DFPV), 12. Dorsal fin front to dorsal fin back (DFDB), 13. Dorsal fin to
anal fin (DFAF), 14. Pelvic fin to anal fin (PVAF), 15. Dorsal back to anal
fin (DBAF), 16. Dorsal fin back to caudal top (DBCT), 17. Dorsal back to
caudal bottom (DBCB), 18. Anal fin to caudal top (AFCT), 19. Caudal
top to caudal bottom (CTCB), 20. Anal fin to caudal bottom (AFCB),
21. Dorsal fin back to pelvic fin (DBPV

64. •Truss lengths measured between these landmark points should either
lie on curved surfaces or be on straight lines lying on a flat plane.
•The distances were measured with the help of vernier callipers (RS
and Cam lab) or brass divider accurately to 0.1 mm .
•Measuring four fishes repeatedly will help assess the accuracy of
measurements and comparing results.
•Measurement errors were calculated by taking the mean of the
standard deviation of the measurements for each fish.
•The relative error is the percentage of the mean truss length that the
tabulated measurement error represents.

65. Image analysis morphormetricmethods
•The development of image analysis systems has facilitated progress
and diversification of morphometric methods and expands the
potential for using morphometry as a tool for stock identification
•Traditional multivariate morphometrics, accounting for variation in
size and shape, have successfully discriminated many fish stocks.
•However, traditional methods have been enhanced by image processing
techniques, through better data collection, more effective descriptions of
shape, and new analytical tools
•It also allow more advanced geometric morphometrics, which include
outline methods and landmark methods

66. •Image analysis is the extraction of meaningful information from
images;
•mainly from digital images by means of digital image processing techniques.
•Image analysis tasks can be as simple as reading bar coded tags or as
sophisticated as identifying a person from their face.
•Computers are indispensable for the analysis of large amounts of
data, for tasks that require complex computation, or for the
extraction of quantitative information.
•There are many different techniques used in automatically analysing
images.

67. •Each technique may be useful for a small range of tasks,
•however there still aren't any known methods of image analysis that are
generic enough for wide ranges of tasks, compared to the abilities of a
human's image analysing capabilities.
•Examples of image analysis techniques in different fields include:
•2D and 3D object recognition,
•image segmentation,
•motion detection e.g. tracking, video, flow, analysis, Estimation, automatic

68. Methods
•Model-based recognition is used to locate the object and stereo
vision system to determine distance and sizes given stereo video
input.
•However, the stereo vision system is very expensive and the matching
procedures also still have error and poor image quality that can affect
the accuracy of measurement

69. •Automated Fish Recognition and Monitoring (FIRM)
•focused on comparison of technique to shape matching but did not focus to
obtain the size of fish.
•This method has five main processing steps:
•image acquisition, object detection algorithm detects the presence of an object (DMA),
identifying the fish with object contour extraction used Canny Edge operator and
identification,
•Tracking of the fish object determines the location of the fish , triggering the
recognition process when an image of the whole fish can be acquired.
•The measurement size and species of fish used shape-based recognition.
•This method is suitable for fish in an aquarium.
•This method must have laboratory equipped with a conveyor belt and other
hardware such as pc, lamp and sensor

70. Stomach content analysis
•The study of the feeding habits of fish and other animals based upon analysis of
stomach content has become a standard practice.
•Stomach content analysis provides important insight into fish feeding patterns
and quantitative assessment of food habits is an important aspect of fisheries
management.
•Accurate description of fish diets and feeding habits also provides the basis for
understanding trophic interactions in aquatic food webs.
•Diets of fishes represent an integration of many important ecological components
that included behavior, condition, habitat use, energy intake and inter/intra
specific interactions.
•A food habit study might be conducted to determine the most frequently
consumed prey or to determine the relative importance of different food types to
fish nutrition and to quantify the consumption rate of individual prey types.

71. •For a better understanding of diet data and for accurate interpretation of fish feeding
patterns, time of day, sampling location, prey availability and even the type of collecting
gear used need to be considered before initiating a diet study or analysing existing diet
data
•Stomach contents can be collected either from the live or fresh died fish.
•Regardless of the method, investigators should ensure that the removal technique
effectively samples all items in the gut.
•Other wise data will be skewed toward items that are more easily displaced from the
stomach.
•Alternatively, live fish can be sacrificed and stomach contents removed for analysis.
•If fish are to be sacrificed, they should be preserved immediately either by freezing or by
fixing in formalin.
•Stomach contents will continue to digest, rendering

72. Sample collection techniques
•As in most fish groups feeding behaviour of juveniles and adults vary
distinctly attention should be taken to encounter more samples which will
include all size groups of the particular fish.
•The specimens either from live or preserved should be measured to its
total length to the nearest 1mm and weight to the nearest 0.1 g.
•Cut open the fish and record the sex and maturity stage of the fish.
•Remove the stomach and preserve them in 5% neutralized formalin for
further analysis.
•For the analysis, a longitudinal cut must be made across the stomach and
the contents are transferred into a Petri dish.
•The contents then keep for five minutes to remove excess formalin and
then examine under binocular microscope.

