landscape metrics indicate differences in patterns and dominant controls of ribbon forests in the...

Landscape metrics indicate differences in patterns and dominant

controls of ribbon forests in the Rocky Mountains, USA

Bekker, Matthew F.1�; Clark, Jess T.

2& Jackson, Mark. W.

1,3

1Department of Geography, Brigham Young University, 690 SWKT, Provo, UT 84602, USA;2US Forest Service, Remote Sensing Applications Center, 2222 W. 2300 S., Salt Lake City, UT 84119, USA;

E-mail [email protected];3E-mail: [email protected];

�Corresponding author: Fax 11 801 422 0266; E-mail [email protected]

Abstract

Question: Do landscape metrics reflect differences indominant factors controlling ribbon forest patternsamong sites?

Location:West Flattop Mountain, Glacier National Park,Montana (Flattop); Medicine Bow Mountains, Wyoming(Medicine Bow); Park Range, Colorado (Park Range).

Methods: High-resolution aerial photography was used todelineate ribbon forest patches, and to calculate landscapemetrics to distinguish between long, narrow, regularpatterns expected from strong microtopographic control,and smaller, more compact, and variable patterns ex-pected from wind-snowdrift interactions.

Results: All but two metrics were significantly different(Po0.05) among the three sites. The rank and magnitudeof differences indicated that ribbons at Flattop and ParkRange are more similar to each other than to those atMedicine Bow. Flattop ribbons were also more elongated,narrower and less variable than those at Park Range,suggesting differences in the type and strength of structur-al control. Previous research showed that Flattop ribbonsoccupy regular lithologic ridges, while our observations ofribbons and analysis of geologic maps suggests weakerand less consistent microtopographic control at ParkRange, and dominant wind-snowdrift interactions withlittle to no microtopographic influence at Medicine Bow.

Conclusions: Landscape metrics indicate differences inpattern among sites that reflect differences in dominantfactors influencing ribbon forest development and main-tenance. Explanations of ribbon forest dynamics are site-specific and are more complex than is currently recog-nized. The sites vary in the level of endogenous versusexogenous control of ribbon patterns, and consequently inthe sensitivity of this phenomenon to climate.

Keywords: Ecotone; Feedback; Landscape ecology;Lithology; Microtopography; Remote sensing; Ribbonforest; Treeline; Wind-snow interaction.

Introduction

The study of vegetation pattern may reveal theprocesses that produced the patterns, and yield in-sight into the biotic and abiotic factors thatconstrain vegetation change (Malanson et al. 2001;Alftine & Malanson 2004). Pattern may also be re-lated to positive feedback between vegetation andenvironment (Wilson & Agnew 1992), which canlead to self-organization and thresholds in ecosys-tem behavior (Loehle et al. 1996; Milne et al. 1996;Malanson 1999; Rietkerk et al. 2004; Rietkerk &van de Koppel 2008). Near species’ range limits,sensitivity to environmental heterogeneity is in-creased (Walker et al. 2003) and physiological stressincreases the prevalence of positive interactions be-tween species (Callaway et al. 2002), both of whichcan produce visually striking, regular vegetationpatterns. Such patterns have been identified in con-trasting environments, including ‘‘tiger bush’’(White 1969) or ‘‘banded vegetation’’ (Tongway etal. 2001) in arid and semi-arid landscapes, ridge andslough patterns (Wu et al. 2006) in the Everglades,‘‘string patterns’’ (Foster et al. 1983) in boreal peat-lands, and ‘‘fir waves’’ (Oshima et al. 1958; Sprugel1976), ‘‘krummholz islands’’ (Marr 1977), ‘‘hedges’’(Holtmeier 1982), ‘‘fingers’’ (Bekker 2005) and‘‘ribbon forest’’ (Billings 1969) in subalpine land-scapes (for a review of linear patterns in subalpineforest see Bekker & Malanson, 2008). This paperfocuses on ribbon forests, which are elongated pat-ches of subalpine forest that develop perpendicularto prevailing winds at several sites in the RockyMountains of North America. Relatively few directstudies of the phenomenon have been published(Billings 1969; Holtmeier 1982; Butler et al. 2003)and although the influence of wind-deposited snowis common to all of the studies, they have suggesteddifferent dominant mechanisms for ribbon forestorigin and maintenance, ranging from completely

Applied Vegetation Science 12: 237–249, 2009& 2009 International Association for Vegetation Science

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endogenous wind-snowdrift interaction to exogen-ous microtopographic control.

Landscape metrics have commonly been used toquantify patterns that may be related to ecologicalprocesses, and have been shown to discriminateamong landscapes influenced by different dis-turbance regimes, topography, land uses and bioticinteractions at both broad and fine scales (O’Neill etal. 1988; Baker 1992; Turner et al. 1996; Malanson& Zeng 2004). This paper reviews previous work onthe three most extensive areas of ribbon forest toidentify suggested dominant mechanisms of ribbondevelopment and maintenance, and uses landscapemetrics to quantify spatial patterns among the sitesand determine whether the patterns reflect differ-ences in dominant controls.

Background

Three different types of ribbon forest have beendescribed, and they are differentiated by site condi-tions and the number of ribbons. Buckner (1977)categorized sites with only a few to several ribbonson relatively steep slopes as ‘‘Type 1’’ and those withmany ribbons on relatively flat slopes as ‘‘Type 2.’’Arno (1984) also described sites in the RockyMountains that contained a single strip of ‘‘ridgetopribbon forest’’ between windswept ridgelines anddeep snowdrifts on the leeward slope. Our study fo-cuses on Type 2 ribbon forest, where the pheno-

menon is most conspicuous because of its develop-ment in extensive patches. Three such sites in theRockies have been previously studied in the UnitedStates: the Park Range, Routt National Forest,Colorado (Buckner 1977) (hereafter Park Range);the Snowy Range, Medicine Bow National Forest,Wyoming (Billings 1969; Earle 1993) (hereafterMedicine Bow); and West Flattop Mountain, Gla-cier National Park, Montana (Butler et al. 2003)(hereafter Flattop) (Fig. 1, Fig. 2).

