LAB EXERCISE #3 – Neutral Landscape Analysis Objectives ...

LAB EXERCISE #3 – Neutral Landscape Analysis

Instructors: K. McGarigal

Overview: In this exercise, you will learn to use the program QRULE and interpret the output inthe context of the case study landscape. QRULE is a program for generating and quantifyingneutral landscapes. Students will become familiar with the concept of neutral landscapes andgain a practical understanding of how to use neutral landscapes to test hypotheses regardinglandscape pattern formation. Specifically, students will test the null hypothesis that the reallandscape(s) is structured randomly (i.e., how likely is it that the landscape pattern could havebeen produced in the absence of any ecological pattern-generating processes), determine how thelacunarity pattern of the real landscape varies in comparison to random and fractal landscapes,and quantitatively show how landscape connectivity varies as a function of the interplay betweenspecies’ life history characteristics and the configuration of habitat.

Objectives

• To learn how to use QRULE and interpret the output.• To become familiar with the concept of neutral landscapes.• To gain a practical understanding of how to use neutral landscapes to test hypotheses

regarding landscape structure and connectivity.

Background Information

In lab #2 we gained an overall familiarity with the biophysical patterns of the case studylandscape. In this lab, we are going to delve more deeply into the agents of pattern formationaffecting vegetation and begin to explore the ecological consequences of those patterns. For thispurpose, we are going make use of neutral landscapes, so a brief discussion of neutral landscapeanalysis is required.

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What are Neutral Landscape Models?

Neutral landscape models are grid-based maps in which complex habitat distributions aregenerated by random, hierarchical, or fractal algorithms. Because the artificial landscapes aregenerated with analytical algorithms, they are thus “neutral” to the biological and physicalprocesses that shape real landscape patterns.

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Why are neutral landscapes useful?

Neutral landscape provide a useful model for the study of ecological responses to landscapepatterns because they are based on the movement, flow, or rate of spread that characterize adiverse array of biological processes. For example, by simulating the dispersal of organismsacross neutral landscapes, we can examine how habitat area and configuration interact to affectlandscape connectivity for organisms with different dispersal abilities. In this way, neutrallandscapes offer a means of conducting a highly controlled experiment, without the logisticaldifficulties of conducting real-world experiments at the landscape scale. [Of course, neutrallandscape experiments are not without their own set of tradeoffs]

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The concept of percolation in neutral landscape models

Percolation, in this context, refers to the physical connection or spanning of the focal class(habitat or land cover type) across the landscape (from side to side) for a given neighbor rule. Assuch, percolation provides a simple measure of connectedness for the study of ecologicalresponses to landscape patterns.

A percolating cluster (patch) is a set of connected cells (patch) that spans the landscape from sideto side. In this figure, the percolating cluster is the large patch of cells depicted in green. In thiscase, connected is defined by the 4-neighbor rule which means that only cells touching on a side(orthogonally) are considered “connected”. Cells touching only at the corner (diagonally) areconsidered “disconnected”.

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Neighborhood rules

Clearly, what constitutes a connection depends on how one defines it. In the previous example,cells were considered connected only if they shared a complete side. This is known as the 4-neighbor rule, because a cell has only 4 neighboring cells that share a side (these are also know asorthogonal neighbors). The 8-neighbor rule allows the four neighboring cells touching only at thecorner (i.e., diagonally adjacent) to be considered as neighbors as well. The 4- and 8-neighborrules are based on the restriction that a neighbor must be physically touching the focal cell to beconsidered “connected”. However, for species (and phenomena) that can easily cross gaps, theneighbor rule can be extended to nearby cells that are within a certain distance of the focal cell.For example, the 12-neighbor rule considers the 8 surrounding cells plus 4 additional cells onecell away in the orthogonal directions. Clearly, there is no limit to how neighborhood rules canbe defined, which provides great flexibility for exploring the relationship between landscapepattern and landscape connectivity for species (or processes) with different life history (e.g., gap-crossing abilities).

