marxan & mpa: strategic conservation planning

MARXAN & MPA:Strategic Conservation Planning

by Falk Huettmann

Decision-Support & Analysis Systems (in Space and Time)

How to manageWhere to managerWhen to manageWhat to manage …=> Million $ Decisions

Use of computers to suggest best possible solution(s), => Make everybody “happy” and safe/make $

A typical Marxan application a): Area Network Site selection, e.g. MPA

A typical Marxan application b): Assessment of existingArea Network locations

Species #Inside Outside

SolutionsA B

Or,No Best Solutionpossible…

A typical Marxan application c): Optimization

Planning Units PLUs

Optimized for(in time):~x layers1000s PLUsSpatial arrangementsWeighting factorsSeveral solutionsMany scenarios

e.g. based on simulated annealing algorithm

Often, can only be resolved through simulations…(no single mathematical solution) => Optimum is assumed, plain wrong, or never reached even… Even small improvements do count

Start

EndLocation A

Location B

Location C

Location D

Order of visitA,C,B,DB,A,C,DC,A,B,D… ?…Change of plans……What If…

(Spatial) Optimization Example: Traveling Salesman Problem

A typical Marxan application d): Best Professional Conservation Practice

Principles of Conservation Planning:

-Efficiency-Spatial arrangement: compactness and/or connectedness-Flexibility-Complementarity-Representativeness-Selection Frequency versus “Irreplaceability” -Adequacy-Optimisation, decision theory and mathematical programming

e.g. 10% of the area, high altitude, low biomass

A typical/traditional MPA application without MARXAN e): =>Scoring

NumberNumber MPA GoalMPA Goal ScoreScore

11 BiodiversiBiodiversityty

11 HighHigh

22 EconomyEconomy 22 MediuMediumm

33 HumansHumans 33 LowLow

44 FishFish 11 HighesHighestt

55 HabitatsHabitats 22 MediumMedium

…… …… ……

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…10s or 1000s of stakeholders, spatial & dynamic goals…

How Marxan works:

1. The total cost of the reserve network (required)2. The penalty for not adequately representing conservation features (required)3. The total reserve boundary length, multiplied by a modifier (optional)4. The penalty for exceeding a preset cost threshold (optional

=> feed with (spatial) Data

http://en.wikipedia.org/wiki/Marxan

How Marxan works:

Target Penalty Name of LayerPLUs101 1000 Deep sea areas102 5000 Albatross colonies 200 60 Fish habitat302 100 Plankton diversity

=> find Optimum

=> show the best solution in GIS

How Marxan works:

Target Penalty Name of LayerPLUs101 1000 Deep sea areas102 5000 Albatross colonies 200 60 Fish habitat302 100 Plankton diversity

=> find Optimum

=> show the best solution in GIS

Data Issues: e.g. Calanus glacialis

Open Access Data Predicted (app. 83% accuracy)

Credit: Imme Rutzen

by R.Hopcroft

How Marxan works:

Target Penalty Name of LayerPLUs101 1000 Deep sea areas102 5000 Albatross colonies 200 60 Fish habitat302 100 Plankton diversity

=> find Optimum

=> show the best solution in GIS

How a Marxan solution can look like

Scenario:10% Ecological

Servicesmaintained for

the Arctic

(Huettmann & Hazlett 2010)

MPA certified …

Optimization Problems applied elsewhere:

-Operations Research-Trading, e.g. Carbon-Stockmarket-Banking-Storage-Traveling Salesman Problem-Political Decisions-Life…

Optimization: Simulated Annealing

What is it ?“Annealing”:e.g. a hot liquid that coolsInto crystals(Mathematical description of this process) Hot

Cold

Optimization: Simulated Annealing

What is it ?

Annealing:e.g. a hot liquidthat cools intocrystals, startingat a random location

http://en.wikipedia.org/wiki/Simulated_annealing

Optimization: Simulated Annealing

What is it ?

Annealing:e.g. a hot liquidthat cools intocrystals, startingat a random location

Optimization: Simulated Annealing

What is it ?

Simulated Annealing:a mathematical processthat “mimics” hot liquidthat cools into crystals,starting at a random location

Optimization: Simulated Annealing

Relevance of a Random Start

Optimum is build additively,based on existing start and new & surrounding data

Optimization: Simulated Annealing

Relevance of the Random Start location

Simulated Annealing:a mathematical processthat “mimics” hot liquidthat cools into crystals,starting at a random location

A different sample at each run

=> A different optimum

=> A different solution

Optimization: Simulated Annealing

Cooling algorithm

Simulated Annealing:a mathematical processthat “mimics” hot liquidthat cools into crystals,starting at a random location

A different sample size at each step

=>A different (local) optimum

=>A different solution

Optimization: Simulated Annealing

Cooling speed

Determines the amount of detail whilesearching for the optimum

A different sample size at each step

=>A different (local) optimum

=>A different solution

Optimization: Simulated Annealing

Why so good ?!

http://4.bp.blogspot.com/_Hyi86mcXHNw/SIqveI8_1bI/AAAAAAAAAKs/LU6WJzOFo-M/s400/Simulated+Annealing.png

Beyond Annealing: Other algorithms & approaches (MARXAN example)

-Scoring-Iterative Improvement-Greedy Heuristics-Richness Heuristics-Rarity Algorithms-Irreplacability

Finding the Optimum: A Point

Optimum of “the data”

e.g. a hyperdimensional cube/problem

Finding the Optimum: A Polygon/Area

e.g. a feasible solution within 2 value ranges (x,y) and 3 linear constraints imposed

A concept widely used in Operations Research andMicroeconomics

Source: WIKI

Finding the Optimum

True optimum of the data (=best solution)Previous, local, optimum

Optimum foundwithin the Search Window

Finding the Optimum

True optimum of the data (=best solution)Previous, local, optimum

Size of theSearch Window

In TN & RF: Number of Trees settings…

Finding “the” Optimum: Always possible ?

True optimum of the data (=best solution)

Finding the Optimum: Algorithms

Derivatives

Derivatives using bootstrapping or jackknifing

(Neural Networks, CARTs)

Simulated Annealing

LP solver

What is Optimization ?Finding the “best”/optimal solution, taken all otherconstraints (which can be thousands) into account=> Often only an approximation

Measured how ? What units ? Derived how ?

per 1 x unit

? y unitsMarginal Gain/Cost…

=>Maximized Marginal Gain/Costs

Cost Function, minimize “costs”

=creates an obvious bias… (~unrealistic)