Spatial fisheries management Spatial fisheries management in practice: an examplein practice: an example

““Optimal” spatial managementOptimal” spatial management

Recall though experiment: A fisherman “owns” Recall though experiment: A fisherman “owns” the ocean. How would he harvest spatially to the ocean. How would he harvest spatially to maximize NPV of profits?maximize NPV of profits?On reserve design:On reserve design:– Many reserve design planning processes are on-Many reserve design planning processes are on-

goinggoing– None are informed by the kind of modeling we can None are informed by the kind of modeling we can

provideprovide– As fisheries move towards private access (zoning, As fisheries move towards private access (zoning,

dedicated access, property rights…) this will be THE dedicated access, property rights…) this will be THE critical questioncritical question

Some approaches people useSome approaches people use

The “Marxan” approachThe “Marxan” approach– Layer maps, score things, define “targets”, Layer maps, score things, define “targets”,

and select parcelsand select parcels– Ignores spatial connections which is the Ignores spatial connections which is the

whole reason reserves can increase profitswhole reason reserves can increase profits

The “Collaborative” approachThe “Collaborative” approach– Policy guy draws linesPolicy guy draws lines– Fishermen draw linesFishermen draw lines– Come to some agreementCome to some agreement

Costello/Polasky F3 paperCostello/Polasky F3 paper

N exhaustive “patches”N exhaustive “patches”In each patch:In each patch:– Cost function for harvestingCost function for harvesting– Growth functionGrowth function– Survival function (or percentage)Survival function (or percentage)

Connectivity matrix (kernels) connecting Connectivity matrix (kernels) connecting all patchesall patchesDynamic optimization model derives Dynamic optimization model derives optimal harvest in each patch over timeoptimal harvest in each patch over time

The result…The result…

Reserves – only optimal under some conditions Reserves – only optimal under some conditions (heterogeneity and connectivity)(heterogeneity and connectivity)– Patch-specific inputs and connectivity matrix will Patch-specific inputs and connectivity matrix will

determine whether reserves are optimal for a given determine whether reserves are optimal for a given applicationsapplications

Outside Reserves – model also derives optimal Outside Reserves – model also derives optimal harvest (by patch over time) in all “fished” harvest (by patch over time) in all “fished” patchespatches

If reserves don’t emergeIf reserves don’t emerge– Model derives optimal spatial managementModel derives optimal spatial management

A paper ideaA paper idea

1.1. Flesh out the interdependencies among these Flesh out the interdependencies among these characteristicscharacteristics

2.2. Assemble the appropriate data layers for a real Assemble the appropriate data layers for a real (sort of) system(sort of) system

3.3. Actually determine how harvest should be Actually determine how harvest should be distributed across space (including reserves)distributed across space (including reserves)

4.4. In principle, could compare optimal spatial In principle, could compare optimal spatial management from this model with alternative management from this model with alternative designs (e.g. reserves sited by habitat only)designs (e.g. reserves sited by habitat only)

A Channel Islands Example?A Channel Islands Example?

1.1. Defining “patches” (on the order of 100 or 1000 Defining “patches” (on the order of 100 or 1000 or so would be fine)or so would be fine)

2.2. Patch connectivity between patches (“Flow”)Patch connectivity between patches (“Flow”)

3.3. Biological layers for each patch (“Fish”) – e.g. Biological layers for each patch (“Fish”) – e.g. for urchinfor urchin

4.4. Economic layers for each patch (“Fishing”)Economic layers for each patch (“Fishing”)

The result would be an optimal spatial The result would be an optimal spatial management plan to maximize profits management plan to maximize profits

Channel Islands with gridChannel Islands with grid

Urchin habitat suitabilityUrchin habitat suitability

Kelp abundanceKelp abundance

Fishing cost in each grid cellFishing cost in each grid cell

Defining “patches”Defining “patches”

We desire a repeatable, transparent method We desire a repeatable, transparent method for defining patchesfor defining patchesSo far, we have:So far, we have:

– Habitat suitability, kelp abundance, costHabitat suitability, kelp abundance, cost

Define a “patch” as a set of grid cells:Define a “patch” as a set of grid cells:1.1. Homogeneous biology (kelp and HSI)Homogeneous biology (kelp and HSI)2.2. Homogeneous economics (cost)Homogeneous economics (cost)3.3. Spatially connectedSpatially connected

Wrote Matlab code to filter 1 & 2, use graph Wrote Matlab code to filter 1 & 2, use graph theory to accomplish 3theory to accomplish 3

Here’s what we’ll needHere’s what we’ll need

Define patchesDefine patchesIn each patch, derive:In each patch, derive:– Stock/Recruit relationshipsStock/Recruit relationships– Survival relationshipsSurvival relationships– Economics variablesEconomics variables

Connectivity matrix across all patchesConnectivity matrix across all patches

Then run Costello/Polasky to derive optimal Then run Costello/Polasky to derive optimal spatial managementspatial managementSimulate system over time using optimal spatial Simulate system over time using optimal spatial rule to derive biological and economic outcomesrule to derive biological and economic outcomes