Ecological Complexity 11 (2012) 91–102

Original Research Article

Investigating species–environment relationships at multiple scales:Differentiating between intrinsic scale and the modifiable areal unit problem

Alex M. Lechner a,b,*, William T. Langford b,c, Simon D. Jones b, Sarah A. Bekessy c, Ascelin Gordon c

a Centre for Mined Land Rehabilitation, Sustainable Minerals Institute, University of Queensland, Sir James Foots Building, Cnr Staff House and College Roads,

St. Lucia, QLD 4072, Australiab School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476, Melbourne, VIC 3001, Australiac School of Global Studies, Social Science and Planning, RMIT University, GPO Box 2476, Melbourne, VIC 3001, Australia

A R T I C L E I N F O

Article history:

Received 26 September 2011

Received in revised form 18 April 2012

Accepted 18 April 2012

Available online 15 May 2012

Keywords:

Multi-scale

Modifiable areal unit problem

Spatial resolution

Spatial uncertainty

Remote sensing

Species–environment relationships

Virtual ecologist

Simulation modelling

A B S T R A C T

In ecology, multi-scale analyses are commonly performed to identify the scale at which a species

interacts with its environment (intrinsic scale). This is typically carried out using multi-scale species–

environment models that compare the relationship between ecological attributes (e.g., species diversity)

measured with point data to environmental data (e.g. vegetation cover) for the surrounding area within

buffers of multiple sizes. The intrinsic scale is identified as the buffer size at which the highest correlation

between environmental and ecological variables occurs. We present the first investigation of how the

spatial resolution of remote sensing environmental data can influence the identification of the intrinsic

scale using multi-scale species–environment models. Using the virtual ecologist approach we tested this

influence using vegetation cover spatial data and a simulated species–environment relationship derived

from the same spatial data. By using a simulation model there was a known truth to use as a benchmark

to measure accuracy. Our findings indicate that by varying the spatial resolution of the environmental

data, the intrinsic scale may be incorrectly identified. In some cases, the errors in the intrinsic scale

identified were close to the maximum value possible that could be measured by this experiment.

Consequently, multi-scale ecological analyses may not be suitable for distinguishing scale patterns

caused by the relationship between an organism and its environment from scale patterns caused by the

effect of changing spatial resolution: a phenomenon referred to as the modifiable areal unit problem

(MAUP). Thus, observed scale-dependent ecological patterns may be an artefact of the observation of

ecological data, not the ecological phenomenon. This study concludes with some suggestions for future

work to quantify the effect of the MAUP on multi-scale studies and develop generalisations that can be

used to assess when multi-scale analyses have the potential to produce spurious results.

� 2012 Elsevier B.V. All rights reserved.

Contents lists available at SciVerse ScienceDirect

Ecological Complexity

jo ur n al ho mep ag e: www .e lsev ier . c om / lo cate /ec o co m

1. Introduction

1.1. Scale

Determining the scale of landscape processes and the scaledependency of ecological responses to the resulting landscapepatterns are central questions in landscape ecology (Turner, 1989;Wu and Li, 2006). At the same time, spatial uncertainty arisingfrom changes of scale is a major concern in the spatial sciencessuch as remote sensing research (Marceau and Hay, 1999;Openshaw, 1984). The aim of our study is to examine how the

* Corresponding author at: Centre for Mined Land Rehabilitation, Sustainable

Minerals Institute, University of Queensland, Sir James Foots Building, Cnr Staff

House and College Roads, St. Lucia, QLD 4072, Australia. Tel.: +61 401 233 019;

fax: +61 733 464 021.

E-mail addresses: a.lechner@uq.edu.au, alexmarklechner@yahoo.com.au

(A.M. Lechner).

1476-945X/$ – see front matter � 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.ecocom.2012.04.002

effects of scale in remote sensing data may lead to misidentifica-tion of scale-dependent ecological patterns.

In this study, we distinguish three important components of scalefrom the spatial sciences and ecology literature: observation scale,analysis scale and intrinsic scale (Dungan et al., 2002; Wu and Hobbs,2007; Wu and Li, 2006). Observation scale describes the size, shape,extent and distance between observational units used to sample aphenomenon (e.g. spatial resolution). Analysis scale refers to theunits used in analysing data and is usually coarser than theobservation scale. For example, when analysing remote sensing datain ecology, the observation scale is the spatial resolution of the imageand the analysis scale employed by an ecological analysis may be thesize of a circular buffer around point locations at which ecologicaldata is sampled. Within each buffer multiple pixels of the remotesensing imagery are found. Intrinsic scale is the scale at whichecological phenomena interact with or perceive the environment. Itis an emergent property of an organism’s relationship with itsenvironment and is measured indirectly through using multipleobservation scales and/or analysis scales.

Table 1Descriptive nomenclature.

Descriptors Definition

Scale Generic term used to describe all three components of scale.

Observation scale Sampling unit used to measure the environment.

Spatial resolution Smallest identifiable feature within an image. In this study we only consider how pixel size and the application of a

smoothing filter affect spatial resolution.

Pixel size Size of spatial units in remote sensing data.

Smoothing filter Remote sensing processing method that is used to enhance images and image classification quality, but results in a

coarsening of spatial resolution.

Analysis scale Size of spatial unit used in an ecological analysis.

Buffer Area in which vegetation fraction cover is measured.

Intrinsic scale Scale at which an ecological process interacts with the environment – measured indirectly with observation and

analysis scale.

Multi-scale studies Studies which are conducted at multiple analysis or observational scales. In some cases to identify the intrinsic scale.

Landscape

Correct landscape Remote sensing dataset that is defined as correct – used to derive the correct ecological response.

Apparent landscape Remote sensing dataset with pixel sizes that differ from the correct landscape and/or has a smoothing filter applied.

Used to derive the apparent ecological response.

Ecological response Dependent variable in the simulated species–environment relationship, analogous to ecological attributes such as

population abundance. Derived from vegetation fraction cover found in a specific buffer size using the correct landscape.