73. •Identify the gut content up to the genus and if possible up to species
level depending up on the state of digestion.
•Various taxa digest at different rates. As such, all recently consumed
taxa may be present in the foregut but only resistant items remain in
the hindgut.
•To avoid bias when both easily digested prey and resistant prey are
present, only the immediate foregut (e.g., stomach) should be
sampled

74. •Prey items in fish stomachs are often not intact.
•Hard parts such as otoliths, scales, cleithra or backbones have diagnostic,
species specific characteristics useful for identifying prey.
•Alternatively, partially digested prey may be identified using unique
biochemical methods such as allozyme electrophoresis, or immunoassays.
•An important fact assessed by the examination of the stomach is the
state or the intensity of feeding.
•This is judged by the degree of distension of the stomach or by the
quantity of food that is contained in it.
•The distension of the stomach is judged and classified as ‘gorged or
distended’, ‘full’, ‘3/4full’, ‘1/2full’ etc by eye estimation.

75. •Fish diets can be measured in a variety of ways.
•Methods of gut contents analysis are broadly divisible into two, viz.,
qualitative and quantitative.
•The qualitative analysis consists of a complete identification of the
organisms in the gut contents.
•Only with extensive experience and with the aid of good references it is
possible to identify them from digested, broken and finely comminuted
materials.
•Quantitative methods of analysis are three types, viz., numerical,
gravimetric and volumetric.

76. The numerical methods
•The numerical methods are based on the counts of constituent items in the gut
contents.
•The numerical methods have been adapted in different ways to assess the
relative importance of food items and these can be classified under four distinct
heads,
•a) Occurrence,
•b) Dominance,
•c) Number and
•d) Point (Numerical) methods.
•e) Frequency of Occurrence.
•Stomach contents are examined and the individual food organisms sorted and
identified.
•The number of stomachs in which each item occurs is recorded and expressed as
a percentage of the total number of stomachs examined.

77. •Frequency of Occurrence,
•Oi = P Ji
•Where, iJ is number of fish containing prey iand
•P is the number of fish with food in their stomach.
•This method demonstrates what organisms are being fed upon, but it gives no
information on quantities or numbers and does not take in to consideration the
accumulation of food organisms resistant to digestion.
•For instance, three organisms in a stomach, say, prawn, rotifers and diatoms, present in the ratio
of 1:200:2000 would all be treated by this method as 1:1:1 with reference to the stomach in
question.
•This method holds good even when there is differential distribution of various food
organisms in the water for the same reason that it is not biased by size or numbers of
organism comprising the food.
•Many have used this method as an indicator of inter-specific competition while some
utilized this method to illustrate the seasonal changes in diet composition.

78. •Number method.
•The number of individual of each food type in each stomach is counted and expressed as
a percentage of the total number of food items in the sample studied, or as a percentage
of the gut contents of each specimen examined, from which the total percentage
composition is estimated.
•This method has been employed successfully by several workers in studies on the food of
plankton feeding fishes where the items can be counted with ease.
•In the basic number method, no allowance is made for the differences in size of food
items.
•So in the studies on the food of fishes other than plankton feeders, the number method
has very limited use.

79. •Dominance method.
•Essentially the dominance method is a partial improvement of the
occurrence method, viz., the lack of consideration of the quantities of
the food items present in the stomach, sought to be remedied.
•The stomach contents comprising the main bulk of the food materials
present, is determined and the number of fish in which each such
dominant food material is present is expressed as a percentage of the
total number of fishes examined.
•The percentage composition of the dominant food materials can also
be expressed by this method as in the occurrence method.

80. •The points method
•is an improvement on the numerical method where consideration is given to the bulk of
the food items.
•The simple form of points method is the one in which the counts are computed falling a
certain organisms as the unit.
•In a more modified form, the food items are classified as ‘very common’, ‘common’,
‘frequent’, ‘rare’, etc., based on rough counts and judgments by the eye.
•In this arbitrary classification the size of the individual organisms is also given due
consideration.
•The contents of all stomachs are then tabulated and as a further approximation, different
categories are allotted a certain number of points and
•the summations of the points for each food item are reduced to percentages to show the
percentage composition of the diet

81. Volumetric methods
•It forms a very suitable means of assessment, this is especially so in
the case of herbivorous and mud feeding fishes where the numerical
methods “become meaningless as well as inaccurate”.
•Even in cases where the numerical methods are suitable, volume has
been considered as an essential factor to be reckoned with, and
•In all improved numerical methods the volume of the food items is
taken in to consideration in some way or other.

82. •Eye estimation method: -
•This is probably the simples and easiest means of determining the
volume of food constituents.
•In this method the contents of each sample is considered as unity, the
various items being expressed in terms of percentage by volume as
estimated by inspection.
•This method of analysis is subjective in nature and the investigators
personal bias is likely to influence the results very greatly.
•This defect can be minimized to a great extent by the examination of
large samples conducted over a long period.

