451PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLASRevista Chilena de Historia Natural78: 451-467, 2005

A quantitative analysis of forest fragmentation in Los Tuxtlas, southeastMexico: patterns and implications for conservation

Un análisis cuantitativo de la fragmentación de la selva de Los Tuxtlas en el sudeste deMéxico: patrones e implicaciones para la conservación

EDUARDO MENDOZA1, JOHN FAY2 & RODOLFO DIRZO1, 3

1Instituto de Ecología, Departamento de Ecología Evolutiva, UNAM, Apartado Postal 70-275,México 04510, Distrito Federal; e-mail: emr_999@yahoo.com.mx

2Center for Conservation Biology, Stanford University, Stanford, California 94305, USA3Current address: Department of Biological Sciences, Stanford University, Stanford, California 94305, USA

ABSTRACT

Habitat loss is a critical threat to tropical biodiversity and its quantification constitutes a central conservationissue. Typically, assessments have been based on deforestation rates statistics. However, this overlooks theeffects brought about by the spatial reconfiguration of the remaining habitat: fragmentation. We present ananalysis of fragmentation in a Neotropical site aimed at: (a) devising a protocol for its quantification, (b)using such protocol to provide insights on the ecological consequences of fragmentation, (c) exploring itsapplicability to address the hypothesis that forest size-inequality decreases with elevation, an indicator ofhabitat accessibility. We applied the Gini coefficient (G) and the Lorenz curve to analyze fragment-sizevariation using a satellite-generated map. We also estimated edge effect, fragment shape and isolation.Remaining forest includes 1,005 fragments, ranging from 0.5 to 9.356 ha (median = 0.89). Size inequality wasvery high (G = 0.928), producing a flattened Lorenz curve. Forty percent of the fragments did not maintain anarea free of a 30-m edge effect, and larger fragments showed a marked deviation from ideal circular forms.Eighty-four percent of the fragments lay further than 500 m from the largest forest tract and their sizedecreased with distance. Fragment size distribution changed with altitude: the Gini coefficient was lowest andforest coverage was greatest at the highest altitude, but inequality peaked at an intermediate elevation. Giventhe current pace of habitat deterioration, application of similar analyses may improve global assessments oftropical ecosystems and their perspectives for biodiversity conservation.

Key words: edge effect, fragment shape, Gini coefficient, Lorenz curve, tropical rain forest.

RESUMEN

La destrucción del hábitat es la principal amenaza para la biodiversidad tropical, por lo que su cuantificaciónconstituye un aspecto central para la biología de la conservación. Usualmente, esta cuantificación se basa enel cálculo de las tasas de deforestación, ignorando los efectos derivados de la reconfiguración espacial delhábitat remanente postdeforestación: la fragmentación. Aquí presentamos un análisis de la fragmentación enun sitio Neotropical para: (a) proponer un protocolo para su cuantificación; (b) utilizar tal protocolo paraexplorar las consecuencias ecológicas de la fragmentación; y (c) explorar su aplicación para evaluar lahipótesis de que la heterogeneidad de tamaños de los fragmentos disminuye con la elevación (indicativo de laaccesibilidad del hábitat). Calculamos el coeficiente de Gini y la curva de Lorenz para analizar la desigualdadde tamaños de los fragmentos, utilizando un mapa generado con una imagen de satélite; además evaluamos elefecto de borde, la forma de los fragmentos y su grado de aislamiento. Encontramos que el bosque remanenteincluye 1.005 fragmentos entre 0,5 y 9,356 ha (mediana = 0,89). La desigualdad de tamaños fue considerable(G= 0,928), con una curva de Lorenz muy abatida. El 40% de los fragmentos no tuvo un área libre de unefecto de borde de 30 m de ancho; los fragmentos más grandes mostraron un desvío considerable con respectoa la forma circular ideal. El 84 % de los fragmentos estuvo aislado, ubicándose más allá de 500 m de distanciadel parche más grande de bosque y su tamaño disminuyó con la distancia. La distribución de tamaños de losfragmentos varió con la elevación: el coeficiente de Gini fue menor y la cobertura relativa de bosque fuemayor en la elevación más grande, pero la desigualdad fue máxima en una elevación intermedia. Proponemosque, en vista de los ritmos actuales de deterioro del hábitat, la aplicación de análisis similares puede mejorarnuestras evaluaciones del estado de conservación de los ecosistemas tropicales y las perspectivas para laconservación de la biodiversidad.