Response correlation curve (RCC) Function that describes correlation between the ecological response and vegetation cover for multiple buffer sizes.

The shape of the curve is used to identify scale patterns, i.e. intrinsic scale.

Correct RCC Function derived using correct landscapes.

Apparent RCC Function derived using apparent landscapes.

Identified intrinsic scale

Correct intrinsic scale Buffer size at which the correct RCC has the highest correlation value.

Apparent intrinsic scale Buffer size at which the apparent RCC has the highest correlation value.

Base buffer Buffer size used to generate the RCC. Corresponds with the correct intrinsic scale.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–10292

In this study we will consider limited aspects of observational

and analysis scales, and will refer to these respectively as spatialresolution, and buffer size, respectively to describe our experi-mental method. While terms like spatial resolution represent justone aspect of the observation scale, the terms buffer size andintrinsic scale make the discussions less abstract and easier tofollow (Table 1). Finally, the term scale when used on its own refersgenerically to all three scale components.

1.2. Scale questions in ecology

According to ‘hierarchy theory’ (O’Neill et al., 1989), ecologicalphenomena interact with or perceive the environment at relativelyisolated, distinct intrinsic scales (O’Neill et al., 1989). For example,mobility, home range and proportion of habitat available arethought to be key drivers for the generation of patterns that varyacross different scales (Addicott et al., 1987; Krawchuk and Taylor,2003; Pearman, 2002; Soderstrom and Part, 2000; Wheatley andJohnson, 2009). Relationships found at one analysis and/orobservation scale are not necessarily observable at other scales,so phenomena need to be measured at the appropriate scales(Levin, 1992; Turner et al., 2001; Wiens, 1989; Wu et al., 2006).This suggests that phenomena need to be analysed at multiplescales to detect scale-dependent ecological patterns (Wiens, 1989;Wu and Li, 2006).

A particular focus among ecological investigations of scale-dependent relationships is the determination of the scale at whicha given ecological phenomenon operates (i.e. the identification ofintrinsic scale(s)). This is often investigated by measuringenvironmental attributes at multiple buffer sizes, and thencorrelating these attributes to ecological measurements (Fig. 1).A common experimental strategy is to sample ecological attributessuch as species diversity at random points across a landscape andcompare these to environmental measurements made over acircular area centred at the point, commonly referred to as a buffer(e.g. Coreau and Martin, 2007; Cushman and McGarigal, 2004;Davis et al., 2007; Holland et al., 2004; Suorsa et al., 2005). The

environmental measurements within the buffer are most com-monly derived from remote sensing data of a single spatialresolution (often the finest spatial resolution available) and areusually area based measurements such as percentage cover ofsingle or multiple vegetation classes. However, other environ-mental variables describing vegetation characteristics such asforest edge may also be measured within the buffer area (e.g. Takiet al., 2007). This type of analysis is performed at multiple buffersizes to test the strength of the relationship at each size(henceforth known as multi-scale buffer sampling design)(Fig. 1). The buffer size where the relationship between theecological attribute and environmental measurement is strongestis identified as the intrinsic scale (Fig. 1b) (e.g. Coreau and Martin,2007; Holland et al., 2004; Suorsa et al., 2005).

At different buffer sizes the relative importance of environ-mental variables such as percentage cover changes as theamount and composition of these variables change. For example,the relationship between home range size and the proportion ofhabitat available at different buffer sizes is thought to be a keyecological factor in determining scale dependent ecologicalpatterns (Pearman, 2002; Soderstrom and Part, 2000). Suorsaet al. (2005) found that the relationship between forest coverand probability of occupancy for the Eurasian tree creeper wasthe strongest at buffer sizes with a similar area to territory size.This type of analyses is more commonly conducted for birdspecies (Coreau and Martin, 2007; Pearman, 2002; Soderstromand Part, 2000; Suorsa et al., 2005), but has also been conductedon other species, such as bees (Taki et al., 2007) and beetles(Holland et al., 2004).

1.3. Scale questions in the spatial sciences

While the previously described form of analysis is intuitivelyappealing, a similar form of multi-scale experiment has been usedto demonstrate something completely contradictory in the spatialsciences. In particular, similar experiments have been used to testthe sensitivity of a statistical analysis to variations in the spatial

Fig. 1. Example of an ecological analysis conducted using a multi-scale buffer sampling design. (a) In this example the ecological response (e.g. species diversity) is measured at

point locations and vegetation cover fraction is measured within a circular buffer of multiple sizes surrounding the point samples. (b) Correlation (r) between species diversity

and vegetation cover are calculated for each buffer size to derive the response correlation curve (RCC). The intrinsic scale is identified as 125 m, which is the buffer size at which

the highest r value occurs.

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resolution of remote sensing data (Marceau and Hay, 1999;Marceau et al., 1994). These studies investigate what is referred toas the modifiable areal unit problem (MAUP) (Openshaw, 1984).

In the MAUP view, the same base data describing an ecologicalprocess can be aggregated or bounded in different ways beforeanalysis, for example, using 1 m pixels versus 30 m pixels.Statistical relationships derived from these areal units withdifferent boundaries and levels of aggregation can lead to differentstatistical conclusions about the same ecological process. Conse-quently, studies investigating the effect of the MAUP using spatialdata from a range of sources, such as remote sensing and censusdata, have found that MAUP effects can render the results of somespatial statistical analyses meaningless (Jelinski and Wu, 1996;Nelson, 2001; Wu et al., 1997).

