Fishing in a stirred Fishing in a stirred ocean: sustainable ocean: sustainable

harvest can increase harvest can increase spatial variation in fish spatial variation in fish

populationspopulations

Heather BerkleyHeather Berkley

Bruce Kendall, David Siegel, Bruce Kendall, David Siegel, Christopher CostelloChristopher Costello

University of California, Santa University of California, Santa

BarbaraBarbara

Spatial Fisheries Spatial Fisheries ModelsModels

• Recently, spatially explicit Recently, spatially explicit fisheries models have gained fisheries models have gained popularitypopularity– Adding space can make more Adding space can make more

realisticrealistic– Necessary to model effects of MPA’s Necessary to model effects of MPA’s

• However, many of these models However, many of these models still emphasize spatial uniformitystill emphasize spatial uniformity

Uniformity AssumptionUniformity Assumption

• Intuition suggests that fishing may Intuition suggests that fishing may homogenize the fish density across spatial homogenize the fish density across spatial domain (by taking adults from where they are domain (by taking adults from where they are most abundant)most abundant)

• If this is true, assuming a uniform domain is If this is true, assuming a uniform domain is okok

• However, if harvesting does NOT homogenize However, if harvesting does NOT homogenize the population, this assumption may be the population, this assumption may be leaving out important information about the leaving out important information about the fishery and population dynamicsfishery and population dynamics

Our Fisheries ModelOur Fisheries Model

• Single species, nearshore Single species, nearshore fisheryfishery

• Linear coastlineLinear coastline

• Sessile adultsSessile adults

• Dispersal only in larval stageDispersal only in larval stage– RockfishRockfish– UrchinUrchin– AbaloneAbalone

all y

tx

ty,xy

ty

ty

tx

tx

tx

tx

1tx

R L K) FH(A

)HM (AHAA

# of adults at # of adults at xx in time in time t+1t+1

# of adults # of adults harvestedharvested

Natural mortality Natural mortality of un-harvested of un-harvested

adultsadults

FecundityFecundityLarval Larval survivalsurvivalLarval dispersalLarval dispersal

Fraction of Fraction of settlers settlers

that recruit that recruit at at xx

# of larvae that successfully # of larvae that successfully recruit to location recruit to location xx from from

everywhereeverywhere

An integro-difference model An integro-difference model describing coastal fish population describing coastal fish population

dynamics:dynamics:

all y

tx

ty,xy

ty

ty

tx

tx

tx

tx

1tx

R L K) FH(A

)HM (AHAA

# of adults at # of adults at xx in time in time t+1t+1

# of adults # of adults harvestedharvested

Natural mortality Natural mortality of un-harvested of un-harvested

adultsadults

FecundityFecundityLarval Larval survivalsurvivalLarval dispersalLarval dispersal

Fraction of Fraction of settlers settlers

that recruit that recruit at at xx

# of larvae that successfully # of larvae that successfully recruit to location recruit to location xx from from

everywhereeverywhere

An integro-difference model An integro-difference model describing coastal fish population describing coastal fish population

dynamics:dynamics:

ty,xK

How to model the How to model the dispersal kernel?dispersal kernel?

• Realistic ocean flows to disperse Realistic ocean flows to disperse the larvaethe larvae

• Didn’t use typical diffusion, which Didn’t use typical diffusion, which assumes:assumes:– Well-mixedWell-mixed– Independence of individualsIndependence of individuals

• Because… the ocean is turbulent: Because… the ocean is turbulent: – Stirred not mixedStirred not mixed– Individuals do not move Individuals do not move

independentlyindependently

Drifters: Measurable Drifters: Measurable Example of Larvae Example of Larvae

DispersingDispersing• Buoys float near Buoys float near

surfacesurface

• Tracked by Tracked by satellitessatellites

• Released at Released at multiple multiple sites/timessites/times

• Give good Give good indication of indication of surface flowsurface flow

http://www-ccs.ucsd.edu/research/sbcsmb/http://www-ccs.ucsd.edu/research/sbcsmb/drifters/drifters/

Drifters released off Drifters released off central California coastcentral California coast

http://www-ccs.ucsd.edu/research/sbcsmb/drifters/makeDepTable.cgi

Implications for Larval Implications for Larval DispersalDispersal

• Physical oceanographers say:Physical oceanographers say:– Flows at location Flows at location xx become decorrelated become decorrelated

•on a temporal scale of about 3 dayson a temporal scale of about 3 days•on a spatial scale of 10-50 kmon a spatial scale of 10-50 km

• So, larvae released in a region within a So, larvae released in a region within a few days tend to travel togetherfew days tend to travel together