Ribbon-like patches in the Rockies were de-scribed by Griggs (1938) and Oosting & Reed(1952), but Billings (1969) was the first to provideformal hypotheses of ribbon forest formation basedon observations at Medicine Bow. His first hypoth-esis suggested that a group of seedlings could esta-blish toward the windward edge of an unforestedarea and then expand laterally (perpendicular to theprevailing wind) through layering or new seedlings,although he did not suggest a mechanism for thislateral expansion. He proposed that as the treesgrew taller they would reduce wind speed, producinga leeward snow drift that would encourage the de-velopment of another ribbon at the far edge of thedrift in mid-summer, while preventing seedling es-tablishment in the ‘‘snow glade’’ closer to the ribbonbecause of late snowmelt. The death of old treeswould produce gaps or ‘‘blowouts’’ within ribbons,funneling wind that would remove leeward snowand allow seedlings to establish in the snow glade.

Fig. 1. Location of the three US ribbon forest study sites: West Flattop Mountain, Glacier National Park, Montana;Medicine Bow Mountains, Wyoming; and the Park Range, Colorado.

238 BEKKER, M. F. ET AL.

He suggested that this process would producebreaks and bends in the ribbons and could causethem to move slowly downwind over time.

Billings (1969) also suggested that ribbon forestcould develop through the gradual breakup ofclosed forest adjacent to an extensive unforestedarea caused by severe fire or edaphic conditions thatfavor meadow vegetation. In this case snow wouldbe swept by wind from the cleared area and de-posited several meters into the adjacent closedforest, killing established trees and eventually‘‘breaking the forest into ribbon-like patches’’ (Bill-ings 1969, p. 206). The suggested processes of

breaking, healing and migrating ribbons, as well asthe destruction of existing mature forest by windand snow, are similar to the ‘‘wave regeneration’’identified in forests near treeline in Japan (Oshima etal. 1958); the eastern United States (Sprugel 1976;Reiners & Lang 1979) and southern Argentina(Puigdefabregas et al. 1999). Although all of Bill-ings’ (1969) work was conducted at Medicine Bow,his paper included an oblique aerial photograph ofFlattop, giving the impression that ribbons devel-oped in similar ways at the two sites.

Earle (1993) suggested a similar hypothesis ofribbon forest development at Medicine Bow, but he

Fig. 2. Examples of ribbon forest shown at the same scale at (a) Medicine Bow, (b) Park Range and (c) Flattop.

- RIBBON FOREST PATTERNS AND CONTROLS - 239

emphasized that several tree clumps could becomeestablished throughout an open area, expand lat-erally where the depth of captured snow wasoptimal, and eventually connect with other treeclumps to form ribbons. His analysis suggested thatexisting ribbons do not encourage the developmentof additional ribbons downwind as Billings pro-posed, but that seedling establishment, and thusribbon expansion, is indeed limited by the snowdriftproduced by the next windward ribbon.

Other work at Medicine Bow has evaluatedBillings’ (1969) second hypothesis of ribbon forestdevelopment in Cinnabar Park. This site consists ofa single ribbon and snow glade on the leeward sideof a meadow, bordered by closed forest. Usingmeasurements of soil plant opal and pH, Miles &Singleton (1975) suggested that the snow glade wascreated as snow was swept from the meadow anddeposited in the adjacent closed forest, as Billings(1969) proposed. They also suggested that the mea-dow migrates as the leeward ribbon and closedforest are destroyed by wind. In contrast, using treeage-structures, and locations of logs and snags, Vale(1978) concluded that the meadow was being in-vaded by trees on the windward side, but that theribbon and snow glade were stable. Doering & Re-ider (1992) analysed soil morphology andstratigraphy and radiocarbon dates of wood frag-ments in the park and concluded that the meadowwas not migrating. They suggested that the presenceof the park is the result of edaphic factors ratherthan wind-snowdrift action.

Another hypothesis for the origin of ribbonspoints to the influence of pre-existing microtopo-graphic variation. Geological and geomorphicfactors strongly influence alpine treelines generally(Holtmeier 2003; Butler et al. 2007), and such con-trols on ribbon forests were emphasized by Buckner(1977) in a study conducted on Buffalo Pass atPark Range. He stated that in all cases the ribbonsoccurred on microtopographic rises, which hepresumed to be associated with intrusive bed-rock outcrops or solifluction terraces. Rocky,topographically raised areas can increase tree estab-lishment and survival through earlier snowmelt(Buckner 1977), protection from wind (Resler et al.2005) or reduced competition with grasses (Coop &Givnish 2007). At one location a powerline right-of-way was cut across several ribbons around 1965,and Buckner (1977) noted earlier snowmelt and ex-clusive tree establishment in areas formerly occupiedby ribbons in the right-of-way – a pattern still evi-dent in 2002 (M. F. Bekker, pers. obs.). Buckner(1977) concluded that ribbons do reduce windspeed,

but their function as snow fences is small except neartreeline, and that ribbon length and inter-ribbonspacing were controlled most strongly by micro-topography, not wind-snowdrift interactions assuggested by Billings (1969) and Earle (1993).

The influence of geology and geomorphologyon ribbon forest patterns was also demonstrated byButler et al. (2003) at Flattop. At this site, analysisof stereoscopic aerial photographs and helicopteroverflights showed ribbons occupying topo-graphically elevated ridges formed by resistantlayers of tilted sedimentary rock that coincide withthe direction of glacial scouring. A change detectionanalysis using aerial photographs from 1966 and1991 of a similar, nearby site showed that ribbon-meadow edges were mostly stable, with no apparentexpansion or migration of ribbons as proposed byBillings (1969). They concluded that ribbon forestsat Flattop are strongly controlled by lithology andgeomorphology, and that snow deposition only actsto maintain the pattern. In contrast to Park Rangeand Flattop, the ribbons at Medicine Bow do notappear to be associated with microtopography, ex-cept for small tree islands on occasional outcrops ofdolomite (M. F. Bekker, pers. obs.; Chris Hiemstra,Research Scientist, Colorado State University, pers.comm., November 6, 2007).

Type 1 ribbon forest has not been as well-stu-died, but Holtmeier (1982, 1985) reported that mostType 1 ribbons are associated with solifluction ter-races or bedrock ridges. He suggested that snowdistribution patterns result primarily by from theinfluence of microtopography on windflow, whilethe effect of the ribbons themselves should be con-sidered secondary.

