Biodiversity of Fishes Stock-Recruitment Relationships Rainer Froese, 17.01.2013

Typical S-R Data Recruits (N) Spawning stock biomass (tonnes)

Distribution of R (recruits) roughly log-normal Skewed

Distribution of S (spawners) skewed roughly log-normal

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

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

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

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

Example Striped bass Morone saxatilis Model α low up Rmax 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 3.81 19.8 16.5 23.9 0.846 Parameters and accounted variance not significantly different Extrapolation VERY different

Example: 12 stocks of Atlantic cod Gadus morhua 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 Rmax for the respective stock.

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

When does R decline? For the hockey-sticks:

Example: North-east Arctic Cod Slim Spa Smax Froese & Proelss 2010)

What is the number of recruits surviving to maturity? The mean maximum number of recruits surviving to maturity (Rm) can be obtained from Rmax and the age- specific mortality rates of juveniles (Mt) where tr is the mean age at recruitment and tm is the mean age at first maturity Froese & Proelss 2010)

What is the unexploited spawner biomass S0? At S0, recruitment replaces deaths. If the mean mortality rate (M) after mean age at maturity (tm) is known, then the total number of individuals (SN0) can be obtained by summing up annual survival Multiplying SN0 with mean body weight Wmean gives S0 Where Pt is the proportion of mature individuals at age t and Mc is the age-specific mortality rate Froese & Proelss 2010)

Example: North-east Arctic Cod Smsy

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 Sdecline by mean body weight gives the number of respective (fished) spawners SNdecline 3. The maximum number of replacement spawners at low spawner densities (αr) is then obtained as

Multiple spawners α > 7 leads to dangerous fluctuations α ~ 1 would be expected for sharks 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). Froese & Proelss 2010)

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

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

Estimating MSY and Fmsy

Time to reach Smsy where Scur is the current spawner biomass and Fcur is the current fishing mortality Froese & Proelss 2010)

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

MSY rmax vs MSY (Y/R)max Data from Froese & Proelss 2010)

Exercises Go to www.ices.dk and select one of these stocks: Western Baltic cod (cod-2224) Baltic sprat (spr-2232) Western Baltic herring (her-3a22) Find stock-recruitment plot Discuss which S-R curve would fit the data Where woud S-decline fall? If S-decline is 0.5 S-msy, what is S-msy?