quickly.
• We advise to be opportunistic when considering planning units. Where possible match the analysis with the management scheme or objective be planned. While it is sensible to consider size and shape from a modeling standpoint, perhaps conducting sensitivity analyses between natural and abstract, uniform units, we also suggest exploring the use of already‐delineated units that may be being used in current management schemes.
A review of various studies and the reasons provided for the choices of planning unit size and shape is provided in Table 7.2. Many the studies outlined do not provide a reason for choosing the size and/or shape of the planning unit. This is likely due to the lack of strong theoretical basis for using a specific selection unit (Stoms 1994, Pressey and Logan 1998).
Box 7.4: A precautionary tale of two different sized planning units in one analysis By Karin Bodtker, BCMCA
The BCMCA decided to use two different sized planning units (i.e., 2 km x 2 km square planning units on‐shelf and 4 km x 4 km square planning units off‐shelf) for an analysis spanning the entire Canadian Pacific EEZ. The decision was made despite solicited Marxan expert advise warning that using two different sizes of planning units could create complicated issues in regards to cost layers and balance’. However, the issues or problems are not well documented and the decision was made to try the analysis with two sizes of planning units for a variety of reasons, including:
• Quite large marine study area overall with a natural break in the physical environment at the base of the slope.
• Resolution of available data was finer for the nearshore and continental shelf regions, and courser for the larger off‐shore deep sea region.
• The original grid was also designed to align with the 4 km x 4 km grid in which some of the fisheries catch and effort data were provided.
• The BCMCA wanted to keep the total number of planning units less than 65 000 for ease of use in Excel spreadsheets.
• Past experience with slow processing speeds when using Marxan with more than 65 000 planning units.
• Many of the ecological features were to be targeted by broad ecosections, of which there are twelve in the study area, and it was reasoned that this would effectively spread solutions over the study area and reduce bias problems related to the different size planning units.
• The work to populate existing planning units with roughly half of the ecological features had already been completed when the advice was received.
When the time came for Marxan calibration, BCMCA tested for an inherent bias in the selection of the two sizes of planning units and did discover a consistent bias. To test this, they created a single feature that occupied each planning unit fully (i.e., the quantity was equal to the area of the planning unit) and targeted that feature using a simple proportional target. The BLM was set to zero and a random distribution of selected planning units was expected. BCMCA expected the summed solutions file to approximate a normal distribution, with the mean equal to the targeted proportion.
However, they found that the small planning units were chosen at nearly twice the rate as big planning units, and the distribution of the values in the summed solution file was clearly bimodal with a mean higher than the targeted proportion. They found the same result whether the scenario ran for 1 million iterations or 500 million iterations.
It may be possible to correct the bias by increasing the boundary cost of the large planning units, but then the correction factor also interacts with the BLM parameter, number of iterations, and number and spatial distribution of real features. BCMCA did not proceed with an analysis using two different sized planning units and, in hindsight, we would recommend using single sized planning units.
7.9 NUMBER OF PLANNING UNITS
Many people ask: What is the maximum number of planning units that Marxan can process? Technically, there was an upper limit of around 20 000 to 30 000 on the number of planning units that early versions of Marxan could handle (version 1.8.10 and earlier), though the optimised version (version 2.0+) has less restrictions and has been successful at processing much larger numbers, over 100 000, or even 150 000 planning units on newer computers with ample RAM memory. However, computer horsepower aside, there are mathematical reasons why Marxan, with its algorithms that try to do a reasonable job with optimality, will struggle to successfully process large numbers of PUs and features into an efficient, and hence meaningful, solution.
The number of possible network solutions is 2 to the power of the number of PUs. Thus, 100 000 PUs is more than 10 to the power 10 000 possible solutions which is greater than number of atoms in universe! That said, there are some cases where the decision space is so constrained by the arrangement of its features that even with huge numbers of PUs, near‐optimal results are still tractable. However, these situations are the exception, and in general, when there are lots of possible network configurations, optimal solutions will be hard to find when using over 50 000 PUs.
