Ecological Complexity 15 (2013) 71–82

Original research article

Interactions between landcover pattern and geospatial processingmethods: Effects on landscape metrics and classification accuracy

Alex M. Lechner a,*, Karin J. Reinke b, Yan Wang b, Lucy Bastin c

a Centre for Mined Land Rehabilitation, Sustainable Minerals Institute, University of Queensland, Queensland 4072, Australiab School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V, Melbourne, VIC 3001, Australiac School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, UK

A R T I C L E I N F O

Article history:

Received 5 October 2012

Received in revised form 4 March 2013

Accepted 13 March 2013

Available online 15 April 2013

Keywords:

Multi-scale

Spatial resolution

Aggregation methods

Spatial uncertainty

Remote sensing

Pattern-process

Simulation modelling

Landscape metrics

Classification accuracy

A B S T R A C T

Remote sensing data is routinely used in ecology to investigate the relationship between landscape

pattern as characterised by land use and land cover maps, and ecological processes. Multiple factors

related to the representation of geographic phenomenon have been shown to affect characterisation of

landscape pattern resulting in spatial uncertainty. This study investigated the effect of the interaction

between landscape spatial pattern and geospatial processing methods statistically; unlike most papers

which consider the effect of each factor in isolation only. This is important since data used to calculate

landscape metrics typically undergo a series of data abstraction processing tasks and are rarely

performed in isolation. The geospatial processing methods tested were the aggregation method and the

choice of pixel size used to aggregate data. These were compared to two components of landscape

pattern, spatial heterogeneity and the proportion of landcover class area. The interactions and their

effect on the final landcover map were described using landscape metrics to measure landscape pattern

and classification accuracy (response variables). All landscape metrics and classification accuracy were

shown to be affected by both landscape pattern and by processing methods. Large variability in the

response of those variables and interactions between the explanatory variables were observed. However,

even though interactions occurred, this only affected the magnitude of the difference in landscape metric

values. Thus, provided that the same processing methods are used, landscapes should retain their

ranking when their landscape metrics are compared. For example, highly fragmented landscapes will

always have larger values for the landscape metric ‘‘number of patches’’ than less fragmented

landscapes. But the magnitude of difference between the landscapes may change and therefore absolute

values of landscape metrics may need to be interpreted with caution. The explanatory variables which

had the largest effects were spatial heterogeneity and pixel size. These explanatory variables tended to

result in large main effects and large interactions. The high variability in the response variables and the

interaction of the explanatory variables indicate it would be difficult to make generalisations about the

impact of processing on landscape pattern as only two processing methods were tested and it is likely

that untested processing methods will potentially result in even greater spatial uncertainty.

� 2013 Elsevier B.V. All rights reserved.

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Ecological Complexity

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

1. Introduction

Land use and land cover maps (LULC) derived from remotesensing sources are routinely used in ecology to investigate therelationship between landscape pattern and ecological processes(Gergel, 2007; Lechner et al., 2012a; Wiens, 2002). LULC maps areused to support the identification of vegetation types and todescribe habitat for ecological analyses including the derivation of

* Corresponding author. Tel.: +61 401 233 019; fax: +61 7 3346 4021.

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

(A.M. Lechner).

1476-945X/$ – see front matter � 2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.ecocom.2013.03.003

landscape metrics (Griffith et al., 2000), change detection analysis(Kennedy et al., 2009), habitat suitability/prediction (Guisan andZimmermann, 2000; Leyequien et al., 2007), population viabilityanalysis (Southwell et al., 2008), and conservation planning(Margules and Pressey, 2000). The outcome of such spatialanalyses, however, depends not only on the landscapes themselvesbut also on the way they are represented. In other words, themethods used to observe and process these landscapes influencesthe outcome of spatial analyses (Friedl et al., 2001; Gergel, 2007;Gustafson, 1998; Lechner et al., 2012a).

Quantifying uncertainty that results from the abstraction of thereal world is critical for ecological analyses that use remote sensingdata (Hess, 1994; Lam et al., 2005; Lechner et al., 2012a) to

Fig. 1. Conceptual diagram showing the relationship between true landscape

pattern and geospatial processes, and their effect on the representation of

landscapes as described by Landscape Pattern Indices (LPI) / landscape metrics and

classification accuracy.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–8272

understand the potential implications for management decisions.The characterisation of uncertainty is essential to provide datausers with confidence in the results of analyses using spatial data.Multiple factors related to the depiction of real geographicphenomenon have been shown to affect the representation ofmapped landscapes causing spatial uncertainty. For example, thereare numerous scale-dependent factors such as pixel size (e.g. Sauraand Castro, 2007; Wickham and Riitters, 1995), the application of aminimum mappable unit (MMU) (e.g. Kendall and Miller, 2008;Prada et al., 2008; Shen et al., 2004; Thompson and Gergel, 2008)and thematic resolution (Bailey et al., 2007; Buyantuyev and Wu,2007) which all affect the characterisation of spatial patterns inLULC maps (Lechner et al., 2012a).