This is important in ecological studies of scale since someecological measurements derived from the arbitrarily sized pixelsof a remote sensing image can be viewed as a specific case of theMAUP. Since such imagery, at various pixel sizes, is commonlyused to map environmental covariates, intrinsic scale effects maybe indistinguishable from effects of the MAUP. Indeed, tests for theMAUP often use multi-scale experimental designs that are similarto studies attempting to identify the scale of ecological interactions(i.e. intrinsic scale). For example, studies testing for the presence ofthe MAUP use differences in correlation coefficients to inferwhether a statistical analysis is not robust to changes in analysisscale. In contrast, ecological studies searching for the correctanalysis or observation scales at which to measure a phenomenoninfer that differences in correlation coefficients are related to theresponse of an ecological phenomenon to particular scales. Whilethe inferences made from these studies differ, there is nosubstantive difference in experimental design for studies withthese two distinct goals. The primary focus of this study will be togive examples of scale-dependent patterns that result from theMAUP and the intrinsic scale.

It is important to note that the MAUP is the result of the manyways in which non-overlapping units can be used to divide a studyarea for the purposes of analyses. It can be divided into two relatedcomponents described by Openshaw (1984) as the: (i) scale

problem and (ii) the aggregation or zoning problem. The scale

problem affects analyses as a result of changes in the spatial unitsthrough the aggregation of small units into progressively largerunits, and vice versa (i.e. changing spatial resolution). The zoning

problem can affect analyses as a result of varying the boundary ofareal units while keeping the number of units constant. In remotesensing, the MAUP is a particular case where the units arecontrolled by spatial resolution.

In this study we focus on the effects of the MAUP arising fromthe differences in spatial resolution. This is tested through acombination of two factors: pixel size and the application of a

smoothing filter. In many studies, the effects of spatial resolutionon analyses are investigated only through differences in pixelsize. Spatial resolution is often considered equivalent to pixelsize (Atkinson, 2004), however, the information content of a pixeland thus its spatial resolution is also affected by landcover foundin neighbouring pixels (Cracknell, 1998; Fisher, 1997). In order totest for the influence of other factors affecting spatial resolutionwe applied smoothing filters. They are a commonly used remotesensing processing technique that increases the influence ofneighbouring pixels and thus their application may potentiallyresult in the MAUP. Smoothing filters can be used in remotesensing to increase global classification accuracy by decreasingthe salt and pepper effect caused by per-pixel based landscapeclassification methods or to remove noise caused by sensor errorin raw remote sensing data (Ivits and Koch, 2002; Zukowskyjet al., 2001).

1.4. Aims

We present the first investigation of the degree to which theMAUP might influence the reliability of multi-scale analysismethods used to identify intrinsic scale. We use real vegetationcover spatial data and a simulated ecological response (i.e. speciesdiversity) derived from these spatial data to give examples wherethe MAUP is problematic. A critical distinction between our workand previous work on intrinsic scale is the use of the virtualecologist approach whereby we simulate ecological data andmodel the effects of the observation of that data on statisticalanalyses (Zurell et al., 2010). By using simulated data this study candistinguish between true effects of the simulated species andenvironment relationship and effects due solely to the spatialresolution of the underlying data. While the simulated ecological

response model represents a simplified version of reality, if thisrelationship cannot be recovered accurately using a simulatedresponse, there can be little confidence in differentiating ecological

Fig. 2. Tree presence (grey)/absence (black) landscapes with percentage tree cover indicated below the landscape title. 30 sampling locations for the ecological model are

indicated on the map by grey circles (500 m diameter).

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–10294

effects from the MAUP effects in real data. We conclude with adiscussion of the implications of our findings for future multi-scalestudies in ecology.

2. Method

2.1. Experimental approach

To test for the effects of the MAUP on the identification ofintrinsic scale, we simulated an ecological response by applying apredefined species–environment relationship to a set of reallandscapes. The simulation model was comprised of 3 parts: (i)landscape definition, (ii) sensor simulator and (iii) ecological response

simulator. We first provide a general overview of our method andthen go into more detail of the three parts.

First, we defined a remote sensed dataset as being the correct

landscape. In our simulation this represents what is actuallypresent on-ground and this information would not normally beavailable when using real-world data. The remote sensing datawere aggregated to an alternative pixel size and processed tocreate a range of realistic geographic representations of the samelandscape. These multiple representations of the same landscapeare designated as apparent landscapes and simulate the use ofimagery derived from satellites with different spatial resolutionsand different remote sensing processing techniques. For example,10 m pixels instead of 30 m pixels. Next, we defined the correct

response correlation curve (RCC), which describes correlation (r)between the ecological response and vegetation cover fraction formultiple buffer sizes derived using a multi-scale buffer samplingdesign with a specific (correct) intrinsic scale (e.g. Fig. 1b). Bycomparing the RCCs generated using the apparent and correct

landscapes, we were able to determine whether it was possible torecover the correct RCC and the correct intrinsic scale when usingapparent landscapes. If the recovered RCC or intrinsic scale changedwhen landscapes with different spatial resolutions were used, thiswould indicate the presence of the MAUP and therefore, anunreliable ecological inference.

2.2. Define landscapes

The landscapes used in the simulation model were a stratifiedsubset from a random sample of sub regions of the regional Tree25

presence/absence tree cover dataset (DSE, 2006). The Tree25

dataset covers most of the state of Victoria, Australia, comprising awide range of land uses including conservation areas, drylandpasture, broad acre cropping and crop pasture. These differing landuses resulted in a wide range of landscape patterns. The datasetwas derived from SPOT panchromatic imagery with a 10 m pixel

Table 2Pixel sizes tested in the simulation model and equivalent satellite sensor. Correct lands

Data source Pixel size (m) Smoothing Total

Landscape A, B, . . ., F 10, 30 Yes/no* 12

size and was classified by automated segmentation, and then thepresence or absence of woody vegetation was labelled by a humaninterpreter. For the purposes of the simulation model, these imageswere declared to represent vegetation cover with 100% accuracy.Initially, 20 random 10 km � 10 km sub-regions of the Tree25

datasets were extracted and then six of those sub regions(henceforth, called Landscape A, B, . . ., F) were chosen so that arange of tree-cover proportions and patterns were sampled (Fig. 2).The sub-regions included a range of ecologically importantlandscape elements, such as small remnant patches and linearstrips.