Palabras clave: efecto de borde, tamaño de fragmento, coeficiente de Gini, curva de Lorenz, selva tropicallluviosa.

452 MENDOZA ET AL.

INTRODUCTION

Habitat loss brought about by anthropogenicactivities is widely recognized as the mostconspicuous and pervasive threat tobiodiversity in the tropics (Laurance &Bierregaard 1997). Upon recognition of itsdeleterious effects, including speciesextinction, local and global climate change, soilerosion, water pollution, and the loss of variousenvironmental services (Malhi & Grace 2000,Lawton et al. 2001), several initiatives havebeen developed to estimate i ts globalmagnitude (e.g., WRI 1990, FAO 1993, 2001,Achard et al. 2002). These assessments haveproduced valuable insights into the generaltrends of tropical forest area loss. However, theestimates they provide remain highly variableand are sometimes inconsistent (WRI 1990,FAO 1993, 2001, Achard et al. 2002, Kaiser2002). On the other hand, and of moreecological significance, global assessments ofnet cover change and their coarse spatialresolution downplay the variety of complexrepercussions arising from the spatialreconfiguration of the remnant habitat afterdeforestation (Vitousek et al. 1997, Borges2000, Dirzo 2001). Indeed, over the last fewdecades, habitat fragmentation –the breakingapart and isolation of formerly continuousforest (Saunders et al. 1991)– has been found tohave a number of negative ecological effects(Turner 1996, Laurance et al. 2002, but seeFahrig 2003). Traditionally, the effects offragmentation have been considered in terms ofthe impact of the size of the remaining forestpatches (Laurance et al. 2002). However,increasing evidence shows that such effectsmay also stem from the spatial distribution(e.g., degree of isolation, location alongaltitudinal gradients) and shape (e.g. edge/arearatio) of the remaining forest patches resultingfrom current land use patterns (Borges 2000,Silva & Tabarelli 2000, Laurance et al. 2002).

These ecological findings, in conjunctionwith the global occurrence of habitatfragmentation make its quantification a topicthat deserves further attention than it has hadhitherto. Local assessments of forest lossincorporating quantitative descriptions offragmentation may be valuable tools for localconservation and management planning butalso for the development of standardized

descriptors of habitat “quality”. Such localassessments may subsequently be used asbaselines to provide more realistic local andglobal assessments of the threats to tropicalbiodiversity resulting from current land usepatterns (Skole & Tucker 1993, Ranta et al.1998, Sánchez-Azofeifa et al. 2001).

Though a number of parameters to describelandscape fragmentation have been alreadyproposed in the scientific literature (Gustafson1998), we present a novel, complementaryapproach based on the application of the Ginicoefficient and the Lorenz curve. Theseanalytical tools were originally developed forthe study of economic wealth distribution andincome inequality (Weiner 1986). However,they have proved to be very useful to describean ample array of ecological situations where ahierarchical organization develops, rangingfrom the skewed distributions of individual sizein plant populations under strong competition(Weiner & Solbrig 1984, Weiner 1986, Weiner& Thomas 1986), to the strength of edge effectsin plant species composition in forests (Matlack1994) or size inequalities among parts (shoots)within plants (Larson & Whitham 1997). Theincreasing familiarity of ecologists with suchtools may permit their use in quantification ofhabitat fragmentation, where a hierarchicaldistribution of patch sizes is likely to develop.In this case the Lorenz curve may provide astandardized graphical representation of areadistribution among fragments whose form, incontrast to histograms, is not influenced byclass sizes and number. In addition,information contained in the Lorenz curve canbe summarized in a single parameter, the Ginicoefficient, that can be readily amenable forcomparison and statistical analysis.