There are many ways in which the choices made during the mapcreation process can affect the characterisation of landscapes andthe ecological analyses conducted with that data. For example, thecommonly used European LULC CORINE mapping product hasspecific characteristics (factors) which affect how it representslandscape such as its mapping scale (1:100,000) and its MMU (25hectares) (European Environment Agency, 1994). Many studiesinvestigate the sensitivity of the characterisation of land cover and/or ecological analysis to these characteristics, however, thesestudies usually test a single factor or two factors in isolation byfixing all other factors except the one’s under investigation (e.g.Buyantuyev and Wu, 2007; Lechner et al., 2012b; Wickham andRiitters, 1995). Often the interaction between factors is notinvestigated. If factors interact, studies that consider a single factorin isolation may produce a result that could otherwise differ whenother factors are fixed at different levels. There are many examplesof studies that have tested multiple factors (e.g. Kendall and Miller,2008; Lechner et al., 2008; Saura and Martinez-Millan, 2001; Wu,2004; Wu et al., 2002), but in most cases implicitly, withoutexplicitly testing for interactions using statistical methods.

The aim of this study was to explicitly investigate the interactionbetween factors affecting the representation of landscape pattern,including geospatial processing methods and the spatial character-istics of the underlying landscapes. In terms of geospatial processingmethods that affect the representation of geographic data, weinvestigated the effects of aggregation methods and the choice ofpixel sizes - common tasks in remote sensing data preparation. Theterm processing method has been used in this paper to describe bothgeospatial processing tasks (e.g. resampling) and related inputparameters (e.g. pixel size). These processing methods were testedin relation to the true landscape pattern as described by the spatialautocorrelation and percentage landcover class area at thelandscape scale (henceforth class proportion) of generated syntheticlandscapes. Multiple synthetic landscapes were generated withknown spatial patterns with a large sample size to provide thestatistical power to allow for generalisations to be made. Theinteractions were described using landscape metrics to measurelandscape pattern and classification accuracy (Fig. 1). It is critical tounderstand the interaction between true landscape pattern and theprocessing methods to determine whether a specific factor (e.g.aggregation method) has the same effect in all landscapes, orwhether certain types of landscapes (e.g. those with high spatial

heterogeneity) are more affected by these processing methodscompared to other landscapes. Furthermore, it is important to assessif these interactions are statistically significant and to assess themagnitude and types of these interactions.

An additional aim of this study was to investigate the effect ofaggregation method on the representation of landscape pattern, ararely tested source of spatial uncertainty. The aggregation methodsthat are used to change pixel sizes for multi-scale studies, arecommonly assumed to have no effect and few studies consider howthe method of aggregating to coarser pixel sizes may affect therepresentation of the same landscape at other pixel sizes (but see

Bian and Butler, 1999; Gardner et al., 2008). This assumption thataggregation method has no effect need to be tested in order tovalidate studies that aggregated data to multiple pixel sizes to testfor the sensitivity of an ecological analyses to pixel size or describean ecological phenomenon at multiple scales (e.g. Cain et al., 1997;Lechner et al., 2008, 2012b; O’Neill et al., 1996; Wickham andRiitters, 1995; Wu, 2004; Wu et al., 2002). In the spatial sciencescommunity, it is common practice for remote sensing data to beaggregated when historical data of low or medium spatial resolutionfrom satellites such as Landsat are combined with higher resolutiondata from newer satellites such as Ikonos and Quickbird for crosscomparison or change detection analyses.

There are numerous methods that can be used to spatiallyaggregate remote sensing data and each has the potential to affectlandscape characterisation. Remote sensing data in its raw formatrepresents the radiometric reflectance values of surface objects. Inorder to create LULC maps these raw values are converted into landcover information classes (e.g. urban vs. forest) with a classificationalgorithm. To aggregate remote sensing data to a new pixel sizethere are two possible strategies: (i) the raw data is aggregated andthen classified or (ii) the raw data is classified at the original pixelsize and then aggregated. Furthermore, the aggregation processmay be performed using a number of standard methods such as amajority filter, nearest neighbour or average filter. The question ofwhether all aggregation methods produce equivalent land coverpatterns has important consequences for studies using multiplepixel sizes, or where original pixel sizes have been changed, and forbetween studies which use different methods.

2. Methods

Using synthetic landscapes we tested for the effects ofprocessing method and real spatial pattern on classificationaccuracy and the characterisation of spatial pattern. The processinvolved four steps: (i) generating synthetic landscapes with arange of spatial heterogeneity, (ii) aggregating data using one ofthree methods, (iii) calculating landscape pattern indices andclassification accuracy and (iv) conducting statistical analysis. Forthe statistical analysis, we applied a multivariate analysis ofvariance (MANOVA) along with an analysis of variance (ANOVA)for specific response variables.

2.1. Landscape generation

The synthetic landscapes used in the model were continuousgray scale fractal landscapes, generated using Saupe’s (1988)

Table 1List of the explanatory variables tested.