83. •Points (Volumetric) method: -
•This method is a variation of the eye estimation method.
•Here instead of directly assessing the volume by sight as in the previous
method,
•each food item in the stomach is allotted a certain number of points based
on its volume.
•E.g. Certain workers have taken into account both the size of the fish and
the fullness of the stomach in the allotment of points.
•The diet component with highest volume was given 16 points. Every other
component was awarded 16, 8, 4, 2, 1 and 0 points depending on the volume
relative to the component with the highest volume

84. •This method is quite useful for analysing omnivorous and herbivores
where measuring volumes of microscopic organisms such as diatoms
and filamentous algae are very difficult

85. •Displacement method: -The displacement method is probably the most accurate
one for assessing the volume.
•The volume of each food item is measured by displacement in a graduated
container such as a cylinder with the smallest possible diameter for accuracy.
•This method is eminently suited in the estimation of the food of carnivorous
fishes.
•But the differential rate of digestion of the food items may sometimes affect he
accuracy of the observations.
•However, if the collections are made when the fish are on feed, this defect can be
easily overcome.
•A knowledge of the volumes of the different size groups of the food items may be
of great help in estimating the volume of the whole item form the semi digested
fragments

86. Gravimetric method
•The gravimetric method consists of the estimation of the weight of each of the
food items, which is usually expressed as percentages of the weight of the total
gut contents as in other quantitative methods
•Generally the wet weigh of the food after removing superfluous water buy
pressing it dry between filter papers is taken for this purpose.
•Dry weight estimation is more time consuming and is usually employed where
accurate determinations of calorific intake is required.
•The limitation of weight as a criterion of analysis has already been referred in the
consideration of the method of assessing the condition of feed.
•Besides these, the accurate weighing of small quantities of food matter is
extremely difficult and impracticable in studies of large collections.
•This method is, therefore generally employed only in conjunction with other
methods to demonstrate seasonal variations in the intensity of feeding

87. Food analysis indices
•Index of fullness.
•This is measured as the ratio of food weight to body weight as an
index of fullness, which is very widely employed. (The ratio of
corresponding volume can also be used.)
•This index can be applied to the food in the stomach, or to that in the
whole digestive tract.
•It is usually expressed as parts per 10,000 (%00, or parts per
decimile); that is

88. •Index of consumption.
•Some authors have used not the actual weight (or volume) of the
stomach contents, but their reconstructed weight: i.e. their estimated
weight at time of ingestion.
•When reconstructed weights are used in the formula above, the index
obtained has been distinguished as the index of consumption
•Reconstructed weights are estimated form the lengths of relatively
indigestible parts of the organisms consumed-for example shells,
chitin, bones, otoliths, scales or stomachs.
•For accuracy it is necessary to make systematic measurements on
whole specimens of various sizes, for each of the food species
consumed.

89. •Index of selection or forage ratio.
•Most fishes have a scale of preference for the organisms in their
environment, so that some are consumed in large numbers, others
moderately, some not al all.
•A quantitative index of such differences called as the forage ratio.
•A study of the quantities of different organisms available to the fish is
made, and also of the various items in their stomachs; then;

90. •Index of electivity,
•Ivlev(1961) proposed a somewhat different quantitative measure of
selection which has been widely used as mean of comparing the
feeding habits of fishes and other aquatic organisms with the
availability of potential food resources in natural habitats
•The index has a possible range of -1 to +1, with negative values
indicating avoidance or inaccessibility of the prey item, zero indicating
random selection form the environment, and positive values
indicating active selection

91. •Manly-Chesson index
•When given a variety of prey types, most fishes select some food
categories over others.
•To measure this selectivity, a variety of indices have been developed that
incorporate measures of prey use and prey availability.
•While prey use can be easily determined from gut content analysis,
accurate description of prey availability can be problematic.
•What we quantify as prey availability may be quite different than what fish
perceive under natural conditions.
•Furthermore, because different prey can occupy different habitats, a single
sampling technique may not adequately quantify the relative abundance of
different prey items in the environment.

92. •Manly-Chesson (Chesson 1983) index is good choice for quantifying
prey preference.
•The Manly-Chesson index is frequently used to quantify prey
preference and can be calculated for two scenarios

93. 1.Constant prey abundance –
•used when the number of prey eaten is very small relative to its total
population or when prey is replaced as in laboratory studies
2.Variable prey abundance –
•used when the number of prey eaten is large relative to its total
population in the environment or, in experimental studies, when prey
are not replaced after being eaten.

94. Compound indices
•In an attempt to consolidate the desirable properties of individual
diet measures (e.g., Ni, Wi. Foi), compound indices were developed
•It combine two or more measures into a single index.
•The belief is that compound indices capture more information than
do single component measures

95. Index of Preponderance
•This index gives a summary picture of frequency of occurrence as well
as bulk of various food items.
•It provides a definite and measurable basis of grading the various
food elements.
•The bulk of food items can be evaluated by 1) Numerical 2)
volumetric and 3) Gravimetric methods.
•As the numerical method is not suited to the index with the
frequency of occurrence it magnifies the importance of smaller
organisms which may appear in enormous numbers.

96. Index of Relative Importance (IRI):-
•This index is an integration of measurement of number, volume and
frequency of occurrence to assist in evaluating the relationship of the
various food items found in the stomach.
•It is calculated by summing the numerical and volumetric percentages
values and multiplying with frequency of occurrence percentage
value

97. Surveys
•Besidescommercialfisheriesstatistics,themainsourceof
informationforstockassessmentarefisheryindependentdata
collectedbyscientificabundancesurveyscarriedoutbyresearchor
commercialvessels.
•Thistypeofdataisnowextensivelyusedaspartofthecommonwork
carriedoutbymanyregionalornationalcommissionsinmanaging
andconservingfishstocksandforlong-termmonitoringofmostof
thecommerciallyimportantstocks

98. •the use, precision, and applicability of survey indices have increased
over time, the quality of survey data has in most cases not yet been
considered good enough for a "stand alone" assessment
•the indices of abundance are used to tune a VPA or other types of
catch at age models

