1. Stock Assessment Workshop 30 th June - 4 th July 2008 SPC Headquarters Noumea New Caledonia

2. Day 5 Sessions 1 Revision

3. Unexploited Fish Population dynamics In unexploited fish populations there are three key processes governing population size (in biomass), being RECRUITMENT, GROWTH and NATURAL MORTALITY. These processes do NOT operate in equiliberium (there is no “balance of nature” in the absence of mans influence), with environmental influences upon each process resulting in natural fluctuations in population size over time (e.g. proof from sediment scales studies of sardine and anchovy). Typically, environmental impacts on RECRUITMENT play the most significant role in natural tuna population fluctuations. Growth Recruitment Biomass Death (Natural mortality) B t+1 =B t +R+G-M

4. Exploited Fish Population dynamics The resilience of a fish population to fishing is very much dependant on its biological features relating to growth, maturity, fercundity, natural mortality, life span etc. Stock Status Overfishing (F 25% too high) Significant probability of overfishing No overfishing

5. Stock Assessment Model – Basic Principle A stock assessment model is a mathematical simplification of a fish population and how it interacts with a fishery. It attempts to provide a realistic representation of the interaction between 4 processes, recruitment, growth, natural mortality and fishing mortality, after being “fitted” to observed data which is believed to be index relative changes in population size and structure over time. Once fitted, the model can then be used to provide managers information about fishery impacts.

6. Stock Assessment Model – Basic Principle Growth Recruitment Whole population Death (Natural mortality) Catch (Fishing mortality) (+) (-) W t = W  [1 – e -K(t-to) ] b

7. Growth, size and age to LL L t = L  [1 – e -K(t-to) ] K: ΔL/Δt Different species grow at different rates, to different sizes. Accurately estimating K (steepness of early growth rates) and max size is critical in stock assessment, effecting biomass at age estimates, vulnerability at age, and other parameters

8. Growth, size and age In MULTIFAN-CL, the VBGF parameters determined from biological research are critical, and can be used in the model as “seed” values. A range can specified for these values which allows the model some flexibility to search for the most appropriate growth relationship (within biologically meaningful bounds) during the model fitting process. Alternately the model can estimate growth parameters directly from the size data supplied to the model

9. Maturity at age Fish stocks are comprised of immature fish (juvenile), maturing fish and mature (adult) fish. The maturity schedule of a stock is critical as it will influence future recruitment. Estimation: Maturity schedule fixed in model, as determined from research into reproductive biology of the species. Immature Maturing Mature BET: 3-4 yrs YFT: 2-3 yrs SKJ: 1 yr ALB: 4-5 yrs STM: 4-5 yrs

10. Maturity There is a close relationship between the current status of the stocks, age/size to maturity, and the level of catch from juvenile age classes. Those stocks with relatively little juvenile mortality (i.e. which concentrate on catching adults) are in better condition Note that juvenile BET mortality is not only an issue for PS associated sets and ID/PH fishery, but also the LL fishery JuvenileAdult JuvenileAdult Bigeye tuna Yellowfin tuna

11. Recruitment Highly differing recruitments at same stock size can be due to difference in environment and impacts of that on egg production/quality by adults and/or survival of larvae and juveniles “….more commonly the number of recruits is effectively independent of adult stock size over most of the observed range of stock sizes”. (Gulland, 1983)

12. B t+1 =B t +R+G-M Estimating Recruitment Key factor in a stock recruitment relationship……steepness of the curve! This will be related to b, the stock size when recruitment is half the maximum recruitment, and a, the maximum possible recruitment. This will effectively determine the capacity of a stock at low size to recover quickly or not, but also the degree to which the adult stock can be fished down before reproductive capacity is effected, and will impact significantly on the estimation of MSY Stock Recruitment R = (aS)/(b+S) R = Recruitment a = Maximum recruitment (over all stock sizes) S = Stock size b = Stock size when recruitment is half the maximum recruitment (i.e.= a/2) Beverton and Holt model of compensatory recruitment

13. Estimation of Recruitment by MULTIFANCL MULTIFANCL estimates recruitment based on both the size of recruiting modes in the size data, and the level of CPUE from catch and effort data, to determine the size of the recruitment coming into the fishery at any point in time. Effectively, the model interprets a high CPUE in a region as “many fish in the region”, and interprets a recruiting mode which makes up a significant proportion of the overall size distribution as “many of the fish in the region are recruits”. Combined, the interpretation is “there are many fish in the region and a significant proportion of them are recruits”. In other words, a strong recruitment is estimated. A high CPUE but weak recruiting size mode (relative to the adjacent modes) would be interpreted as a weaker recruitment Strong recruitment (if CPUE high) Weak recruitment?