Variable Description Measurement type

Spatial heterogeneity (H) Landscape spatial autocorrelation H = 0.01, 0.5, 1

Class proportion (CP) The percentage area per class in a binary scheme Class proportion = 0.25, 0.5

Pixel size (PS) The scaling factor used to aggregate the original image pixel value Pixel sizes = 3, 6, 9

Original image: extent = 999

Factor 3: extent = 333

Factor 6, extent = 111

Factor 9, extent = 37

Aggregation method (AM) The order of image processing and generalisation method used Methods = Aggregate with mean then classify

(Agg_then_Classify), classify then majority

(Classify_then_Majority), classify then nearest

neighbour (Classify_then_NN)

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–82 73

fractional Brownian motion with midpoint displacement (mid-pointfM2D) algorithm implemented in IDL. The same algorithm isused in synthetic landscape generation programs used in ecologysuch as RULE (Gardner, 1999) and the recent version QRULE(Gardner and Urban, 2007) and there are numerous exampleswhere it has been used to test spatially explicit ecologicalphenomenon (e.g. Ferrari et al., 2007; King and With, 2002; Neelet al., 2004). The midpointfM2D algorithm can generate syntheticlandscapes using a range of fractal dimensions determined by theparameter H, ranging from 0 to 1. In map terms the fractaldimension equates to landscape patterns with different levels ofspatial autocorrelation (i.e. spatial heterogeneity). Syntheticlandscapes with an H value of 0 have a negative spatialautocorrelation; maps with values of 0.5 are random and mapswith H values of 1 are highly spatially autocorrelated. 100synthetic landscapes were generated for each H value (0.01, 0.5and 1.0) to systematically test the effect of a range of spatialautocorrelations. The initial landscapes generated had a size of999 � 999 pixels and a range of pixel values from 0 to 255 (e.g. 8bit).

This study used synthetic landscapes as it allowed for thegeneration of a large sample size and the control of spatialautocorrelation and proportion of habitat. Large numbers ofindependent landscapes representing a wide range of spatialautocorrelation and class proportion are difficult to acquire fromnatural systems and thus the practice of testing landscape ecologytheory using synthetic landscapes has been advocated (Halleyet al., 2004; Hargrove et al., 2002; With, 1997). However, theresults of this study may represent a subset of the total variationthat occurs in nature. Real landscapes that have been fragmentedby human impacts often have gradients, regionalised variationsand include more regular geometric patterns from humandisturbance. A similar phenomenon has been found by otherauthors (e.g. Diaz-Varela et al., 2009; Shen et al., 2004), wherebythe effects of scale were found to be greater in real landscapes thansynthetic landscapes. Similarly, Riitters, Vogt et al. (2007) foundthat patterns generated using RULE (midpointfM2D algorithm)were different to patterns in real landscapes.

2.2. Generating landscapes with different class proportions and pixel

sizes with multiple aggregation methods

In the next step the original landscapes were aggregated andclassified to create different representations of the same landscape(Table 1). The synthetic image was aggregated using 3 aggregationmethods: (i) aggregation by averaging pixel values, then classifi-cation (Agg_then_Classify), (ii) classification, then aggregationusing a majority rule (Classify_then_Majority) and (iii) classificationthen aggregation using a nearest neighbour rule (Classify_then_NN)(Fig. 1). The landscapes were aggregated by a factor of 3, 6 and 9(pixel size). A binary classification scheme was used with two

classes equivalent to habitat and non-habitat. This is a commonclassification scheme used in landscape ecology (Antrop, 2007).The images were thresholded so that a proportion of the totallandscape area was labelled as habitat. The proportions testedwere 0.25 and 0.5 (0.75 was not tested as it mirrors the effect of0.25 on analysis). The classification method represents a simplifi-cation of remote sensing classification approaches using only asingle thresholded band. The simulation included manipulations ofspatial heterogeneity, class proportion, pixel size, and aggregation

method, resulting in 3 H values � 2 class proportion � 3 pixel

size � 3 aggregation method = 54 combinations (Table 1). 100landscapes were generated for each of the 3 levels of spatialautocorrelation. Thus, there were a total of 5400 landscapes testedin this study.

2.3. Landscape metrics and classification accuracy

In remote sensing, classification accuracy quantifies thedifference between the value recorded by a remote sensingderived map and the real value of the geographic phenomenon. Inthis study the true value was derived at the original image’s pixelsize before it was aggregated. While classification accuracymeasures thematic correctness of an image, it is also importantto quantify the effect of uncertainty on the correctness of thecharacterisation of spatial pattern.

The different aspects of spatial pattern can be quantified usinglandscape metrics, and over 100 metrics are available (e.g. Clericiet al., 2007; McGarigal and Marks, 1994). McGarigal et al. (2002)defined eight categories of landscape pattern which metrics mayrepresent. Others have divided landscape pattern into differentgroups based on qualitative and statistical studies (e.g. Cushmanet al., 2008; Li and Reynolds, 1994; Manning et al., 2006; Neel et al.,2004). We endeavoured to select metrics that measure differentaspects of landscape pattern, as many metrics are closely relatedand some redundant (Manning et al., 2006; Neel et al., 2004).