101. •Theextentofstandardisationvariesbetweensurveysbutincludesnormally
restrictionsonvesseltypeandsize,samplinggear,timeperiodforthe
survey,proceduresforlaunchingandretrievingthesamplinggear,sample
treatment,anddataanalysis.
•Someofthebasicassumptionsare:
•efficiency(catchability)ofthesamplinggearisconstantwithintheframessetbythe
standardisation,
•alloraconstantproportionofthepopulationisavailabletothesamplinggearover
timeandamongsurveys,
•afixedsurveyperiodremovesseasonalvariability,and
•whenastandardisationregimeisfollowed,temporalintegrityofabundance
estimatesismaintained

102. Trawl surveys
•Bottom trawl surveys are widely used for monitoring demersalstocks
when only an index of abundance is required
•In this method, an estimate of the proportionality factor (catchability)
is required to scale the survey estimate of abundance to absolute
abundance.
•In general, catchability(q) describes how the abundance and size
composition of a species differs from within the population and the
survey catch

103. where a is the area swept by the survey trawl, and q is the catchabilitycoefficient
If fish are also in the water column above the catching height of the trawl,
Equation 4 can be written
where the availability (qa) gives the proportion of fish available to the trawl and qeis the catchabilityof the
available fish. Due to a lack of exact information, the area covered a (in Eq. 4 and 5) is often assumed to be the area
swept by the trawl's wings or doors during a standard tow, and qeis given the conservative value 1 (meaning all fish
are assumed caught) or a more or less arbitrary value

104. Organisationof a demersaltrawl survey
campaign

105. Check list for the preparation of a survey

106. Data recorded
•Itdependsonsettingobjectives.
•Logsheetsaredesignedtosummarisetheplanofactivities(distributionof
duties)forthewholecruise.
•Detailsofindividualstation.
•Coverstandardformsummaryinformationforeachhaul:vesselposition,
startingandendingtimeofhauls,totalcatch,sub-samplingweight,and
speciescomposition.
•Detailedinformationonthecatch.Length,weights,sex,sexualmaturation,
growth.

107. Biomass estimated by the swept area method
•This direct method for estimating stock abundance has been
developed by Alversonand Pereira (1969) and is described in Sparre
and Venema(1998).
•The swept area is the length of the path times the width of the trawl
(Figure 5) and can be estimated from
•where v is the velocity of the trawl over the bottom swept, t is the time the
trawl is on the bottom, and wsis the wing spread of the trawl (the width of
the path covered by the trawl).
•For estimation of the biomass, the CPUA (catch per unit of area) is used

111. Estimation of maximum sustainable yield
based on biomass estimates

112. Age
•Ageorrelativeageofthefish,bylength,weight,numbers,etc,isusedto
determinethetimescaleoverwhichthevariousprocesseshavetaken
place.
•Thedeterminationofageisthereforeacentralprerequisiteforfurther
computationsinanalyticalstockassessmentmodels
•Therearethreeapproachesormethodsforageingfish,eachwithits
particularadvantagesanddisadvantages:
•Directobservationsofindividualfish,eitherheldinconfinementorfrommarking
/recaptureexperiments.
•Ageingofindividualfishbasedonannualpatternsinhardstructurese.g.otoliths,
scales,bonesetc.
•Identificationofcohortsbasedonlengthfrequencydistributionsfromoneorseveral
samplesrepresentingawiderangeofthepopulation..

113. •The first method is by far the oldest,
•initially described by fish culturists more than 250 years ago
•The inherent problem of this approach is the problematic extrapolation from observed values to
the true population values.
•Cultivated or tagged fish seldom have the same growth rate as their wild or untagged relatives.
•The second approach is now the preferred and most widely used method.
•It is based on the observation that temporal variations in the growth rate of the fish are reflected
in the deposition of material in the hard parts.
•This leads to alternating bands or growth zones of varying transparency.
•In temperate waters, where the growth rates are closely correlated with the change of seasons,
these bands correspond to annuli, i.e. one may count the zones, and because a set of zones is
formed each year, one obtains an estimate of absolute age.
•Annual growth cycles are seldom as pronounced in subtropical and tropical waters, but the
formation of zones may depend on other stimuli such as monsoons, river outlets, food supply,
stock density, spawning, etc.
•These zones are often unclear, a problem that makes the method inapplicable in most cases.

114. •ThediscoverybyPannella(1971)ofminutegrowthzonesinmany
species,includingtropical,withafrequencyofabout360peryear,
•hasnowledtoamethodwithwhichthesezonesarecountedandregardedas
dailygrowthzones.
•Theapplicationseemsverypromising,butrequiresagood
microscopeandremainsverylabourdemanding

115. •Thethirdapproachisbasedonananalysisofmodes(peaks)inalengthfrequency
distribution.
•Mostspeciesseemtobespawningregularlyandduringarelativelyshortperiod
oftime.Iftheprogenyexhibitaroughlyuniformgrowthrate,itisassumedthat
eachmodeinalengthdistributionrepresentsaseparatecohort.
•Themethodrequireslengthsofalargenumberandsizerangeoffishfromthe
populationandlittleoverlapinthesizesoffishfromadjacentagegroups.
•Thislastrequirementisusuallyonlymetintheyoungerpartofthepopulation
becausethegrowthratesdecreasewithage,sothemodes(cohorts)tendto
merge.
•Thismethodhasbeengivenincreasingattention,partlybecauseitisoftenthe
onlyalternativefortropicalstocks,butalsobecausethenecessarydataareeasily
obtainedandthehandlingofbigsampleshavebecomeeasythankstothe
introductionofcomputerisedtechniques

116. Definition and designation of age:
•Note the important distinction between 'age group or cohort' and
'year-class':
•Age group or cohort refers to the actual age in years and contains fish of the
same age, regardless of the year in which they were born.
•year-class refers to the group of fish produced in a particular year.(E.g. 1981-
year class, 1982-year-class...). Hence, two fishes belonging to the same age
group also belong to the same year-class.
•As they grow older, they will belong to progressively older age groups,
but remain in the same year-class.
•A consistent system is needed for designation of age, regardless of
the method used for age determination.