14. Recruitment (R) The strong influence of recruitment upon biomass trends is evident for YFT in WCPO RecruitmentBiomass

15. Natural mortality (M) Definition: The process of mortality (death) of fish due to natural causes (e.g. predation, disease, senescence). Expressed as a rate (i.e. proportion of the size/age class dying per time period). Allows an understanding of the relative impacts of fishing (e.g. compare natural v fishing mortality rates) Z t =M t +F t Estimation: Can be estimated within the model (model allowed to select a value that maximises the model fit to the data (e.g. CPUE series), possibly with some constraints specified for M to vary within) ….OR ….. YFT ….Can be estimated outside the model and included as a constant by one of a number of methods: 1. Maximum age 2. Length based 3. Application of the M:K ratio 4. Tagging studies 5. Z v. effort series analyses

16. Fishing Mortality Fishing mortality rate (proportion of population removed by fishing, either as retained or discarded dead catch) tends to vary with age due to size (age) based selectivity of fishing gears. There are a number of key equations which relate catch and fishing mortality rate to fishing effort, biomass, catchability and selectivity. Catch: C=qEB Total F: F = qE = C/B F at Age: F a = q t E t S a Where q = catchability, E = Effort, s = selectivity at age **Any increase in q,E or S a will result in a proportional increase in Fa. Hence for BET, for which total F is 25% too high, managers looking to reduce E by 25% (resulting in proportional 25% reduction in F)

17. F adults; F juveniles Initial F is high for older age classes, due to the predominance of the longline fishery. However the purse seine fishery on floating objects, and particularly drifting FADs since 1995, has led to high F on juvenile age classes also (Note: age classes are quarters) Fishing Mortality F – BET SC-2 2006

18. Selectivity – Bigeye 2006

19. Selectivity and MSY MSY from any given stock is selectivity dependent. In other words, MSY depends on and will change with changes in selectivity of the gear(s) operating in a fishery. The “maximum” MSY will be achieved if a fishery can fish only on the age group for which there is the greatest positive differential between biomass added by growth, and biomass lost by natural mortality (scaled by numbers at age). Gears which tend to remove very young fish (before yield per recruit potential is realised) or older fish (where natural mortality based loss of biomass outweighs gains from growth)

20. Catchability – what is it? Catchability …..is defined as the average proportion of a stock that is taken by each unit of fishing effort. q = C/EB It will be a value between 0-1 (0 being no catch and 1 being the entire stock), and typically will be very small….e.g.; 0.000001 As noted before “ q ” is critical in relating fishing mortality to fishing effort and relating the index of abundance (catch rates) to stock biomass

21. Catchability The Problem! Catchability can change (increase or decrease) over time, meaning that our key assumption in stock assessment, that catch per unit effort will vary proportionally with stock size, is no longer true. What can cause changes in catchability? Some causes include: 1. Changes in fishing method (e.g. depth, time of setting) 2. Changes in fishing technology (e.g. Improved fish finding technologies) 3. Experience and skill increases over time. 4. Environmental changes effecting fish distribution These are reasons why we collect information on methods and gears from fishermen, so we can account for changes in fishing over time that might impact catchability. q relates CPUE to Biomass and F to Effort, via: C/E=qB F=qE

22. Many stock assessments rely on the assumption that catch per unit effort (CPUE) will vary proportionally with biomass (as illustrated below), providing an index of observed data to which models can be “fitted”. However the previous section on catchability highlighted that there are many factors (e.g. changes in fishing methods, environmental variability, fish behaviour etc) which effect catch rates other than biomass. Catch rate standardisation is a statistical process by which variation in CPUE due to factors other than abundance (biomass) variations are removed from the CPUE index, leaving an index which does relate closely to abundance Catch rate standardisation Biomass CPUE Time CPUE Biomass

23. Catch = catchability x effort x biomass C = qEB This equation relates catch rates to the stock biomass, via: C/E = qB Stock assessment models rely on the assumption that CPUE will vary over time proportionally with biomass, so CPUE acts as an index of abundance Only if q (catchability) is constant, which is unlikely Biomass CPUE Time CPUE Biomass Catch rate standardisation and Biomass

24. CPUE standardisation – Longline YFT From: Langley et al. (2005) Yellowfin tuna – Region 3 (comprises the majority of historical biomass) shows a clear difference between the nominal (decreasing trend) and standardised (flatter trend) CPUEs. This is because the effect of depth of setting (Japan switched to deeper sets in 70s and 80s, resulting in lower YFT CPUE but higher BET CPUE) had been removed by the CPUE standardisation. Hence the standardised series suggests biomass has not declined to the extent suggested by the nominal series

