1. Biodiversity of Fishes Stock-Recruitment Relationships
Rainer Froese

2. Definitions
A stock is a population of aquatic animals (mostly fish) that is exploited (fished) by humans (fishers)
The stock size is referred to as biomass and is measured in tonnes
Reproductively active fish (spawners) constitute the spawning stock
Recruits are young fish that have survived and are about to join the spawning stock (measured in numbers, e.g. millions)

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

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

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

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

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

8. 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

9. What Determines Recruitment?
Eggs need to encounter right salinity, temperature, current, wind, and absence of predators
After absorption of the yolk sac, larvae need to find food within days or reach a “point of no return”
Juveniles grow up in small nursery areas with limited carrying-capacity (shelter & food)
As a result of mostly starvation and predation, the number of recruits that a population can produce in a given ecosystem is limited
Because of this limited recruitment, populations can not grow much larger than 4 times the population size needed to produce the minimum number of eggs needed for the maximum number of recruits

10. 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 Revisiting safe biological limits in fisheries)

11. 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

12. 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.

13. 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 .

14. How to Fit a Hockey-Stick
Blim
Bpa
Fitting a rule-based hockey stick: (4) Connect Blim to origin, check fit with low recruitment.

15. How to Fit a Hockey-Stick
Blim
Bpa
Bmsy
Fitting a rule-based hockey stick: (5) Use 2 * Bpa = 516 as proxy for Bmsy.

16. 52% of the stocks were outside of safe biological limits, and 12% were
2016
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
MSY. Also, 52% of the stocks were outside of safe biological limits, and 12% were
severely depleted. Fishing mortality in 2013 exceeded natural mortality in 73% of
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.
52% of the stocks were outside of safe biological limits, and 12% were
severely depleted.

17. Exercises
Go to Community, Advisory process, Latest advice, Advice 2014;
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 status of the stock?