1. New Methods for Estimating the Status of Data-poor Fisheries
Rainer Froese, GEOMAR
Aquatic Ecosystems Research Laboratory
UBC, Vancouver, 09 March 2018

2. Too many stocks, too few data
New legislation in Canada, US and Europe requires management of all exploited stocks
In Europe, of about 400 exploited stocks, only 100 have sufficient data for traditional age-structured stock assessment
New and old simple approches are needed to get reasonable assessments with less time and data
New data-light but computation-heavy methods come to the rescue:
BSM: Estimates status and exploitation from catch and abundance
CMSY: Estimates status and exploitation from catch and resilience
LBB: Estimates status from length frequency

3. Principles of Surplus Production Modelling

4. Thomas Robert Malthus (1766 – 1834, English Economist)

5. World Population Growth
"The power of population is indefinitely greater than the power in the earth to produce subsistence for man"

6. Pierre François Verhulst (1804 – 1849, Belgian Mathematician)
(1844) k k k k k

7. Logistic Curve Propertiesk k
BioDivPopGrowthMSY.xls

8. Milner Baily Schaefer (1912 – 1970, US Fisheries Scientist)

9. The Schaefer Model: Surplus Production
BioDivPopGrowthMSY.xls

10. The Schaefer Model: CPUE
Catch per unit of effort (CPUE in e.g. kg/h)
BioDivPopGrowthMSY.xls

11. The BSM Method in a Nutshell
Given a time series of Catch and CPUE, the parameters r = rmax and k are estimated from
𝐵 𝑡+1 = 𝐵 𝑡 +𝑟 𝐵 𝑡 1− 𝐵 𝑡 𝑘 − 𝐶 𝑡
where Ct is catch in year t, B = CPUE / q, q is the catchability coefficient, and the other parameters are as defined above
Using a Bayesian approach, the r-k combination that minimizes the difference between the observed biomass and the one predicted by the equation is chosen as best estimate

12. Advantages of BSM
Can utilize short and interrupted time series of abundance
Can estimate catchability q
Gives the desired fisheries reference points MSY, Bmsy and Fmsy
Gives the ecological reference points rmax and k
Gives stock size as B and status as B/Bmsy and B/B0
Gives exploitation as F and F/Fmsy
Gives time series of biomass and exploitation

13. Sole (Solea solea)
in the Irish Sea:
Graphical results of
BSM analysis for use
by management

14. The CMSY Method in a Nutshell
CMSY estimates biomass from catch and resilience
It needs priors for resilience

15. Life History Correlates of Resilience rmax
r = 2 Fmsy (Schaefer 1954) r ̴ 2 M because M ̴ Fmsy (Gulland 1971) r ̴ 3 K because K ̴ 2/3 M (Jensen 1996) r ̴ 9/tmax because tmax ̴ 3/K (Taylor 1958) r ̴ 3.3/tgen because tgen ̴ 1/K (Roff 1984) r = f(Fecundity < 1000) (Musick 1999) These relations were used to predict r in FishBase for currently close to 1000 species. Qualitative resilience (Very low, Low, Medium, High) and their r ranges are available for all species.

16. The CMSY Method in a Nutshell
If abundance is unknown, a prior range for r is derived from life history traits, a prior range for k is derived from maximum catch, and prior ranges for Bt/k (beginning and end of catch time series) are derived from expert knowledge. 𝐵 𝑡+1 = 𝐵 𝑡 +𝑟 𝐵 𝑡 1− 𝐵 𝑡 𝑘 − 𝐶 𝑡 All r-k combinations that are compatible with the life history traits (r, M, K), the catches (Ct) and the expert knowledge (Bt/k) are identified by a Monte-Carlo approach. An r-k combination representative of high r values is chosen as best estimate.

17. Flathead grey mullet
(Mugil cephalus)
in the Southern Gulf
of Mexico:
Graphic Results of
CMSY analysis for
use by working group.

