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Fisheries Reference Points(Single- and multi-species)

Fish 458, Lecture 23

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(Fisheries) Reference Points

Quantities that provide guidelines for targets and limits on harvesting

(are usually fishing mortality rates or biomasses).

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Traditional Reference Points

(BMSY / MSY)

BMSY – the biomass at which Maximum Sustainable Yield, MSY, is achieved.

0

5

10

15

20

25

30

0 20 40 60 80 100

Biomass

Yie

ld

BMSY

MSY

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Traditional Reference Points

(BMSY / MSY)

Calculating MSY and BMSY given a biomass dynamics model:

MSY is defined as:

1 ( )t t t tB B g B C

( ) ( )0;MSY MSYdC B dg B

dt dt

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Yield-Per-Recruit Reference Points

0

0.5

1

1.5

2

0 0.2 0.4 0.6

Exploitation rate

Yie

ld-p

er-

recr

uit

Fmax

F0.1 is defined by:

F0.1

0.1( ) ( 0)0.1

d YPR F d YPR F

d F d F

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Spawner Biomass-per-Recruit Reference Points

0

20

40

60

80

100

120

0 0.2 0.4 0.6

Explotation Rate

Spa

wne

r-bi

omas

s-pe

r-re

crui

t Scaled to 100% for F=0

F40%

Typical choices include: 35%, 40%

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Stock-Recruitment Relationship Reference Points

0

0.20.4

0.60.8

1

1.21.4

1.6

0 0.25 0.5 0.75 1

Spawner biomass

Rec

ruitm

ent

Fhigh

Flow

Fmed

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Combining Yield-per-Recruit and Stock-

Recruitment-I Spawner biomass, S, = Spawner

biomass per recruit multiplied by recruitment, R:

Substitute into a Beverton-Holt stock recruitment relationship:

*S S R S

S RR

S R

or

SR

S

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Combining Yield-per-Recruit and Stock-

Recruitment-II To calculate a yield vs. spawner

biomass plot:1. Set the exploitation rate to 02. Calculate the yield-per-recruit and the spawner

biomass-per-recruit as a function of exploitation rate3. Compute recruitment given spawner biomass-per-

recruit and the stock-recruitment relationship.4. Multiply yield-per-recruit and spawner biomass-per-

recruit by recruitment to calculate yield and spawner biomass.

5. Increase the exploitation rate and repeat steps 2-4.

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Combining Yield-per-Recruit and Stock-

Recruitment-III

BMSY

MSYF0.

1

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Combining Yield-per-Recruit and Stock-

Recruitment-IV

0

0.3

0.6

0.9

1.2

1.5

0 25 50 75 100

Spawner Biomass

Yie

ld

Steepness = 0.5 / 0.8 / 0.95

How sensitive is the yield curve to steepness

BMSY

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Other Biomass Reference Levels

20% B0 – when selecting policies consider the probability of dropping below 20% B0 (a “level one does not go below”).

An example: Accept no policy that has a greater than 10% probability of dropping below 20% B0 over a 20-year projection period.

Problems with approaches based on a fixed proportion of B0: arbitrary, too cautious for some species, not cautious enough for other species.

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Multi-species Reference Points

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Multispecies Yield-Per-Recruit-I

Multispecies yield-per-recruit extends single-species yield-per-recruit by linking the fishing mortality rates for each species: s s s

a aF q S E

fishing mortality on fish of species and age ,

vulnerability on fish of species and age ,

catchability coefficient for species , and

fishing effort.

sa

sa

s

F s a

S s a

q s

E

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Multispecies Yield-Per-Recruit-II

1

1

( )1, , 1

( ) ( ), , 1

( ),

1 if 0

if 1

if

(1 )

s sa

s s s sx x

s sa

M Fs st a t a

M F M Fs st x t x

sM Fs t sa

t a t as sa a

a

N N e a x

N e N e a x

FC w N e

M F

Notes: 1. The species are independent, except through the

impact of fishing.2. We have adopted a continuous formulation here

rather a discrete formulation – why?

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An Example of Multispecies Yield-per-

Recruit Pink ling

Slow growing (=0.14), long lived (M=0.15yr-1), domed shaped vulnerability pattern.

Spotted warehou Fast growing (=0.3), medium lived

(M=0.15yr-1), asymptotic vulnerability ogive.

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The yield-per-Recruit Curve

0

25

50

75

100

0.00 0.50 1.00 1.50

F (ling)

Yie

ld-p

er-

recr

uit

Ling

Spotted warehou

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The Spawner Biomass-per-Recruit Curve

0

25

50

75

100

0.00 0.50 1.00 1.50

F (ling)

Sp

aw

ne

r B

iom

ass

-pe

r-re

cru

it

Ling

Spotted warehou

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Multispecies Yield-per-recruit(Advantages and Disadvantages)

Disadvantages: It is often very difficult to estimate the

catchability coefficients. A value-per-recruit analysis may be more

appropriate but that requires specifying the relative size of the recruitment of each species.

Discarding is ignored – this is, however, often an important aspect of technological interactions.

No account is taken of the impact of reduction of spawner biomass on recruitment.

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Multispecies Yield-per-recruit(Advantages and Disadvantages)

Advantages: It allow us to predict the overall

consequences of changes in fishing effort in terms of yield- and spawner biomass-per-recruit.

The approach can be extended to handle discarding and the stock-recruitment relationship.

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Readings Clark (1991). Hilborn and Walters (1992);

Chapter 14. Pikitch (1987). Quinn and Deriso (1999); Chapter

11. Sissenwine and Shepherd (1987)