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Neighborhood Rules

Because neighborhood rules determine what constitutes a single cluster (or patch), they affectmeasured characteristics of the landscape pattern. For example, as shown in the top figure, thereis a strong threshold-like relationship between the area-weighted mean cluster size and P, theproportion of the landscape comprised of the focal class. Specifically, for a randomly patternedlandscape, as P increases, at first there is no measurable increase in the area-weighted meancluster size because the additional area is largely individual cells and very small patches.However, at some point, as P increases further, the small patches begin to coalesce into largerpatches and the area-weighted mean cluster size increases. The P at which this begins to happendepends on the neighborhood rule, because the 12-neighbor rule will fuse patches together intolarger clusters long before the 4-neighbor rule. The size of the largest cluster exhibits a similarrelationship. Specifically, for a random landscape, the P at which a percolating cluster forms,

critknown as the critical percolation threshold (P ), varies as a function of the neighbor rule. For

critthe 4-neighbor rule, P occurs when P . 0.6. When an 8-neighbor rule is used to identify

critclusters, the value of P drops to . 0.4, and so on.

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Random landscapes

This simplest neutral landscape is a simple random one, in which the pattern is completelyrandom. For a single focal class, call it “habitat”, each cell is randomly assigned to “habitat” orbackground depending on the user-specified probability of occurrence, or proportion of thelandscape to be assigned as habitat (P). For a multi-class landscape, each cell is randomlyassigned to one of the classes based on user-specified proportions. Simple random landscapes areoften used as a null model, whereby the landscapes are neutral to ALL pattern-generatingprocesses.

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Hierarchical (curdled) random landscapes

Another kind of neutral model can be used to produce hierarchically structured maps.Hierarchically structured random maps, also known as curdled maps, can be produced by arecursive procedure in which a series of scales are defined and then cells are assigned a classrandomly within each scale. The sequence of steps requires several parameters to control theprocess, including the number of hierarchical levels, L, the size of each level, M, and theprobability of being assigned to a class at each level, P.

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As shown in this example, by varying L, M and P, a bewildering array of hierarchicallystructured patterns can be generated. The overall proportion of habitat in the map is determinedby the product of the P’s for each level. Similarly, the overall map dimension (i.e, length of oneside in number of cells (is determined by the product of the M’s for each level. By varying theP’s across levels, a variety of patterns can be created for maps with the same dimensions andhierarchical levels.

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Fractal landscapes

A third kind of neutral landscape model can be used to create fractal maps. Fractal random mapsexhibit varying degrees of continuous spatial autocorrelation between classes. The procedure forgenerating fractal maps is discussed in Turner et al. (2001). Essentially, by varying the parameterH, representing the spatial autocorrelation, and P, the proportion of the landscape in each class,one can create a wide variety of patterns, ranging from extremely rough patterns in which theclasses are highly fragmented, to extremely smooth patterns in which the classes are highlyclumped or contagious in their distribution. Again, procedures exist for creating both single classand multi-class fractal maps. Perhaps more than any other neutral landscape model, fractallandscapes have been used in a wide variety of applications, for example, to explore the effects ofhabitat area and fragmentation on landscape connectivity for orgnisms.

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QRULE Statistics – Rulerun.log

We will be using the program QRULE developed by Bob Gardner, first developed (and namedRULE) and applied in the late 1980's. QRULE rule produces four different output filescontaining the results of the neutral landscape analysis. We are going to make use of two of theseresults files in this exercise.