117. •the fish are designated by reference to annual marks
•A fish in its first growing season belongs to age-group 0
•A fish in its second growing season belongs to age-group 1 or simply age 1
and so on.
•It has been proposed and has become more or less generally
accepted, that 1st January is the date in which age designation
changes.
•This is in the northern hemisphere.
•In the southern hemisphere, it would correspond to 1st July.

119. Length frequency analysis
•Thesemethodsarebasedontheobservationthatthelengthcomposition
ofapopulationoftenexhibitsmodes(peaks)amongtheyoungerage
groups.
•Theparticularshapeistheresultofrecruitment,growth,mortalityand
sampling(whichmaybebiasedbyselectivityorthedistributionofthe
sampledfish).
•Thebasicassumptionunderlyingthestatisticalapproachestolength
frequencyanalysisisthat,theseasonalvariationsinthespawningpattern
aresopronouncedthatthemodaldistributionisequivalenttoa
recruitmentfrequencydiagram.
•Thebasicunitinfrequencyanalysisarethecohorts,i.e.abatchof
specimensofapproximatelythesameagethathaveenteredthestockand
whichbysize/agecanbediscriminatedfromtherestofthestock

120. •The birthday of a single fish in a cohort is considered as a random
variable within the range of a spawning period and with the
probability function approximating a normal distribution
•because of different birthdays, the individuals within a cohort do not
have exactly the same age at the same time, and because of different
growth, the individuals also do not have the same length at the same
age.
•As a result, a certain spread in lengths is expected.

121. Methods
•There are several methods for finding the number of cohorts, their relative contribution, and the
mean length of each cohort at different times in one or several composite length frequency
distributions:
•Visual methods
•The `Petersen` method.
•Modal progression analysis.
•Graphical methods:
•Bhattacharya method
•Cassie method
•(Tanaka method (parabola method))
•Computerisedversions:
•NORMSEP (FORTRAN)
•MIX (FORTRAN)
•ELEFAN I. V (BASIC)
•LFSA (BASIC)
•FiSAT(BASIC)

122. •Allmethodsrequirethat:
•Thesamplingisconductedinarelativelyshorttime
span.
•Thespecieshasaspawningpatternthatmakesit
possibletodetermineseparatepeaksof
recruitment.
•Everycohorthasauni-modaldistributionpattern.

123. The Petersen method (1892).
•This is the simplest, fastest but inherently also the most inaccurate of
the methods. It assumes that:
•Length at age varies around a single mean value.
•Fish of the same length have approximately the same age.
•Then, by simply counting the number of discernible modes and
relating these to the respective lengths and frequencies, a rough
estimate of the numbers and mean length of each cohort is obtained.
•Care must be taken that the modes in fact belong to successive age
groups and not to dominating cohorts separated by more scarce
broods.

124. The modal progression analysis (MPA).
•This is also a visual analysis, but based on a series of samples from the same
population taken at known time intervals.
•The method is particularly applicable for short-lived species or for species which
show considerable variation in cohort abundance (the method is especially useful
with shrimps).
•When arranging the samples on the same length scale one over the other in successive order
and with their relative distances proportional to the time span in sampling sessions,
•it may be possible to follow the progress of one or several dominant cohorts over length.
•By measuring or calculating the means, a direct impression of the growth is obtained. If, in
addition, information of the approximate time of spawning or age at recruitment, ages to the
lengths can be designated.
•MPA is also used for connecting mean length over time after having estimated
the number of cohorts and their mean length from one of the graphical methods
(e.g. Bhattacharya).

125. Graphical methods: Bhattacharya method

127. •ThisregressionisthemainelementoftheBhattacharyamethod.
•Whenthefrequenciesinthelengthintervals(dl)areassumedtobe
normallydistributed,theyareregardedasthefunctionvalues.
•Then,bytheuseofthelogarithmsofthefrequencies,computingthe
differenceoftwoadjacentpairsbysubtraction(i.e.(ln(dl+1)–ln(dl)),
andbyplottingsofthedifferenceagainsttheupperlimitofdl,a
scatterdiagramthatcanbelinearisedbyregressionisobtained.
•Theinterceptandslopeoftheregressionlinewillthenbeanestimate
ofthecorrespondingvaluesofthetruenormaldistribution,
approximatingthefrequencydistribution.

128. ThecalculationsrequiredforaBhattacharyaplottoobtainthe
normallydistributedcomponentsofacompositelength
frequencydistribution.