2.3. Sensor and processing simulator

Next, a sensor and processing simulator was used to createdifferent representations of the original six landscapes. Thisinvolved two steps. First, the 10 m pixels of the Tree25 classifiedlandscapes were aggregated to 30 m pixels using a majority rulereducing the number of pixels to 1/9 of the original total. This pixelsize matches the Landsat TM/ETM+ sensors’ pixel size and iscommonly used in landscape ecology (Table 2). In the second step,the dataset was smoothed using a majority filter creating anadditional representation of the landscapes. The majority filteruses a 3 � 3 moving window filter to replace the value of a pixel inthe centre of the window based on the majority value of all pixelsin the window. This operation leaves the pixel size unaltered. Thusfor each of the 6 landscapes, A, B, . . ., F, there were four variants:10 m and 30 pixel sizes, which are both smoothed and unsmoothed(Fig. 3). This results in 24 different landscapes.

2.4. Simulating the ecological response and testing for the MAUP

The crux of the simulation is to reproduce common elements ofanalyses with real ecological data that use a multi-scale bufferdesign. To make the explanation easier to follow, we will firstdescribe the methods using a concrete but fictitious examplerather than abstract names.

Suppose that in a real situation, the normalised abundance of aparticular bird species at any location was equal to the fraction ofthe landscape that was vegetated within 125 m of that point. Inother words, there is a very simple linear, scale-dependentrelationship, y = x, between an ecological response y (abundance;normalised from 0 to 1) and the independent variable x (vegetationcover fraction) at a given intrinsic scale (125 m). An ecologist couldtry to identify that intrinsic scale by

1) conducting a bird survey at 30 randomly chosen fixed locationson the ground to estimate the abundance

capes did not include smoothing filter (*).

true landscapes Total apparent landscapes Sensor equivalent

24 SPOT XS, Landsat

Fig. 3. Example of remote sensing simulator outputs: landscape C aggregated from 10 m to 30 m with a smoothing filter applied.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–102 95

2) choosing 10 different analysis scales (buffer sizes) anddetermining the vegetation cover fraction within each buffersize at the same locations using a classified remote sensedimage, and finally

3) determining the buffer size whose 30 vegetation cover fractionshas the highest correlation with the 30 measured values ofabundance.

The above experiment can be mimicked for a particular map of alandscape by arbitrarily choosing an intrinsic scale (buffer size) andan equation to declare as our ecological response. Because thecentral premise of this study is that the identification of theintrinsic scale of the underlying ecological process may be affectedby the observation scale of the map, we compared the results ofdoing the same experiment on different maps of the same place.Additionally, by using different intrinsic scales to generate thecorrect ecological response any effects due to the idiosyncrasies ofone particular scale choice could be assessed.

So, mimicking the structure of a real world experiment, eachsingle experiment in our study is uniquely specified by

1) one intrinsic scale designated as correct,2) one landscape,3) one realisation of that landscape designated as correct.

The full set of experiments consists of the combinations of allpossible values of those three attributes chosen as follows:

1) possible base buffer radii of [25 m (1964 m2), 125 m (49 087 m2)and 225 m (159 040 m2)]

2) possible landscapes are the six Tree25 landscapes: [A, B, C, D, E, F]3) possible correct landscapes are: [(10 m pixel, unsmoothed),

(30 m pixel, unsmoothed)]

which results in 3 � 6 � 2 = 36 experiments in total.Fig. 4 shows a schematic representation of the process of

simulating the ecological response and testing for the MAUP afterthe application of the sensor simulator. This process involved foursteps, which we describe below.

Step 1a. In each experiment, the first step is to declare thecorrect value of the ecological response and the intrinsic scale. Togenerate the ecological response for any given landscape thefollowing procedure was used.

Thirty sample locations are selected randomly within thelandscape. This number is similar to many landscape-level studies(e.g. Pearman, 2002; Taki et al., 2007). The locations wereconstrained to be far enough apart so that the largest buffer placedaround them (250 m radius) would not overlap with the buffer ofany other point. This is a common practice in ecological experimentsto reduce the effect of spatial autocorrelation and avoid violating theassumption of independence for regression models.

The proportion of vegetation cover within these buffer areas isrecorded for each location at each of three base buffer sizes [25 m(1964 m2), 125 m (49 087 m2) and 225 m (159 040 m2)] to use asthe basis for three different experiments with three differentintrinsic scales. For each experiment, the base buffer size used isdeclared to be the correct intrinsic scale for that experiment.

To simulate the ecological response that would be measured ateach location, we arbitrarily choose the simplest possible linearform commonly used in species–environment studies, that is, y = x,where y is the ecological response and x is vegetation cover fractionat one of the three base buffer radii specified above (25 m, 125 m,225 m). The ecological response itself abstractly representscommonly measured ecological attributes, such as occupancy(Suorsa et al., 2005), population abundance (e.g. Heikkinen et al.,2007; Holland et al., 2004) and species diversity (e.g. Lawler et al.,2004; Pearman, 2002).

In studies of this kind, measurements of vegetation coverfraction are commonly used as an explanatory variable to assessthe impact of vegetation cover on ecological attributes. Because weuse the simple y = x form in our simulations and the vegetationfraction recorded at that buffer size is used as the input variable x,the vegetation cover fraction itself becomes the value of theecological response for all of these simulations (e.g. Fig. 1a).

In a real experiment, we would not know the intrinsic scale, butin the simulation model the intrinsic scale is determined by thebase buffer size used in the computation of the ecological response.While, the identification of the intrinsic scale in real experiments isconducted by deriving the RCC. To derive the RCC, vegetation coverfraction was measured at 10 buffer sizes (25 m, 50 m, . . ., 250 m)and correlated with the original vegetation cover fraction valuesof the ecological response. Correlation was calculated usingSpearman’s r as the assumption for linear regression was notmet. The assumption was not met because the distributions ofvegetation cover fraction values were often non-normal and plotsof the residuals demonstrated that the data were often hetero-scedastic.

