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Inherent Uncertainties in Nearshore
Fisheries: The Biocomplexity of
Flow, Fish and Fishing
Dave Siegel1, Satoshi Mitarai1, Crow White1, Heather Berkley1, Chris Costello1,
Steve Gaines1, Ray Hilborn2, Bruce Kendall1, Steve Polasky3, Bob Warner1 &
Kraig Winters4 1 = [UCSB], 2 = [UW], 3 = [UMn] & 4 = [SIO/UCSD]
Flow, Fish & Fishing (F3) Biocomplexity
Flow, Fish & Fishing
• Human-natural system biocomplexity projectOceanography, population dynamics, marine ecology, fishery management, fisherman behavior & economics all wrapped up together
• Focus on California nearshore fisheries & role of uncertainty in management [but in a general way]
• Today – environmental uncertainties & their role on the stocks & harvest of a long-lived fish
Stock / Harvest Modeling
Next generation stocks = survivors - harvest + new recruits
SURVIVORS are surviving adults from previous time
HARVEST are those extracted from the fishery
NEW RECRUITS are a function of fecundity of the survivors, larval dispersal & mortality, settlement & recruitment to adult stages
Model System• Long lived, sessile, harvested fish
– M = 0.05 y-1, density dependence parameterized using Beverton-Holt on larval settling densities
• Larval dispersal scales (Gaussian kernel)
– PLD = 60 d, Dd = 150 km & Tspawn = 60 d
• Virgin carrying capacity set to 100 units
– Fixes fecundity
• 1-D coastline domain
– 2000 km long, x = 5 km & absorbing BC
Harvesting
• Total allowable catch (TAC) = f(recruitment)
TAC = 20% of the measured recruitment
Enables TAC to be set dynamically
• Spatial harvest allocation = f(adult density)
Fishermen fish where there are the highest fish densities & harvest up to the set TAC
So-called “ideal free distribution”
Base Case
Diffusive larval kernel, no sources of uncertainty
Adults (~60)
Recruitment (~4)
Settlement (~6)
Harvest (~0.9)
Flow
Fish
Settlement
HabitatRecruitment
Harvest
RegulationFisherm
en
Market INFO
Climate
Variability in
Fecundity CV = 50%
Climate Case
Adults
Recruitment
Settlement
Harvest
Diffusive larval kernel - fecundity variability (CV = 50%)
0 10 20 30 40 50 60 70 80 90 10040
60
80regional means - diffusive kernel
Adu
lts
0 10 20 30 40 50 60 70 80 90 1000
5
10
Rec
ruitm
ent
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
Har
vest
0 10 20 30 40 50 60 70 80 90 1000
0.5
Larv
al P
rodu
ctiv
ity
years
Regional means are same as the base case
Adults (~60)
Recruitment (~4)
Settlement (~6)
Harvest (~0.9)
Recruitment variability sets TAC
Flow
Fish
Settlement
HabitatRecruitment
Harvest
RegulationFisherm
en
Market INFO
Climate
Short time scales of
the process makes larval
transport stochastic
Larval Connectivity is a
StochasticDriven by flow scales, short spawning durations & the low probability of survival
Model stochastically which matches Gaussian kernel when # of settlement events is large
Siegel et al. [in review]
Mitarai et al. [in prep.]
Destination Location (km)
Sou
rce
Loca
tion
(km
)
Self s
ettle
men
t
Patchy Settlement Case
Adults
Recruitment
Settlement
Harvest
Patchy larval kernel - PLD = 60 d, Dd = 150 km & Tspawn = 60 d
0 10 20 30 40 50 60 70 80 90 10030
40
50regional means - patchy dispersal
Adu
lts
0 10 20 30 40 50 60 70 80 90 1001.5
2
2.5
Rec
ruitm
ent
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
Har
vest
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
Larv
al P
rodu
ctiv
ity
years
Adult densities are lower, why?
Climate Case Patchy Case
• Settling densities are 2x the base case due to the spatial focusing of successful settlement events
• Larval density dependence on post-settlement recruitment rates reduces overall adult populations
Role of Density Dependence
Flow
Fish
Settlement
HabitatRecruitment
Harvest
RegulationFisherm
en
Market INFO
Climate
Sample recruitment at only 5% of the sites to set the
TAC
Uncertainty Case
Adults
Recruitment
Settlement
Harvest
Patchy larval kernel, varying fecundity & assessment area = 5%
0 10 20 30 40 50 60 70 80 90 10020
40
60regional means - patchy dispersal
Adu
lts
0 10 20 30 40 50 60 70 80 90 1000
5
Rec
ruitm
ent
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
Har
vest
0 10 20 30 40 50 60 70 80 90 1000
0.5
Larv
al P
rodu
ctiv
ity
years
• Regional scale harvest & recruitment are weakly correlated• Times when fishery is closed when TAC = 0 • Increases risk to sustainability of the stock & fishing profits
Uncertainty Case
• Stock-recruitments do not exists for these systems • No relationship between total harvest and recruitment• Shows danger of setting TAC based on little data (5% sites)
Stock-Recruitment & Harvest- RecruitmentRelationships for Uncertainty Case
?
Conclusions to Date
•Created a caricature of a CA nearshore fishery
Climate forcing creates temporal variations though its effects are linear (time average = base case)
Flow-induced stochastic settlement creates spatial-temporal variability to stocks, recruitment & harvest
Larvae/larvae density dependence mitigates extreme settlement event densities
• Information is critical
Poor information leads to overfishing & profit losses
Thank You!!
Berkley et al. Spatiotemporal scales of stocks & recruitment – Poster Today
OS36K-12
Mitarai et al. Role of larval behavior on dispersal scales – Talk Tomorrow OS43I-01
1pm HCC318
www.icess.ucsb.edu/~satoshi/f3Photo credit: Steve Churchill
Mathematically...
t 1 t t t t t ti i i j ji i
j
A (1 M)(A H ) Y F K P L
t t
i i
ti
ti
ti
tj
[#/km]
[#/km]
[#/year]
( A H )
[spawned larvae/adult]
[settled larvae/spawner]
A Adult densityat sitei
H Harvest Yield
Y Escapedadult density
M Natural mortality
F Fecundityat site j
P Larval mortality
L
ti
tji
[adult/settler]
[(settler/km)/total settled larvae]
Post-settlementrecruitment
K Dispersion kernel
• Determine # of settlement packets
N = (T/) (L/) f
NUMBER OF SETTLEMENT PACKETS
T: Larval release duration : Lagrangian correlation time L: domain size : Rossby radius f: survivability of packet
Siegel et al. [in rev.], Mitarai et al. [in prep.]
DIFFUSION LIMIT
Packet model
1 season 6 seasons 12 seasons 120 seasons
1 season 6 seasons 12 seasons Diffusion
Flow simulation Diffusion model