Previous research on ribbon forest has sug-gested complex and variable controls of their originand maintenance at different sites, and has dis-proved some of Billings’ (1969) hypotheses. Yet,recent literature does not recognize this complexity.For example, in his overview of ribbon forests in theRockies, Peet (2000) emphasized Billings’ (1969)hypothesis of fire-wind-snowdrift interactions, in-cluding the suggestion that snowdrifts encourage thedownwind development of new ribbons in an un-forested area, despite the conclusions of Buckner(1977), Holtmeier (1982, 1985) and Earle (1993) thatthey do not. He also repeated Billings’ (1969) inclu-sion of an oblique aerial photograph from Flattop,although all of the research he cited was conductedat other sites, again suggesting homogeneity in pat-terns and controlling factors in different areas.Walker et al. (2001) and Smith et al. (2003) invokedBillings’ (1969) second hypothesis to suggest that


ribbon forest dynamics are similar to fir waves(Sprugel 1976), migratory strips resulting from thedestruction of closed forest by deep snowdrifts, de-spite the conclusions of Vale (1978) and Doering &Reider (1992) that this model would produce only asingle, stable ribbon and snow glade on the edge of aclearing.

We identify two limitations in the current stateof knowledge of ribbon forest origin and dynamics.First, recent summaries of ribbon forest develop-ment have not recognized studies that proposehypotheses of ribbon origin and maintenance dif-ferent from those suggested by Billings (1969). Thismay be due in part to unfamiliarity with the studiesthat are unpublished (Buckner 1977; Earle 1993) orare not in English (Holtmeier 1982, 1985). Thesedifferent hypotheses have important implicationsfor the level of endogenous versus exogenous con-trol of vegetation pattern and dynamics (Zeng et al.2007) and, consequently, the sensitivity of these rib-bon forest systems to variations in climate(Malanson et al. 2007). Second, research on Type 2ribbon forest has always been conducted within onesite or mountain range, without consideration ofhow patterns and processes compare with othersites. Buckner (1977), Earle (1993) and Butler et al.(2003) have all suggested the need for further re-search on ribbon forest, particularly comparisonsamong ribbon forest types or sites, and Earle (1993)specifically emphasized the need to quantify andcompare spatial patterns.

In this paper, we address that need by usinghigh-resolution imagery and analysis of landscapemetrics to identify differences in ribbon size (meanarea, length and width), shape (patch shape index,perimeter and length-width ratio) and consistency(contagion; and mean and standard deviation ofpatch orientation) among the three previously stu-died Type 2 ribbon forest sites, to determine whetherthese patterns reflect suggested dominant controls.Sites where lithology is a dominant control overribbon development should contain relatively long,thin, ribbons with consistent orientation because oftheir expansion along narrow, linear topographicrises broken only by geomorphic alteration of thelandscape. In contrast, sites where wind-snowdriftinteraction is dominant should contain smaller,more compact ribbons with more variable orienta-tion, owing to gaps and blowouts (Billings 1969) andlocally variable winds. Because ribbons at Flattopand Park Range have been reported to be influencedby underlying structure, while studies at MedicineBow have only implicated wind-snowdrift interac-tions, we expected to find that ribbon patterns at

Flattop and Park Range would be more similar toeach other than those at Medicine Bow.

Study Sites

Flattop is an uplifted synclinal peak thatconsists of Precambrian sedimentary and meta-sedimentary rock, straddling the Continental Divideand sloping gradually to the west (Whipple 1992;Butler et al. 2003). Ribbons at Flattop are foundbetween 1830 and 2135m. Medicine Bow consists ofuplifted Precambrian metamorphic rock (Houston& Karlstrom 1992) and ribbons are found between3200 and 3385m on flat areas and gentle slopes withvariable aspects. Park Range is dominated by Pre-cambrian igneous and metamorphic rocks (Snyder1980a, b) and ribbons are located between 3050 and3200m, primarily on gentle west-facing slopes justwest of the Continental Divide. All three sites wereheavily modified by Pleistocene glaciation (Atwood& Atwood 1937; Ross 1959; Mears 2001). Averagemaximum snow depth is 122 cm for Flattop, 88 cmfor Medicine Bow and 134 cm for Park Range; theaverage annual precipitation is 145, 102 and 150 cm,respectively (SNOTEL 2007). All three sites experi-ence dominant westerly winds (Buckner 1977;Hiemstra et al. 2002; Butler et al. 2003) and forestsat all three sites are dominated by Abies lasiocarpa[Hook.] Nutt. and Picea Engelmannii Parry exEngelmann (Billings 1969; Buckner 1977; Butleret al. 2003).

Methods

DOQ Mosaic

To capture the spatial patterns in each land-scape, we mapped ribbon patches by classifyingremotely sensed imagery. To ensure a common scaleand spectral profile, panchromatic 1:24 000 USGSDigital Orthophoto Quadrangles (DOQs) were usedas the base imagery. This scale translates into 1-mimage pixels, which is sufficient to easily identify in-dividual ribbons.

Adjacent DOQs represent different flight linesthat can produce noticeable seams in a mosaic, par-ticularly if the photos were taken on different dates.All photos for Libby Flats were taken on the sameday and Park Range included two sets of photos ta-ken 7 days apart. Flattop included two photos taken4 years apart (1991 and 1995), but this is an in-sufficient amount of time for any noticeable changes


to occur in ribbon-meadow boundaries (Butler et al.2003). Moreover, both photos were taken at thesame time of year (late August), and no major dis-turbances occurred at the site between the two dates.Visual inspection revealed very little difference inribbons at the boundaries of images. We also colorbalanced all images and no conspicuous seams thatwould obscure analysis were present in the finalmosaic.

Ribbon forest boundary delineation

Polygons were digitized around whole areas ofribbon forest based on visual interpretation, in-corporating only discrete ribbons and excludingthose that were clearly connected to adjacent con-tinuous forest. Ribbons at Flattop exist in onecontinuous area, while bothMedicine Bow and ParkRange include several separate groups of ribbonforest. The digitized polygons were then used to ex-tract each discrete region of ribbon forest into aseparate image for analysis.

Patch delineation

To create the thematic elements showing eachribbon forest patch, we performed an ISODATAunsupervised classification on all images. This pro-cedure creates clusters of features with similarspectral variances. Our analysis only consideredtree/non-tree, so the relatively simple unsupervisedclassification technique was sufficient. We created50 initial classes and examined them to find thespectral separation between tree/non-tree. Once the50 original classes were assigned to either tree ornon-tree, we recoded all the classes into just two.Each site mosaic was visually inspected followingclassification and corrected through on-screen digi-tization. Misclassified pixels, e.g. water bodies andmoist meadows with spectral responses similar tothat of trees on a panchromatic DOQ, were easilyidentified and were recoded to the appropriate class.Some forest patch edges were obscured by tree-sha-dows, thus some small areas of meadow areprobably misclassified as forest.