• These groups of larvae settle together These groups of larvae settle together at a few locations (NOT evenly at a few locations (NOT evenly distributed along coast)distributed along coast)

• Connections among sites are Connections among sites are stochastic and intermittentstochastic and intermittent– Some sites get lots of recruits from Some sites get lots of recruits from

xx– Others get noneOthers get none

• This “spiky” recruitment better This “spiky” recruitment better fits empirical larval settlement fits empirical larval settlement datadata

• In this model we can compare In this model we can compare both the “spiky” and “smooth” both the “spiky” and “smooth” dispersal kernelsdispersal kernels

““Spiky” vs. “Smooth” Spiky” vs. “Smooth” RecruitmentRecruitment

4 Fishing Policies4 Fishing Policies

• Implemented 4 fishing policiesImplemented 4 fishing policies

• Each controlled by 1 parameter: Each controlled by 1 parameter: h = Harvest Fractionh = Harvest Fraction

• Definition of h differs between Definition of h differs between policiespolicies

• Constant EffortConstant Effort– Same fraction of adults is Same fraction of adults is

harvested (h) at all locationsharvested (h) at all locations

Fishing Policy #1Fishing Policy #1

• Constant EscapementConstant Escapement– Escapement level same for each Escapement level same for each

location: (1 – h) (virgin K) location: (1 – h) (virgin K)

Fishing Policy #2Fishing Policy #2

• Constant Total Allowable Constant Total Allowable CatchCatch– TAC set for the whole region: TAC set for the whole region:

(h) (virgin K) (size of (h) (virgin K) (size of domain)domain)

– Harvest is concentrated on Harvest is concentrated on locations with most fishlocations with most fish

Fishing Policy #3Fishing Policy #3

• Constant Local HarvestConstant Local Harvest– TAC set for the whole region, TAC set for the whole region,

divided equally between all divided equally between all locationslocations

Fishing Policy #4Fishing Policy #4

ParametersParameters

• Ran model for 50 yearsRan model for 50 years• Domain size: 2000 km broken Domain size: 2000 km broken

into 5km sectionsinto 5km sections• Absorbing BoundariesAbsorbing Boundaries• Post-Settlement Density Post-Settlement Density

Dependence (Ricker)Dependence (Ricker)• Calculated spatial varianceCalculated spatial variance• Graphs show means of 50 Graphs show means of 50

simulations at each harvest simulations at each harvest fraction (h)fraction (h)

Post-settlement Post-settlement Density DependenceDensity Dependence

• When adults are near carrying When adults are near carrying capacity, recruitment at a location capacity, recruitment at a location x x will be lowerwill be lower

• As harvest reduces adult density, As harvest reduces adult density, the effect of density dependence on the effect of density dependence on recruitment decreases and recruitment decreases and individual recruitment “spikes” individual recruitment “spikes” become largerbecome largerHarvest Adults Density Dependence Harvest Adults Density Dependence

RecruitmentRecruitment

Maximum HarvestMaximum Harvest

• Optimal harvest fraction (where Optimal harvest fraction (where yield is the highest) also yield is the highest) also maximizes the spatial variance in maximizes the spatial variance in adults and recruitmentadults and recruitment

• Maximum recruitment also occurs Maximum recruitment also occurs in this region (due to decreased in this region (due to decreased density dependence effect)density dependence effect)

ConclusionsConclusions

• Spatial pattern of fishing policies Spatial pattern of fishing policies determines how variance in determines how variance in escapement changes with increased escapement changes with increased fishingfishing

• Counter-intuitively, all fishing policies Counter-intuitively, all fishing policies showed:showed:– Increasing the harvest Increasing the harvest increasesincreases the the

spatial variance in fish densities until spatial variance in fish densities until severe over harvest/extinction (does NOT severe over harvest/extinction (does NOT spatially homogenize)spatially homogenize)

– Maximum yield occurs at peak spatial Maximum yield occurs at peak spatial variance variance

• Therefore, spatial variation is important Therefore, spatial variation is important and needs to be considered in fisheries and needs to be considered in fisheries models and management decisionsmodels and management decisions

Thanks!Thanks!

Crow White, Steve Gaines, Bob Warner, Ray Crow White, Steve Gaines, Bob Warner, Ray

Hilborn, Steve Polasky, Kraig Winters, Erik Hilborn, Steve Polasky, Kraig Winters, Erik

Fields Fields

Flow, Fish, & FishingFlow, Fish, & Fishing

A Biocomplexity in the Environment ProjectA Biocomplexity in the Environment Project