129. •Column A represents the length intervals.
•Column B is the frequency distribution of elements in each interval (called
N1+ to indicate that it consists of the first component N1 + the rest. N1 is
the component that needs to be isolated).
•Column C gives the logarithmic values.
•Column D gives the difference of the logarithmic values between two
adjacent intervals.
•Column E gives the length against which the values of column D should be
plotted (i.e. the upper limit of the smallest length group).
•Column F gives the calculated (theoretical) values of the differences of the
logarithmic values between two adjacent intervals, obtained by insertion
into the regressed line equation.

130. •Column G is a back calculation to the logarithmic values of the
frequencies in the first component (N1), obtained by choosing a clean
value (i.e. a value where the elements are considered only to belong
to N1) and adding the calculated values of the differences step-wise
forward. By this, an estimate of the number of elements in each
interval, which only belong to N1, is obtained.
•Column H is the anti-logarithm of the values in column G, i.e. the
frequencies of N1 now adjusted to conform to a normal distribution.
•Column I gives the frequencies of N2+, i.e. the components of N1
have been subtracted. The idea now is to repeat the whole procedure
with N2+ in order to isolate N2 and so on.

132. Computerisedversions of length frequency
analysis
•This is only a brief superficial presentation of some of the approaches developed:
•ELEFAN (Electronic LEngthFrequency ANalysis) developed by Paulyand David
(1981) and with later refinements and extensions (ELEFAN I, IV). (BASIC)
•LFSA (Length Frequency Stock Assessment) developed by P. Sparre(1987a)
(BASIC).
•The MAXIMUM-LIKELIHOOD-METHOD: NORMSEP developed by Tomlinson (1971)
and later extensions and modifications by MacDonald and Pitcher (1979),
Schnuteand Fournier (1980) and Sparre(1987b). (FORTRAN)
•FiSAT(FAO/ICLARM Stock Assessment Tools) (Gayaniloand Pauly1997) is a
package combining ELEFAN and LFSA together with additional features and a
more user-friendly interface. FiSATis presently being converted into the Windows
platform.
•The ELEFAN method is basically a modal progression analysis.

133. •The ELEFAN method is basically a modal progression analysis.
•The LFSA can be considered as a computer-assisted version of the
Bhattacharya method, with the underlying assumption (model) that
the length frequency distribution of each cohort is normally
distributed.
•It is like ELEFAN, a package of BASIC programs, primarily intended for
tropical fish stock assessment, where the emphasis is placed on the
analysis of time series of length frequency samples

134. Limitations of length frequency analysis
•It is sometimes difficult to separate the components of a composite frequency
distribution.
•This applies especially to the older parts where the overlaps become increasingly
bigger.
•Recall that a normal distribution was characterisedby the three variables:
numbers, mean value and variance.
•Intuitively, one would expect that proper identification and resolving would
become troublesome when either the mean values are lying relatively close or
when increasing variance will extend the overlapping areas or a combination of
both.
•To assess the reliability of resolving the components, a separation index has been
introduced and is an automatic feature in the Bhattacharya method implemented
in FiSAT

136. •Growth is a change in biomass due to both change in numbers from
recruitment and mortality and increment in weight
•is a phenomenon of primary interest in studies concerning production of
animals and plants.
•The growth of a population or an individual is often represented by
mathematical models describing the average change per unit of time.
•Well known examples are the logistic equation for population growth
in numbers (biomass dynamic models and ecological concepts) and
the Von BertalanffyGrowth Function (VBGF) (Bertalanffy1938) for
individual growth in length or weight.

137. •There are two types of growth to be considered:
1. Population growth in numbers or weight
2. Individual growth in length or weight
•Population growth depends on the combination of natality(birth rate), mortality
rate and immigrations/emigrations, and when weight is considered, also on the
sum of individual growth increments.
•Individual growth is within wide limits determined genetically, but is influenced
by several factors:
•Food availability (quality/quantity)
•Temperature (fish are poikilotherms)
•Variable allocation of surplus energy (somatic or gonadal tissue growth and/or for
locomotion and maintenance)
•Sexual differences
•Density and size distribution (hierarchical behaviourand/or competition)

138. •Growth is often divided into
a) somatic growth
b) gonad growth
•In many speeiesthe somatic growth slows down or almost ceases when
maturation is reached and the gonads start growing fast.
•Length (l) and weight (w) can be related using the expression
•W = a' + b log l orW a lb
•The regression coefficient b is often used as a measure of fish condition.
Usually it is close to 3. In mature fish there are cyclical changes, i.e. b > 3
during gonad development and b < 3 after spawning.

139. •In this equation, the parameters a and b, usually termed as length weight parameters are
to be estimated with the available length-weight data.
•The parameter a is a scaling coefficient for the weight at length of the fish species. The parameter
b is a shape parameter for the body form of the fish species.
•In theory, one might expect that the exponent b would have a value of roughly b = 3
•because the volume of a 3-dimensional object is roughly proportional to the cube of length for a
regularly shaped solid.
•Length is one dimensional whereas weight which depends on volume is three dimensional. Hence,
there is thinking that weight of a fish is proportional to cube of the length of the fish.
•That is, there exists cubic relationship between weight and length of a fish. For an ideal fish which
maintains the same shape b=3.
•Most species of fish do change their shape as they grow and so a cube relationship
between length and weight would hardly be expected.
•It has also been found that while b may be different for fish from different localities, of
different sexes, or for larval, immature and mature fish, it is often constant for fish
similar in these respects.