The high resolution of the imagery allowed se-parate patches to be visualized where tree canopieswere more than 1m apart. Some groups of neigh-boring small patches were very close to one anotherand were actually parts of elongated patches (rib-bons) clearly distinguishable at a broader scale.Other small and compact patches were more iso-lated from one another. Although they did not fitthe general definition of a ribbon as an elongated

patch, we did not eliminate them because of Earle’s(1993) hypothesis that small tree clumps coulddevelop into ribbons. To retain the isolated clumpswe applied a 3�3 maximum filter to the classifica-tion and then applied a 3�3 majority filter toconnect neighboring groups, and create a morecontinuous and accurate representation of ribbons(Fig. 3).

Metric computation

Patch- and landscape-scale metrics were se-lected that could differentiate the more elongated,narrow ribbons with consistent orientation in sitescontrolled by underlying structure, from smaller,more compact ribbons with variable orientation insites dominated by wind-snowdrift interactions. TheFRAGSTATS (McGarigal & Marks 1994) software wasused to calculate mean patch area, length, width,perimeter and shape index, as well as the landscape-scale metrics contagion (Li & Reynolds 1993) andlength-width ratio. We also calculated the mean andstandard deviation of patch orientation (SFWMD2004).

Mean patch area, length and width were chosento characterize overall ribbon sizes. Because regularlithological patterns can be disrupted by geo-morphic processes, and microtopography can bequite variable, these simple metrics only provide astarting point for differentiating controls on ribbonpatterns.

Patch shape index, perimeter and length-widthratio all contribute to a description of patch shape.The shape index measures deviation from standardgeometric shapes, in this case a square because ras-ter imagery, indicated by a value of 1.0, was used.There is no limit to the upper range of shape values,so ribbons with values farthest from 1.0 are inter-preted to be the most elongated. Perimeter indicatesedge complexity while length and width indicateribbon size and elongation. Length and width werecalculated on vector representations of the classifiedribbons using scripts acquired from EnvironmentalSystems Research Institute’s (ESRI) website (http://www.esri.com).

Contagion and the mean and standard devia-tion of patch orientation both indicate theconsistency of ribbon patterns in the landscape.Contagion evaluates the probability that cells of agiven cover type in a landscape will be adjacent tocells of the same cover type (higher values) versus adifferent cover type (lower values). If cover typestend to occur in a few large patches, contagion va-lues will be higher because cells of the same cover


type will frequently be adjacent. Conversely, alandscape with many small patches will yield lowercontagion values because cells of one cover type willfrequently be adjacent to cells of a different covertype. The mean and standard deviation of patch or-ientation were computed using the length vectorscreated for the patch-scale analysis.

Substrate

Butler et al. (2003) described the influence of li-thological, structural and geomorphic features onribbon patterns in flattop. To identify the effects ofunderlying structure on ribbon patterns at the othersites, geological and topographic maps for ParkRange (Snyder 1980a, b) and Medicine Bow (Hous-ton 1968) were analysed. The scale of the geologicalmaps (1:48 000 for Park Range and 1:63 360 forMedicine Bow) was insufficient to resolve micro-topography, but both maps displayed features thatcould indicate microtopographic variation such asglacial deposits, igneous dikes, and the direction ofglacial scouring. Overlays of ribbon forest patcheswere used to identify the association between rib-bons and lithologic, structural or geomorphicfeatures, calculate the percentage of ribbon forest ondifferent substrates (i.e. glacial deposits, rock type)and evaluate the orientation of ribbons relative tothe dominant direction of Pleistocene glacial ad-vance.

Results

The number of ribbons varied considerablyamong the three sites. Medicine Bow has the most(12 722), followed by Park Range (10 504) and Flat-top (2238). However, the sizes of areas covered byribbons also differed among the sites, with ParkRange the largest (3390 ha), followed by MedicineBow (3023 ha) and Flattop (321 ha). To facilitate amore direct comparison of ribbon numbers acrosssites, the percentage of each study site covered byribbons was calculated. Flattop was highest(36.8%), followed by Park Range (32.7%) andMedicine Bow (23.8%) (Table 1).

Park Range ribbons were the largest in area(mean 1061.8m2), length (mean 40.1m) and width(mean 10.7m), while Medicine Bow ribbons were thesmallest (mean 532.5m2) and shortest (mean 26.3m).Flattop andMedicine Bow had identical mean patchwidths (8.2m). All patch-scale metrics among siteswere significantly different (Po0.05 Mann-WhitneyU test) except shape between Flattop and Park

Fig. 3. Example of a ribbon forest site (Medicine Bow)with neighborhood maximum and majority filters appliedto emphasize ribbons rather than individual trees. Thethree frames represent the original image (top), after ap-plication of a 3�3 maximum filter (middle), and afterapplication of a 3�3 majority filter (bottom).


Range and mean width between Flattop and Medi-cine Bow (Table 2).

The patch shape metric illustrated that ribbonsat Flattop and Park Range were more elongated(less square) than Medicine Bow. Orientationshowed that Medicine Bow ribbons were alignednearly exactly north-south while Park Range andFlattop ribbons were aligned northwest-southeast.Orientation standard deviation showed Flattop rib-bons being more consistently oriented in the samedirection (m5 201) than those at Park Range(m5 291) or Medicine Bow (m5 351).

Flattop had the lowest contagion value (36.76),followed by Park Range (44.07) and MedicineBow (52.71). This indicates that tree and non-treecells were more clumped at Medicine Bow, moredispersed at Flattop and intermediate at ParkRange.

To summarize the overall similarities and dif-ferences in metrics among the three sites, themagnitude of the difference in metric values betweenpairs of sites (Table 3) were calculated and ranked.Flattop and Park Range were the most similar forseven of ten metrics, while they were the most dif-ferent for only one (ribbon width, for whichMedicine Bow and Flattop were identical). Con-

versely, Flattop and Medicine Bow were the mostsimilar for only two metrics and the most differentfor six. Differences between Park Range and Medi-cine Bow were primarily intermediate (most similarfor one metric and most different for four).