In total we selected nine metrics (Table 2) to ensure that everybroad category of landscape pattern was measured based on thefragstats software (McGarigal et al., 2002) and studies by Neel et al.(2004) and Lausch and Herzog (2002). Landscape metrics related toclass diversity were not computed, as the synthetic landscapesused in this study only have two categories.

2.4. Statistical analysis

A range of statistical analysis techniques were used to exploreand quantify the relationship between the explanatory andresponse variables. In the first step a principal component analysis(PCA) was conducted to ensure that the response variables(landscape metrics and classification accuracy) represented arange of responses to changes in the explanatory variable and thusdescribed different aspects of landscape pattern. As there were

Table 2List of response variables used in the study. For the landscape metrics the different aspects of landscape pattern that they represent are described.

Metric McGarigal

et al., 2002 (Fragstats)

Neel et al., 2004 Lausch and

Herzog, 2002

Description

Area-weighted mean patch

area (AREA_AM)

Area/density/edge Primarily related to

class area

N/A Mean patch area weighted relative to total

area

Number of patches (NP) Area/density/edge N/A Patch area

metrics

Describes the total number of patches

Edge density (ED) Area/density/edge Related to the interaction

of CP and H parabolic

response along P

Edge and

shape

The linear distance of edge (boundary

between patches and matrix) per unit area

of landscape

Mean perimeter area ratio

(PARA_MN)

Shape Trend from high CP and

H to low CP and H

N/A The average perimeter to area ratio of

calculated for each patch within a

landscape

Standard deviation of perimeter

area ratio (PARA_SD)

Shape Primarily related to

class aggregation

N/A The standard deviation of the perimeter to

area ratio of calculated for each patch

within a landscape

Aggregation index (AI) Contagion/interspersion Trend from high CP

and H to low CP and H

N/A AI equals the number of like adjacencies,

divided by the maximum possible number

of like adjacencies

Area-weighted mean euclidean nearest

neighbor (ENN_AM) or ENN_MN

Isolation/proximity Strongly nonlinear

at high H and low CP

N/A ENN_AM is the area weighted mean

straight line distance from one patch to the

closest patch

Mean Euclidean nearest neighbor

(ENN_MN)

Isolation/proximity Strongly nonlinear

at high H and low CP

N/A ENN_MN is the mean straight line distance

from one patch to the closest patch

Patch cohesion index (COHESION) Connectivity Strongly nonlinear

at low CP and H

N/A Patch cohesion index describes the

physical connectedness of patch types

Classification accuracy (ACCURACY) N/A N/A N/A Number of pixels classified correctly

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–8274

multiple response and explanatory variables a multivariateanalysis of variance (MANOVA) was performed to examine theeffects of the explanatory variables on the related set of responsevariables. Box’s M-test may be used to test the homogeneityassumption, but with equal sample sizes (as in this study) theMANOVA is robust to violations of this assumption. For thoseexplanatory variables with significant statistical results, analysis ofvariance (ANOVA) was subsequently used to identify their effectson the specific response variable of interest. Firstly, the maineffects of each explanatory variables alone were investigated. Thentwo, three and four way interactions were analysed to quantifyhow the variables interact to affect response variables. As well asnumerical statistical analyses, both main effects and interactionswere also plotted to visually help assess the effects of theexplanatory variables on the response means. In the paper we willfocus the discussion on two-way interactions as they are the

Fig. 2. Ordination plot from a principal components analysis (PCA) of landscape

metric and classification accuracy data in the plane of principal component 1 and

principle component 2. Principle components 1 and 2 describe 71.6% of the total

variation.

easiest to understand and follow. For the assumptions underlyingANOVA such as normal distribution and equal variances, largesample size and balanced design of our simulated data provideprotections against the violation of these assumptions. Thestatistical analyses were carried out using the statistical programMinitab 15 (Minitab Inc).

3. Results

3.1. Preliminary analyses of all response variables

The principal component analysis of the landscape metrics andclassification accuracy showed that the first two components 1 and2 describe 71.6% of their total variation. The ordination plot ofprincipal components 1 and 2 shows that the response variablesare spread evenly and thus the landscape metrics selectedrepresent a range of different aspects of landscape pattern(Fig. 2). However, ENN_AM and ENN_MN, and AI and ACCURACYare correlated.

3.2. MANOVA

The MANOVA analyses found that all effects, including the mainand multi-way interactions, were significant. Thus, all explanatoryvariables (spatial heterogeneity, class proportion, pixel size andaggregation method) affect accuracy and the selected landscapemetrics significantly. Next, we look further into the ANOVA resultsthat describe more specific associations.

3.3. Main effects

The ANOVA results show that all main effects from spatial

heterogeneity, class proportion, pixel size and aggregation method

were significant (p < 0.0009) for each of the response variableswith the exception of PARA_SD (P = 0.383) (Appendix 1). As well asthe tests of significance, the main effects were explored graphicallyusing standardised means, as each response variable uses adifferent measurement scale (Fig. 3).