140. •In practice, fish that have thin elongated bodies will tend to have values of b that
are less than 3 while fish that have thicker bodies will tend to have values of b
that are greater than 3.
•Thus this also help to determine whether somatic growth is isometric (b=3) or
allometric.
•Values of b smaller, equal and larger than 3 indicate isometry, negative allometry
and positive allometryrespectively.
•When b>3, large specimens increase in height or width faster than in length,
either as the result of a change in body shape with size, or because the large
specimens in the sample are in better condition than the small ones.
•Conversely, when b<3, either the large specimens have changed body shape, i.e.,
become more elongated, or the small specimens were in better nutritional
condition at the time of sampling.

141. •The determination of growth of a single fish is of little use.
•What is needed is some measure of mean size at age and a method of
modelling or estimating the average growth rate of a species or particular
stock.
•This is based on the assumption that although individual growth differs,
there are reasonably confined limits to the range of growth rates at age in
a particular habitat.
•Also, fish are generally considered to grow indefinitely (i.e. growth never
ceases completely), but with continuously decreasing rates with age.
•Therefore, what is required, is a large and representative material in both
numbers and age range to carry out growth calculations

142. Approaches to growth estimation
1.Direct observations from experiments of either confined or
tagged/recaptured fish.
•Unless one is specifically dealing with cultured stocks, the first approach is
questionable.
•The estimates are of doubtful value when extrapolating to wild stocks
because of the difficulties in simulating natural conditions.
•This approach must be evaluated with extreme care to insure that the actual
marking method is not affecting health, behaviouror mobility.
•Only few of actual marking methods cause little or no retardation of growth.

143. 2.Length-at-age data.
•With precise and valid age determination and a large unbiased random sample, this
is the most satisfactory method.
3.Back calculations from analysis of hard parts,
•using the ratios between the lengths of fish and the spacing between the growth
zones of the otoliths, scales etc.
•This approach is often used. It requires certain assumptions about constant iso-or
allometricgrowth to be fulfilled.
4.Estimating average length at arbitrary age from length frequency
analysis (statistical) with known or assumed periodicity.
•This is often the only alternative when dealing with tropical or other stocks not
exhibiting a regular zone pattern in their hard parts

144. Back calculation of growth
•If the ratio between the fish length and some dimension of otoliths, scales or
other parts showing cyclical marks is known, this can be used for back calculation.
•Annual, monthly or daily marks can be used, and the ratio makes it possible to
calculate the fish length at the time when a given mark was formed
•The following procedure could be used:
1.Measure fish length and diameters, radii or another simply measurable
dimension in otoliths, scales, vertebrae or other structure where cyclical marks
are found. A wide range of fish lengths should be used.
2.Plot corresponding values and fit a regression. If a simple regression cannot be
fitted, try to measure another dimension.
3.Measure the diameters (or other dimensions) of annual or daily marks, and use
the regression to calculate the fish length when this ring was formed

145. Lee's phenomenon:
•Fish caught at older age of ten gives a lower back-calculated length for a
given age than fish caught at a younger age.
•This is called Lee's phenomenon.
•Possible causes are of three different types:
•Technical
•Use of incorrect scale: body relationships in back-calculation of growth.
•Biased sampling –
•Where fish of different sizes are not represented in samples of scales or otolithsin
proportion to their abundance. Usually it is the smaller fish of an age-group that
appear in samples less frequently than larger ones.
•The reason may be either that the sampling gear in use catches large fish more
effectively, or the larger fish may have a different distribution or habits -of ten
associated with the fact that more of them are mature and so take part in migrations
or spawning manoeuvresthat make them more easily caught.

146. •Selective mortality
•Where the mortality rate among the larger fish of an age-group is different from that
among the smaller.
•Size-selective mortality may arise either from natural mortality factors, or (when
fishing is a significant source of mortality in the population) from differing catch
abilities of fish of different sizes.
•Selective mortality, unlike the other two causes of Lee'sphenomenonis a
property of the fish population rather than of the technique.
•In a situation with sampling error the back calculated lengths are usually
close to the true lengths at age than those derived by direct observations.
•When there is a Lee's phenomenon caused by any of the other factors
listed above, the direct observations are usually closest to the truth.

147. Von Bertalanffygrowth estimates
•Von Bertalanffy(1938) proposed a simple asymptotic function or
model to describe the growth of fish by length, (i.e., a curve for which
the slope continuously decreases with increasing age, approaching an
upper asymptote parallel to the x-axis) (Figure 1).
•Curves of weight at age also approach an upper asymptote, but form
an asymmetrical sigmoid shape with an inflectionoccurringat a
weight equal to about one third of the asymptotic weight (Figure 1).

149. •Input data for growth models may include length, weight, or age
measurements.
•Length measurements may include total length, fork length, depth,
girth, width, and height.
•Weight measurements may include total body weight, wet weight,
dry weight, organ weight, shell weight, and meat weight.