First, the Rulerun.log file contains a number of statistics (landscape metrics) for the neutrallandscapes generated, including those listed here. The first four statistics reported are for thesingle largest cluster in the landscape: Mass fractal dimension is a measure of aggregation orshape complexity, where the higher the fractal dimension the more clumped or aggregated thedistribution of mass; Radius of gyration is the average distance between cells in the cluster and isa measure of cluster extensiveness; larger values are associated with clusters that extend overgreater distances. The next four statistics are self-explanatory. The next statistic, correlationlength, is equal to the area-weighted mean radius of gyration. We will discuss this metric indetail in the next lab. For now, suffice it to say that correlation length is a measure of the physicalconnectedness of the landscape (or focal class) and is often interpreted as the distance on averagean organism (or process) can traverse the landscape from a random starting point and remain inthe same class (i.e., not leave the cluster). The last metric, percolation frequency is given as thepercentage of neutral landscapes containing a percolating cluster and, as such, is often interpretedas a simple measure of the physical connectedness of the landscape.

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The Rulerun.log file contains first- and second-order summary statistics for each land coverclass. For each of the 10 landscape metrics, the mean, standard deviation, coefficient of variation,minimum and maximum values across the replicate landscapes are reported. Because eachreplicate landscape is generated independently, each one represents a single, independent,stochastic realization of the neutral landscape model. If enough replications are done, the analysiscan be treated as a Monte Carlo simulation, where the summary statistics provide a description ofthe random permutation distribution of each landscape metric. These statistics can be comparedto those from real landscapes to test hypotheses about pattern-generation in the real landscapes,as you will do below.

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QRULE Statistics – Lacun.dat

Second, the Lacun.dat file contains the results of the lacunarity analysis. Lacunarity, you willrecall from lecture, is a scale-dependent measure of contagion (or spatial aggregation) and istypically plotted as the natural log of lacunarity against the natural log of box size. The resultinglacunarity curve expresses spatial contagion as a function of scale. The Lacun.dat file containsfour unnamed columns. The first is the box size (scale) given in distance units. The second is thecorresponding raw lacunarity value. The third is the normalized lacunarity value, derived bysimply dividing the lacunarity by the maximum lacunarity value (which is always the lacunarityfor the box size of 1). The normalized lacunarity merely rescales the lacunarity output so that thevalues range from 1 to 0. Recall that lacunarity varies as a function of P (proportion of thelandscape occupied by the focal class); specifically, lacunarity increases as P decreases. Thus,normalized lacunarity adjusts for variation in P. This may be useful if one wishes to compare therelative spatial contagion among landscapes independent of their variation in P. The fourthcolumn is the variance to mean ratio and is constant for all box sizes.

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Detailed Instructions

Step 1. Establish the objective of the analysis

In lab #2 we learned that there is an almost limitless number of ways to define the landscape foranalysis and that our choice of definition can have important quantitative (and qualitative)consequences, and thus that the landscape should always be defined on the basis of clearly statedobjectives. Thus, the first step is to establish the objective of the analysis. We are currently in theplanning stages of a study on the effects of forest loss and fragmentation on breeding birds in theConnecticut River watershed. The overall purpose of this study is to determine the effects offorest loss and fragmentation caused by urban/residential and agricultural development onbreeding bird community structure and the abundances of several bird species associated withinterior forested habitat. We are particularly interested in determining whether thresholds exist inavian response to habitat loss and fragmentation and determining if the existence and nature ofany threshold response to habitat loss is effected by habitat configuration (i.e., fragmentation).

In this exercise, we are going to focus on the following specific questions (but note that themethods and principles applied and learned in this exercise are broadly applicable to a widerange of related questions):

1. Is the configuration of forest cover different from a randomly structured landscapecontaining the same number of patch types in the same proportions? In other words, howlikely is it that the configuration of forest cover in each real landscape could have beenproduced in the absence of any ecological pattern-generating processes?

2. Does the configuration of forest cover expressed across spatial scales (as measured bylacunarity) reveal anything about the nature of the pattern-forming agents?

3. Does landscape connectivity vary as a function of the interplay between species’ lifehistory characteristics and the configuration of habitat for forest-associated species?