Ribbons at Park Range andMedicine Bow werenot associated with any mapped lithological orstructural features. Ribbons at Park Range were as-sociated with gneiss, schist and other metamorphicrocks (38%), glacial till and moraines (31%), granite(28%) and rocky deposits (3%). In contrast, ribbonsat Medicine Bow were primarily found on glacial tillor drift (57%) and the rest was associated withquartzite and other metamorphic rocks (29%), do-lomite (11%) and igneous rocks (4%). At both sitessome of the most clearly defined groups of ribbonswere associated with mesotopographic convexities,and ribbons were relatively rare in ravines or de-pressions. Ribbons at both sites were also primarilyoriented perpendicular to the dominant direction ofice movement.

Discussion

The statistically significant differences amongnearly all metrics indicate the importance of localprocesses in determining specific ribbon patterns,and emphasize the problem with proposing a singlemechanism to explain all ribbon forests. Analysis ofthe ranked order and magnitude of differences inmetric values among sites reveals non-random var-iation that is consistent with dominant controlssuggested by previous work at each site. As ex-pected, most metrics for Flattop and Park Range aremore similar to each other than for either site com-pared with Medicine Bow. This is consistent withthe conclusions of Butler et al. (2003) and Buckner(1977) that underlying structure plays an importantrole in ribbon forest patterns at these sites. How-ever, the results also reveal consistent differencesbetween Flattop and Park Range ribbons that

Table 1. Calculated patch- and landscape-scale metricsfor the three study sites.

Flattop Park Range Medicine Bow

Patch-ScaleCoverage of ribbons (%) 36.8 32.7 23.8Mean perimeter (m) 153.5 182.9 115.9Mean area (m2) 532.5 1061.8 466.6Mean length (m) 34.8 42.0 26.4Mean width (m) 8.2 11.2 8.2Mean orientation (1) 343.63 349.69 359.89Orientation SD 20.30 28.93 35.46Mean patch shape 1.695 1.618 1.471

Landscape-scaleLength-width ratio 4.27 3.76 3.21Contagion 36.76 44.70 52.71

Table 2. Statistical comparison (Mann-Whitney Z scores)of patch-scale metric means between pairs of study sites.

Flattop versusPark Range

Flattop versusMedicine Bow

Park Range versusMedicine Bow

Shape � 0.367� � 15.262 � 27.096Length � 2.859 � 8.323 � 18.69Width � 12.46 � 0.473� � 20.34Perimeter � 14.392 � 44.208 � 26.155Area � 11.968 � 42.300 � 24.863Orientation � 6.397 � 15.156 � 15.241

All values are significantly different (Po0.05) except �.

Table 3. Comparison of the similarity of metrics amongthe three study sites.

Flattop-ParkRange

Medicine Bow-Park Range

Medicine Bow-Flattop

Most similar 7 1 2Intermediate 2 5 2Least similar 1 4 6

Values indicate the number of times the difference between metrics attwo sites was smallest (most similar) or largest (least similar) amongthe three paired comparisons.


suggest differences in the nature of structural con-trol at these sites.

Microtopographic variation can be influencedby many factors, including lithology, differentialweathering and erosion, volcanic intrusions, glacialdeposition and mass movement such as solifluction.Butler et al. (2003) attributed the microtopographicpatterns at Flattop primarily to lithology, and sec-ondarily to glacial scouring. Ribbons at this siteoccupy ridges of resistant, tilted bedrock while in-tervening meadows occur in depressions underlainby less resistant rock. Pleistocene glaciers at this siteadvanced in the same direction as the strike of thesebedding planes, causing greater erosion of the lessresistant strata and amplifying the microtopo-graphic variation.

In contrast, Buckner (1977) was uncertain of theprecise relationship between underlying structureand microtopography at Park Range. He did notethat the ribbons do not correlate with the principalgeological structure, which runs northeast-south-west, but he suggested that joints or intrusive dikesmay run north-south, corresponding with the axis ofuplift of the range. He also suggested that some ofthe raised areas may be solifluction terraces. Ouranalysis of geologic maps published after Buckner’sstudy (Snyder 1980a, b) confirmed that ribbons donot correspond with any mapped lithological, jointor dike features. This suggests that solifluction ter-races, and to a lesser extent glacial deposition, mostlikely caused the microtopographic variation asso-ciated with the ribbons. These features should bemore subtle and more variable in shape and sizethan ridges produced by lithology, and thus the rib-bons at Park Range would be expected to be morevariable than those at Flattop.

Most ribbons at Medicine Bow occur on glacialdeposits, and microtopographic variation asso-ciated with these deposits certainly exists at this site.The lack of association between ribbons and micro-topography at Medicine Bow compared withFlattop and Park Range may be explained in part bydifferences in snowpack among the sites. Meanmaximum snow depth at Park Range is 139% ofMedicine Bow, and at Flattop it is 152% of Medi-cine Bow. At these sites with higher snowfall,microtopographic rises provide earlier melt-outdates and consequently longer growing seasons fornewly established seedlings that may be critical forribbon development. In contrast, snowfall at Medi-cine Bow appears to be low enough that wind-snowdrift interactions provide suitable levels ofsnowpack for tree establishment and survival re-gardless of microtopography.

The differences in dominant controlling factorsfor ribbon forest development among the three sitesmay be summarized as: (1) strong structural controlvia lithology and complementary glacial scouring atFlattop; (2) less consistent structural control, per-haps via solifluction terraces and glacial depositionat Park Range; and (3) little to no structural controlat Medicine Bow. The differences in metric valuesamong the three sites are consistent with this inter-pretation.

As expected, mean ribbon length and perimeterat structurally controlled Flattop and Park Rangewere greater and more similar than at Medicine Bowwhere wind-snowdrift processes dominate. Ribbonwidths and areas, however, were more similar be-tween Flattop and Medicine Bow, emphasizing thedifferences in the type of structural control betweenFlattop and Park Range. Flattop ribbons follownarrow ridges of bedrock while Park Range ribbonsfollow broader microtopographic rises. The land-scape-scale length-width ratio strengthens thisinterpretation, as Flattop and Park Range were themost similar for this metric, and Flattop had thehighest values and Medicine Bow the lowest.

Mean ribbon orientation also illustrates con-sistent similarities and differences among the threesites. Ribbon-snow glade patterns will develop mosteasily if the ribbons are oriented perpendicular tothe prevailing wind. Because westerly winds dom-inate at all three sites, ribbons that are mostly orentirely controlled by wind-snowdrift interactionsshould be aligned closest to north-south. Incontrast, ribbons affected by underlying structurecan develop along microtopographic rises thatare not as strongly perpendicular to the wind.Mean orientation was most similar between Flattopand Park Range, and Medicine Bow ribbonswere most closely aligned north-south, whileFlattop ribbons were furthest from north-south.Thus, the two structurally controlled sites are themost similar, ribbons with the strongest structuralcontrol are furthest from north-south, andthose with the least structural control are closest tonorth-south.

