Yield Practical Session 1

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FMSP stock assessment tools Training workshop
Yield Practical Session 1
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Yield Software Practical Session

• The Yield Software practical session will last
  half a day.
• During the session we will look in detail at
• Data requirements for the yield software.
• Then using the pre-prepared Yield Software
  tutorial we will investigate some example yield
  analysis with the pre-prepared example dataset.

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Loading and Saving Datasets

• To create a new dataset, open the Yield Software
  and enter parameters as described in the pull
  down menu then just save the parameters.
• To load an existing dataset into the Yield
  Software select File Load Parameters from the
  menu and select the appropriate file.
• To save a dataset created or modified with the
  Yield Software, select File Save Parameters
  from the menu and enter an appropriate filename
  DO THIS OFTEN, AND WHEN HAPPY DATA ARE CORRECT.

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Entering and saving data

• First we will enter a new dataset. Open the Yield
  software from the Programme menu or from the
  MRAGLtd subdirectory
• To create a new dataset, open the Yield Software
  and enter parameters as described in the pull
  down menu then just save the parameters.
• We will now enter an example data set for
  Lethrinus mahsena from Seychelles

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Yield Software Parameters (1/7)

• To enter or modify the parameters for the yield
  software you must select the appropriate option
  from the Parameters menu. Options exist for the
  following sets of parameters
• Von Bertalanffy
• Length-Weight
• Natural Mortality
• Maturity and Capture
• Seasonality and
• Stock-Recruit Relationship.

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Yield Software Parameters (2/7)

• Von Bertalanffy
• You will be asked to enter the parameters for the
  von Bertalanffy growth curve L8, K and T0. The
  growth curve will be displayed on the form.
• Each parameter can be entered as a point estimate
  or as a distribution. This is done by clicking
  on the radio button next to the text box or the
  distribution button.

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Yield Software Parameters (3/7)

• Length-Weight
• You will be asked to enter the two parameters (a
  ß) for the length-weight equation
• W a Lß

• Again these two parameters may be entered as
  point estimates or as distributions.

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Yield Software Parameters (4/7)

• Natural Mortality
• You will be asked to enter a value or
  distribution for the rate of natural mortality
  M.
• Alternatively you can enter the temperature
  parameter, which (when combined with L8 and K,
  that you have already entered under von
  Bertalanffy) is used in Paulys equation to
  estimate the natural mortality rate.

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Yield Software Parameters (5/7)

• Maturity and Capture
• Maturity and capture can be entered as ages or
  lengths by toggling the button.
• You will be asked to enter a value or
  distribution for the length / age at maturity and
  length / age at first capture.
• These whether point or distribution will provide
  knife-edge selection within the model.

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Yield Software Parameters (6/7)

• Seasonality of the Fishery
• You will be asked to enter the time period over
  which the fishery is to be analysed (months,
  years etc).
• You will then be asked to indicate the breeding
  and fishing seasons based on the timescale
  indicated previously.

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Yield Software Parameters (7/7)

• Stock-Recruit Relationship
• You will be asked to define the stock recruit
  relationship for the species.
• Choices exist for three different stock-recruit
  relationships, Beverton-Holt, Ricker and Constant
  with their associated parameters.
• You can also modify the coefficient of variation
  for stochastic recruitment.

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Checking Parameters

• Built in to the software application is a
  facility to cross-check parameters against each
  other.
• This should be run with every dataset before
  starting to analyse it.
• This will for instance check that the length at
  first capture and maturity and less than L8, and
  that the mortality rate allows fish to survive to
  reach maturity.
• If any parameters are not accepted, they will
  need to be checked.
• If all OK SAVE FILE select File Save
  Parameters from the menu and enter an appropriate
  filename

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Yield Example Dataset
Now we will enter the pre prepared data-set. The
yield software example dataset is based around
Lethrinus mahsena. This species is one of the
main species taken in fisheries for snappers and
emperors in the western central Indian Ocean, on
banks of the Chagos Archipelago, the Seychelles,
and Mauritius.
A data file containing estimates of parameters
and their uncertainties for L. mahsena,
LmahDat.txt, has been distributed along with the
software.
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Loading and saving data

• We will now load this existing dataset
• To load an existing dataset into the Yield
  Software select File Load Parameters from the
  menu and select the appropriate file.
• Load LmahDat from the MRAGLtd subdirectory, take
  a quick look at the data, Crosscheck parameters.
• SAVE File Save Parameters from the menu and
  enter an appropriate filename DO THIS OFTEN,
  AND WHEN HAPPY DATA ARE CORRECT

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Number of Simulations

• The number of simulations is set by the user, by
  selecting Number of simulations from the
  Options menu.
• Number of simulations is the number of times that
  the model is run to calculate the various
  different parameters the data used in each
  run is sampled from the range of values
  entered. It will be slightly different for each
  run.
• This enables us to explore the question of
  uncertainty in our data
• The greater the number of runs, the better, but
  obviously more runs take more time.