The response variables exhibited a range of behaviours inresponse to different levels of class proportion (Fig. 3). AREA_AM

Fig. 3. Line plots of standardised means for the response variables of accuracy and landscape metrics for each explanatory variable. Standardised values were calculated by

subtracting the mean and dividing by the standard deviation.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–82 75

showed the greatest sensitivity to class proportion with astandardised mean value more than double the next most sensitiveresponse variable (Fig. 3). As class proportion increases, there was alarge decrease in the standardised mean of AREA_AM. In contrast,most response variables such as PARA_SD (Fig. 4) and NP wereunaffected or minimally affected by class proportion. Generally,class proportion had a smaller effect on the response variablescompared to the other explanatory variables with the exception ofAREA_AM (Fig. 5).

Pixel size showed a greater spread and range of standardisedmeans than other explanatory variables at lower and higher pixel

sizes (PS = 1 and PS = 3) with a slightly smaller spread of values (all

Fig. 4. Line plots of PARA_SD means for the explanatory variables class proportion, aggrega

the explanatory variable pixel size.

approaching zero) at the mid-point pixel size (PS = 2). PARA_MNand PARA_SD showed the greatest decrease in standardised meansas pixel size increased (Fig. 3). While the response variables ofAREA_AM, ENN_AM and ENN_MN showed an increase in values aspixel size increased, in some cases such as PARA_SD the main effectof pixel size was far greater than other explanatory variables with adecrease in mean PARA_SD from 372,386 to 67,360 compared to anincrease from 150,244 to 252,006 for spatial heterogeneity whichhad the second largest main effect (Fig. 4).

Spatial heterogeneity showed the greatest mix of responsevariable behaviour at different levels (Fig. 3) with some responsevariables relatively unaffected and the opposite case with other

tion method, pixel size and spatial heterogeneity. The largest main effect can be seen in

Fig. 5. Line plots of AREA_AM means for the explanatory class proportion, aggregation method, pixel size and spatial heterogeneity. The largest main effect can be seen in the

explanatory variable class proportion.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–8276

variables. ACCURACY and AI behaved almost identically, shiftingfrom low standardised mean values to large values as the levelschanged. Like pixel size, the smallest spread of values was aroundthe mid-point at H = 0.5. In some cases such as AI large differenceswere observed only for spatial heterogeneity (Appendix 2).

The explanatory variable aggregation method showed only smalldifferences in standardised means response behaviour. Unlike theother explanatory variables, this variable is categorical and thusonly the magnitude of the difference between levels can beconsidered, not the trends. The methods Agg_then_Classify andClassify_then_Majority behaved almost exactly the same. However,Classify_then_NN usually had the opposite effect on the standar-dised mean. For example, ED, PARA_MN and COHESION all hadnegative standardised means for Agg_then_Classify and Classi-fy_then_Majority and a positive standardised mean for Classi-

fy_then_NN.

Table 3Summary table of two-way interactions. Blank cells indicate no significant interactions (p

F-ratio reported for the combination of explanatory variables per response variable is d

lowest by a light grey cell with circle). Where CP = class proportion, AM = aggregation m

NP Para_MN Para_SD ENN _MN ENN _AM

CPxAM

CPxPS

CPxH

AMxPS

AMxH

PSxH

In summary, the explanatory variables pixel size and spatial

heterogeneity had the greatest magnitude of differences in theirstandardised mean compared to the explanatory variablesaggregation method and class proportion. Class proportion onaverage had the smallest main effect in comparison to the otherexplanatory variables and certain landscape metrics were almostunaffected by changes in class proportion. A large range of maineffect behaviour for different response variables was observed.There were examples of a response variable where a large maineffect was observed for all but one explanatory variable (e.g. Fig. 4(PS), Fig. 5 (P) and Appendix 2 (H)). In other cases all main effectswere present for all explanatory variables such as EMN_MN(Appendix 3). While most response variables behaved differentlyin response to each explanatory variable, ACCURACY showedalmost identical behaviour to AI across all explanatory variablesexcept for Aggregation method (Pearson correlation for all values:

-value > 0.05), light grey and black cells indicate significant interactions. The highest

enoted by the black cells. The second highest is denoted by dark grey cells and the

ethod, H = spatial heterogeneity and PS = pixel size.

ED Area_AM Cohesion AI Acc uracy

Fig. 6. Two-way interaction plot of NP.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–82 77

0.947, P < 0.0009). Additionally, NP and ED also shared nearidentical trends for all explanatory variables (Pearson correlationfor all samples: 0.956, P < 0.0009). Conversely, some responsevariables had almost equal standardised means for all levels forone explanatory variable, but for another explanatory variabletheir behaviour was completely opposite. For example, PARA_MNand PARA_SD had nearly exactly the same standardised meanvalues for pixel size, but for spatial heterogeneity, when oneresponse was positive the other was negative. Finally, for allresponse variables the direction of change remained the same witheach change in level (for the two explanatory variables with morethan one level: pixel size and spatial heterogeneity). In other words,there was either a negative or positive trend.