The standard deviation of ribbon orientationstrengthens the interpretations based on orientationmean. Ribbons controlled by lithology should varylittle from the consistent strike of bedding planes,particularly when this directionality is enhanced byglacial scouring. Ribbons controlled by solifluctionand glacial deposition should be more variable asthey follow these less rigid features, but they shouldbe less consistent than ribbons controlled by wind-snowdrift interactions, with locally variable winds


and blowouts. As expected, lithologically controlledFlattop varied the least, wind-snowdrift controlledMedicine Bow varied the most, and Park Range andMedicine Bow were the most similar.

Flattop had the highest shape index values,while Medicine Bow had the lowest, indicating thatFlattop ribbons are the most elongated and Medi-cine Bow ribbons are the most compact. Values weremost similar for Flattop and Park Range. As withthe length-width ratio, this pattern can be explainedby the establishment of ribbons at Flattop on long,thin lithologic ridges, at Park Range on longer butwider microtopographic rises and at Medicine Bowin areas without structural control.

Contagion also ordered the sites according tothe level of structural control. Flattop had the low-est value, followed by Park Range and MedicineBow. Flattop is characterized by consistently thinribbons separated by consistently thin meadows.Thus, tree cells are frequently adjacent to meadowcells, producing a low contagion value. Conversely,the highest contagion value at Medicine Bow can beexplained by the abundance of larger meadows,some that exceed a kilometer in width (Fig. 4), re-sulting in many adjacent meadow cells. Ribbonshave been unable to develop over relatively largerareas at Medicine Bow because seedling establish-ment and survival is closely associated with existingtrees (Germino et al. 2002). The intermediate valuefor Park Range reflects the intermediate level ofstructural control; ribbons are spaced in correspon-dence with microtopographic features that are lessconsistent than at Flattop.

The three sites are also ordered according to le-vel of structural control by the percentage of areacovered by ribbon versus meadow. Flattop, with themost structural control, was the highest, MedicineBow, with the least structural control, was the low-est, and Park Range was intermediate. In areaswhere mictrotopography does not strongly influenceribbon development, suitable sites for seedling es-tablishment and survival may be rare and dependenton optimal snowpack conditions or existing vegeta-tion (Hattenschwiler & Smith 1999; Germino et al.2002), resulting in relatively few ribbons per unitarea.

We have emphasized variation in ribbon pat-terns at the site scale that reflect differences incontrolling factors. However, ribbon forest patternswithin each site were not homogeneous, and eachsite includes some ribbons with similar character-istics to those in a different site. While this studysuggests that a given process or feature may exertdominant control over broad-scale patterns, the

strength of that factor may vary within a site. Fur-ther research is needed to investigate finer-scale,within-site variability in ribbon forest patterns.

The results of this study have important im-plications for ribbon forest dynamics. Ribbons thatare strongly controlled by underlying structureshould be relatively stable features in the landscape,and ribbon migration through endogenous snowremoval and deposition as proposed by Billings(1969) should be greatly reduced or non-existent, aswas suggested by Butler et al. (2003) for Flattop.Moreover, structurally controlled ribbons shouldbe less responsive to exogenous changes such as

Fig. 4. Flattop and Medicine Bow ribbons both displayedin white at the same scale, illustrating the greater con-sistency and uniformity of Flattop ribbons compared withMedicine Bow ribbons.


increases in temperature or reductions in snowpack.Forest population dynamics should also differamong sites that are controlled by different factors.

Parts of Medicine Bow have been well-studied interms of wind-snowdrift interactions (Hiemstra et al.2002, 2006), seedling establishment and survival(Hattenschwiler & Smith 1999; Germino et al. 2002;Smith et al. 2003) and ribbon forest dynamics (Billings1969; Earle 1993). The results of this study emphasizethe need for similar research in other ribbon forestsites and, more importantly, the need to design studiesthat will capture the range of spatial variability andtemporal dynamics within and among sites.

Conclusions

Landscape metrics indicate differences in pat-tern among the three previously studied Type 2ribbon forest sites in the Rocky Mountains, whichreflect differences in dominant controlling factors ateach site. Ribbon forest characteristics are more si-milar at Flattop and Park Range, where micro-topographic features are associated with the rib-bons, than at Medicine Bow, where wind-snowdriftinteraction is the dominant control over ribbon de-velopment. Differences are also clear betweenFlattop, where ribbons are associated with regular,resistant lithologic ridges, and Park Range, whereribbons occupy more spatially variable microtopo-graphic rises associated with solifluction and glacialdeposition.

Recent summaries of ribbon forest developmenthave implied that the models of ribbon forest originand dynamics proposed by Billings (1969) explainthe phenomenon throughout the Rocky Mountains,despite studies that have disproved some of thesehypotheses. Landscape metrics calculated for Medi-cine Bow in this study do reflect patterns that wouldbe expected from wind-snowdrift interactions.However, patterns at Park Range and Flattop sug-gest that microtopographic variation is moreimportant than wind-snowdrift processes in produ-cing and maintaining ribbon forest patterns at thesesites. These results, combined with the conclusionsof Holtmeier (1982, 1985) that most Type 1 ribbonsare also controlled by microtopography suggest thatthe mode of ribbon forest dynamics at MedicineBow is an exception, rather than the rule. This studyillustrates the importance of a landscape perspectivein identifying variation in pattern that reflects dif-ferences in process, and highlights the need forfurther research that reconsiders hypotheses of rib-bon forest development in light of this variation.

Acknowledgements.We appreciate constructive comments

from two anonymous reviewers. This research was sup-

ported by a GraduateMentoring Grant to J.T. Clark from

Brigham Young University.

References

Alftine, K.J. & Malanson, G.P. 2004. Directional positive

feedback and pattern at an alpine tree line. Journal of

Vegetation Science 15: 3–12.

Arno, S.F. 1984. Timberline: mountain and arctic forest

frontiers. The Mountaineers, Seattle, WA, USA.

Atwood, C.K. &Atwood Jr., W.W. 1937. Land utilization

in a glaciated mountain range. Economic Geography

13: 365–378.

Baker, W.L. 1992. Effects of settlement and fire

suppression on landscape structure. Ecology 73:

1879–1887.