To our knowledge, no attempt has been madeto quantitatively describe habitat fragmentationusing these tools. In this study we combine theuse of such techniques with other quantitativedescriptors of the spatial configuration andshape of forest fragments to assess theconservation status of a Neotropical site.Specifically, this study focuses on a rain forestsite of relevance for the Neotropics at large. Theconcerned study site, Los Tuxtlas (state ofVeracruz, México), constitutes the northernmostlimit of the distribution of this ecosystem in theAmericas (Dirzo & Miranda 1991a) and is oneof most studied sites in the Neotropics (see

453PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

González et al. 1997). We addressed fourparticular questions: (i) how is remaining forestarea distributed among fragments? (ii) to whatextent the incorporation of edge effect mayreduce effective fragment area and number? (iii)to what extent the ratio area/perimeter offragments deviates from the corresponding ratioof circular fragments (which minimize areaexposure) of the same size? (iv) how are forestfragments distributed in space as a function ofdistance from the largest tract of remainingforest? In addition, we developed an exercise totest the applicability of the Gini coefficient and

the Lorenz curve by comparing such parametersacross a deliberately defined stratification of theterrain in terms of altitudinal bands. In particularwe evaluated the expectation that the value ofthe Gini coefficient (and its graphicalrepresentation, the Lorenz curve) would belower, indicating the lowest inequality, aselevation increases, given that elevation is anindicator of land inaccessibility and thussusceptibility to human influence. A test of thishypothesis is relevant for sites that, like LosTuxtlas, include a topographic/elevationgradient.

Fig. 1: Location of the study area in southeast Mexico and UNAM’s field station (FS). The isolinesrepresent 200-m elevation bands, starting from 200 m (the outermost, adjacent to the coastline) till1,400 m (the innermost). Shaded areas represent major human settlements.Ubicación del área de estudio en el sudeste de México y de la estación biológica de la UNAM (FS). Las isolíneas indicanintervalos de 200 m en altitud, a partir de los 200 m y hasta los 1.400 m. Las zonas con achurado representan los pobladosmás grandes.

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MATERIAL AND METHODS

Study area

This study encompasses an area of 83,644 ha ofcontinental land that includes the northernmostportion of the Sierra de Los Tuxtlas, in southernVeracruz, Mexico (Fig. 1). The Sierra de LosTuxtlas is a diagonal mountainous rangecomposed of a series of volcanic cones runningin a NW-SE direction, the most conspicuous ofwhich are the San Martín (included in this study)and the Santa Marta (a large tract of forestlocated towards the southeast of the study site),both with an altitude close to 1.650 m (Dirzo &García 1992). These volcanoes represent thenorthwestern and southeastern extremes,respectively, of the Sierra de Los Tuxtlas.Between such volcanoes lies the Catemaco Lake,the fourth largest in the country.

Average temperature ranges between 24 and26 °C in most of the study area, with lower values(20-22 °C) at higher altitudes. Annualprecipitation ranges between 3,000 and 4,500 mmbut may be even higher in some sectors of thearea (Soto & Gama 1997). Originally, thepredominant vegetation type was lowland tropicalrain forest with marked altitudinal variants,including mixed pine-oak patches, cloud forestand elfin forest. Mangrove vegetation isassociated to the Sontecomapan lagoon located onthe eastern portion of the study area (Fig.1)(Dirzo et al. 1997, Ibarra-Manríquez et al. 1997).Additional vegetation variants are related toedaphic factors such as soil depth and thepresence of lava outcrops (Dirzo et al. 1997,Ibarra-Manríquez et al. 1997). For a detaileddescription of the area see Dirzo et al. (1997).

Los Tuxtlas has a long history of exposureto human activities, in particular those relatedto cattle ranching. This dates from the firstquarter of the sixteenth century, but i tsignificantly expanded during the decade of the1950’s, when it began to experience anaccelerated growth, marking the start of anextensive transformation of the natural habitatsin the region (Guevara et al. 1997).

Image classification and generation of forestmap

To generate the forest map of our study area weused a previously geo-referenced sub-scene

from a yr 2000 Landsat-7 image (obtained fromthe Institute of Geography, UNAM), with sixbands and a pixel size of 30 x 30 m. For theclassification of this image we conducted asupervised classification using the IDRISI 32(Clark Labs, The Idrisi Project) image-processing protocol. We selected representativeareas of the following land-cover classes astraining fields: (1) water bodies, (2) matureforest, (3) secondary forest, (4) mangrove, (5)pasture and agriculture and (6) barren soil. Insome cases we used subdivisions of the mainland-cover classes to deal with morehomogeneous land-cover subcategories.Selection of the training fields was based on thevisual interpretation of color composites,digital aerial photography (yr 2000) and fieldwork.