Step 2a. The correct RCCs are derived for each of the 6 landscapesA, B, . . ., F, at two different pixel sizes (10 m and 30 m) using onlythe unsmoothed versions of these maps. The correct RCCs aremeasured by undertaking Step 1 at three base buffer sizes (25 m,125 m and 225 m), thus creating six functions for each of thelandscapes A, B, . . ., F (2 pixel sizes � 3 base buffer sizes).

Step 2b. The apparent RCCs are derived using four variants foreach of 6 landscapes A, B, . . ., F: smoothed and unsmoothed at pixelsizes of 10 m and 30 m. In Step 2a the correct RCC was derived onlyfor unsmoothed versions of these maps. Now we create a set ofapparent RCCs using the apparent landscapes to compare to thecorrect RCC using the following method:

1) First, a landscape is assigned as the correct landscape (C), leavingthree apparent landscapes (A1, A2, A3). For example, if landscape

Fig. 4. A schematic diagram that describes the relationship between Figs. 5 and 7. See Section 2 for further details. Step 1. Generate the ecological response for any given

landscape using vegetation cover fraction at 30 points. Step 2. Derive correct RCCs for each of the 6 landscapes A, B, . . ., F, at two different pixel sizes (10 m and 30 m) and three

buffer sizes (25 m, 125 m and 225 m), using only the unsmoothed versions of these maps (2 pixel sizes � 3 buffer sizes). Next, derive the apparent RCCs using the apparent

landscapes (A) to compare to the correct RCC (T) using the following method. Step 3. Compare shape of correct and apparent RCCs and buffer size of correct and apparent intrinsic

scales. Step 4. Compare buffer radii for the smallest and largest apparent intrinsic scales to the correct intrinsic scale. Note that each circle in example Fig. 6 corresponds to the

maximum correlation value on a different RCC.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–10296

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–102 97

B at 10 m was selected, this becomes the correct landscape, thenthe three associated apparent landscapes are: unsmoothed at30 m, smoothed at 10 m, and smoothed at 30 m.

2) As described in Step 2a select the correct landscape and measurevegetation fraction using one of three buffer sizes (25 m, 125 mand 225 m). The vegetation cover fraction value at the 30locations becomes the dependent variable, the ecological

response. Next, measure vegetation cover fraction at 30locations using a particular buffer size and the apparent

landscape. Vegetation cover fraction is measured at the 30locations using the apparent landscape and correlated with theecological response measured in step 1a. This is repeated formultiple buffer sizes (25 m, 50 m, . . ., 250 m) to derive theapparent RCCs.

3) The previous step is then repeated for each of the three buffersizes (25 m, 125 m and 225 m) used to derive the ecological

response.4) Finally, applying the previous two steps on each of the three

apparent landscapes using the ecological response derived forbuffer sizes: 25 m, 125 m and 225 m and pixel sizes: 10 m or30 m. This results in six sets of one correct RCC and threeapparent RCCs for each of the six ecological responses (3 buffersizes � 2 pixel sizes).

Step 3. The buffer size at which the correct ecological responses

are derived is the correct intrinsic scale as it will have a correlationcoefficient value of 1 and thus the highest correlation coefficient.At this buffer size we are using the same data for both dependent(ecological response) and independent variables. If the buffer size ischanged the correlation coefficient decreases. The buffer sizeidentified as having the highest r value using the apparent RCC istermed apparent intrinsic scale.

Step 4. The effects of the MAUP are measured by comparingthe differences between the correct and apparent RCCs. The peaksand troughs of the RCC correspond to the response of ecologicalphenomenon to buffer size as in other ecological studies (e.g.Holland et al., 2004; Pearman, 2002). From the apparent RCC,multiple intrinsic scales may be identified if multiple peaksoccur, however, the correct RCC was derived with a singleintrinsic scale. For cases where two or more buffer sizes have themaximum value (i.e. in cases where the shape of the curveplateaus and does not peak), the intrinsic scale is identified as theaverage of the maximum range of these values. Differences inthe intrinsic scale identified between the correct RCC and theapparent RCC as well as the shape of the function indicate thepresence of the MAUP.

Fig. 5. Scatter plots of synthetic ecological response versus vegetation cover fraction (%) f

in the top left corner. The ecological response was derived at a pixel size of 10 m and the bu

pixels and no smoothing. (b) Landscape D, with 30 m pixels and smoothing applied (appa

point inside a plot represents a single sampled location on the map at the given buffe

3. Results

The strength of relationships between vegetation cover andthe ecological response changed with buffer size and pixel size.For example, Fig. 5 (landscape D) presents 2 out of 144 sets ofscatter plots (6 landscapes (Landscape A, B, . . ., F) � 6 buffer sizesand pixel combinations � 3 apparent and 1 correct landscapes)produced in this study used to describe the relationship betweenvegetation cover fraction and the ecological response. Fig. 5ashows the correlations generated for a range of buffer sizes toproduce the correct RCC. The function was generated bycorrelating vegetation cover fraction at 125 m with vegetationcover fraction at all buffer sizes. In this case the ecological

response was derived from a buffer size of 125 m and thus thecorrelation coefficient was 1 and there was a perfect linearrelationship. This buffer size is identified as the intrinsic scale.When buffer size increased or decreased the correlation betweenvegetation cover fraction and the ecological response becameweaker. Changing the pixel size by using an apparent landscape

with a pixel size of 30 m compared to a pixel size of 10 m atwhich the ecological response was derived and applying asmoothing filter resulted in incorrectly identifying the intrinsic

scale at a buffer size of 175 m (Fig. 5b). At this radius the highestcorrelation coefficient of 0.90 was recorded.

The scatter plots presented in each row of Fig. 5 can besummarised as a single curve by plotting the correlation coefficientversus buffer size for the correct or apparent landscapes to derivethe RCC. Curve a in Fig. 6 refers to the scatter plots of Fig. 5a andcurve b in Fig. 6 refers to scatterplots of Fig. 5b. This is a commonmethod of depicting the relationship between buffer size andcorrelation (e.g. Holland et al., 2004; Pearman, 2002). However,previous studies use only a single spatial resolution and testmultiple buffer sizes which is equivalent to a single curve in Fig. 6.

