1. Stock Assessment Workshop 25th-30th June 2007 SPC Headquarters Noumea New Caledonia

2. Day 5 Session 1 Biological reference points

3. Overview Review of reference points Why calculate them?
Reference points considered by WCPFC
Reference points calculated by OFP
How are they calculated?
What can you do with RPs?
Target or Limit reference points?
The precautionary approach and reference points
Reference points used by other RFMOs

4. Review of reference points (RPs)
Reference points are used to judge the status of a stock
They are also used to provide advice to management from the outputs of stock assessments
In age-structured models, information on the SRR, growth and mortality are required

5. Why calculate RPs? How else can you assess the condition of a stock?
How else can you assess the impacts of fishing and/or fisheries on a stock?
How else can you evaluate the performance of fishery management?

6. What RPs does the WCPFC use?
The WCPFC convention lists several reference points
Maintain or restore stocks at levels capable of producing MSY [Article 5(b)]:
i.e. Maintain Bcurrent  BMSY
Eliminate overfishing and excess fishing capacity [Article 5(g)]:
i.e. Maintain Fcurrent  FMSY
Assess the impacts of fishing on target and non-target stocks and associated species [Article 5(d)]
i.e. 1 - Bcurrent / B0 ;

7. What RPs does the WCPFC use?
The WCPFC convention also lists several other points that may potentially develop into RPs;
Long-term sustainability of highly migratory species [Article 5(a)]
Minimise wastes, discards and catches of non-target species, in-particular protected species [Article 5(e)]
Protect biodiversity and marine environment [Article 5(f)]
e.g. Maintain total discards (mt) below 2005 levels?

8. What RPs does the WCPFC use?
In addition;
develop stock-specific reference points [Article 6.1(a)]
ensure that, when reference points are approached, they will not be exceeded [Article 6.3]
adopt … conservation and management measures and recommendations for non-target species and species dependent on or associated with the target stocks, with a view to maintaining or restoring populations … above levels at which their reproduction may become seriously threatened [Article 10.1(c)]:
Maintain SSBcurrent  SSBMSY?

9. RPs calculated by OFP

10. RPs calculated by OFP
MSY - The maximum average catch that can be removed under given environmental conditions over an indefinite period, without reducing a stock’s ability to reproduce
at MSY,
Catches are maximised (for the fishery specific combinations of F and selectivity)
Catches and natural mortality are balanced by recruitment and growth

11. Bt+1=Bt+R+G-M-C Death (Natural mortality) Recruitment (+)
Whole population
(-)
Catch
(Fishing mortality)
(-)
Growth
(+)
Movement

12. RPs calculated by OFP FMSY – the fishing mortality (or effort) at MSY.
This can be thought of as the level of fishing effort needed to achieve MSY
FMSY is influenced by the selectivities of different gears and method fisheries (depending on the component of the stock [e.g. adults, juveniles] each gear or fishery targets)
BMSY – the biomass (adult, juvenile or total) of the stock at MSY

13. WCPO example: Skipjack (SA WP-4, SC-1)
The horizontal line at 1.0 indicates the overfished state reference point

14. How are reference points calculated?
General
Estimates of various quantities are generated from the outputs of a stock assessment
Ratios are constructed to provide information about the level of fishing, the biomass of the stocks and other values, relative to these parameters at MSY
e.g. Fishing effort
Fcurrent/FMSY : provides a ratio of the current level of fishing effort compared to the level required to achieve MSY
If > 1, overfishing is occurring
IF<1, overfishing is not occurring

15. Information required for constructing RPs from age-structured models
Growth: how fast do fish grow and contribute to the biomass of the stock?
[i.e. contribution of additional biomass at age of new and existing fish, weight–at-age]

16. Information required for constructing RPs from age-structured models
Mortality: what is the rate of mortality, both M and F?
[i.e. how fast is biomass removed from the population, mortality rate (Z= M+F)-at-age] F M

17. Information required for constructing RPs from age-structured models
Maturity: What is the proportion of mature fish–at-age?

18. Information required for constructing RPs from age-structured models
SRR: how many new recruits will be produced at a range of adult stock sizes?
[i.e. how many new fish will contributed to the population at different levels of adult biomass]
SRR

19. How are reference points calculated?
Natural
mortality
Fmulti
Fishing
mortality
Further analyses
Impact,
Historical
Time-series
Growth
BMSY
SBMSY
MSY
Maturity
ogive
SRR

20. How are reference points calculated?
1. An age-specific vector of fishing mortality (F) is calculated for the entire model region (i.e. a series of F estimates for each age class)
This is really the F-at-age estimates from the model for a recent period of time.
Typically it is an average of F for each age class averaged over a useful time period for fishery purposes. In the WCPO, this is typically over the previous 3 years
[Can also omit the most recent year, as often the end of a time-series is very influential]
[This is often referred to as “current” or “recent” fishing mortality in SA reports].