156. Estimating Growth Equation Parameters

157. Estimating Growth Equation Parameters

159. •Thekeyparametersusedwhendescribingdeatharecalledthemortalityrates.
•Thechanceofdyingasafunctionoftime,i.e.themortalityrate,is,otherthings
beingequal,closelycorrelatedtothepredictabilityoftheenvironment,i.e.the
frequencyofrandomfluctuationsthatsomehowendangersthesurvivalofthe
population
•The factors contributing to mortality can be divided into two main categories,
although it must be stressed that this subdivision is purely for simplification:
•Abiotic factors (physical environment)
•temperature
•salinity
•oxygen
•light
•stability and disturbances

160. •pollution
•Biotic factors (other organisms)
•predation
•cannibalism
•density
•starvation
•competition
•Diseases
•In the context of mortality rates, the number of survivors of a cohort
as a function of time is a significant factor

161. Definitions:
•Ntis used to designate the number of survivors from a cohort attaining age t.
•Tris used for the time of recruitment, meaning the age at which fish enter the
fishery on the fishing grounds and will probably encounter fishing gears.
•Thus, NTris the number of recruits from a cohort.
•Often the symbol R is used to designate the recruitment (R = NTr).
•Tcis used for the age when the cohort actually enters the fishery and and
becomes catchable.
•Tcis called the age of first capture and marks the beginning of the exploited
phase.
•The difference between Trand Tcdepends on the selectivity of the fishing gear.

162. •Z is called the instantaneous rate of total mortality, the total mortality
coefficient, or simply the total mortality rate.
•F is called the instantaneous rate of fishing mortality, or simply the fishing
mortality rate.
•M is called the instantaneous rate of natural mortality, or simply the
natural mortality rate.
•All mortality rates are in units per time, normally per year.
•mortality rates are strongly size-dependent with an overall general decline
in the rates as a function of size.
•The natural mortality of a cohort will therefore tend to decline with
increasing age

163. Quantitative measures of mortality
•Over a given time interval, a proportion of the fish alive (N1) at the
beginning of the time interval (t1) will die by various natural causes or
by fishing pressures, while the rest will survive (N2) until the end of
the time interval (t2).
•Mathematically, one has N1 = P + D + O + C + N2
•where P,D,O = numbers dying from predation, diseases, and other causes, and
C = numbers caught by fishing.

164. •There are two ways of expressing the fishing mortality:
•Relative mortality
•The most obvious and easily understood expression is represents the
mortality as a fraction or a percentage of the initial number; for
example, the total death rate over time interval [t1, t2]is defined as
•the ratio between the numbers of individuals that have left the
cohort and the initialnumber.
•The closely related quantity, survival, is defined as

165. •the ratio between the numbers of individuals that were present at
time t2 and the initial number at time t1.
•The possible values of mortality and survival are from 0 to 1, or if
expressed in percentages, from 0 to 100.

166. Instantaneous mortality
•The instantaneous rates, i.e. the mortality rates applied over a very
short period of time (dt), where the numbers in the population do not
change significantly.
•In that case, the numbers dying from any one cause are not affected
by the numbers dying from any other cause and the deaths will be
proportional to the instantaneous rates.
•A decrease in the population numbers can then be considered as
proportional to the total mortality coefficient Z

168. •The figure illustrates the impact of fishing to the survival rates, compared tonatural decay without
fishing.
•The line N+Catchillustrates the relative proportion of fish landed under anexploitation rate of 0.5 (F
= M), compared to the survivors.
•It is important to note that the catch is much smaller than the difference between survivors with or
without exploitation because the probability of dying from natural causes does not change, and the
total number dying is a function of N.

169. •Equations above are among the most basic equations in fish
population dynamics.
•From them, expressions of the relative rates (e.g. annual) can be
obtained:

170. Properties of exponential decay model
•If the average rate of mortality (Zi) is constant in the time interval Ti,
where Ti = ti-ti+1, then
•Number of survivors (Ni+1) at the end of time interval Ti is
•Number of dead in the time interval Ti is
•Number of accumulated survivors in the time interval Ti is
•Average number of survivors in the time interval Ti is

171. •When splitting total mortality (Zi) into the components of fishing
mortality (Fi) and natural mortality (Mi), where Zi = Fi+ Mi , then
•The number caught by fishing in the time interval Ti can be expressed
as

172. Estimation of mortality rates
•EstimationofZfromcatchandeffortdata
•Itispossibletoestimatethetotalaveragemortalityratewhenthenumber
offishinacohortisavailablefortwodifferentmomentsinitsexploited
phaseundertheassumptionthatfishingandnaturalmortalityareconstant
intimeforcertain(older)agegroups.
•Equationscanberewrittenas:
•For the estimation of Z with this formula, it is not necessary to know the
absolute values of N(t1) and N(t2); only their ratio is required.
•This permits an estimate, Z, from the CPUE data,since
•CPUE = q ⋅Nt

173. CPUE data from research surveys
•If the CPUE data from a research survey at two different time periods
where q can be assumed constant is known, and it is possible to
determine the cohorts from ageing the fish

176. Natural mortality
•The natural mortality coefficient, or instantaneous rate of natural mortality
(M), is an important, but poorly qualified parameter in most mathematical
models of fish population dynamics.
•The natural mortality rate has clear correlations with other life history
parameters:
•M is proportional to the following factors:
•Growth and therefore indirectly to the VBGF parameters K and L∞
•Size or weight, which is partly a function of longevity
•Ageatmaturation,whichisalsoafunctionoflongevity
•Reproductive effort (the relative distribution of energy into gonad or somatic tissue)
•Temperature which determines the metabolic rate and therefore growth
•Environmental stability which may also affect longevity
•Intrinsic population growth rate r

177. •There are three different approaches to estimate M in fish
populations:
•Analysis of catch data from commercial fisheries, sampling programmes, or
mark and recapture experiments.
•Correlation with other life history parameters.
•Estimation of predation from stomach content analysis and consumption
experiments