Previous to the classification we applied theSEPSIG option of IDRISI 32 to the six-bandimage and to a vegetation index (the NDVI), inorder to select the subset of bands with the bestpotential to separate land cover categories, andto create final signature files for each landcover type (Eastman 1999). We used thesignatures to carry out a maximum likelihoodclassification of the pixels (MAXLIKE optionof IDRISI 32). We repeated this process untilwe found a satisfactory match between pixelassignation to a given forest category andvisual inspection of digital and analog aerialphotography (2000 and 1991, respectively).Given that the main concern of this study wasmature forest area, we aggregated all non-forestcategories (except water bodies) thusgenerating a map with just three elements:mature forest, non-forest and water. Theresulting map was then subjected to anaccuracy assessment.

For such an assessment we physicallylocated 48 ground-truthing points scatteredthroughout the study area (30 in mature forest,14 in secondary forest and four in water) andemployed the ERRMAT option of IDRISI 32 toassess the agreement between field informationand land-cover designation in our map(Eastman 1999). To have an additionalindicator of the accuracy of the classification,we obtained the Kappa Index of Agreement ingeneral, and for each land-cover category inparticular (Eastman 1999). This indexcompares the proportion of correctly classifiedpixels (based on ground-truthing data) against

455PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

the proportion of pixels expected to fall in thecorrect class just by chance. Possible values ofthe index range between zero (no differencewith the expected random pattern) to one (100% accuracy) (Congalton & Mead 1983).

As a final step of this phase of the work weexcluded all classified forest fragments with anarea equal to or smaller than 3,600 m2 (4pixels), based on two criteria: (a) any fragmentequal to or smaller than 3,600 m2 is completelyinfluenced by edge effects (see below) and (b)individual pixels classified as forest frequentlyrepresent isolated trees. The final map (rasterfile) was transformed to a vector format usingIDRISI 32 (Clark Labs, The Idrisi Project) tofacilitate subsequent manipulation.

Distribution of remnant forest area amongfragments

In order to describe patterns of variation infragment size we employed the Lorenz curveand the Gini coefficient (Weiner & Solbrig1984, Weiner 1986). The Lorenz curve allows avisual inspection of the departure of fragmentsfrom perfect equality (meaning in this case thatall fragments have the same forest area), asrepresented by a diagonal that connects the (0-0) and (100 -100) coordinates of a fragments-area plot. Such a procedure involves thegraphical representation of the cumulativepercentage of area against the cumulativepercentage of the “population” of forestfragments ranked in an upward sequenceaccording to their size. Associated to this, theGini coefficient provides a quantitativeestimation of the departure from perfectequality. The Gini coefficient has a minimumvalue of cero when all the individuals (i.e.,fragments in this case) contribute in the samerelative magnitude to the total population“wealth” (i.e., forest area) and a theoreticalmaximum of 1 when all but one of theindividuals (fragments) have a 0 contribution tothe total population wealth (Slack & Rodrigue2002). The Gini coefficient can readily becalculated as follows (Slack & Rodrigue 2002):

where N = number of fragments, Yi = observedproportional area of each fragment, Xi =expected proportional area of each fragment if

area were distributed equally, σY=accumulated proportions of Y values and σX=accumulated proportions of X values. Anestimate of the standard deviation for the Ginicoefficient was generated using the DAD 4.2software following Duclos et al. (2002).

Analysis of edge effect

It is known that the penetration distance ofedge effects varies widely depending on thevariable under examination. In addition, edgeeffect intensity varies as a consequence of edgeage and the type of surrounding matrix(Laurance et al. 2002). Such effects of edgewill determine effective fragment size andnumber. As a conservative approach, we tookadvantage of the existence of a recent studycarried out in our study site, in which thevariation in temperature and relative humiditywere systematically measured at 1-m distancesestablished on transects moving from the edgetowards the interior of a series of fragments(Ruiz 2003). Several transects were used perfragment, including a range of fragment sizes.The large data set derived from these transectsallowed for best-fit models of distance versustemperature/humidity to be performed. Fielddata for this study were gathered in 2001, onlyone year apart from the date of the image weused for the present study. This analysisdetected an asymptote in the response of thesevariables at 30 m. Nevertheless, in order toexplore the possibility that the penetrationdistance for other variables would be greater,we developed an additional exercise ofexploring the changes in the number offragments and their variation in size, usingdistances of 60 and 100 m.