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Simulations, Simulating under uncertainty
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Simulations, Simulating under uncertainty

• We will now go into Yield and look at what the
  effects of both the number of runs and
  statistical uncertainty in input parameters have
  on the output analyses.
• This is jumping ahead into analysis at this
  point dont worry about interpreting the results
  we look at that next. Here we are exploring
  only the effects of
• Number of runs
• Statistical uncertainty in input parameters
• Yield Select Equilibrium/YPR F with 100 runs

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Simulations, Simulating under uncertainty
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Simulations, Simulating under uncertainty
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Summary Practical Session 1

• At the end of this session you should be familiar
  with

• Loading and saving datasets
• Entering and saving data
• Yield software parameters
• Checking parameters
• Simulating under uncertainty

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FMSP stock assessment tools Training workshop
Yield Practical Session 2 Equilibrium Analyses
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Yield Software Practical Session

• The Yield Software practical session will last
  half a day.
• During the session we will look in detail at
• Data requirements for the yield software.
• NOW.
• Then using the pre-prepared Yield Software
  tutorial we will investigate some example yield
  analysis with the pre-prepared example dataset.

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Yield per Recruit Analysis (1/6)

• We will now look at the Yield-per-Recruit
  Analysis
• Select from the Equilibrium menu
  Yield-per-Recruit vs F
• This will display a dialog box as below to enter
  the range and steps in F you wish to analyse.
  Accept the defaults.

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Yield per Recruit Analysis (2/6)

• This will create a series of graphs against the
  values of F selected showing the following
• Yield per recruit
• Spawning stock biomass (SSB)
• Fishable biomass (FishB) and
• Total biomass (TotalB).
• These can be viewed as absolute values or as
  fractions of the unexploited biomass.

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Yield per Recruit Analysis (3/6)
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Yield per Recruit Analysis (4/6)

• On each of the graphs the solid line shows the
  mean values obtained with the confidence bands
  either side. The confidence intervals are by
  default set to 95 thought his can be changed by
  selecting from the menu.
• The data can also be viewed in a tabular format
  by pressing the Medians and Intervals button.
• The Input Parameters button will also show the
  individual input parameters used. Note this will
  not be the same for everybody!!!

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Yield per Recruit Analysis (5/6)

• What do these results mean?
• Median YPR as fraction of unexploited fishable
  biomass.
• Tends to a maximum at values of F gt 1.3
• Natural Mortality Rate M was based on a mean of
  0.39.
• Therefore F is approximately three times M, which
  is quite high.

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Yield per Recruit Analysis (6/6)

• The other three biomass plots show the effect of
  increasing F.
• If we look at SSB-per-recruit it is clear that
  levels of F producing high values of yield per
  recruit are only found where the SSB is
  substantially reduced in terms on its unexploited
  biomass.
• Note that the levels of recruitment in a YPR are
  assumed constant. This is very unlikely with
  such as small SSB.
• Similar patterns are shown for total / fishable
  biomass.

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Yield per Recruit Reference Points (1/13)

• Next we will look at the reference points that
  can be calculated from Yield per recruit
  analyses.
• Maximum yield per recruit.
• F0.1 or F0.x
• Target spawning biomass
• Target fishable biomass
• Target total biomass
• Note that for some of the results we get a number
  of impossible results.

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Yield per Recruit Reference Points (2/13)

• Select from the Equilibrium menu
  Yield-per-Recruit Reference Points
• This will bring up the dialog box below to allow
  you to select which reference points you wish to
  calculate.

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Yield per Recruit Reference Points (3/13)

• Select the defaults as before and press OK to
  start calculating.
• As before you will see the progress box appear.

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Yield per Recruit Reference Points (4/13)

• When complete a set of five graphs will be
  displayed for the Maximum Yield per Recruit
  reference point.
• These show the following histograms
• Maximum yield per recruit
• Value of F that produces the maximum yield per
  recruit
• Spawning stock biomass per recruit
• Fishable biomass per recruit and
• Total biomass per recruit.