Considering issues of scale and precision, blocking fine‐scale raster data into sub‐
catchments and hexagons really does not cause you to lose any data and it should not be seen as a problem. Ultimately, it is all about the spatial scale of decision‐making. If decision‐making in a large study area is still on the scale of individual hectares then the problem has to be divided into sub‐regional analyses. However, usually this is not the
case. If required, sequential or greedy algorithms can work on such huge numbers of PUs but it is very unlikely that the solutions produced would be anywhere near optimal.
Thus, good practice would dictate either aggregating data into larger PUs or sub‐
dividing the study area. If you do decide to use a large number of PUs, you will need to do extensive testing to find the number of iterations required whereby the good solutions begin to converge. Even with the latest desktop computers, getting meaningful near‐optimal solutions could increase processing time dramatically, perhaps 24 hours or longer per Marxan scenario.
Table 7.2: Summary of planning unit choices in various studies.
AUTHOR/
TITLE SHAPE SIZE REASON PROVIDED Leslie et al.
2003.
Square 1-km2 and 100- km2
No – preferred 1 km2 to 100 km2 because solution area decreased.
Airame et al.
2003.
Square 1 x 1 min Socioeconomic information collected at this scale because they are the CA Department of Fish and Game planning units.
Beck and Odaya 2001.
Bays/
Eco-region
Vary Goal of project was to identify priority sites (i.e., eco-regions) for conservation.
Ardron et al.
2002.
Hexagon 250 ha No
Lewis, et al.
2003.
Hexagon 30 km2 and 10 km2, reefs
Used different planning units to reflect the spatial scale of management and administrative and physical boundaries. No reason for choosing hexagon.
Chan et al.
2006.
Square 1 x 1 min Socioeconomic information collected at this scale because they are the CA Department of Fish and Game planning units.
Richardson et al.
Square 2 x 2 min No
Stewart and Possingham 2003.
Square 5 x 5 km No
Geselbracht et al. 2005.
Hexagon 1500 ha Hexagons provide more natural appearing clumps as sites have six sides shared among individual units. The size of the PU was selected to provide fine enough detail for state-wide analysis while not overwhelming processing capabilities with
excessive units that may add little to analytical resolutions.
CLF and WWF 2006.
Square 5 x 5 min Size consistent with regional planning for which outputs were intended and scale and constraints of available data.
Tallis, H, Ferdana, Z, Gray, E 2008.
Hexagon 500 Ha
Hexagons, &
Hexagons split at the shoreline to account for terrestrial and coastal features
Hexagons integrated terrestrial and near shore area selection. Reasons for size: (1) consideration of scales of input data for ecological features; (2) promoting ecological accuracy between terrestrial and coastal realms by splitting units at the shoreline thereby accounting for a natural shared boundary
AUTHOR/
TITLE SHAPE SIZE REASON PROVIDED Ferdana
2005
Hexagon, and shoreline unit
750 Ha Hexagons, &
Hexagons and Variable length shorelines
Hexagons integrated terrestrial and near shore area selection. No reason for size
Shoreline was a more natural unit with ecological boundaries
Ferrar and Lötter 2007
DEM
modeled sub- catchments
5820 ha Freshwater assessment needed to protect intact wetlands and rivers, within healthy sub-
catchments Pence
(2008)
Segmented satellite image or landcover image (eCognition)
23 ha (range 0.25-550 ha)
Land-cover based planning units; ensuring homogenous contents of planning units (also ensure features not artificially dissected by planning unit boundaries); improves translation of product into management plan/guidelines
Klein et al.
(2008)
Sub- catchments
Average of 50 km2 and 800 km2 in the intensive and extensive land- use zones, respectively
To facilitate the protection of the integrity and function of ecosystem processes occurring on a sub-catchment scale