Bekker, M.F. 2005. Positive feedback between tree

establishment and patterns of subalpine forest

advancement, Glacier National Park, Montana,

USA. Arctic, Antarctic, and Alpine Research 37: 97–

107.

Bekker, M.F. & Malanson, G.P. 2008. Linear forest

patterns in subalpine environments. Progress in

Physical Geography 32: 635–653.

Billings, W.D. 1969. Vegetational pattern near alpine

timberline as affected by fire–snowdrift interactions.

Vegetatio 19: 192–207.

Buckner, D.L. 1977. Ribbon forest development and

maintenance in the Central Rocky Mountains of

Colorado. PhD Dissertation. University of Colorado,

Boulder, CO, USA.

Butler, D.R., Malanson, G.P., Bekker, M.F. & Resler,

L.M. 2003. Lithologic, structural, and geomorphic

controls on ribbon forest patterns in a glaciated

mountain environment. Geomorphology 55: 203–217.

Butler, D.R., Malanson, G.P., Walsh, S.J. & Fagre, D.B.

2007. Influences of geomorphology and geology on

alpine treeline in the American West: more important

than climatic influences? Physical Geography 28: 434–

450.

Callaway, R.M., Brooker, R.W., Choler, P., Kidvidze, Z.,

Lortie, C.J., Michalet, R., Paolini, L., Pugnaire, F.L.,

Newingham, B., Aschehoug, E.T., Kikodze, D. &

Cook, B.J. 2002. Positive interactions among alpine

plants increase with stress. Nature 417: 844–848.

Coop, J.D. & Givnish, T.J. 2007. Gradient analysis of

reversed treelines and grasslands of the Valles Caldera,

New Mexico. Journal of Vegetation Science 18: 43–54.

Doering, W.R. & Reider, R.G. 1992. Soils of Cinnabar

Park, Medicine Bow Mountains, Wyoming, USA:

indicators of park origin and persistence. Arctic and

Alpine Research 24: 27–39.

Earle, C.J. 1993. Forest dynamics in a forest-tundra ecotone,

Medicine BowMountains, Wyoming. PhD Dissertation.

University of Washington, Seattle, WA, USA.


Foster, D.R., King, G.A., Glaser, P.H. &Wright Jr., H.E.

1983. Origin of string patterns in boreal peatlands.

Nature 306: 256–258.

Germino, M.J., Smith, W.K. & Resor, A.C. 2002. Conifer

seedling distribution and survival in an alpine-treeline

ecotone. Plant Ecology 162: 157–168.

Griggs, R.F. 1938. Timberlines in the northern Rocky

Mountains. Ecology 19: 548–564.

Hattenschwiler, S. & Smith, W.K. 1999. Seedling

occurrence in alpine treeline conifers: a case study

from the central Rocky Mountains, USA. Acta

Oecologica 20: 219–224.

Hiemstra, C.A., Liston, G.E. & Reiners, W.A. 2002. Snow

redistribution by wind and interactions with

vegetation at upper treeline in the Medicine Bow

Mountains, Wyoming, USA. Arctic, Antarctic, and

Alpine Research 34: 262–273.

Hiemstra, C.A., Liston, G.E. & Reiners, W.A. 2006.

Observing, modelling, and validating snow

redistribution by wind in a Wyoming treeline

landscape. Ecological Modelling 197: 35–51.

Holtmeier, F.-K. 1982. ‘Ribbon Forest’ and ‘Hedges.’

Strip-like distribution patterns of trees at the upper

timberline in the RockyMountains. Erdkunde 36: 142–

153.

Holtmeier, F.-K. 1985. Climatic stress influencing the

physiognomy of trees at the polar and mountain

timberline. In: Turner, H. & Tranquilini, W. (eds.)

Establishment and trending of subalpine forest: research

and management. Proceedings of the 3rd IUFRO

Workshop. pp. 31–40, Eidgenossische Anstalt fur das

forstliche Versuchswesen, Berichte, 270..

Holtmeier, F.-K. 2003. Mountain timberlines: ecology,

patchiness, and dynamics. Kluwer Academic

Publishers, Dordrecht, the Netherlands.

Houston, R.S. 1968. Geologic map of the medicine Bow

Mountains, Albany and Carbon counties, Wyoming.

Geological Survey of Wyoming, Laramie, WY, USA.

Houston, R.S. & Karlstrom, K.E. 1992. Geologic map of

Precambrian metasedimentary rocks of the Medicine

Bow Mountains, Albany and Carbon Counties,

Wyoming. US Geological Survey Miscellaneous

Investigations Map I-2280. US Geological Survey,

Washington, DC, USA.

Li, H. & Reynolds, J.F. 1993. A new contagion index to

quantify spatial patterns of landscapes. Landscape

Ecology 8: 155–162.

Loehle, C., Li, B.L. & Sundell, R.C. 1996. Forest spread

and phase transitions at forest-prairie ecotones in

Kansas, USA. Landscape Ecology 11: 225–235.

Malanson, G.P. 1999. Considering complexity. Annals

of the Association of American Geographers 89: 746–

753.

Malanson, G.P. & Zeng, Y. 2004. Uncovering spatial

feedbacks at alpine treeline using spatial metrics in

evolutionary simulations. In: Atkinson, P.M., Foody,

G., Darby, S. & Wu, F. (eds.) GeoDynamics. pp. 137–

150. CRC Press, Boca Raton, FL, USA.

Malanson, G.P., Xiao, N. & Alftine, K.J. 2001. A

simulation test of the resource-averaging hypothesis

of ecotone formation. Journal of Vegetation Science

12: 743–748.

Malanson, G.P., Butler, D.R., Fagre, D.B., Walsh, S.J.,

Tomback, D.F., Daniels, L.D., Resler, L.M., Smith,

W.K., Weiss, D.J., Peterson, D.L., Bunn, A.G.,

Hiemstra, C.A., Liptzin, D., Bourgeron, P.S., Shen,

Z. & Millar, C.I. 2007. Alpine treeline of western

North America: linking organism-to-landscape scales.

Physical Geography 28: 378–396.

Marr, J.W. 1977. The development and movement of

tree islands near the upper limit of tree growth in

the southern Rocky Mountains. Ecology 58: 1159–

1164.

McGarigal, K. &Marks, B.J. 1994. FRAGSTATS: spatial

pattern analysis program for quantifying landscape

structure. Oregon State University, Corvallis, OR,

USA.

Mears Jr., B. 2001. Glacial records in the Medicine Bow

Mountains and Sierra Madre of southern Wyoming and

adjacent Colorado, with a traveler’s guide to their sites.