3.4. Interactions

The results of the ANOVA showed a range of two-wayinteractions whereby certain response variables did not havesignificant two-way interactions or minimal interactions, whileother response variables had large interactions at one or morelevels. Table 3 provides a summary of all the two-way interactionsand indicate where the greatest effects may lie with respect to thetwo-way combinations of explanatory variables. The table shows,that whilst almost all two-way interactions were significant, thegreatest effects in response variables appeared for class propor-

tion � spatial heterogeneity, aggregation level � spatial heterogeneity

and to a lesser degree, aggregation method � aggregation level andaggregation method � spatial heterogeneity. The response variableArea_AM showed the greatest range in effect (according to F-ratios) followed by NP and PARA_MN. ENN_MN showed the leasteffect amongst the response variables.

Table 4 presents a summary of the three-way interactions andindicates where the greatest effects may lie with respect to thethree-way combinations of explanatory variables. Class propor-

tion � aggregation method � pixel size and class propor-

tion � aggregation method x spatial heterogeneity had the smallesteffect on the response variables which, when considered with the

two-way interaction table suggests that, in general, the combinationof class proportion and aggregation method had less effect than othercombinations of explanatory variables for all response variables.

In the next section we took a subset of the data examining theresponse variable interactions in more detail. ACCURACY, NP andAREA_AM were selected as they represent good examples of thedifferent types of behaviours exhibited by the response variables ingeneral. As well as statistical analyses, the behaviour of theresponse variables was explored visually using plots of theirinteraction. The interaction plots describe the means for each levelof the explanatory variable with the level of a second explanatoryvariable held constant. Two way interactions can be graphicallyidentified whereby the lines representing different levels of anexplanatory variable are not parallel (e.g. Fig. 6, pixel size versusspatial heterogeneity).

3.4.1. Interactions for number of patches

All two-way interactions for NP were significant (Table 3) withsome interactions resulting in large differences in means at specificlevels for one or more explanatory variables (Fig. 6). Thecombination pixel size � spatial heterogeneity showed the greatestamount of interaction compared to all other explanatory variables.There was a decrease in the mean NP reported as spatial

heterogeneity increased. However, at H = 0.01 the differencebetween PS = 1 (mean NP = 5031) compared to PS = 2 (meanNP = 948) and 3 (mean NP = 390) was much greater. The otherlarge effect observed was for the combination of spatial hetero-

geneity � aggregation method. In this instance, NP was almost thesame for all aggregation methods, where H = 0.5 and H = 1.0.However, the mean NP for H = 0.01 was greater than other H valuesand even larger for aggregation method, classify_then_NN. Most ofthe large interactions occurred when H = 0.01 i.e. where individualpixels were likely to be isolates as individual patches. Interactionsbetween class proportion and other explanatory variables, whilesignificant, were all very small compared with the otherexplanatory variables as demonstrated by the parallel lines inthe interaction plots.

Table 4Summary table of three-way interactions. Blank cells indicate no significant interactions (p-value > 0.05), grey and black cells indicate significant interactions. The highest F-

ratio reported for the combination of explanatory variables per response variable is denoted by the black cells and the lowest by grey cells with a circle. Where CP = class

proportion, AM = aggregation method, H = spatial heterogeneity and PS = pixel size.

NP Para_MN Para_SD ENN _MN ENN _AM ED Area_AM Cohesion AI Acc uracy

CPxAMxPS

CPxAMxH

CPxPSxH

AMxPSxH

.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–8278

3.4.2. Interactions for PARA_MN

PARA_MN is an example of a response variable in which themagnitude of the two-way interactions were very small or in somecases not present. Both class proportion � aggregation method (P-value = 0.729), and class proportion � pixel size (P-value = 0.066)were not significant. All other two-way interactions weresignificant (P < 0.0009). Pixel size � spatial heterogeneity had thelargest interaction (Fig. 7). An increase in the pixel size resulted inlower mean PARA MN, and an increase in spatial heterogeneity

resulted in a decrease in mean PARA_MN. However, at H = 1.0 thedifference between mean PARA_MN for pixel size and the otherpixel sizes were much less. The size of this interaction contrastswith the small magnitude of other interactions. The interaction ofthe explanatory variable class proportion with other explanatoryvariables, was either not significant or very small.

3.4.3. Interactions for ACCURACY

The response variable ACCURACY provides an example where arange of large and small two-way interactions were found for a

Fig. 7. Two-way interacti

single response variable (Fig. 8). All two-way interactions weresignificant (P < 0.0009), with the exception of aggregation meth-

od � class proportion (P < 0.370). Spatial heterogeneity � class

proportion showed the greatest interaction. For H = 0.5 andH = 1.0 there was very little change in accuracy regardless of theclass proportion as shown by the parallel lines in the plot. However,for H = 0.01 there was a decrease in accuracy at a larger class

proportion. A similar pattern of interaction could be seen in spatial

heterogeneity � pixel size with very little change in ACCURACY forH = 0.5 and H = 1.0 and a decrease in ACCURACY at a larger pixel

size. Spatial heterogeneity � aggregation method showed a similarpattern, however the interaction was only present for classi-

fy_then_NN. Although statistically significant, minimal interactionbetween other explanatory variables was present.