Once we decided to use these threepenetration distances we created a series of 30,60, or 100 m inner strips, parallel to the edge ofeach fragment, with the ArcView 3.2a (ESRI)buffer option. We subsequently discounted thearea of such strips from the area of eachfragment using Patch Analyst 2.2 (Elkie et al.1999). Through this process we obtained thecore fragment area (i.e., fragment area free ofedge effect). We analyzed relative frequenciesof whole-area fragments (WF) and core-areafragments (CAF) using histograms inconjunction with the Lorenz curves. We alsocalculated the value of the Gini coefficient for

G = 1- Σ (σYi-1 + σYi) (σXi - σXi-1)N

i=0

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the case of WF using the procedure describedabove

Analysis of fragment shapes

Although there exists a variety of indices todescribe variation in fragment shape we decidedto develop an approach that allowed a graphicdescription of the departure of forest fragmentshapes from the ideal (for our purposes a circle,given that this shape maximizes the area/perimeter ratio for any given area). For thispurpose we calculated the area (A)/perimeter (P)ratio for each of the observed fragments usingPatch analyst 2.2 (Elkie et al. 1999) and weplotted those values on a chart with log of thearea as the X-axis and log of the A/P ratios asthe Y-axis. We also calculated the A/P

relationship for circular fragments with the samesizes as the observed fragments and plotted theresulting values onto the same graph. Bycomparing against the expected A/P ratio of acircular fragment of the same area, wecontrolled for the effect of size variation. Theline that results from connecting pointsrepresenting A/P ratios for circles of differentsize with the graph’s origin defines the highestpossible limit for A/P values. Thus, an estimateof the departure of each fragment from its idealform was obtained based on the distancebetween any observed data point and itscorresponding value on the graph’s diagonal.The resulting distances, in percentage, weregrouped into the 25, 50, 75 and 100 % quartiles,in order to compare departures among fragmentsof different class-sizes.

Fig. 2: Map depicting the study area and the current (i.e., year 2000) spatial distribution of forestfragments in Los Tuxtlas. The round-shaped forest mass to the center-left of the map corresponds tothe San Martín volcano and the enclosed area to UNAM’s field station.Distribución espacial de los fragmentos de bosque en Los Tuxtlas. La porción redondeada de bosque al centro-izquierda delmapa corresponde al volcán San Martín y el área en el recuadro a la estación de la UNAM.

457PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

Fragment isolation

In order to have an estimator of the level ofisolation of the fragments with respect to thelargest tract of remaining forest (see Fig. 2) wecreated a set of concentric bands (of 500-mwidth) around such fragment (using ArcView3.2a utilities). The bands were irregular inshape, following the irregular edge of thelargest fragment. We then quantified thenumber of fragments falling within each band.Large fragments lying on more than onedistance interval were assigned to the firstdistance interval they contacted.

Altitudinal variation of remnant forest and itsdistribution among fragments

We explored the relationship between the spatialdistribution of remnant forest and fragmentswith altitude employing a geo-referenced digitalelevation model (DEM) of the zone (with a pixelsize of 90 x 90 m) obtained from the Institute ofGeography, UNAM, and our vegetation map.We used ArcView 3.2a (ESRI) to reclassify theDEM in five strata according to the followingaltitude intervals: 0-330, 331-660, 661-990, 991-1,320 and 1,321-1,650 m. After suchreclassification we calculated the proportion ofthe area of study falling within each interval,excluding water bodies. We used ArcView 3.2a(ESRI) to overlay the area falling in each of theintervals with the forest map. After this wecalculated the proportional coverage of forest foreach altitude interval (assuming that the wholeterrestrial area at each altitude interval could bepotentially covered by forest). Additionally, werepeated the procedure described in the previoussection, dealing with the analysis of distributionof forest area among fragments, in order togenerate the Lorenz curves and the Ginicoefficients for each one of the altitudeintervals.