The effect of the MAUP is illustrated by comparing curvesdescribing the correlation coefficient versus buffer radii forapparent landscapes to curves for correct landscapes. This effectwas tested for multiple RCCs and multiple landscapes (Fig. 7Landscape B; plots for other landscapes can be found in thesupplementary material). Using apparent landscapes usuallydecreased correlation coefficients across most buffer sizes (e.g.Fig. 7b, c, e, f). Furthermore, the intrinsic scale was misidentifiedin one or more apparent landscapes in every case except when theRCC was derived with a pixel size of 30 m and buffer size of 25 m(e.g. Fig. 7b).

Not only did correlation coefficient values change with the useof apparent landscapes, but so did the shapes of the apparent RCC. In

or landscape D. The line of best fit plotted in dark grey and Spearman’s r is presented

ffer size of 125 m for both row a and b. (a) Landscape D, correct landscape, with a 10 m

rent landscape). Each plot represents results at the buffer size for that column. Each

r size.

Fig. 6. Landscape D. Correlation (Spearman’s r) versus buffer radius for a range of

correct and apparent RCCs for an ecological response derived at a pixel size of 10 m

and the buffer size of 125 m. Curve (a) in bold is the correct RCC based on the correct

landscape used to derived the ecological response. This curve is the equivalent of

Fig. 5a. Curve (b) is derived using an apparent landscape with 30 m pixels and

smoothing applied is the equivalent of Fig. 5b. The intrinsic scale is identified as the

buffer size with the highest r value. The buffer size of the true intrinsic scale is

indicated by the dotted vertical line. The apparent intrinsic scales identified for each

of the apparent RCCs is indicated with a circle.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–10298

some cases the shape of the functions changed greatly, from asimple exponential to a complex polynomial resulting in theappearance of multiple peaks in the function indicating two ormore intrinsic scales rather than a single intrinsic scale asrepresented by the correct landscape. For example, in Fig. 7a, anecological response was derived for a pixel size of 10 m and a buffersize of 25 m for landscape B. The correct intrinsic scale was 25 m,but when using the corresponding apparent landscapes with a pixel

Fig. 7. Landscape B. Correlation (Spearman’s r) versus buffer radius for a range of correct a

RCC at a buffer radius and pixel size indicated above each plot. The other RCC describe r va

of the true intrinsic scale is indicated by the dotted vertical line.

size of 30 m and no smoothing filter applied, there were two peaksin correlation coefficient values which indicate intrinsic scales atbuffer sizes 100 m and 200 m.

The effect of applying the smoothing filter was dependent onthe pixel size of the correct landscape. Pixel size had a greaterimpact on the RCC than the application of the smoothing filter. Inmost cases, applying a smoothing filter decreased correlationcoefficients. In some cases, it changed the intrinsic scale identifiedwhen the pixel size of the apparent landscapes did not match thecorrect pixel size (e.g. Fig. 7f; Pixel size 10 m and smoothing filterapplied).

The effects of using apparent landscapes varied betweenlandscapes and depended on the buffer size and pixel size usedto derive the RCC. For some landscapes, such as Landscape B, theeffect on analysis of using apparent landscapes resulted in nodifferences in intrinsic scale identified for one combination of bufferand pixel sizes (30 m pixel, 25 m buffer). Meanwhile, errors of125 m in the intrinsic scale were identified for another combination(30 m pixel, 125 m buffer) (Fig. 8b). Using one or more apparent

landscapes for Landscape C resulted in erroneously identifying theintrinsic scale for all combinations of buffer and pixel sizes in atleast one apparent landscape in (Fig. 8c). In contrast, the intrinsic

scale was identified correctly for all combinations of buffer andpixel sizes in Landscape E (Fig. 8e).

4. Discussion

4.1. Overview

The results of this study demonstrate that spatial uncertaintyarising from the MAUP has the potential to produce misleading

nd apparent RCCs. Curves in bold are based on the correct landscape used to derive the

lues versus buffer size relationship derived with apparent landscapes. The buffer size

Fig. 8. Comparison of buffer radii (Y-axis) for the smallest and largest apparent intrinsic scales and the correct intrinsic scale identified for all landscapes and all derived RCCs

combinations. For example, each of the 6 plots in Fig. 7 are summarised as six sets of three bars in plot (b). The first of the three bars describes the smallest intrinsic scale

identified from the apparent RCC. The second bar describes the correct intrinsic scale. The third bar describes the largest intrinsic scale identified from the apparent RCCs. The

specific pixel and buffer size at which the RCC was derived is described in the x axis. Differences between the second bar and the first and/or third bar represent the size of

errors in identifying the intrinsic scale. While, if all three bars are of the same height there was no error in identifying the intrinsic scale.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–102 99

results in ecological analyses. We found that the observedecological responses repeatedly exhibited the MAUP and thatthese responses were not just a property of the buffer size butalso of spatial resolution. More specifically, we detected a highlevel of variability in the effect of using apparent landscapes onthe accuracy of the identified intrinsic scales between landscapesand for different combinations of pixel sizes and buffer sizesused to derive the RCC. In some cases, the differences in pixelsize only affected the strength of the relationship between theecological response and vegetation cover fraction. In other casesthe intrinsic scale was misidentified altogether with error valuesranging from 0 to 175 m, where 225 m was the maximummeasured value. Furthermore, in other cases multiple intrinsic

scales were identified when in reality there was only a singleintrinsic scale. The effects of the MAUP could also be seenqualitatively in the large differences in the shape of the apparent

and correct RCCs. Finally, changing pixel size appeared to havethe greatest effect on the outcome of analyses and thesmoothing filter only had a similar effect size for specificcombinations of landscapes and derived ecological responses.This is interesting as both 30 m unsmoothed pixels and the 10 msmoothed pixels result from a similar level of degradation butusing different methods.

