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

2. Day 1 Sessions 1-3 Revision

3. Fish Population dynamics

4. Unexploited Fish Population dynamics
Growth
Recruitment
Biomass
Death
(Natural mortality)
Bt+1=Bt+R+G-M
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.

5. Exploited Fish Population dynamics
An exploited fish population is effected by the same population dynamics processes, but additionally, by fishing mortality also.
Stock assessment must take into account the interaction between all four processes when providing advice to managers and politicians in relation to F, as in general, changes in populations over time are likely to be influenced by both fishing and by environment/other factors impacts on RECRUITMENT, GROWTH and NATURAL MORTALITY! (e.g R and BET)
It is the job of stock assessment to tease apart the respective influences of fishing, recruitment, growth and natural mortality to enable appropriate management responses to changes in population size and status.
***A population’s response to its environment may in fact be changed by the impacts of fishing so the two processes are interrelated
Growth
Recruitment
Whole population
Death
(Natural mortality)
Catch
(Fishing mortality)
(+)
(-)
Bt+1=Bt+R+G-M-C

6. 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

7. Exploited Fish Populations Equiliberium biomass, yields and MSY

8. Equiliberium biomass, yields and MSY
Recruitment
Biomass
MSY
Yield
Bmsy
Fishing Effort

9. Stock Assessment Model – Basic Principles

10. 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.
It is the balance between these “input” and “output” processes in nature that will determine changes in the real populations size over time. Hence if the model parameters (and equations) can be “tuned” to produce the same fluctuations in biomass as is indicated by our biomass index (standardised CPUE), then we can have some faith that our model is a realistic representation of the real population, and we can use it to predict impacts of the fishery, both past, present and future (allowing analyses of management options). If it is a good representation of the real population, we should be able to simulate different fishing conditions/levels in the future and see how our model population responds. If our model has a good fit, we’d have some confidence that how our model population responds would be very similar to how the real fish population will respond to different management actions.

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

12. Growth, size and age

13. Growth, size and age
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 to L
Lt = L[1 – e-K(t-to)]
K: ΔL/Δt

14. 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

15. Maturity

16. 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.
Mature
BET: 3-4 yrs
YFT: 2-3 yrs
SKJ: 1 yr
ALB: 4-5 yrs
STM: 4-5 yrs
Maturing
Immature

17. 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
Juvenile
Adult
Bigeye tuna
Juvenile
Adult
Yellowfin tuna

18. Recruitment

19. Recruitment
“….more commonly the number of recruits is effectively independent of adult stock size over most of the observed range of stock sizes”. (Gulland, 1983)
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

20. Estimating Recruitment
Bt+1=Bt+R+G-M
Estimating Recruitment
Beverton and Holt model of compensatory 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)
Recruitment
Stock
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

21. 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
Weak recruitment?
Strong recruitment (if CPUE high)

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

23. Natural Mortality

24. 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)
Zt=Mt+Ft
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

25. Fishing Mortality

26. 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: Fa = qtEtSa
Where q = catchability, E = Effort, s = selectivity at age
**Any increase in q,E or Sa 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)

27. Fishing Mortality (Fa = qtEtSa)
Constant S at age, and E and q over time
Age specific S (mimic LL)
Increasing effort (25units/yr)
Increasing q (5%/yr)

28. Fishing Mortality
F adults; F juveniles
F – BET SC
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)

29. Fishing Mortality Impacts of fishing on total biomass x gear
F – BET SC

30. Comparing (current) F to
Fishing Mortality
Comparing (current) F to
F required to achieve
maximum sustainable
yield (MSY)
F – BET SC

31. Fishing Mortality - Z (F + M) - M only Impacts of fishing
F – BET SC

32. Selectivity

33. Selectivity
The probability of capture by a particular fishing gear is known to depend on size/age of the fish (i.e. gears are size selective). This selectivity is an important component in age specific fishing mortality estimation
F=qEs
The key problem raised by size selectivity of fishing gears is that the size composition of the catch will not reflect the size composition of the population as a whole.
Including a parameter to describe gear selectivity helps us to account for this in our stock assessment models
The size based selectivity of a fishing gear can be described by means of a “selection curve”, which gives for each size class (or in age structured models these can be converted to age classes where the relationship between age and size is known) the proportion of the age/size class which is available to the gear….