RESULTS

Image classification and accuracy

The error matrix produced an estimate ofoverall misclassification of 7 % (range 0 -14 %;95 % confidence interval). The main source ofmisclassification was inclusion of old

secondary vegetation within the mature forestcategory (21 % commission error for secondaryforest category). The values of the Kappa indexof agreement for each cover category, using theforest map as the reference image, were 100,100 and 72 % for water, mature forest, andsecondary forest, respectively. On the otherhand, the corresponding values for the samecategories using the ground-truthing map as thereference image were 100, 75, and 100 %,respectively. Therefore, there was a value of 87% for the overall Kappa index of agreement;that is, we got 87 % more accuracy in theclassification, as compared with that expectedby chance alone (see resulting forest map inFig. 2). From the point of view of forestclassification, inclusion of old secondary forestresults in some level of over-estimation ofremaining mature forest area.

Distribution of remnant forest area amongfragments

Considering the entire study area, we found thatboth inequality parameters, the Lorenz curve andthe Gini coefficient (Fig. 3A), are very close tothe values that indicate maximal inequality. Thisimplies an extreme contrast in the distribution offorest area among fragments, with the greatmajority of them having a very small area andjust a few having a very large area. Specifically,ca. 90 % of the fragment population onlyaccumulates around 10 % of the total forestedarea, while the remaining 10 % of the fragmentsaccount for as much as 90 % (Fig. 3A). This isconsistent with the fact that one single fragmentrepresents more than 60 % of the existing forestarea (cf. Fig. 2). Consequently, we observe (Fig.3A) an almost complete occupation of the arealying on the sub-diagonal portion of thecumulative percentages plot (shaded area in Fig.3A) in the case of the Lorenz curve, and a valuevery close to 1,0 in the case of the Ginicoefficient (Fig. 3A).

Edge effects

The subtraction of strips of 30 m in width fromthe edge of each fragment (to simulate edgeeffects) produced several changes in thefrequency-distribution of forested areas (Fig.4A). One of the most evident is that once allthe fragments that are unable to maintain a part

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Fig. 3: Lorenz curves describing area inequalities among forest fragments. The extent of the shadedarea indicates the magnitude of the departure from perfect equality and is reflected in the Ginicoefficient (G) [± standard deviation]. Panel (A) corresponds to the complete study area and panels(B)-(F) represent each of the altitudinal bands.Curvas de Lorenz que describen la desigualdad en el área de los fragmentos. El tamaño del área sombreada indica lamagnitud del desvío de una distribución perfectamente equitativa y corresponde al valor del coeficiente de Gini (G) [± 1desviación estándar]. La parte (A) corresponde el área completa y (B)-(F) corresponden a los diferentes pisos altitudinales.

459PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

Fig. 4: (A) Frequency-distribution of whole fragments (i.e., ignoring edge effects) (empty bars) andof core-area fragments (shaded bars). Numbers in the X-axis indicate the upper class limit; the firstclass includes areas ≤ 10-3 ha. The insert shows descriptive statistics of both distributions; (B)Lorenz curves corresponding to whole fragments (upper) and core areas (lower), the value of G [± 1standard deviation] corresponds to the latter. Shaded area corresponds to departure from perfectequality.(A) Distribución de frecuencias de las áreas de los fragmentos (ignorando el efecto de borde) (barras blancas) y áreasnúcleo (barras negras). Los números en el eje de las X indican el límite superior de la clase; la primera clase incluye lasáreas ≤ 10-3 ha. El recuadro muestra la descripción estadística de ambas distribuciones. (B) Curvas de Lorenz correspon-dientes a los fragmentos enteros (curva superior) y a las áreas núcleo (curva inferior). El valor de G [± 1 desviaciónestándar] corresponde a las áreas núcleo. El área sombreada indica el grado de contraste con respecto a la máxima equidad.

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of its area free of such effect (heretofore core-area) are discarded, the number of fragmentsdramatically falls from 1,005 to 597 (see insertin Fig. 4). Furthermore, the shape of thefrequency-distribution was also modified in anumber of ways. The highest value of thedistribution decreased by 21 %, moving from9,356 to 7,354 ha. The lowest value alsochanged, passing from nearly 0.25 ha to almost0 ha, and creating a previously non-existing lefttail of the distribution (Fig. 4A). Thecontraction of the range led to an almost 50 %reduction of the skewness (see insert in Fig. 4).The median values were more sensitive toqualitative/quantitative changes in thefrequency-distribution, showing an 83 %decrease, while mean values showed a slightchange, only of 10 %. Nevertheless, aconsiderable amount of variation remains in thefrequency distribution of core-area fragments(Fig. 4A). The consideration of this edge effectresulted in an even more flattened Lorenz curvethan the corresponding to whole fragments (cf.Figs. 3A and 4B). In accordance with thiseffect on the Lorenz curve, the value of Gexperienced an increase of 5 % passing from0.928 to 0.978, almost reaching the maximum

