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

Flow

Fish

Settlement

HabitatRecruitment

Harvest

RegulationFisherm

en

Market INFO

Climate

Flow

Fish

Settlement

HabitatRecruitment

Harvest

RegulationFisherm

en

Market INFO

Climate

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

ROMS simulations from Mitarai et al. JMS [2006]

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

MODEL PREDICTIONS

Summer Winter

Accounts for spatial structures

CONNECTIVITY MATRIXSummer Winter

Larval Transport & Fish Life Cycles