Public information circular no. 4. Wyoming State

Geological Survey, Laramie, WY, USA.

Miles, S.R. & Singleton, P.C. 1975. Vegetative history of

Cinnabar Park in Medicine Bow National Forest,

Wyoming. Soil Science Society of America Pro-

ceedings 39: 1204–1208.

Milne, B.T., Johnson, A.R., Keitt, T.H., Hatfield, C.A.,

David, J. & Hraber, P.T. 1996. Detection of critical

densities associated with pinon–juniper woodland

ecotones. Ecology 77: 805–821.

O’Neill, R.V., Krummel, J.R., Gardner, R.H., Sugihara,

G., Jackson, B., DeAngelis, D.L., Milne, B.T., Turner,

M.G., Zygmunt, B., Christensen, S., Dale, V.H. &

Graham, R.L. 1988. Indices of landscape pattern.

Landscape Ecology 1: 153–162.

Oosting, H.J. & Reed, J.F. 1952. Virgin spruce-fir of the

Medicine Bow Mountains, Wyoming. Ecological

Monographs 22: 69–91.

Oshima, Y., Kimura, M., Iwake, H. & Kuriowa, S. 1958.

Ecological and physiological studies on the vegetation

of Mt Shimagare. I. Preliminary survey of the

vegetation of Mt. Shimagare. Botanical Magazine

Tokyo 71: 289–300.

Peet, R.K. 2000. Forests and meadows of the Rocky

Mountains. In: Barbour, M.G. & Billings, W.D.

(eds.) North American terrestrial vegetation. 2nd edn,

pp. 75–121. Cambridge University Press, New York,

NY, USA.

Puigdefabregas, J., Gallart, F., Biaciotto, O., Allogia, M.

& del Barrio, G. 1999. Banded vegetation patterning in

a subantarctic forest of Tierra del Fuego, as an

outcome of the interaction between wind and tree

growth. Acta Oecologica 20: 135–146.

Reiners, W.A. & Lang, G.E. 1979. Vegetational patterns

and processes in the balsam fir zone, White

Mountains, New Hampshire. Ecology 60: 403–417.


Resler, L.M., Butler, D.R. & Malanson, G.P. 2005.

Topographic shelter and conifer establishment and

mortality in an alpine environment, Glacier National

Park, Montana. Physical Geography 26: 112–125.

Rietkerk, M. & van de Koppel, J. 2008. Regular pattern

formation in real ecosystems. Trends in Ecology and

Evolution 23: 169–175.

Rietkerk, M., Dekker, S.C., de Ruiter, P.C. & van de

Koppel, J. 2004. Self-organized patchiness and

catastrophic shifts in ecosystems. Science 305: 1926–

1929.

Ross, C.P. 1959. Geology of Glacier National Park and the

Flathead Region, Northwestern Montana. US

Geological Survey Professional Paper, vol. 296. US

Geological Survey, Washington, DC, USA.

SFWMD. 2004. 2004 Everglades consolidated report.

South Florida Water Management District, West

Palm Beach, FL, USA.

Smith, W.K., Germino, M.J., Hancock, T.E. & Johnson,

D.M. 2003. Another perspective on altitudinal limits

of alpine timberlines. Tree Physiology 23: 1101–1112.

SNOTEL. 2007. SNOTELDataNetwork.U.S. Department

of Agriculture Natural Resources Conservation Service.

URL: http://www.wcc.nrcs.usda.gov/snotel/

Snyder, G.L. 1980a. Geologic map of the central part of the

northern Park Range, Jackson and Routt Counties,

Colorado. US Geological Survey Miscellaneous

Investigations Series Map I-1112. US Geological

Survey, Washington, DC, USA.

Snyder, G.L. 1980b. Geologic map of the northernmost

park range and southernmost Sierra Madre, Jackson

and Routt Counties, Colorado. US Geological Survey

Miscellaneous Investigations Series Map I-1113. US

Geological Survey, Washington, DC, USA.

Sprugel, D.G. 1976. Dynamic structure of wave-

regenerated Abies balsamea forests in the north-

eastern United States. Journal of Ecology 64:

889–911.

Tongway, D.J., Valentin, C. & Seghieri, J. (eds.) 2001.

Banded Vegetation Patterning in Arid and Semiarid

Environments. Ecological Processes and Consequences

for Management. Ecological Studies 149. Springer-

Verlag, New York, NY, USA.

Turner, M.G., Wear, D.N. & Flamm, R.O. 1996. Land

ownership and land-cover change in the Southern

Appalachian Highlands and the Olympic Peninsula.

Ecological Applications 6: 1150–1172.

Vale, T.R. 1978. Tree invasion of Cinnabar Park in

Wyoming. American Midland Naturalist 100: 277–284.

Walker, D.A., Billings, W.D. & DeMolenaar, J.G. 2001.

Snow–vegetation interactions in tundra environments.

In: Jones, H.G., Pomeroy, J.W., Walker, D.A.

& Hoham, R.W. (eds.) Snow ecology: an inter-

disciplinary examination of snow-covered ecosystems.

pp. 266–324. Cambridge University Press, New York,

NY, USA.

Walker, S., Wilson, J.B., Steel, J.B., Rapson, G.L., Smith,

B., King, W.M. & Cottam, Y.H. 2003. Properties of

ecotones: evidence from five ecotones objectively

determined from a coastal vegetation gradient.

Journal of Vegetation Science 14: 579–590.

Whipple, J.W. 1992. Geologic map of Glacier National

Park, Montana. US Geological Survey Miscellaneous

Investigations Series Map I-1508-F. US Geological

Survey, Washington, DC, USA.

White, L.P. 1969. Vegetation arcs in Jordan. Journal of

Ecology 57: 5461–5464.

Wilson, J.B. & Agnew, A.D.Q. 1992. Positive-feedback

switches in plant communities. Advances in Ecological

Research 23: 263–336.

Wu, Y.G., Wang, N.M. & Rutchey, K. 2006. An analysis

of spatial complexity of ridge and slough patterns in

the Everglades ecosystem. Ecological Complexity 3:

183–192.

Zeng, Y., Malanson, G.P. & Butler, D.R. 2007.

Geomorphological limits to self-organization of alpine

forest-tundra ecotone vegetation. Geomorphology 91:

378–392.

Received 15 December 2007;

Accepted 28 November 2008.

Co-ordinating Editor: A. Moody


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