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Yield per Recruit Reference Points (5/13)
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Yield per Recruit Reference Points (6/13)

• The largest frequency (for F in the range 1.6
  2.6) has around 30 observations. Over 50 of the
  time, the F producing the maximum
  yield-per-recruit exceeded 2.4. This confirms
  the impression given by the yield-per-recruit
  plots discussed above.
• The SSB-per-recruit histogram also confirms the
  impression given by the earlier plots the
  largest of all the values of SSB-per-recruit was
  less than 11 of its unexploited value. This is
  not a good recommendation for management of a
  stock.

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Yield per Recruit Reference Points (7/13)

• The maximum YPR therefore was clearly not very
  useful for this stock.
• Lets look at the next reference point we selected
  F0.1.
• Select F0.1 from the side menu by clicking on the
  radio button.
• Again another five graphs are displayed for this
  reference point.

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Yield per Recruit Reference Points (8/13)
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Yield per Recruit Reference Points (9/13)

• Looking at the results from the analysis
  presented
• The most frequently occurring value of F0.1 has a
  mean of 0.39, and the maximum of over 0.5. These
  are obviously more sensible values of F relative
  to the level of natural mortality that we
  selected earlier.
• What are the percentiles for F here?
• Lets display the results in a spreadsheet and
  calculate them.

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Yield per Recruit Reference Points (10/13)

• As for the yield per recruit analysis itself the
  data can also be viewed in a tabular format by
  pressing the Medians and Intervals button.
• The Input Parameters button will also show the
  individual input parameters used to generate the
  results shown.
• Copy out the values of F from the table display
  into a spreadsheet, paste into a spreadsheet and
  work out the mean, median and percentiles.

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Yield per Recruit Reference Points (11/13)

• Lets look at the third reference point we
  selected the target spawning biomass (set at 20
  of unexploited).
• Again just select the Target Spawning Biomass
  button from the menu on the right hand side.
• The five same graphs are displayed as for F0.1.

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Yield per Recruit Reference Points (12/13)
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Yield per Recruit Reference Points (13/13)

• The most obvious result in this form is in the
  histogram for SSB-per-recruit/SSB0. As it
  should, it shows that in every case, this ratio
  was 20.
• Looking at the histogram of values of F that
  produce this, we see that most frequently, these
  fell in the range 0.37 0.43, and all fell
  between 0.25 and 0.79. As one would have
  expected, these reference point F values are
  slightly higher than those for F0.1.
• Using the table of results, the median
  SSB-per-recruit reference point F was 0.45 with
  95 confidence interval 0.31 0.70.

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Equilibrium Yield Analysis (1/4)

• Select Equilibrium yield from the Equilibrium
  menu and accept the range of F values shown.
• The progress dialog box will appear while the
  simulations are performed.
• After a while the following form appears, and you
  should select the Fraction of unexploited
  biomass button.

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Equilibrium Yield Analysis (2/4)
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Equilibrium Yield Analysis (3/4)

• The main difference between yield and
  yield-per-recruit methods is that for the yield
  methods recruitment is allowed to vary with the
  defined stock-recruit relationship.
• The plot of relative yield against F suggests
  that in 97.5 of the simulations, the stock was
  nearly extinguished when F reached a level of 2.
  
• For the median, the maximum yield occurred at an
  F around 0.4, and for the lower 2.5ile, F had
  to lie in the range 0 0.8 to produce any
  sustainable yield at all.

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Equilibrium Yield Analysis (4/4)

• The median value of the maximum yield is
  estimated at around 1300t, but the percentile
  range is between 600 and 2200t which is a very
  large range for setting management measures.
• The other plots show a similar story. In
  particular, to achieve a median SSB/SSB0 ratio of
  20, the corresponding F value seems to be around
  0.4.
• One other interesting point to note is the shape
  of the plot of yield against F. The standard
  Schaeffer biomass dynamic model suggests that the
  yield curve is symmetric. This curve is clearly
  asymmetric, with a peak shifted towards lower
  values of F.

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Yield Reference Points (1/8)

• We will now look at the Yield Reference Points.
• Select Equilibrium Yield Reference Points.
• Select the default values from the menu displayed
  and wait for the simulations to be carried out
  and the progress dialog to be replaced by the
  following set of graphs. Note that an additional
  reference point has been asked for that
  producing a fishable biomass at 50 of its
  unexploited level.