3.4.4. Interaction summary for all variables

While there was a large range of variability in the main effectsand interactions more complex interactions such as disordinal/cross-over interactions where the interaction plot lines intersect

on plot of PARA_MN.

Fig. 9. Three-way interaction plot of AREA_AM for class proportion � pixel size � spatial heterogeneity.

Fig. 8. Two-way interaction plot of ACCURACY.

A.M. Lechner et al. / Ecological Complexity 15 (2013) 71–82 79

were rarely observed. Cross-over interactions were only observedfor AREA_AM (Fig. 9), however the magnitude of the difference wasvery small. Furthermore the direction of trends was always thesame; i.e. trends remained consistent regardless of the level ofinteraction. Even though three-way interactions were significant,the patterns described by two-way interactions and the maineffects are still valid. The magnitudes of three-way interactionswere consistently small in comparison to two-way interactions asshown in the three-way interaction plots of AREA_AM (Fig. 9).Three-way interactions can be identified by comparing two plotsand if the differences in slopes are not the same in both plots, a

three-way interaction is present. Fig. 9 shows very small three-wayinteractions, though significant (P-value < 0.0009). Finally, alltwo- and three-way interactions for spatial heterogeneity and pixel

size resulted in consistent positive or negative trends in the averagevalue of the response variable across levels. There were no Vshaped or ^ shaped trends. Although, these trends were not linear.

4. Discussion

The results of this study demonstrate that the representation oflandscapes as used in pattern-process analyses in ecological

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applications is as much a property of the true landscape pattern asof the processing methods used to observe and represent thatlandscape. We found that the most important explanatoryvariables were spatial heterogeneity (a property of the generatedlandscapes) and pixel size (a property of the processing method).These explanatory variables tended to result in large main effectsand large interactions. In contrast, class proportion had the leasteffect on the response variables. However, there was largevariability in landscape metric behaviour and each responsevariable appeared to have unique behaviour in terms of its maineffects and interactions.

This study builds on previous research into the effects of spatialscale on the characterisation of landscape pattern (e.g. Lechneret al., 2009; Saura and Castro, 2007; Wickham and Riitters, 1995).Furthermore, it provides evidence of the effect aggregation method

has on the characterisation of landscape pattern which becomescritical for multi-scale studies. The behaviour patterns for manylandscape metrics in relation to changes in the explanatoryvariables could readily be explained. For example, a decrease in NPis expected when the number of pixels within a landscape isreduced through coarser pixel sizes. The observed sensitivity oflandscape metrics provides a good indicator of how pattern-process based analyses in landscape ecology may be affected by therepresentation method.

4.1. The importance of interactions

The results of this study demonstrated that there were nocomplex cross-over interactions and the main effects werealways in one direction (note: cross-over was observed withAggregation method but as this is categorical the order ismeaningless and thus the observation of cross-over is irrele-vant). Studies that have tested multiple factors graphicallywithout the tests of statistical significance used in this study,have found similar patterns (Lechner et al., 2008; Saura andMartinez-Millan, 2001; Wu et al., 2002). Thus, as long as theprocessing method is the same (e.g. same pixel size and sameaggregation method), only the magnitude of the differencesbetween landscapes should change. For example when compar-ing two landscapes, regardless of the pixel size used for bothlandscapes, more heterogeneous landscapes will always becharacterised by remote sensing data as more heterogeneousthan less heterogeneous landscapes. However, the absolutevalues of landscape metrics are as much a property of thelandscape as of the processing method (e.g. pixel size).

Land cover maps produced with different processing methodscan characterise landscape pattern differently. Maps producedthrough Agg_then_Classify and Classify_then_Majority are likely tocharacterise landscape pattern in similar ways, while Classi-

fy_then_NN is likely to characterise landscape patterns verydifferently. Our results suggest that it won’t matter whether theoriginal multi-spectral data is classified first then aggregated orvice versa when using the first two methods. This is one of the firststudies focusing on these effects specifically for discrete categori-cal landscapes. Other studies in this area such as Bian and Butler(1999) investigated differences in aggregation methods forsynthetic gray scale (continuous) landscapes, while Gardneret al. (2008) focused only on rescaling methods for classifiedbinary landscapes. A previous study by Jones et al. (2006) focusedon a small number of landscapes and the effects of aggregationmethod on accuracy. Future research in this area need to expand onthe simple classification method of thresholding as there are likelyto be other sources of uncertainty such as differences in remotesensing classification method (e.g. object orientated versus pixelbased) and sensor characteristics, that potentially affect suchcomparisons.

