An explanation of the outputs produced by MARXAN (section 3)

As described in section 1, MARXAN uses simulated annealing to identify efficient conservation portfolios and this process consist of three main elements described below:

1) Iterative improvement

MARXAN starts by creating a portfolio based on randomly selecting a number of planning units. It then improves on this random selection by using iterative improvement, ie one that is based on repeating the same simple set of rules a number of times to reduce the cost of the planning portfolio. In MARXAN's case the rules are:

1. Calculate the cost of the planning portfolio.
   
   
2. Choose a planning unit at random and change its portfolio status (ie change a protected unit to being unprotected or change an unprotected unit to being protected).
   
   
3. Calculate the new cost of the changed planning portfolio.
   
   
4. If the new portfolio has a lower cost than the original portfolio then make the change permanent. Otherwise, do not make the change.

This is one iteration and MARXAN can be used to repeat the process a number of times, so that the portfolio cost is gradually reduced. In general, a conservation planning exercise will use a large number of iterations (the CLUZ default is one million) but the illustration below shows the results of a process based on three iterations.

This illustration uses the planning example described in section 2 of this explanation, which focussed on 9 planning units and 3 species. Each planning unit has a PU cost of 1, the BLM = 1.5 and the SPF cost = 10.

The random portfolio produced by MARXAN, which has a total cost of 32, is shown in iteration one and the following diagrams show each of the three iterations in turn:

Iteration 1:

Randomly selected unitTotal cost = 32Total cost = 23

Iteration 2:

Randomly selected unitTotal cost = 23Total cost = 26

Iteration 3:

Randomly selected unitTotal cost = 23Total cost = 22

The three iterations produced two improvements to the portfolio and reduced the total portfolio cost from 32 to 22. Increasing the number of iterations would probably have reduced the cost even further, although setting a very large number of iterations does not bring corresponding improvements in the cost of the final portfolio.

2) Random and occasional cost increase

The iterative improvement illustrated above is unlikely to identify the most effective portfolio. This is because it cannot make changes that increase the portfolio cost in the short term but would allow long term improvements.

MARXAN overcomes this problem by including a process that allows changes to the portfolio that increases the cost value. This is incorporated into the iterative process, so that when MARXAN checks whether the random change to the portfolio reduces the total cost it will occasionally allow changes that make the portfolio more costly. MARXAN is more likely to accept changes that will increase the portfolio cost at the beginning of the iterative process, as this is when these "backward steps" are most likely to produce long-term benefits. In addition, MARXAN is influenced by the size of the cost increase and is also more likely to accept large cost increases at the beginning of the process.

This feature of allowing backward steps in the iterative improvement process is illustrated below using the same set of 9 planning units containing three species. The distribution of these three species is shown again on the left.

The diagram shows two iterations, where the first increases the cost of the portfolio from 24 to 27 but is still accepted. The second iteration is a standard example of iterative improvement, with the portfolio cost going from 27 to 14, but the previous backward step made this large improvement possible.

3) Repetition and irreplaceability scores

Finally, MARXAN can run the process described above a number of times, which also increases the chances of finding a low-cost portfolio. MARXAN then identifies the most efficient portfolio from the different runs but the information from each of the runs can also be used to provide important information. MARXAN does this by counting the number of times a planning unit appeared in the different portfolios produced by the different runs.

This is illustrated below, where MARXAN carried out five runs and identified five portfolios that are shown on the left. All of these portfolios met the representation targets but the best one, that is the one with the lowest cost, is shown on the right. Also on the right is the "summed solution" output, which shows the number of times each unit appeared in those five portfolios. You can see that this "summed solution" output provides important information about each of the planning units, whereas the best result only shows whether each unit belongs to the best portfolio.

Best resultSummed solution

This summed solution is useful in that it lets planners distinguish between units that are important for producing low-cost portfolios and those that could be swapped with other, similar units. For example, the figures below show the two types of MARXAN output that are displayed in CLUZ. The best result, ie the least-costly portfolio identified, shows a potential conservation plan for a region but the summed solution results show which parts of that plan are most important (in red) and which could be swapped with other units (in yellow).

The best resultSummed solution (highest scores in red)

The summed solution scores are similar to the irreplaceability scores produced by the C-Plan conservation planning software. The main difference is that irreplaceability scores are based on determining the total number of different portfolios that would meet the representation targets. The irreplaceability score for a particular unit is then calculated as the number of possible portfolios that contain the unit divided by the total number of possible portfolios. The summed solution in MARXAN is not based on the total possible number of portfolios but the number of runs specified by the user. In addition, each of these runs is designed to produce a low-cost portfolio.

Final details on the MARXAN parameters used by CLUZ

CLUZ has been designed to provide all of the important features of MARXAN in a way that can be understood by beginners. This means that it uses one mathematical approach to identifying low-cost portfolios, as this generally produces the best results. In addition, CLUZ does not allow the user to change several of the underlying parameters but lets MARXAN identify the best parameters instead. However, some experienced user may wish to experiment with changing these parameters and this can be done by running MARXAN independently and importing the results into CLUZ.

Experienced users may also be interested in knowing the MARXAN settings that CLUZ uses, so that they can investigate other approaches. These settings are that CLUZ uses simulated annealing, with the adaptive annealing option, followed by the iterative improvement run and no cost threshold. Anyone interested in learning more about the extra features in MARXAN should read the MARXAN manual.

We also recommend that you try the Reserve design game that has been developed by Wayne Rochester and Hugh Possingham at The University of Queensland.