#### Transcript Revisiting Stock-Recruitment Relationships

Biodiversity of Fishes Stock-Recruitment Relationships Rainer Froese, 15.01.2015 Typical S-R Data Recruits (N) Spawning stock biomass (tonnes) Distribution of R (recruits) roughly log-normal Skewed 2500 2500 1500 Frequency (n) Frequency (n) Frequency (n) 2000 2000 1000 500 1500 1500 1000 1000 500 500 0 0 1 2 3 Rnorm 4 5 00 -5.00 -5 -2.50 -3 0.00 0 LNSnorm Rnorm 2.50 3 5.00 5 Distribution of S (spawners) roughly log-normal 2500 2500 2000 2000 Frequency (n) Frequency (n) skewed 1500 1000 500 1500 1000 500 0 0 1 3 Snorm 4 5 0 -5.00 -2.50 0.00 LNSnorm 2.50 5.00 The Hump (Ricker, 1954) R S e S R Se Rmax 2.178 S 2.178 Rmax ln R ln ln S where A = ln Rmax Assumptions: a) negative S-R relationship at high S b) highest recruitment at intermediate S S 2.178 e A The Asymptote (Beverton & Holt 1957) R S 1 S R S S 1 Rmax ln R ln ln S ln(1 where A = ln Rmax Assumption: Positive S-R relationship at high S Rmax S eA ) The Hockey-Stick (Barrowman & Myers 2000) Recruits (N) R2 Rmax R1 S Spawners (N) Assumptions: a) Constant R/S at low S b) Constant R at high S The Smooth Hockey-Stick (Froese 2008) R Rmax (1 e Rmax ln R A ln(1 e where A = ln Rmax Assumptions: a) Practically constant R at high S b) Gradually increasing R/S at lower S S ) e A S ) Example Striped bass Morone saxatilis S-R Model comparison for Morone saxatilis (striped bass) n=17 1982 --> 1998 [Stock: STRIPEDBASSUSA2] 25 20 15 Froese Ricker R B&H 10 observed 5 0 0 10 20 30 40 50 60 S Model α low up Rmax low up r2 B&H 3.67 2.60 4.73 24.9 17.3 36.0 0.834 Froese 3.40 2.64 4.15 17.4 13.5 22.6 0.843 Ricker 3.22 2.64 3.81 19.8 16.5 23.9 0.846 Parameters and accounted variance not significantly different Extrapolation VERY different Use of Hockey-Stick in Management Conceptual drawing of the hockey stick relationship between spawning stock size and recruitment. SSBlim marks the border below which recruitment declines, SSBpa marks a precautionary distance to SSBlim, and 2 * SSBpa can be used as a proxy for SSBmsy, the stock size that can produce the maximum sustainable catch [ContHS.xlsx]. (Froese et al. 2014.) How to Fit a Hockey-Stick Fitting a rule-based hockey stick: (1) calculate geometric mean of recruits in upper half of biomass range: gmean R = exp(average(log(R)) for R at SSB > 383 = 373 How to Fit a Hockey-Stick Blim Fitting a rule-based hockey stick: (2) Extend shaft to lowest biomass with same or higher recruitment. This gives Blim. How to Fit a Hockey-Stick Blim Bpa Fitting a rule-based hockey stick: (3) Multiply Blim = 184 with 1.4 to get a precautionary Bpa = 258 . How to Fit a Hockey-Stick Blim Bpa Fitting a rule-based hockey stick: (4) Connect Blim to origin, check fit with low recruitment. How to Fit a Hockey-Stick Blim Bpa Fitting a rule-based hockey stick: (5) Use 2 * Bpa = 516 as proxy for Bmsy. Bmsy 2014 Abstract The appropriateness of three official fisheries management reference points used in the north-east Atlantic was investigated: (i) the smallest stock size that is still within safe biological limits (SSBpa), (ii) the maximum sustainable rate of exploitation (Fmsy) and (iii) the age at first capture. As for (i), in 45% of the examined stocks, the official value for SSBpa was below the consensus estimates determined from three different methods. With respect to (ii), the official estimates of Fmsy exceeded natural mortality M in 76% of the stocks, although M is widely regarded as natural upper limit for Fmsy. And regarding (iii), the age at first capture was below the age at maturity in 74% of the stocks. No official estimates of the stock size (SSBmsy) that can produce the maximum sustainable yield (MSY) are available for the north-east Atlantic. An analysis of stocks from other areas confirmed that twice SSBpa provides a reasonable preliminary estimate. Comparing stock sizes in 2013 against this proxy showed that 88% were below the level that can produce 52%ofofthe thestocks stockswere wereoutside outsideofofsafe safebiological biologicallimits, limits,and and12% 12%were were MSY. Also, 52% severely depleted. depleted. Fishing mortality in 2013 exceeded natural mortality in 73% of severely the stocks, including those that were severely depleted. These results point to the urgent need to re-assess fisheries reference points in the north-east Atlantic and to implement the regulations of the new European Common Fisheries Policy regarding sustainable fishing pressure, healthy stock sizes and adult age/size at first capture. Exercises Go to www.ices.dk, Community, Advisory process, Latest advice Select a stock with a stock-recruitment graph, e.g.: Western Baltic cod (cod-2224) Western Baltic herring (her-3a22) North Sea cod (cod-347d) • Fit hockey-stick to stock-recruitment plot • Discuss Blim, Bpa and Bmsy compared to official estimates • What is the current status of the stock?