Studies that investigate the sensitivity of a single explanatoryvariable in isolation will be affected by the value of otherexplanatory variables that are fixed. As all the explanatoryvariables interact, predictions and generalisations of the effectof explanatory variables are difficult to make. Different compo-nents of landscape pattern as described by landscape metrics weremore sensitive to either processing methods or the spatial patternof the landscape. For example, NP was susceptible to allinteractions in contrast to PARA_MN in which no or minimaleffects were observed. The presence of interactions means that thetrue landscape pattern interacts with processing method and thusit will be difficult to isolate purely landscape pattern driven effectsfrom the effects of processing methods when conducting ecologi-cal analyses and thus address spatial uncertainty.

In this study we chose a few key explanatory variables that arecommonly the subject of research on the effects of scale (e.g. Cainet al., 1997; Lechner et al., 2008; O’Neill et al., 1996; Wickham andRiitters, 1995; Wu, 2004; Wu et al., 2002). However, there arenumerous sources of spatial uncertainty described in the literaturethat also have the potential to effect analyses such as scale-dependent factors (Lechner et al., 2012a) that include patchlocation, minimum mappable units and thematic resolution (e.g.Buyantuyev and Wu, 2007; Lechner et al., 2009; Wu et al., 2000). Ifwe had chosen to conduct this experiment with a different set ofexplanatory variables such as thematic resolution and MMU theinteractions may have been different. Furthermore, the largevariability and complexity in their responses indicate if a differentset of metrics was tested the result would describe a differentrange of unique behaviours. This is likely to be the case, eventhough the landscape metrics used in this study represented arange of responses (as described by the ordination plot). Forexample, one focus of research in landscape ecology is theidentification of the smallest set of landscape metrics that candescribe all of the different forms of landscape pattern (e.g.Cushman et al., 2008; Lausch and Herzog, 2002; Neel et al., 2004).No consensus exists on the choice of metrics (McGarigal et al.,2002) and the results of some studies contradict each other(Cushman et al., 2008). The reason for the lack of consensus hasbeen attributed to each study investigating a limited suite oflandscape metrics on a different set of landscapes with their ownunique pattern characteristics (Cushman et al., 2008).

4.2. Accuracy

A key response variable investigated in this study was that ofACCURACY. Classification errors measured in this study were theresult of differences in pixel size and aggregation method alone.Classification accuracy is one of the only variables describing errorin remote sensing landcover maps that is routinely measured. Anaccuracy assessment is considered a minimum requirement forremote sensing land cover dataset (Cunningham, 2006). However,the behaviour of ACCURACY was very different to other landscapemetrics other than AI. Thus, classification accuracy statements arenot likely to be a good prediction of the accuracy of landscapepattern characterisation. Maps may have high classificationaccuracy yet low accuracy in terms of landscape patterncharacterisation as the accuracy assessment does not take intoaccount the spatial distribution and variation in mapping errors(Steele et al., 1998). There is a need to develop better descriptorsdescribe error in metrics.

This study did not look at the impact of errors that occur duringthe classification process. For example, when using real remotesensing data the algorithms used to classify multispectral data intoland cover classes are never 100% accurate due to the effects ofnoise, geometric error, vagueness of landcover classes etc. Thistype of classification error can be considered as another untested

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explanatory variable that has the potential to interact and affectthe accuracy of landscape pattern characterisation. For example, astudy by Langford et al. (2006) found that in some cases mapclassification error can cause a thousand-fold increase in error inthe calculation of landscape metrics.

5. Conclusion

This study focused on the interaction of geospatial processingmethods and true landscape pattern. The findings are particularlyrelevant to landscape ecology, a discipline which focuses on therelationship between spatial pattern and ecological processes, as ithighlights the sensitivity of landscape metrics to change depend-ing on commonly applied data processing decisions. This paperextends existing knowledge in this area by describing theinteraction effects of multiple combinations of data processingfactors using statistical methods. The variability in response, andthe interaction of the explanatory variables, indicate it is difficultto make generalisations about the effect of spatial uncertainty onthe characterisation of landscape pattern. The results suggest thatcomparisons of landscape metric values between landscapesprocessed using the same methods are likely to remain consistentas long as only ranking of the landscapes are used. For example,landscape A is more heterogenous than landscape B and Caccording to a set of landscape metrics. However, the interactionof processing methods mean absolute values of these metrics aremeaningless as they are dependent on processing methods usedand need to be interpreted with caution. Finally, unless differencesdue to processing methods are accounted for (e.g. rescaling)comparisons between landscapes processed using differentmethods may be spurious. The patterns found with in our analysisof landscape metrics may potentially be considered analogous todifferent types of spatial models conducted in the field oflandscape ecology. Thus, spatial uncertainty resulting from theinteraction of these explanatory variables needs to be consideredwhen the accurate characterisation of landscape pattern usingspatial datasets is a key input into spatially explicit ecologicalmodels. The next step is to test these findings using reallandscapes.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.ecocom.2013.03.003.

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