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Yield Reference Points (2/8)
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Yield Reference Points (3/8)

• The first two graphs show that the median maximum
  sustainable yield is estimated at about 1400t at
  an F of 0.47.
• This however seems to result in a SSB at less
  than the 20 level we have assumed as a safe
  level to avoid a collapse in the stock. The
  fishable biomass at FMSY is at around 30 of
  pre-exploitation levels, a long way below the
  assumed level of the Schaefer model. (Note you
  need to toggle display option to Fraction of
  unexploited biomass to see these)
• Lets now look at the Target Spawning Biomass
  reference point.

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Yield Reference Points (4/8)
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Yield Reference Points (5/8)

• The 20 target spawning biomass reference point
  gives a reasonable value for F of approximately
  0.43, which is within reasonable bounds compared
  to M.
• Check the confidence intervals for F in the
  results table.
• The final reference point to look at is the 50
  fishable biomass reference point.

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Yield Reference Points (6/8)
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Yield Reference Points (7/8)

• Again, we would expect this to be achieved at a
  lower value of F, given that the median fishable
  biomass ratio producing MSY was estimated earlier
  to be 30.
• Now, the mode occurs at an F around 0.211. Using
  the table of results, the median was estimated to
  be 0.20, with 95 confidence interval 0.15
  0.26.
• All these analyses are heavily dependent on the
  input parameters and we should test the
  sensitivity of these.

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Yield Reference Points (8/8)

• One of the parameters that is more doubtful than
  others is the R0 parameter (number of recruits
  before exploitation) of the stock recruit
  relationship.
• This was set at 25 million initially.
• Try values of 2.5, 10 and 250 million and
  investigate the results. Are the reference
  points sensitive to the R0 parameter?

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Summary Practical Session 2

• Equilibrium models
• Yield-per-recruit analyses (constant recruitment)
• Yield analyses (deterministic recruitment)
• Biological Reference Points (BRPs)
• Yield (MSY)
• Biomass (SSB20, Fishable Biomass, Total Biomass)
• Fishing Effort (F0.1)

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FMSP stock assessment tools Training workshop
Yield Practical Session 3 Transient Analyses
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Transient Analysis (1/6)

• We have assumed so far that the population has
  been in equilibrium.
• Let us calculate the transient SSB reference
  point.
• We will look for a probability (10) that the
  stock will remain above a proportion of SSB (20)
  for twenty years.
• Select the Transient SSB Reference Point from the
  Transient menu and accept the default values as
  above.

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Transient Analysis (2/6)

• This will then perform the simulation giving a
  probability estimate based on our parameters.
• Here for instance we have calculated that an F of
  0.271 would give a probability that the
  population will drop below 20 in one or more
  years in the next twenty.

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Transient Analysis (3/6)

• This suggests that, with even relatively modest
  amounts of recruitment variability the risks of
  the SSB falling below specified low levels can be
  rather greater than might have been imagined.
• The value we have obtained is rather less than
  the median FMSY (0.41), but then we would expect
  that because that F on average reduces the SSB to
  less than 20 of its unexploited level even when
  there is no recruitment variability. With
  variability there is always the possibility of a
  number of bad recruitment years occurring one
  after the other.

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Transient Analysis (4/6)

• We can now look at projecting a strategy for
  fisheries management into the future on our
  imaginary stock.
• Select Transient Projections from the menu.
• Then project the stock into the future by using
  the value of F you obtained in the Transient SSB
  Reference Point. We assume that this will on
  average allow the SSB to drop below 20 of SSB0
  in 10 of the years.
• What do you find?

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Transient Analysis (5/6)

• Try the same analysis for the values of F for the
  FMSY and the SSB/SSB0 20 target reference points
  you obtained.
• What happens to the stock?
• Try a few other scenarios to see what happens,
  e.g. unrestricted fishing at very high values of
  F or periods of no fishing between periods of
  high fishing.

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Summary Reference Points
Estimated Fishing Mortality Rates (F) from
Equilibrium and Transient Analyses when Lc 22.8
cm
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Summary - Managing under uncertainty

• Managers base their decisions on certain
  reference points that indicate a particular
  course of action. Yield derives these. However we
  have seen that statistical uncertainty in the
  biological data estimated for a fishery, and
  inter-annual variation in the SRR can lead to
  considerable uncertainty in the values of the
  reference points and thus in management
  decisions.
• Yield quantifies this uncertainty and enables
  managers to make more informed decisions about
  how best to manage.
• Yield can be a powerful tool when used properly
  and in conjunction with other stock assessment
  tools.