1. Revisiting Stock-Recruitment Relationships Rainer Froese 24.02.09 Mini-workshop on Fisheries: Ecology, Economics and Policy CAU, Kiel, Germany

2. Overview A review of S-R models and their properties Estimating S decline Estimating unfished biomass S 0 and S msy Estimating annual reproductive rate α r Estimating r max Estimating MSY and F msy Estimating time to reach S msy MSY and F msy from ICES data Some results

3. Typical S-R Data (N) (tonnes)

4. Skewed roughly log-normal Distribution of R

5. Distribution of S skewed roughly log-normal

6. The Hump (Ricker, 1954) Assumptions: a) negative S-R relationship at high S b) highest recruitment at intermediate S where A = ln R max

7. Assumption: Positive S-R relationship at high S The Asymptote (Beverton & Holt 1957) where A = ln R max

8. The Hockey-Stick (Barrowman & Myers 2000) Assumptions: a)Constant R/S at low S b)Constant R at high S

9. The Smooth Hockey-Stick (Froese 2008) Assumptions: a)Practically constant R at high S b)Gradually increasing R/S at lower S where A = ln R max

10. Parameters and accounted variance not significantly different ModelαlowupR max lowupr2r2 B&H3.672.604.7324.917.336.00.834 Froese3.402.644.1517.413.522.60.843 Ricker3.222.643.8119.816.523.90.846 Example Striped bass Morone saxatilis Extrapolation VERY different

11. Bold line is Smooth Hockey-Stick with n = 414, α = 4.5, Rmax = 0.85 Dotted line the Hump with n = 414, α = 3.1, Rmax = 1.4. Data were normalized by dividing both R and S by R max for the respective stock. Example: 12 stocks of Atlantic cod Gadus morhua

12. Conclusion of detailed comparison (Froese et al. in prep.) With regard to resilience of stocks to overfishing (α) and the carrying capacity of the environment for recruits (R max ) The Asymptote tends to overestimate both α and R max The Hump gives conservative estimates of α but tends to overestimate R max The Piece-wise Hockey-Stick gives the most conservative estimates of α and R max The Smooth Hockey-Stick tends towards intermediate estimates of α and conservative estimates of R max.

13. When does R decline? For the hockey-sticks:

14. Example: North-east Arctic Cod S lim S pa S max

15. What is the number of recruits surviving to maturity? The mean maximum number of recruits surviving to maturity (R m ) can be obtained from R max and the age- specific mortality rates of juveniles (M t ) where t r is the mean age at recruitment and t m is the mean age at first maturity

16. What is the unexploited spawner biomass S 0 ? At S 0, recruitment replaces deaths. If the mean mortality rate (M) after mean age at maturity (t m ) is known, then the total number of individuals (SN 0 ) can be obtained by summing up annual survival Multiplying SN 0 with mean body weight W mean gives S 0 Where P t is the proportion of mature individuals at age t and M c is the age-specific mortality rate

17. Example: North-east Arctic Cod S msy

18. What is the maximum number of replacement spawners per spawner? 1. For the hockey-sticks, a simple relationship between maximum recruitment and spawner biomass is given by 2. Dividing S decline by mean body weight gives the number of respective (fished) spawners SN decline 3. The maximum number of replacement spawners at low spawner densities (α r ) is then obtained as

19. Multiple spawners Standardized replacement spawner abundance over spawner abundance for 56 stocks of 25 iteroparous species. The curves are smoothed hockey sticks with Rmax = 1 and α as indicated. Median α = 2.1 (1.7 – 2.8).

20. One-time spawners Median α = 4.2 (3.6 – 5.2)

21. What is the intrinsic rate of population increase r max ? In semelparous species (one-time spawners ) In iteroparous species (multiple spawners) (Myers & Mertz 1998)

22. Estimating MSY and F msy

23. Time to reach S msy where S cur is the current spawner biomass and F cur is the current fishing mortality

24. MSY from ICES data ICES gives the maximum yield per recruit (Y/R) max and maximum recruitment R max can be obtained as geometric mean of recruitment at stock sizes beyond S pa. Then MSY = R max (Y/R) max

25. MSY r max vs MSY (Y/R) max

26. r max and F msy from ICES data ICES provides a fishing mortality F pa that stabilizes the stock at a low size S pa F pa must then be smaller than but close to r max F pa thus is a conservative estimate of r max

27. r max vs F pa

28. Some Results For 53 ICES stocks with available data 47 stock sizes are below S msy These will need 0.7 – 22 years to reach S msy if fishing is halted (median = 6.0 years) Current fishing mortality in these stocks is much larger than F msy Landings from these stocks could be 1 million tonnes higher (+16%) at MSY

29. Relevance of MSY MSY and the related Biomass are goals for overfished stocks and lower limits for healthy stocks This is prescribed in the Law of the Sea. The Johannesburg Declaration of 2002 set the deadline of 2015 to reach this objective. The EC instead aims to reach Fmsy

30. Thank You