21. How are reference points calculated?
2. A series of “Fmulti” are established.
Fmulti area series of multipliers (usually from 0 to 50 in steps of 0.1 ) that are used to generate a wide range of theoretical Fs, both lower (0 – 0.9) and higher (1.1 – 50) than the current level of F (which is Fmulti=1).
[Fmultis are scalars of fishing mortality (effort)]
e.g. F0.3 = 0.3 * Fcurrent
[The range of Fmulti used are usually enough to generate a dome-shaped yield curve – we’ll come to this later!]

22. How are reference points calculated?
3. The schedule of natural mortality at age is also required.
This is the M-at-age series either included in the model (fixed value(s)) or M-at-age estimated from the model.
This can also simply be a single fixed value for all age classes

23. How are reference points calculated?
4. The M-at-age series is added to each Fmulti-at-age series.
This gives the total mortality (Z) for each age class for each level of Fmulti.

24. How are reference points calculated?
4. The abundance at age per recruit function is estimated for each Fmulti-at-age series.
This is to provide a proportion surviving to each age for a cohort of fish, under each Fmulti-at-age series.
The abundance of fish in age class 1 is defined as 1 (all alive).
Then the mortality of all previous age classes are pooled to estimate the remaining proportion of fish within a cohort surviving to each age class, for each Fmulti series

25. How are reference points calculated?
4. The abundance at age per recruit function is estimated for each Fmulti-at-age series.
[Exponent of the Sum of total mortality of all previous age classes]

26. How are reference points calculated?
5. The biomass at age per recruit function is estimated for each Fmulti-at-age series.
This is simply taking the abundance at age per recruit function estimated for each Fmulti-at-age series in the previous step and multiplying it by the weight-at-age (i.e. incorporating growth)
This provides the mean biomass of each original recruit at age for each Fmulti series

27. How are reference points calculated?
6. The spawning biomass at age per recruit function is estimated for each Fmulti-at-age series.
taking the abundance at age per recruit function estimated for each Fmulti-at-age series in the previous step, and multiplying it by the weight-at-age (i.e. incorporating growth) and multiplying by the proportion mature- at-age (maturity ogive)
This provides the mean spawning biomass of each original recruit at age for each Fmulti series

28. How are reference points calculated?
7. The sum of the spawning biomass at age per recruit function, estimated for each Fmulti-at-age series, is applied to the SRR to estimate recruitment for each level of Fmulti.
Number of recruits =  - /(spawning biomass per recruit)
(at each level of Fmulti)
This provides an estimate of the number of recruits expected for the spawning biomass for the stock for each level of Fmulti

29. How are reference points calculated?
8. The equilibrium abundance at age is estimated by applying the number of recruits to the abundance at age per recruit calculated previously.
This applies the mortality schedule and moves the estimate number of recruits through each time step, incorporating the mortality schedule to give the total number of each age class at each level of Fmulti.

30. How are reference points calculated?
9. The equilibrium biomass at age is estimated by multiplying the equilibrium abundance at age by the weight at age.
This provides an estimate of biomass at age for each level of Fmulti.

31. How are reference points calculated?
10. The equilibrium catch (numbers) at age is estimated by applying the ratio of F to Z by the difference in abundance between age class a and a+1, for each level of Fmulti.
Catcha = (Fa/(Ma + Fa))* (Numbersa – Numbersa+1)
This formula takes into account the F at time and estimated number of fish that survive to the next age class

32. How are reference points calculated?
11. The equilibrium catch (weight) at age is estimated by multiplying the equilibrium catch-at-age by the weight-at-age.
This estimates the catch in weight at age at each level of Fmulti

33. How are reference points calculated?
12. The sum of the equilibrium catch (weight) at age is estimated for each Fmulti.
This estimates the YIELD at each level of Fmulti. This is plotted against Fmulti
“Dome-shaped”
yield curve

34. How are reference points calculated?
13. Estimates of Biomass and Spawning Biomass are plotted against Fmulti.

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

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

37. How are reference points calculated?
16. A range of ratios and time-series can be calculated from the data and fishery data.