21. Proof of Concept: Application to 400 Stocks
Froese, R., Garilao, C., Winker, H.,
Coro, G., Demirel, N., Tsikliras, A.,
Dimarchopoulou, D., Scarcella, G.,
Sampang-Reyes, A
Exploitation and status of European
stocks. World Wide Web electronic
publication,

22. Nice Fit
Sole (Solea solea)
in the North Sea

23. Special Case: Regime Shift
Peruvian anchovy (Engraulis ringens) in Central Peru.
Anchovy-dominated , Sardine-dominated , Anchovy-dominated

24. Special Cases: Monotone Increase
Indian mackerel
(Rastrelliger kanagurta)
in Southern Vietnam

25. Special cases: Monotone decrease
Muksun (Coregonus
muksun) in the Kara Sea

26. Length-based Bayesian Biomass (LBB) (submitted)

27. Conceptual Framework
Conceptual framework for the analysis of length frequency data from the commercial fishery, here modeled with life history traits of western Baltic cod (Gadus morhua). The green curve shows the decline in cohort numbers without fishing. The blue curve shows the decline with fishing, the yellow curve shows the fish vulnerable to the gear, and the red curve is the catch in numbers resulting from a certain fishing effort. The vertical dashed lines indicate the length (Lx) where fish become vulnerable to the gear, the length (Lc) where 50% of the individuals are retained by the gear, the length (Lopt) where the unexploited cohort would have maximum biomass, and the asymptotic length (Linf)

28. The Visible Length-Frequencies
Schematic representation of the length-frequency distribution in commercial catch, with indication of the sections that are subject to no gear selection (dotted red curve), partial gear selection (solid red curve), and full gear selection (dashed red curve). Note the difference between the length at half of the peak of the catch curve and the slightly larger true Lc used in the model [Sim_19.xlsx].

29. Decline in Numbers at Full Selection
The decline in numbers over fully-selected length-classes
is only a function of the total mortality rate (Z)
relative to the growth rate in length (K)

30. The LBB Master-Equation
By dividing both sides of the Equation by their respective sums, F cancels out.
Using a Bayesian approach with priors derived from previous or aggregated LFs,
Linf, Lc, M/K, F/K and F/M= (F/K)/(M/K) are estimated simultaneously.

31. Mortality Estimates Are Not Recent
Mortality estimates of LBB are of limited use for management, because they are not recent but the average of the exploited length (Lx to Linf) and corresponding age range.

32. Standard Yield per Recruit Equation
Average growth and mortality parameters are, however,
the required input for yield per recruit equations.
A combination of these standard equations then gives
the current biomass relative to unexploited biomass (B/B0)

33. Optimum Length at First Capture Lc_opt
The length where cohort biomass is maximum in an unexloited population is given by Holt (1958) as:
This is also the length where cohort fecundity is maximum and thus this is the natural average length of spawners.
Froese et al. (2016) present an equation for the length at first capture that will maximize catch and biomass for a given F and will result in Lopt being the mean length in the exploited population:

34. Proxy for Bmsy
A proxy for the biomass that can produce the maximum sustainable yield can be calculated from standard equations by assuming that Lc = Lopt and F/M = 1.0
The relative biomass and the length at first capture estimated by LBB can then be used directly for management of data-poor stocks:
If relative stock size B/B0 is smaller than Bmsy/B0, reduce catches
If length at first capture Lc is smaller than Lc_opt, start fishing at larger sizes.

35. Performance of LBB
LBB results for relative biomass or stock status have been validated against simulations and against 34 real stocks
LBB reproduced the “true“ parameter values of the simulations
LBB gave stock status results similar to full stock assessments

36. Example for Haddock in the North Sea
An example of graphical output produced by LBB, here for North Sea haddock, for the years 2010 to The upper left panel shows the accumulated LF data used to estimate priors Lc, Linf. and Z/K. The upper middle and right panels show the LF data for the first and last year in the time series. The red curve shows the fit of Equation 8, which provides estimates Z/K, M/K, F/K, Lc, and Linf. From Linf and M/K, Lopt is calculated and shown as reference. The lower left panel shows Lmean (bold black curve) relative to Lopt, and Lc (black curve) with approximate 95% confidence limits (dotted curves) relative to Lc_opt.. The lower middle panel shows relative fishing pressure F/M (black curve), with approximate 95% confidence limits (dotted curves), with indication of the reference level where F = M (green horizontal line). The lower right panel shows relative biomass B/B0 (black curve) with approximate 95% confidence limits (dotted black curves) with indication of a proxy for Bmsy (green dashed line) and a proxy for Bpa (red dotted line).

37. Conclusion
BSM gives good estimates of stock status and exploitation based on catch and abundance data
CMSY gives reasonable estimates of stock status and exploitation based on catch and resilience in data-poor situations
LBB gives preliminary estimates of stock status based on length frequency data from the fishery
LBB results provide objective B/B0 priors for CMSY

38. Rainer Froese rfroese@geomar.de www.fishbase.de/rfroese/
Thank You
Rainer Froese