Step 2. Establish the study design and define the digital landscapes

We delineated a somewhat arbitrary study area encompassing 214,900 ha surrounding the citiesof Amherst, North Hampton, Holyoke, and Springfield. This study area includes the towns with apreponderance of agricultural land and experiencing the greatest urban/residential sprawl in theConnecticut River watershed in Massachusetts. To facilitate study site selection and to aid in ourunderstanding of landscape structure gradients within the study area, we compiled a GIS databaseconsisting of the following data layers:

(1) 1985 Land use/cover map (created by our Resources Mapping Lab using aerial photointerpretation). For our purposes, we have aggregated land use/cover classes into 6 broadclasses (forest, open, residential, urban, wetland, water) and converted the original vectorcoverage, mapped at a minimum resolution of $0.5 acre (varied among cover classes), to a

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raster grid with a 50 m cell size (0.25 ha).

(2) 1-km square grid superimposed over the study area.

For the purpose of this exercise, we arbitrarily selected 3 5-km square (2,500 ha; 100 rows x 100columns) landscapes based on the land use/cover map using the 1-km square grid. The selectedlandscapes, hereafter referred to as ‘real’ landscapes, represent a gradient in the areal extent offorest cover, as follows:

Grid Name %LandscapeForested (p)

%LandscapeOther (1-p)

Reg21 20.52% 79.48%

Reg66 65.58% 34.42%

Reg78 78.04% 21.96%

Note, the size of the sample landscapes represented a comprise between two factors: 1) the desireto make the sample areas large enough to capture meaningful habitat patterns, and 2) the desire tolimit the size to 100 x 100 cells for computational efficiency in the QRULE software (below).

In addition, ‘open’ land cover was the predominant nonforest cover type in each landscape. Thus,the principle agent of forest loss in these landscapes was agricultural development. It can beassumed that the conversion of forest to open cover occurred historically during the period ofagricultural expansion in the region (mid 1800's). Each landscape was analyzed usingFRAGSTATS to quantify the composition and configuration of the landscape based on the landuse/cover classes and the patch-, class-, and landscape-level results are included as attached filesfor reference use.

Open up in ArcMap the project file “...\neutral\neutral.mxd”

Take some time to review each layer for the purpose of familiarizing yourself with the samplelandscapes.

Step 3. Conduct the neutral landscape analysis

The next step is to conduct the neutral landscape analysis. This step is broken into three partscorresponding to the three study questions. The first part involves testing the real landscape fornonrandom patterns, the second part involves comparing the lacunarity curves betweencorresponding real and neutral landscapes, and the third part involves examining the relationshipbetween landscape pattern and landscape connectivity. Each of these parts involves runningQRULE to generate and analyze neutral landscapes.

To facilitate running all of the QRULE simulations needed for this exercise and managing the

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QRULE output files, we have written a function for batch processing (or “file redirection” inQRULE parlance) in the R language and statistical computing environment (note, it is assumedthat you have pre-installed the R software). Note, detailed instruction on the use of R is waybeyond the scope of this exercise, so the instructor will guide you through the following steps.

Open the R interface: Start ( Programs ( R ( R 2.4.0 (or higher)

Open the R script provided: File ( open script ( .../neutral/scripts/qrule.analysis.r

Run the following lines from the script:source('c:/work/landeco-umass/exercises/neutral/scripts/qrule.R')batch.rule(path='c:/landeco/exercises/neutral',infile=’batchfile.txt’)

Note, substitute the path in the above lines for the local path on your computer.

Now be patient for 10-15 minutes while the computer does all the work for you. While thebatch file is running, the R console window will show an hourglass when the mouse/cursor isplaced over the window, or in Rstudio the “Stop” sign will be visible in the console. Whenthe prompt (‘>’) is returned, the batch file is done processing and you can proceed to the nextstep. If the program should fail for any reason, no worries, the results (from a previous run)are included in the output folder.

3.1 Test for nonrandom patterns

The next step is to test the following null hypothesis:

The configuration of habitat in each real landscape is not different from a randomlystructured landscape containing the same percentage of habitat. In other words, how likely isit that the configuration of habitat in each real landscape could have been produced in theabsence of any ecological pattern-generating processes.