value of 1,0 (highest inequality). These changesarise as a consequence of the remarkablereduction in core area experienced by small/medium fragments, the consequent generationof very small core areas, and the relativelyslight impact on the largest fragment. Thisreduces the contribution to total forest area dueto most of the fragments and exacerbates thesize contrast among fragments in the oppositeextremes of the distribution.

The incorporation of an edge effect of 60 mleaves a total of 633 fragments, a number largerthan the one produced by an edge effect of 30m. This situation is the result of a more intensepulverization of formerly larger fragments.Nevertheless, median size of fragments shiftedfrom an original value of 0.89 ha to a value of0,11 ha and the size of the largest fragmentdiminished from 9,356 ha to 5,243 ha, a 44 %reduction. In comparison, the incorporation ofan edge effect of 100 m has extreme effects onboth the number of fragments and on the size ofthe largest fragment. Thus, the number offragments falls to 224 (a 78 % reduction) andthe size of the largest fragment diminishes to3,814 ha (a reduction of 59 %). In contrast,median size reached a value of 0.20 ha.

Fig. 5: Plot depicting the departure of the observed A/P fragment ratios from that of circles withequivalent areas (diagonal line). Numbers represent percent departure from expected for circularshapes, grouped per quartile.Descripción de la magnitud del desvío de los cocientes A/P de los fragmentos con respecto a los correspondientes acírculos con la misma área. Los números representan el porcentaje del desvío total que corresponde a cada cuartil.

461PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

Fragment shapes

The A/P ratios of the fragments grouped ineach of the first three quartiles of thefrequency-distribution have a relatively lowdeparture from the points on the diagonal inFigure 5, corresponding to A/P ratios forcircles with the same area. Deviations offragment A/P ratios from the correspondingratios for equivalent circles in the first threequartiles vary between 18.4 and 23.7 %. Incontrast, A/P ratios for fragments belonging tothe fourth quartile show a larger deviation (Fig.5), with an overall departure of 37.6 %. Thismeans that the 25 % largest fragments deviaterelatively more from their correspondingcircular fragments than fragments belonging tothe first three quartiles (i.e., of the smaller sizeclasses).

Fragment isolation

The number of fragments decreases withdistance from the largest remnant forest tract(Fig. 6). Although the distance interval thatindividually holds the greater percentage offragments (i.e., 16.4 %) is that between 0 and500 m, the majority of the remaining fragmentslies further than 500 m away from the largestremnant tract. Such isolation of fragments isfurther exacerbated by the existence of a

negative relationship between average fragmentsize and distance interval (Spearmancorrelation, r = -0.46, P = 0.019, n = 26). On alarger spatial scale it is conceivable that thedepicted level of isolation of forest fragmentsmay change, in particular for the fragmentslaying at the lower right corner of the studyarea (Fig. 1 and 2), due to the proximity ofanother relatively large forest fragment (theSanta Marta volcano) falling outside the studyarea. However, given that the largest fragmentin this study and the Santa Marta volcano lienearly equidistant from the above-mentionedfragments, we do not expect a significantmodification of this result.

Relationship between elevation and distributionof remnant forest and fragments

The patterns of land use in the region have ledto a distinctive pattern of distribution of theremnant forest area in relation to altitude (Fig.7). The area that lies below 660 m, comprising76 % of the whole study area, only retains 34.3% of the forested area. In comparison, the studyarea lying above 990 m, which represents just7.3 % of the whole study area, holds 35.1 % ofthe extant forested area. A remaining 30.6 % ofthe current forested area lies on the interval of661-990 m (Fig. 7). This fact implies that theforest coverage in the lowlands has been

Fig. 6: Frequency distribution of forest fragments in the study area according to their distance tothe largest remnant forest tract (n = 1,002).Distribución de frecuencias de los fragmentos de acuerdo a su distancia con respecto al remanente de bosque más grande (n= 1.002).

