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

2. 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.

3. 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.

4. 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

5. 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.

6. Yield Software Parameters (2/7) Von Bertalanffy You will be asked to enter the parameters for the von Bertalanffy growth curve L ∞, K and T 0. 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.

7. Yield Software Parameters (3/7) Length-Weight You will be asked to enter the two parameters ( α & β ) for the length-weight equation; W= α L β Again these two parameters may be entered as point estimates or as distributions.

8. 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 L ∞ and K, that you have already entered under “von Bertalanffy”) is used in Pauly’s equation to estimate the natural mortality rate.

9. 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.

10. 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.

11. 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.

12. 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 L ∞, 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

13. 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.

14. 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

15. 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.

16. # Simulations, Simulating under uncertainty

17. 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 don’t 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

18. # Simulations, Simulating under uncertainty

20. 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

22. Yield Practical Session 2: Equilibrium Analyses FMSP stock assessment tools Training workshop

23. 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.

24. 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.

25. 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.

26. Yield per Recruit Analysis (3/6)

27. 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!!!

28. 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 > 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.

29. 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.

30. 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. F 0.1 or F 0.x Target spawning biomass Target fishable biomass Target total biomass Note that for some of the results we get a number of impossible results.

31. 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.

32. 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.

33. 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.

34. Yield per Recruit Reference Points (5/13)

35. 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.

36. 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 F 0.1. Select F 0.1 from the side menu by clicking on the radio button. Again another five graphs are displayed for this reference point.

37. Yield per Recruit Reference Points (8/13)

38. Yield per Recruit Reference Points (9/13) Looking at the results from the analysis presented; The most frequently occurring value of F 0.1 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.

39. 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.

40. 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 F 0.1.

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

42. 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.

43. 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.

44. Equilibrium Yield Analysis (2/4)

45. 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 2.5%’ile, F had to lie in the range 0 – 0.8 to produce any sustainable yield at all.

46. 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.

47. 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.

48. Yield Reference Points (2/8)

49. 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 F MSY 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.

50. Yield Reference Points (4/8)

51. 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.

52. Yield Reference Points (6/8)

53. 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.

54. Yield Reference Points (8/8) One of the parameters that is more doubtful than others is the R 0 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 R 0 parameter?

55. 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)

57. Yield Practical Session 3: Transient Analyses FMSP stock assessment tools Training workshop

58. 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.

59. 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.

60. 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 F MSY (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.

61. 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 SSB 0 in 10% of the years. What do you find?

62. 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.

63. Summary – Reference Points Reference Point2.5 %Median97.5 % Equilibrium F0.1 Equilibrium 20% SSB per recruit Equilibrium FMSY Equilibrium 20% SSB Equilibrium 50% Fishable Biomass Transient 20% SSB 0.31 0.27 0.25 0.15 0.40 0.45 0.41 0.37 0.20 0.26 0.54 0.70 0.54 0.26 Estimated Fishing Mortality Rates (F) from Equilibrium and Transient Analyses when Lc = 22.8 cm

64. 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.