First, in the batch file already processed, for each real landscape we generated 100 iterations of asimple random landscape containing 1 patch type in the proportion listed in the previous tableusing QRULE and these parameters:

Parameter Input Parameter Input

Map type S #Reps 100

Dimensions 100 100 Output map G

Neg seed any large number Output file name asciimap.txt

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Nearest neighbor 2 Analysis (A)ll

#Classes 1 Grid resolution (m) 50

Classprobabilities

0 = 1- pth

1 = pth

Important: if you were to run QRULE interactively, when prompted for the number ofhabitat types and their probabilities, input ‘1' as the number of types, and then be sure to inputthe correct probabilities for class = 0 (all background or, in this case, nonhabitat) and class =1 (habitat). These proportions should sum to 1.

Important: if you run QRULE interactively, rename the ‘rulerun.log’ file to a unique filename after each run; otherwise, QRULE will overwrite them during each run.

Second, in the batch file already processed, in addition to these random landscapes, we alsoanalyzed each real landscape using the following input parameters:

Parameter Input Paramter Input

Map type I #Reps 1

Input file reg21.txt, reg66.txt,or reg78.txt

Output map G

Dimensions 100 100 Output file name asciimap.txt

#Classes 6 Analysis (A)ll

Nearest neighbor 2 Resolution 50

Important: if you were to run QRULE interactively, rename the ‘rulerun.log’ file and‘lacun.dat’ file to unique file names after each run, or they will get overwritten after each run.

Next, view the generated neutral landscapes. QRULE outputs the maps (for the last replicationonly) in both ArcGrid and ascii formats. The ArcGrids will have file names that look like?.arcgrid.map, and the ascii files will have file names that look like ?.asciimap.txt. There are twooptions for viewing these maps.

• You can view these maps in your ArcMap project (...\neutral\neutral.mxd). Note, theneutral.mxd project already has them preloaded. Since these grids do not have any spatialreference system, they will not project onto your case study landscape. To view thesegrids you will need to select each grid in turn and “zoom to layer” (right click on layername and select “zoom to layer” option).

• Alternatively, you can view these maps in R using a function that we have written for thispurpose. To do this, run the script provided in qrule.analysis.r. For example, the first plotis generated by running the following lines:

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rulemap(path='c:/work/landeco-umass/exercises/neutral/output/',infile=c('reg21','ran21','reg66','ran66','reg78',’ran78'))

Let’s decompose this so that you understand this function call. This call runs the Rfunction called rulemap, which has two arguments that control the plotting, as follows:

path = specifies the directory containing the lacunarity.csv files for the inputlandscapes. Note, substitute the path in the function above for the local path onyour computer.

infile = vector of input landscapes that you want to plot; in this case, selecting eachpair of real landscape (e.g., reg21) and corresponding random (e.g., ran21)landscapes.

Lastly, using the statistical summary in the ‘rulerun.log’ files (see the appendix for a descriptionof the rulerun.log file), determine whether the configuration of the each real landscape is likelyunder the assumption of random pattern generation. Specifically, compare the values of eachmetric in the ‘rulerun.log’ file for each real landscape with the corresponding mean and range ofvalues obtained from the simple random landscapes. Use the following files for this comparison:

• reg21.rulerun.log vs. ran21.rulerun.log• reg66.rulerun.log vs. ran66.rulerun.log• reg78.rulerun.log vs. ran78.rulerun.log

Note, in the rulerun.log files generated for the real landscapes (reg21, reg66 and reg78), summarystatistics will be computed for each of the six land cover classes. For this exercise, we are onlyinterested in the “forest” cover class, which is listed as “land cover type 4" in the output. Be sureto base your comparisons with the random landscapes on this cover type; otherwise, thecomparisons will be meaningless.