In light of such divergent findings demonstrating instanceswhere the MAUP had large effects on ecological analyses, thereis a need to assess whether scale patterns reported usingecological analyses result from scale-dependent ecologicalphenomenon (i.e. intrinsic scale) or the MAUP. We considerthat the investigative strategy of using a simulation model wasexemplary in detecting these apparently divergent effects ofscale that were undetectable when using a multi-scale buffersampling design.

4.2. Scale and ecological analysis

The results of our study are relevant to ecological analyses usingmultiple and single analysis or observational scales. We testedcommonly used pixel sizes in landscape ecology based on standardoperational remote sensing sensors and demonstrated that theoutcome of analyses will be different when using pixel sizesequivalent to either a SPOT or a Landsat sensor. Landscape levelresearch, however, is typically only conducted at fixed observation

and analysis scales (i.e. single pixel size and buffer size). These areoften arbitrarily selected according to readily available genericdatasets or sensors without any investigation of the sensitivity ofanalysis to different scales (Comber, 2008; Pontius et al., 2008;Schmit et al., 2006). Our study showed that it is critical to test forscale sensitivity and that studies that use fixed scales such as asingle buffer or pixel size may unknowingly overlook a scale-dependent ecological relationship or the MAUP.

The most common recommendation in landscape ecology totest for intrinsic scale is to conduct studies at multiple analysis orobservation scales (Levin, 1992; Wiens, 1989; Wu et al., 2006). Infact, multi-scale studies tend to use a small number of scales andtest a single scale-dependent factor such as pixel size or buffersize. In contrast, our results suggest that the relationshipbetween the intrinsic scale, buffer size and spatial resolutionsmay vary substantially along a continuum. The intrinsic scale

may change with multiple buffer sizes, often abruptly, and thusthe results of studies using a small selection of buffer sizes maylead to erroneous conclusions being drawn due to the absence ofdata at untested sizes. For example, in Fig. 7, plot b, correct RCC,there was a change in r values from 0.8 to 1.0 between bufferssize 75 m to 125 m, where 0.7 was the lowest r value recordedby this curve.

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–102100

More robust studies that use a continuum of analysis scales toidentify intrinsic scale(s) cannot guarantee that observed patternsat a particular analysis scale are not spurious due to the presence ofthe MAUP. This study utilised a simulation model and thus therewas a known truth based on the simulated ecological response touse as a benchmark to measure accuracy. When conducting multi-scale ecological analyses using real data, the intrinsic scale

identified is a property of both how the intrinsic scale is measuredand the underlying scale-dependent process, so there is no way ofknowing whether scale-dependent patterns observed are affectedby the MAUP.

4.3. Simulation modelling: simplifying complex ecological

relationships

A novel aspect of our study is the use of the virtual ecologistapproach using a simulation model to investigate the effects ofspatial resolution on measuring the intrinsic scale. Simulated dataallows some elements of the complexity of real world phenomenato be studied. Our simulation model represents an idealizedscenario for conducting ecological analyses, where no ‘unknown’sources of uncertainty were present in the spatial data or in theecological model. Consequently, there was no measurement errorand all the parameters and all statistical relationships were known.Additionally, the correct landscapes represent the true geographicrepresentation that perfectly describes how the species perceivesthe environment. By contrast, such relationships are typicallynever known with absolute certainty when using real data andecologists can only make inference about causal processes basedon empirical data. In studies using real data the effects of spatialuncertainty on ecological analyses are likely to be much greaterand more difficult to distinguish than in simulation studies. Afeature of simulation modelling is that if simple theoreticalrelationships cannot be derived correctly using simulation models,there can be little confidence in recovering these from morecomplex ‘real’ data (Austin et al., 2006).

In comparison between this study and other studies, themeasurements of correlation were much higher indicating astronger relationship resulting from the absence of other unmea-sured factors that commonly influence species–environmentrelationships. The shape of the curves of buffer size versuscorrelation coefficient reported here appear to be distributed moresmoothly (i.e., less erratically), albeit having qualitatively similartrends to other studies that have conducted similar types ofanalyses on a continuum of buffer sizes using real data (e.g.Holland et al., 2004; Pearman, 2002). However, the derivedcorrelation coefficients were much higher in our simulation modelwith a consistently smaller range than these other studies. Themaximum range of r for any landscape tested in this study wasapproximately 1.0–0.57. Other studies investigating the relation-ship between an ecological attribute and vegetation cover hadlarger ranges and smaller r values. For example, Holland et al.(2004) calculated Pearson’s r values of �0.0–0.3, Pearman (2002)calculated r2 values of �0.35–0.7 and Taki et al. (2007) calculated r2

values of 0.045–0.165. Additionally, differences between buffersizes and correlation coefficients tended to be smaller for thesimulation model compared to real studies. For example,landscape D with an RCC derived using a pixel size of 10 m andbuffer size of 125 m with the true landscape at a buffer size of 25 mthe r value was 0.78 while for all the other buffer sizes valuesranged from 0.95 to 1 (Figs. 5a and 6). Comparison between otherstudies, however, is made difficult due to the variety of correlationmeasures used such as r2 and Pearson’s r.

