1

About a new model of fish size spectra, and fishing

impacts

Eric Benoît, Université de La Rochelle

Marie-Joëlle Rochet, IFREMER NantesFRANCE

2

Pope and Knights, 1982

3

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

log(size)

log(

num

bers

)

Qualitative prediction: fishing changes the slope of size spectra

4

• Why should size spectra be linear?– needs allometric processes =w

• How should fishing impact linear size spectra?

Continuous time-dependent models

Log(w)

5

Allometric losses and generalised growth

Platt and Denmann, 1978

B iom ass flux

B iom ass in thespectral band w

w

biom

ass

u(w

)

size w

7

Predation, growth and mortality

Silvert and Platt (1980), Beyer (1989)

w

biom

ass

()

uw

size ww / q q w

8

Predation, growth and mortality

Distributed prey size

w

biom

ass

()

uw

size ww q/ qw

9

The equations

2

00

0

,,,

,,,

txuedqtxutqxuqeAe

dqtxutqxuqeKAex

txt

u

xqx

qx

u

x

gu

t

u

Balance

x

qx dqtqxuqeAetx ,, Mortality

0

,, dqtqyuqeKAetyg qy Growth

x=ln(w)

10

Linear spectrum

• There is a unique real such thatis a solution of the model (linear spectrum)

• is not sensitive to the parameters’ values and is consistent with observed values

xeu 0

02 01

AdqqedqqeK qq

11

Simulating size spectra

• Plankton input• Baseline « reasonable

parameters »

Log(w)

u

12

How do perturbations affect the size spectrum?

• Time step = 2 days• 3 years simulations

• Oscillatory initial condition

• Oscillatory plankton input

• Stabilizing processes: fixing large predators / biodiversity / non-predation mortality

a

b

13

0

1

2

3

4

5

0 2 4 6 8 10

w (kg)

F

a high fishingmortality

How does fishing impact the size spectrum?

14

How does fishing affect the size spectrum?

f

0

0.2

0.4

0.6

0.8

0 2 4 6 8 10

w (kg)

F

•realistic fishing mortality

•time step = 3 days•10 years simulation•years 5-10 shown

15

The impact of fishing on size spectra

• If biomass flux driven by size-dependent predation:

• Fishing decreases linearity• Slope

– has less meaning– cannot be well estimated– is not a good indicator.