Questions to answer:3.1 Do you reject the null hypothesis and, if so, on the basis of what empirical evidence? Be

sure to interpret your result in terms of the landscape metrics; i.e., what do the metricstell you about landscape pattern? Also, is your evidence against the null hypothesisequally strong among the three real landscapes or does it differ with changes in theproportion of the landscape that is forest, and if it differs, why?

Questions to ponder (but not answer):3.2 Is this hypothesis test likely to be affected by the scale (i.e., grain and extent) of the

analysis? If so, how? For example, if you increased or decreased the grain and/or extent,would you expect the same outcome? Under what circumstances might you expect theresults to change with scale?

3.3 Is this hypothesis test likely to be affected by the landscape definition? For example, if thefocal habitat was restricted to late-seral, closed-canopy deciduous forest, would youexpect the same outcome, and why?

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3.2 Examine the lacunarity curves

The next step is to compare the lacunarity of each real landscape with comparable simple randomand fractal neutral landscapes.

First, in the batch file already processed, for each real landscape we generated 100 iterations of asimple random landscape and 3 fractal landscapes at varying levels of spatial contagion, usingthe following input parameters:

Parameter Random

Fractal

Lowcontagion

Medcontagion

Highcontagion

Map type S M M M

Dimensions* 100 100 ---- ---- ----

#Levels ---- 7 7 7

H ---- 0.1 0.5 0.9

Wrap map ---- N N N

Neg seed large number large number large number large number

Nearest neighbor 2 2 2 2

#Classes 1 1 1 1

Classprobabilities

0 = 1- pth

1 = pth

0 = 1 - pth

1 = pth

0 =1 - pth

1 = pth

0 = 1-pth

1 = pth

#Reps 100 100 100 100

Output map G G G G

Output file name asciimap.txt asciimap.txt asciimap.txt asciimap.txt

Analysis (L)acunarity (L)acunarity (L)acunarity (L)acunarity

Resolution 50 50 50 50

*Note, QRULE does not require the ‘grid dimensions’ parameter as an input for fractallandscapes; the ‘number of levels’ parameter determines the grid size. Unfortunately, thealgorithm employed in QRULE cannot create fractal landscapes with dimensions 100x100.Instead, 7 levels will produce a 128x128 grid. For our purposes, we will ignore thedifferences in grid sizes.

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Important: if you were to run QRULE interactively, note the same considerations discussedfor step 3. In particular, be sure to rename the ‘lacun.dat’ and ‘arcgrid.map’ files to uniquefile names after each run; otherwise, QRULE will overwrite them during each run.

Next, view the generated neutral landscapes. Remember, there are two options for viewing thesemaps.

• You can view these maps in your ArcMap project (...\neutral\neutral.mxd).• Alternatively, you can view these maps in R using a function that we have written for this

purpose.

Lastly, using the lacunarity results reported in the ‘lacun.dat’ files, determine how the lacunaritypattern of each real landscape varies in comparison to the random and fractal landscapes (see theappendix for a description of the lacun.dat file). Specifically, you should plot the natural log oflacunarity against the natural log of box size in cell units. Note, the lacun.dat files report rawlacunarity values and box size is given in meters (not cell units). In addition, note that in thelacun.dat files created from each of the real landscapes (reg?.txt) there will be 6 blocks ofobservations (rows) corresponding to the 6 cover types. You are only interested in the 4 classth

listed. Thus, using the lacun.dat files directly requires considerable care and lots of tedious datamanagement. Don’t despair, to facilitate generating the lacunarity plots amidst all of this datamanagement nightmare, we have written a function in R.

