Biodiversity of Fishes Stock-Recruitment Relationships

Rainer Froese, 15.01.2015

Typical S-R Data

(N)

(tonnes)

Spawning stock biomass

Recruits

0

500

1000

1500

0 1 2 3 4 5

Rnorm

Fre

quency

(n)

0

500

1000

1500

2000

2500

-5 -3 0 3 5

Rnorm

Fre

quency

(n)

0

500

1000

1500

2000

2500

-5.00 -2.50 0.00 2.50 5.00

LNSnorm

Fre

quency

(n)

Skewed roughly log-normal

Distribution of R (recruits)

0

500

1000

1500

2000

2500

-5.00 -2.50 0.00 2.50 5.00

LNSnorm

Fre

quency

(n)

0

500

1000

1500

2000

2500

0 1 3 4 5

Snorm

Fre

quency

(n)

Distribution of S (spawners)

skewed roughly log-normal

The Hump (Ricker, 1954)

S

eSR

max178.2 R

S

SeR

Ae

SSR

178.2lnlnln

178.2max

R

Assumptions: a) negative S-R relationship at high Sb) highest recruitment at intermediate S

where A = ln Rmax

Assumption:Positive S-R relationship at

high S

SS

R

1

maxR

max

1R

SS

R

)1ln(lnlnlnAe

SSR

The Asymptote (Beverton & Holt 1957)

where A = ln Rmax

Spawners (N)

Re

cru

its

(N

)

The Hockey-Stick (Barrowman & Myers 2000)

SR 1

max2 RR

Assumptions:a) Constant R/S at low Sb) Constant R at high S

The Smooth Hockey-Stick (Froese 2008)

)1ln(lnS

e AeAR

)1( maxmax

SReRR

Assumptions:a) Practically constant R at high Sb) Gradually increasing R/S at lower S

where A = ln Rmax

S-R Model comparison for Morone saxatilis (striped bass) n=17 1982 --> 1998[Stock: STRIPEDBASSUSA2]

0

5

10

15

20

25

0 10 20 30 40 50 60

S

R

Froese

Ricker

B&H

observed

Parameters and accounted variance not significantly different

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

Example Striped bass Morone saxatilis

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

Fitting a rule-based hockey stick: (2) Extend shaft to lowest biomass with same or higher recruitment.This gives Blim.

Blim

How to Fit a Hockey-Stick

Fitting a rule-based hockey stick: (3) Multiply B lim = 184 with 1.4 to get a precautionary Bpa = 258 .

Blim Bpa

How to Fit a Hockey-Stick

Fitting a rule-based hockey stick: (4) Connect B lim to origin, check fit with low recruitment.

Blim Bpa

How to Fit a Hockey-Stick

Fitting a rule-based hockey stick: (5) Use 2 * Bpa = 516 as proxy for Bmsy.

Blim Bpa Bmsy

AbstractThe appropriateness of three official fisheries management reference points used inthe north-east Atlantic was investigated: (i) the smallest stock size that is stillwithin 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 examinedstocks, the official value for SSBpa was below the consensus estimates determinedfrom three different methods. With respect to (ii), the official estimates of Fmsyexceeded natural mortality M in 76% of the stocks, although M is widely regardedas natural upper limit for Fmsy. And regarding (iii), the age at first capture wasbelow the age at maturity in 74% of the stocks. No official estimates of the stocksize (SSBmsy) that can produce the maximum sustainable yield (MSY) are availablefor the north-east Atlantic. An analysis of stocks from other areas confirmed thattwice SSBpa provides a reasonable preliminary estimate. Comparing stock sizes in2013 against this proxy showed that 88% were below the level that can produceMSY. Also, 52% of the stocks were outside of safe biological limits, and 12% wereseverely depleted. Fishing mortality in 2013 exceeded natural mortality in 73% ofthe stocks, including those that were severely depleted. These results point to theurgent need to re-assess fisheries reference points in the north-east Atlantic and toimplement the regulations of the new European Common Fisheries Policy regardingsustainable fishing pressure, healthy stock sizes and adult age/size at first capture.

2014

52% of the stocks were outside of safe biological limits, and 12% wereseverely depleted.

ExercisesGo 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?