FMSP stock assessment tools

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FMSP stock assessment tools Training Workshop
LFDA Theory
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LFDA Theory Session 1 Contents

• What does LFDA do?
• Why use LFDA?
• LFDA Data Requirements
• Von Bertalanffy growth curves
• Length based methods of estimation
• Methods used in LFDA

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What does LFDA do?

• It uses length frequency data to provide
  estimates of
• Von Bertalanffy growth parameters (both
  non-seasonal and seasonal)
• Total mortality, Z ( FM).
• These estimates can then be used in subsequent
  packages (eg Yield) to provide further information

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The analytical stock assessment approach using
LFDA and Yield
Biological data, management controls (size
limits, closed seasons etc)
Length frequency data
Data / inputs
LFDA
Yield
Assessment tools
Intermediate parameters
L8, K, t0 (growth)
Indicators
Z ( - M ) Fnow(Eq)
Per recruit Fmax F0.1 FSPR
With SRR FMSY Ftransient
Reference points
Compare to make management advice on F e.g. if
Fnow gt FMSY, reduce F by management controls
if Fnow lt FMSY, OK
Management advice
Figure 4.1
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Why use LFDA?

• Many standard stock assessment methods use age
  composition data.
• In tropical waters, good ageing materials
  (otoliths, scales etc) are not always available
• Due to the minimal seasonal effects, making
  ageing unreliable
• Getting large enough datasets can be rather
  expensive
• Length composition data can often be converted
  into age composition data via a growth curve, and
  assessment methods can be modified to work with
  length data.
• Length data are relatively cheap and easy to
  collect.

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Data Requirements (1/3)

• Sample sizes
• Sufficient sample size to eliminate biases.
• Ensure data are correctly raised for each
  sampling period.
• Distributions (numbers and timing)
• How should you organise your sampling to get the
  right numbers and timings?
• Cost

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Data Requirements (2/3)

• LFDA datasets contain a number of length
  frequency distributions (LFDs).
• LFDA requires that all distributions in a dataset
  have the same length class intervals and minimum
  length.
• LFDA also needs to know at what time of year the
  catch that makes up each distribution was taken.
  This is known as the sample timing.
• For LFDA, sample timings are expressed as a
  fraction of a year, e.g. 0.5, with separate years
  being separated by a full unit e.g. 1.5.

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Data Requirements (3/3)
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Data format

• Data can be imported from a spreadsheet, database
  or word processing file.
• Need
• length-classes as row headings
• sample timings as column headings.

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Example data and plot
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Von Bertalanffy Growth Curves (1/4)

• Non-seasonal growth curves
• Simplest and common for tropical marine
  fisheries.
• Non-seasonal von Bertalanffy Growth Curve.
• Seasonal growth curves
• More common for temperate, cold water or
  freshwater habitats.
• Sinusoidal constant growth but periods where
  growth rate slows down.
• Hoenig and Choudary Hanumura (1982).
• Periods of zero growth Growth stops for part
  of the year.
• Pauly et al. (1992)

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Von Bertalanffy Growth Curves (2/4)

• Mathematical equation to describe the length (L)
  of fish as a function of age (t)
• Lt L8 1 exp (- K (t t0))

• Lt Length at time t
• L8 Asymptotic maximum length
• K Growth rate parameter
• t Time ( corresponding to the age of fish)
• t0 time at which the fish has zero length.

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Von Bertalanffy Growth Curves (3/4)

• Lethrinus mahsena
• Sky emperor (Dame berri, Lascar)
• K 0.194
• L8 30.8 cm
• T0 -0.332 y
• Data from Seychelles 1998 (www.fishbase.org)

L8 30.8cm
T0 -0.332
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Von Bertalanffy Growth Curves (4/4)
Seasonal growth with a period of zero growth
starting in the middle of the year.
Seasonal growth with a slow-growth period in
the middle of the year.
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Length Based Methods of Growth Parameter
Estimation

• Graphical Methods
• Gulland and Holt, Ford-Walford, Chapman,
• von Bertalanffy, Bhattacharya, Cassie
• Modal Separation
• MacDonald and Pitcher, Fournier and Breen
• Computer Based Methods
• Many different methods in computer packages such
  as LFDA, and the FAOs package FiSAT.

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• Go to practical presentation

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LFDA Theory Session 2

• Estimating mortality rates
• Methods used in LFDA

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Mortality Rates

• Definition of a cohort
• A cohort is a batch of fish all of
  approximately the same age and belonging to the
  same stock. (FAO, 1992)
• Definitions of M, F and Z
• M is the natural mortality rate, i.e. the
  proportion of individuals that would die of
  natural causes without any other influence.
• F is the fishing mortality rate, i.e. the
  proportion of individuals that would die due to
  fishing.
• Z is the total instantaneous mortality rate
  i.e. the proportion of individuals in a cohort
  that will on average die in a particular time
  period.

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Estimation Methods for Total Mortality Z

• There are a number of different methods for
  calculating mortality estimates from length
  frequency data.
• Length Converted Catch Curve
• Beverton-Holt
• Powell Wetherall

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Length Converted Catch Curve (LCCC) (1/3)

• Where direct estimation of ages is possible, you
  can estimate the mortality rate based on the
  numbers surviving at each age class.
• In tropical waters this is often not possible and
  alternative techniques have been developed using
  length data as a replacement for age based data.
• One such method is called the length converted
  catch curve or the linearised length converted
  catch curve.

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Length Converted Catch Curve (LCCC) (2/3)

• The conversion of length data into ages is a
  fairly complicated mathematical process, changing
  lengths into ages using the average growth curve
  for the entire cohort.
• The end result of the process is a simple plot of
  the log of the number of survivors of different
  length classes against age. The mortality rate
  is the negative slope of the line plotted between
  the length at which the first length class is
  fully exploited and the length at which age
  classes start to become converged.

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Length Converted Catch Curve (LCCC) (3/3)
Data not used as not under full exploitation
Data not used as too close to L8
Data used to calculate Z
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Beverton-Holt

• Beverton and Holt (1956) showed that there is a
  relationship between length (L) and total
  mortality (Z) and length at first capture (L).

• Need to have accurate estimates for both K and L8
  from the von Bertalanffy growth equation to use
  this method.

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Powell-Wetherall (1/3)

• Powell (1979) developed a method, extended by
  Wetherall et al. (1987), for estimating growth
  and mortality parameters using the idea that the
  shape of the right hand tail of a length
  frequency distribution was determined by the
  asymptotic length L and the ratio between the
  total mortality rate Z and the growth rate K.
• This model has the same assumptions as the
  Beverton-Holt model in that we must have good
  estimates for K and L8.
• The results of this method provide estimates for
  each distribution of L8 and the ratio of Z/K.

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Powell-Wetherall (2/3)

• By manipulating the Beverton-Holt equation given
  previously it can be shown that

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Powell-Wetherall (3/3)

• Therefore taking all fish between L and the
  point of convergence towards L8 as for the LCCC
  method, we can calculate estimates for L8 and Z/K
  for each length frequency distribution in our
  dataset.
• If we have already estimated L8 and K from
  previous analyses we can therefore estimate Z.

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LFDA Theory Session Summary

• Von Bertalanffy Growth Curves
• How we can use length frequency data.
• History of evolution of estimation.
• Estimation of growth parameters.
• Theory of methods used in LFDA.
• Estimation of mortality estimates.
• Theory of methods used in LFDA.