To plot the lacunarity of reg21, reg66, reg78 (from step 3.1) against the corresponding randomand fractal grids (from step 3.2), run the script provided in qrule.analysis.r. For example, the firstplot is generated by running the following lines:

lacun<-lacun.plot(path='c:/work/landeco-umass/exercises/neutral/output/',infile=c('reg21','ran21','frac21low','frac21med','frac21high'),classes=c(4,1,1,1,1),norm=TRUE,main='Lacunarity -- reg21')

Let’s decompose this so that you understand this function call. This call runs the R functioncalled lacun.plot, which has several arguments that control the plotting, as follows:

path = specifies the directory containing the lacunarity.csv files for the input landscapes.Note, substitute the path in the function above for the local path on your computer.

infile = vector of input landscapes that you want to plot; in this case, selecting the reallandscape (reg21) and the corresponding random (ran21) and fractal (frac21low, etc.)landscapes.

classes = vector of class values for the corresponding input landscapes; in this case, the reallandscape (reg21) contains six classes and we are telling the program to plot class = 4,while the random and fractal landscape contain a single class = 1.

norm = logical value (TRUE or FALSE) saying whether to normalize the log transformedlacunarity values, which means to divide the values by the value for the smallest box size

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so that the y-intercept is always equal to 1; this can be important if the proportion ofhabitat differs among landscapes and you want to view the lacunarity curves on the samegraph.

By default, this function will plot a separate curve for every replicate landscape. Recall that weran 100 replicates of each random and fractal landscape. Consequently, this figure can get toobusy with so many reps. An alternative is to plot the mean across reps. To do this, simply add theargument reps=’mean’, as is done in the second function call provided in the script. Thissimplifies the plot considerably and makes the comparison among landscapes a little easier. Butdon’t forget that the mean is just that, the mean, and there is stochastic variability about thatmean.

Once you have look at all the plots, corresponding to each of the real landscapes, you are ready toanswer the questions.

Questions to answer:4.1 How do you interpret a lacunarity plot, in general (it doesn’t matter which one, here I am

interested in knowing what can be learned from a lacunarity plot)? Be specific andcomplete; what are all the bits of information you can derive from a lacunarity plot?

4.2 Based on the lacunarity of the real landscapes in comparison to the random and fractallandscapes, what does the lacunarity analysis reveal about the nature of the pattern-forming agents in light of what the specific pattern-forming agents are in this particularlandscape?

Questions to ponder (but not answer):4.3 Are the lacunarity results likely to be affected by the scale (i.e., grain and extent) of the

analysis? For example, would you expect the same outcome if you increase or decreasethe grain and/or extent? Under what circumstances might you expect the results tochange with scale?

4.4 Are the lacunarity results likely to be affected by the landscape definition? For example,if the focal habitat was restricted to late-seral, closed-canopy deciduous forest, wouldyou expect the same outcome, and why?

3.3 Examine the relationship between landscape pattern and connectivity

The last step is to quantitatively show how landscape connectivity varies as a function of theinterplay between species’ life history characteristics and the configuration of habitat.

First, use QRULE to determine whether or not the landscape percolates in relation to increasinggap-crossing abilities (i.e., varying nearest neighbor rules). To do this, in the batch file alreadyprocessed, we generated a series of a simple random landscapes using the following inputparameters:

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Parameter Input Paramter Input

Map type S Class probabilities 0 = .60th

1 = .40th

Dimensions 128 128 #Reps 100

Neg seed any large number Output map N

Nearest neighbor 1, 2 or 3 Analysis (R)ule

#Classes 1 Resolution 50

Important: if you were to run QRULE interactively, rename the ‘rulerun.log’ file to a uniquefile name after each run; otherwise, QRULE will overwrite them during each run.

If you are really motivated, you can extend this analysis using additional user-specified nearestneighbor rules, but you will have to read the user guidelines to figure out how to do this.

Second, use QRULE to determine whether habitat configuration has any affect on therelationship between gap-crossing ability and landscape connectivity. To do this, in the batch filealready processed, we generated a series of contagious fractal landscapes using the followinginput parameters:

Parameter Input Paramter Input

Map type M #Classes 1

# Levels 7 Class probabilities 0 = .60th

1 = .40th

H 0.5 #Reps 100

Wrap map N Output map N

Neg seed any large number Analysis (R)ule

Nearest neighbor 1, 2 or 3 Resolution 50

Important: if you were to run QRULE interactively, be sure to rename the ‘rulerun.log’ fileto a unique file name after each run.