34. Selectivity – Bigeye 2006

35. 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)

36. Catchability

37. Catchability – what is it?
…..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.;
As noted before “q” is critical in relating fishing mortality to fishing effort and relating the index of abundance (catch rates) to stock biomass

38. 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

39. Catchability
q = C/EB
q = 2/30x28 =

40. Catchability
What happens to catchability when the depth of the gear is increased into the habitat of the target fish?
q = C/EB
q = 7/30x28 =

41. CPUE Standardisation

42. Catch rate standardisation
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
Time
CPUE
Biomass
CPUE
Biomass

43. Catch rate standardisation and Biomass
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
CPUE
Biomass
CPUE
Biomass
Time

44. Catch rate standardisation
Why does q (catchability) vary?
Changes in fishing methods and techniques
[LL - Depth of setting, HBF, hook type, hook size, light-stick use, bait type, time of set, latitude, longitude, proximity of other vessels, proximity to features…………]
[PS – set type, time of set, latitude, longitude, proximity of other vessels, proximity to features, presence of other species ………]
Biological factors – size ,maturity, age, habitat preference
Environmental factors – habitat availability, oceanographic factors, prey abundance…………………
All potentially interact to influence CPUEs
Therefore CPUE may and does vary independent of changes in actual abundance of target species

45. 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

46. CPUE data and MFCL
Bigeye tuna – Unsurprisingly, there is significant correlation between the standardised CPUE and model estimates of biomass

47. Model Fitting

48. 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:
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.
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?”

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

50. Key Concept 6: Fitting models to data
Models used to deduce relationship and find best fit 25
Square of the error
= 102 = 100 20
Sums of Squares of the error
= = 200 15
Square of the error
= 102 = 100 10 5

51. Key Concept 6: Fitting models to data
Models used to deduce relationship and find best fit 25
Square of the error
= 52 = 25 20
Sums of Squares of the error
= = 250 15
Square of the error
= 152 = 225 10 5

52. Key Concept 6: Fitting models to data
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.

53. Assumptions and Uncertainty

54. Assumptions and Uncertainty
There are 4 key areas of an assessment which you should examine to determine the “goodness” of the assessment:
The assumptions made within the assessment
Sensitivity analyses undertaken to test the importance of each assumption
Model fit and maximum likelihood
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.

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

56. 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

57. 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

58. Sensitivity Analyses

59. 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.

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

61. 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.

62. Different model runs with MSYs calculated

63. Biological Reference Points

64. How are reference points calculated?

65. How are reference points calculated?
The Maximum yield is the MSY
The corresponding level of Fmulti is the estimate of FMSY

66. How are reference points calculated?
The biomass and spawning biomass at FMSY are the estimates of BMSY and SBMSY

67. MSY for different species (from SC-1)
BET: 65,000 mt
YFT: 260,000 mt

68. Fmulti and subsequent yields: SA1 WP – 4
Albacore
MSY
FMSY
(about 20 times current F)
Fmulti

69. Fmulti and subsequent biomass estimates: SA1 WP – 4, Albacore
FMSY
BMSY
BsMSY
Fmulti

70. What can you do with RPs?
1. Investigate the impacts of individual fisheries (or all fisheries) on the biomass levels (e.g. what would the biomass be if there was no fishing?; Only LL fishing? etc)
Reduction in biomass due to fishing.
Significant impacts after 1980.
Biomass

71. What can you do with RPs?
2. Estimate how much of the reductions in biomass can be attributable to different method fisheries
% Impact

72. What can you do with RPs?