About a new model of fish size spectra, and fishing impacts
-
Upload
duncan-nguyen -
Category
Documents
-
view
33 -
download
0
description
Transcript of About a new model of fish size spectra, and fishing impacts
1
About a new model of fish size spectra, and fishing
impacts
Eric Benoît, Université de La Rochelle
Marie-Joëlle Rochet, IFREMER NantesFRANCE
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
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
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