If you are really motivated, you can extend this analysis using additional user-specified nearestneighbor rules, but you will have to read the user guidelines to figure out how to do this.

Lastly, using the correlation length (cor_len) and frequency of map percolation (perc/freq) resultsreported in the ‘rulerun.log’ files, determine how the gap-crossing ability (using nearest neighbor

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rules as a surrogate) of a species influences the connectivity of the landscape and whether thisrelationship varies in relation to the spatial contagion of habitat (i.e., random versus fractallandscape patterns). For this examination, it will be useful to fill out the following table and thenplot percolation frequency and correlation length (y-axis) against nearest neighbor rule (x-axis)for the random versus fractal landscapes (series).

Correlation Length Percolation Frequency

NeighborhoodRule

Random Fractal Random Fractal

4

8

12

Questions to answer:5.1 Using the correlation length and frequency of map percolation, determine how the gap-

crossing ability (using nearest neighbor rules as a surrogate) of a species influences theconnectivity of the landscape and whether this relationship varies in relation to thespatial contagion of habitat (i.e., random versus fractal landscape patterns).

5.2 What are the implications of these findings for understanding the consequences of habitatfragmentation on organisms and for managing forest in this landscape?

Assignment

As a team, complete the exercise above and answer each of the questions. One team will beselected to present an oral report and the remaining teams will submit a single written lab reportcontaining answers to the questions above.

The report should be well organized and presented in a clear, grammatically correct and concisemanner. There is no minimum or maximum page limit, although you should be able to completethe assignment in less than 2-4 single-spaced pages, not including tables and/or figures. Theconcepts discussed in lecture and in the readings should be integrated into the discussion of theresults to the extent possible and as appropriate to support your presentation. Full referencesshould be included for all literature cited. Tables and figures should all have captions. Define allcritical terms/concepts with references as appropriate.

Written reports must be submitted electronically; a hard copy is optional. Reports shouldeffectively demonstrate that an interdisciplinary approach was used. In other words, I want asingle integrated presentation that effectively demonstrates that the entire group discussed theresults and reached some kind of consensus over the interpretation of those results. The reportshould not consist of several separate efforts combined at the end for purposes of thepresentation.

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Appendix

QRULE output statistics include several files, depending on the optional output selected.Unfortunately, the fields are either undefined (i.e., not given headers) or are difficult to interpret.The following table gives the field names and definitions for each file. In addition, we havetranslated the lacun.dat data into lacunarity.csv with additional columns for replicate number,box.size and class.

Rulerun.log (rule output)L.C.size = Largest cluster (patch) size (m)L.C.edge = Largest cluster edge (m)L.C.fract = Largest cluster mass fractal dimensionL.C._rms = Largest cluster mean squared radius of gyration (m)TTL clstr = Total number of clusters (patches)TTL edgs = Total amount of edge (m)Sav size = Area-weighted mean cluster size (ha)S_Freq = Total number of cells of corresponding classCor_len = Correlation length (area-weighted mean radius of gyration)(m)Perc = Frequency of map percolation

Patch_cfd.dat (cluster level statistics)Size = Cluster size (ha)Cfd = Cumulative frequency distribution (proportion of habitat)Edges = Cluster edges (m)Fractal = Cluster mass fractal dimensionRMS = Cluster mean squared radius of gyration (average distance (m) between cells)

Lacun.dat (lacunarity output)1 column = box size (m)st

2 column = untransformed lacunaritynd

(box size of 1)3 column = normalized lacunarity (L/L )rd

4 column = variance/mean ratioth

Lacunarity.csv (lacunarity output reformatted)rep = replicate #class = class (cover type)box.size = box size (m)raw.lac = untransformed lacunarity

(box size of 1)norm.lac = normalized lacunarity (L/L )var/mean = variance/mean ratio

Lab. 3 Pg. 24