38. How are reference points calculated?
These calculations take into account age-specific estimates of;
Mortality (F and Z)
Growth
Maturity ogive
the SRR to estimate recruitment at the resulting levels of spawning biomass
Thus, as Fmulti varies, yield also varies
[Think of Fmulti as levels of fishing effort relative to the ‘current’ level]

39. How are reference points calculated?
Recent research – Theoretical maximum sustainable yields (for YFT) that could be generated by harvesting the stock at individual age classes and the proportion of the total biomass of that age class that would be harvested to achieve the theoretical MSY. The current MSY (402,000 mt per year) is represented by the dashed horizontal line.

40. How are reference points calculated?
Recent research - Average age class of fish harvested by each fishery. The dashed vertical line represents the “critical age” (11 quarters); the critical age is the age of capture that generates the maximum yield from the stock.

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

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

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

44. WCPO example: Skipjack (SA WP-4, SC-1)
B/BMSY and F/FMSY are calculated over the entire time-series of fishery data, (Bs/BsMSY also)

45. How are reference points used?
Changes in RPs through time are due to;
Changes in gear use and subsequent changes in selectivities, fishing mortality, impacts on the growth of the stock (via the distribution of size at age of fish) and catches (e.g. compare LL to PS catches for BET and YFT).
Increasing catches through time and subsequent impacts on estimates of biomass due to the SRR

46. e.g. YFT in WCPO
Change in MSY due to changes in proportion of catches by method fisheries, due to differences in selectivity and therefore F

47. What can you do with RPs?
Impact analysis: how much has the stock been reduced from unfished (virgin) levels by fishing?
1- Bcurrent/Btime 0
~ 65% reduction since
fishing commenced
Most reductions since 1975

48. What can you do with RPs?
2. 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

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

50. What can you do with RPs?
4. Examine historical trends in significant reference points
F/FMSY

51. What can you do with RPs?
4. Examine historical trends in significant reference points

52. 5. Assess RPs against management objectives
What can you do with RPs?
5. Assess RPs against management objectives
Maintain or restore stocks at levels capable of producing MSY [Article 5(b)]:
Maintain B  BMSY
Eliminate overfishing and excess fishing capacity [Article 5(g)]:
Maintain F  FMSY
Assess the impacts of fishing on target and non-target stocks and associated species [Article 5(d)]
Assess B / B0

53. Impacts
Management
objectives

54. What reference points are used elsewhere?
Who
What
Notes UN
FMSY
Minimum standard
ISC
BMSY
F0.1
SSBmin
Suggested; none formally adopted although reported in some cases
IATTC
MSY
AMSY
SBRX%
FAMSY
None formally adopted although reported in some cases

55. Other considerations in regard to RPs
Trend to more conservative RPs
ISC: 30% to 40% SSB
ISC: Buffer reference points
Ecosystem considerations: ‘leave more biomass in the system’. BMSY reduced from B/2 to B/2.5 ?
RPs as limits, not targets.
Maintain F<FMSY, not aim for F = FMSY. This may provide some insurance if variables beyond fisheries change, affecting stock productivity and reducing estimated MSY (e.g. unfavourable oceanographic conditions)

56. Limit & Buffer RPs e.g. The NAFO Scientific Council Flimit = FMSY
Fbuffer as "a fishing mortality rate below Flimit that acts as a buffer to ensure that there is a high probability that Flimit is not reached
Flimit
Blimit
Bbuffer
Fbuffer
Yield 
Biomass 

57. RPs for different species?
The characteristics of some species may make some RPs more or less useful
Protected species
Maintaining MSY may be (socially) inappropriate.
Reduction and minimisation of catches may be a better objective
A more reasonable RP may be to maintain the catch of these species below a certain level
e.g. Maintain catch rates of seabirds < 0.05 birds per thousand hooks
[Seabird target bycatch level set by the Australian government for L fisheries within the EEZ]

58. RPs for different species?
Discard species
Reduction and minimisation
RP – may be to stay below a certain level of discards per time period
(e.g. less than X kg per set?)
This RP is likely to be more about social acceptability than truly about stock status for discard species

59. Summary RPs are a way of summarising the outputs of a stock assessment
They allow;
the status of a stock to be assessed
The impacts of fishing on a stock to be estimated
The performance of the stock against management objectives to be assessed
RPs vary through time due to changes in fisheries, catches and the incorporation of new information
RPs are not management tools, but provide scientific advice to management to develop harvest strategies