An explanation of the outputs produced by MARXAN (section 2)

How MARXAN works

Section 1 of this explanation illustrated the process of simulated annealing using an analogy based on designing a robot to find low-lying areas on the surface of Mars. Part of the iterative process that the robot used involved measuring its elevation, as it needed this information to calculate whether changing its location would result in moving to a lower-lying position.

MARXAN needs similar information to calculate whether a particular change to a portfolio would improve its effectiveness. It does this by calculating the cost of each portfolio, where effective portfolios have the lowest costs. The portfolio cost consists of the following parts:

1) The combined planning unit cost
Each planning unit is assigned a cost value, based on its area, financial value, the opportunity cost of it being protected (eg lost income from farming) or any other relevant factor. MARXAN calculates the combined cost of all the planning units in the portfolio.

2) The boundary cost
The boundary cost measures the amount of edge that the planning units in a portfolio share with unprotected units. This means that a portfolio containing one connected patch of units will have a lower boundary cost than a number of scattered, unconnected units. The cost is quantified as the length of edge in metres, kilometres or any other measurement systems. MARXAN then multiplies this value by the Boundary Length Modifier (BLM) constant, which is a user-defined number. Increasing this number increases the cost of having a fragmented portfolio.

3) Species penalty factor (or target penalty cost)
MARXAN calculates whether the target for each conservation feature is met by a portfolio and includes a cost for any target that has not been meet. A separate penalty value can be set for each conservation feature, although CLUZ aims to produce portfolios that meet all the targets by automatically setting a very high penalty for each target. The MARXAN literature refers to these penalty values as species penalty factors.

The total cost of a portfolio combines these three costs and is calculated as:

Combined planning unit cost + (boundary cost * BLM) + Combined species penalty factors

An example of calculating portfolio costs

This example uses a hypothetical planning exercise based on three vertebrate species (a mouse, a fish and a butterfly) and nine planning units. The distributions of the three species is shown below:

Each one of the planning units is 1 km x 1 km, so the planning unit (PU) cost of each unit is set as 1, the boundary is measured in kilometres and the boundary length modifier value is set as 1.5. The targets are that each species should be represented at least once in the portfolio and the species penalty factor for all three species is 10.

The diagrams below calculate the portfolio cost for two portfolios selected at random:

Portfolio A

Total PU cost = 4Boundary cost = 12 * BLMSPF = 10

Portfolio B

Total PU cost = 4Boundary cost = 8 * BLMSPF = 0

Portfolio A contains 4 units, has a boundary length (shown in red) of 12 and fails to represent the fish. Portfolio B contains 4 units, has a boundary length of 8 and meets all of the representation target. Therefore, the total cost for each portfolio is:

Portfolio A total cost = 4 + (12 * 1.5) + 10= 32

Portfolio B total cost = 4 + (8 * 1.5) + 0= 16

Incorporating viability into MARXAN costs

MARXAN can also incorporate population and ecological viability issues into the planning process. It does this by letting the user specify the minimum viable clump size for each conservation feature and only counting viable clumps when determining whether the conservation targets have been met. This feature can also be used to set targets for the number of clumps, so that a target for a particular species could be 20,000 ha of habitat made up of at least 3 clumps of a minimum size of 6,000 ha.

Extra features of MARXAN

The description above slightly simplifies the process that MARXAN uses to calculate the total portfolio cost, as it fails to mention the Cost Threshold Penalty (CPF). The CPF function allows the user to set the maximum total portfolio cost, so that an extra cost is added if the portfolio cost goes beyond the specified threshold. This means the user can ensure that MARXAN identifies portfolios that are less costly than a specified value, although these portfolios may be less effective at meeting the other specified targets.

The CPF feature is not included when CLUZ runs MARXAN (ie CLUZ sets the CPF value as 0). This is because the CPF cost is based on the total planning portfolio cost, which combines the planning unit and boundary costs. Beginners generally find it difficult to estimate the preferred total cost because it involves two separate elements which are measured in different ways. For example, the planning unit cost might be measured in dollars while the boundary cost is measured in kilometres. Advanced users who want to incorporate the CPF feature can run MARXAN independently and import the results into CLUZ.

The next page will show how MARXAN uses this information to identify low-cost planning portfolios, based on the elements of iterative improvement, occasional random backward steps and repetition.