Untested forms of uncertainty that are common in real datawith more complex, sometimes multivariate relationships havethe potential to amplify the impact of the MAUP on analyses. For

example, ecological relationships may be non-linear and difficultto derive statistically because of confounding factors such asspatial autocorrelation (Legendre et al., 2002; Wintle et al., 2005).Our study used a simple univariate linear model to describe thespecies–environment relationship commonly used by otherauthors (e.g. Holland et al., 2004; Pearman, 2002; Taki et al.,2007), however, many studies use multiple explanatory variablesthat may increase the potential for the MAUP. Our model used onlya single spatial dataset as an explanatory variable, while manyother studies utilise spatial data from multiple sources withdifferent analysis and observation scales. Every spatial datasetincluded in a model has the potential to introduce MAUP effects.Furthermore, the MAUP can be the result of other scale-dependentfactors not tested in this study, such as patch location, minimummappable units and thematic resolution (e.g. Buyantuyev and Wu,2007; Lechner et al., 2009; Wu et al., 2000). Our study only testedtwo scale-dependent factors (pixel size and the application of asmoothing filter) and found that the effect of applying thesmoothing filter was dependent on the pixel size at which theecological response was derived and the pixel size of the apparent

landscapes. Thus, spatial uncertainty factors interact and poten-tially may be difficult to predict and/or magnify when occurringtogether, further complicating ecological analyses.

While our study investigated spatial uncertainty arising fromthe MAUP, untested sources of spatial uncertainty which are notrelated to scale may further degrade analyses in unpredictableways. There are many forms of error that result from the processof generating binary habitat maps such as those used in thisstudy and commonly used in landscape ecology (Antrop, 2007).Spatial uncertainty can be the result of factors, such asclassification error (e.g. Langford et al., 2006; Shao and Wu,2008) and variations and ambiguity in landcover class defini-tions (e.g. Colson et al., 2009; Comber et al., 2005). For example,Langford et al. (2006) found that in some cases map classificationerror can cause a thousand-fold increase in error in thecalculation of landscape metrics.

Ecologists spend considerable effort testing uncertainty inecological data (Chapman et al., 2005) while often ignoring theeffects of spatial uncertainty. Users of spatial data often blindlyaccept them as error free (Adams and Gillespie, 2006; Evans, 1997),even though uncertainty in spatial data may in some cases be asimportant or more important than errors in other modelparameters (Schmit et al., 2006). Previous studies comparing theimpact of spatial uncertainty versus model or parameter uncer-tainty show that both may impact ecological analyses. However,whether spatial or non-spatial factors are a greater source of errormay depend on the specific study. For example, a study byRuckelshaus et al. (1997) found that their model was moresensitive to error in model parameters compared to spatial inputs.Conversely, Minor et al. (2008) found that the habitat map was thelargest source of error for their spatially explicit population model.Thus, to ensure ecological studies are robust to uncertainty, there isa need for testing of spatial data to become as common as testingfor uncertainty in non-spatial model parameters.

4.4. Recommendations

Further research is needed to expand on our findings anddevelop methods for reducing the effects of MAUP. The currentapproach commonly used to address the MAUP involves testinganalyses for scale sensitivity by altering observation and/or analysis

scale. The research shown here demonstrates that this approach isstill useful in detecting the MAUP, but it does not provide a solutionto the MAUP, as the causal process cannot be determined using thismethod. There is a need to develop methods to determine thecause of scale-dependent patterns and develop methods to reduce

A.M. Lechner et al. / Ecological Complexity 11 (2012) 91–102 101

the effects of the MAUP. Alternative approaches to simple binarymap classification methods may reduce the effect of the MAUP.These include using more complex landcover classificationmethods rarely utilized in ecology such as fuzzy classifiers (Foody,1998) that can describe sub-pixel landcover area (e.g. Robinson,2007), new approaches to rescaling data (e.g. Gardner et al., 2008)and/or methods for performing multi-resolution analyses withcategorical data (e.g. Pontius and Connors, 2009).

The findings in this study demonstrate examples of where theMAUP is problematic, but do not identify if it is widespread inecology. Neither do the findings provide generalisable results dueto the sample size and the specific environments that thelandscapes represent. The study design used was specificallychosen so that the deterministic mechanisms (i.e. changing pixelsize) could be explicitly described and to demonstrate the use ofthe virtual ecologist approach for evaluating multi-scale models. Inthis study we used six landscapes with a range of fragmentationpatterns to demonstrate that the MAUP effect is not confined to aspecific landscape pattern. However, a broader range of studiesusing greater number of landscapes, controlling for influentialfactors is necessary to attempt to make generalisations that canpredict how landscape pattern influence the effects of the MAUP.Further development of our model using synthetic landscapes tocontrol for spatial patterns with large sample sizes can provide anunderstanding of the properties of the MAUP. Additional avenuesof development required to create generalisations include testingother types of ecological models such as non-linear and/ormultivariate models and testing the effect of other scale-dependent factors which affect spatial resolution. These scale-dependent factors may result from the application of remotesensing and GIS methods such as imposing a minimum mappableunit, applying a low pass filter on raw imagery and resampling fororthorectification. A key obstacle to developing generalisations isthe wide range of landscape patterns and the idiosyncratic naturein which analyses may respond to these patterns and the way theyare observed. Thus, generalisations using quantitative approacheswill always be problematic due to the vast array of untestedsources of uncertainty.

5. Conclusion

This study used the virtual ecologist approach to investigatewhether multi-scale ecological analysis methods can be reliablyused to identify the intrinsic scale. It found that the commonpractice of conducting multi-scale studies to identify the intrinsic

scale can in some cases produce flawed results because of theeffects of the MAUP. Thus, multi-scale ecological analyses may notbe able to distinguish scale-dependent patterns caused by therelationship between an organism and its environment and scale-dependent patterns resulting from the MAUP. This is in contrast tothe assumption that performing multi-scale analyses such as usingmultiple buffer sizes will address scaling issues. This study showsthat scale-dependent ecological patterns identified in ecologicalstudies may be an artefact of the way ecological phenomenon areobserved, which results from a combination of scale-dependentfactors such as pixel size, the application of a smoothing filter andbuffer size.

Acknowledgements

This work was supported by the Australian Research Council’sDiscovery grant DP0450889, the Australian Research Council’sLinkage grant LP0882780 and the Australian CommonwealthEnvironment Research Fund: Landscape Logic research hub.Thanks to Patrick Audet and special thanks to the anonymousreviewers for their comments.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,

in the online version, at http://dx.doi.org/10.1016/j.ecocom.

2012.04.002.

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