25. Stock Assessment Model – Basic Principle The process by which we find combinations of parameter values that allow the model to closely predict our CPUE trends is called fitting the model to the data. There are two main methods by which stock assessment scientists do this: 1.Minimisation of Sums of Squares of Errors Basically, this approach asks “What combination of values result in there being the smallest difference (degree of error) between the model estimated CPUE series and the real CPUE series?” This approach involves a search for the parameter values which minimise the sums of squared differences between the observed data and the data as predicted by the model and parameters. It is almost impossible in any slightly complex system to create a model that exactly fits the real data….there is always some error. The objective of the SSE approach is to find parameter values that minimise the total error. 2.Maximum likelihood approach This approach asks “What combination of values for all of these parameters would most likely result in the observed CPUE values occuring?”

26. Models used to deduce relationship and find best fit Observed values Predicted values Difference between the observed and predicted value is the “residual error” Key Concept 6: Fitting models to data SSE = Sum (Observed-Predicted) 2

27. 2. Maximum Likelihood Method For this approach, parameters are selected which maximise the probability or likelihood that the observed values (the data) would have occurred given the particular model and the set of parameters selected (the hypothesis being tested) The set of parameter values which generate the largest likelihood are the maximum likelihood estimates: So.. Likelihood = P{data|hypothesis} Which means “the probability of the data (the observed values) given the hypothesis (the model plus the parameter values selected)”. E.g. Think of the flip of a coin Whats the probability of getting heads? Of getting tails? Stock assessment models can use fairly complex mathematics to determine the probability of, for example, the observed CPUE series occuring, given a particular model. Key Concept 6: Fitting models to data

28. Assumptions and Uncertainty There are 4 key areas of an assessment which you should examine to determine the “goodness” of the assessment: 1.The assumptions made within the assessment 2.Sensitivity analyses undertaken to test the importance of each assumption 3.Model fit and maximum likelihood 4.Uncertainty – how it is incorporated, represented and discussed The very first thing that you should look for is that these elements are actually discussed and represented within the assessment paper to start with! It is then a matter of interpreting what the statements regarding these four issues mean for how confident you can be in using the assessment for management advice etc. We are going to concentrate on these topics over the next day or so.

29. What assumptions made in SAs? (YFT, 2006)

30. Where does uncertainty come from? Sources of uncertainty include (from FAO); Measurement errors (in observed quantities), e.g. uncertainty around the robustness of PH/ID catch and effort data; discarding, rounding of weights Process errors (or natural population variability, e.g. in recruitment) e.g. uncertainty around the SRR Model errors (mis-specification of assumed values or population model structure), e.g. uncertainties around the values of M Estimation errors (in population parameters or reference points, due to any of the preceding types of errors) e.g. a result of carrying these errors thorough the model

31. What does uncertainty do to assessments? Uncertainties do exactly that – they make the confidence of any estimated measure, or output, less certain This is not to say that an estimate is necessarily wrong or bad Simply, that the value may be less accurate or precise than we would like It implies that using this point-estimate in the assessment MAY affect parameter estimates or the overall outcomes It does not automatically imply that an assessment is wrong or bad Uncertainties are not necessarily bad

32. What can sensitivity analyses tell us? The sensitivity analyses indicate if the uncertainty around the level of a major input variable (e.g. M) results in significant changes to the model outputs If there are not significant changes, the variable has little influence, despite the level of the variable being uncertain. That is, the outputs and conclusions of the stock assessment are not greatly impacted by uncertainty in the level of this variable.

33. Sensitivity analyses (e.g. MLS) For example, how do different starting values of M influence RPs ? Outputs are compared both qualitatively and quantitatively

34. Sensitivity analyses Sensitivity analyses also assist in indicating in which areas of the assessment would more information result in a more robust assessment For example, if different M values had a significant impact on the outcome of an assessment then more research into estimating M would be recommended. If different M values had little impact on the outcome of an assessment, then more research into M would be provide little improvement to the assessment. Other areas could be considered for improvement. This could not be clearly decided unless sensitivity analyses were undertaken.

35. Different model runs with MSYs calculated

36. How are reference points calculated?

37. The Maximum yield is the MSY The corresponding level of Fmulti is the estimate of F MSY

38. How are reference points calculated? The biomass and spawning biomass at F MSY are the estimates of B MSY and SB MSY

39. What can you do with RPs?