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largely eradicated. Moreover, looking at theextremes of the elevation gradient, it is strikingthat the area laying above 1,320 m has almostfull-forest coverage (97.3 %), while the areabelow 330 m retains less than 2 % of its surfacecovered by forest (Fig. 7). The contrastingpatterns of relative coverage depicted in Figure7 are reflected in the negative relationshipbetween available terrain to be potentiallycovered by forest and altitude (Spearmancorrelation, r = -1.0, P < 0.001, n = 5) and fromthe positive relationship between altitude andproportion of actual forest coverage (Spearmancorrelation, r = 1.0, P < 0.001, n = 5). Thisresults from the fact that only the mostinaccessible, topographically complex areashave escaped deforestation.

The Gini coefficient and the Lorenz curvewere sensitive to variation in forested areaamong fragments across the altitudinal gradient(Fig. 3B-F). The Gini coefficient shows anincreasing tendency with a peak at the interval991-1,320 m (i.e., 0.9525) (Fig. 3E), followedby a considerable decrease at the highestelevation (0.4692) (Fig. 3F). Such altitudinaltendency is reflected in the Lorenz curve,which shows an increasing reduction of thearea under the curve up to 1,320 m, followedby a noticeable increase in the highestelevation. The contrast between the two

extreme data points (Fig. 3E versus Fig. 3F)stems from the fact that at the 991-1,320altitudinal band one single “fragment”, out of atotal of 27, accumulates close to 96 % of thetotal forested area available in such interval.However, more important than this is theabsolute size variation: the one largest fragmentis ca. 4,800 times larger than the other ones. Onthe other hand, the lowest value of G at thehighest elevation is a consequence of theexistence of just two fragments within thisaltitudinal interval. In this case, although thelargest fragment shows a similar, 97 %monopolization of area, its contrast with theother fragment is only 31-fold. Thus, the lowestvalue of fragment size inequality correspondsto the altitudinal belt that holds the lowestabsolute area of remnant forest (cf. Fig. 7).

DISCUSSION

The picture delineated by our forest map, theLorenz curve, and the Gini coefficient indicatethat the remaining forest in Los Tuxtlasrepresents a heavily fragmented landscape inwhich an archipelago of forest islands areimmersed in a sea of cattle grasslands. Evenwhen the map provides a dramatic pictorialview of the current spatial configuration of the

Fig. 7: Relative distribution of the study area by altitudinal levels (empty bars) and the percentcoverage of remaining forest area in each of the corresponding altitudinal levels (shaded bars).Distribución relativa del área de estudio por piso altitudinal (barras blancas) y el porcentaje de cobertura de bosquecorrespondiente (barras negras).

463PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

remnant vegetation, the Gini coefficientprovides a quantitative indicator of the imagethat, in addition, will be readily comparable tothat obtainable from areas subjected to thesame analysis. Quantitative descriptors such asG can provide a statistic that complements thewidely used deforestation rate which, usefuland conventional as it is, does not conveyinformation on the patterns of fragmentation.To the extent that we incorporate descriptors ofthis kind as widely as possible, our overallperception of the conservation state of tropicalforests can be more realistic.

In the case of Los Tuxtlas, our analysisshows that forests fragments fall into one oftwo contrasting categories: (A) that representedby a few relatively large fragments and (B) thatconstituted by a very large amount ofperipheral, small fragments, individuallyretaining a very low proportion of theremaining forest. As a consequence of thispattern, an overwhelming majority of the forestfragments in Los Tuxtlas falls well below thesizes in which significant declines in theabundance and species richness of understorybirds, butterflies and dung beetles in othertropical forests have been documented (Klein1989, Newmark 1991, Daily & Ehrlich 1995).In particular, forest fragments where howlermonkeys (Aloautta palliata) can be found inLos Tuxtlas (Estrada et al. 1999) are on averagemore than 40- times larger than the medianfragment size (0.89 ha). An additional andmore general picture of the impact offragmentation in Los Tuxtlas on the non-volantmammalian fauna can be gained through thecomparison of current fragment sizes and theinferred habitat-area requirements of suchfauna. If we use the published average densitiesof Neotropical forest mammals (Robinson &Redford 1989) we find that 26 selected specieswhose historical occurrence has been reportedfor Los Tuxtlas, would not be able toaccommodate a population with a minimumsize of 50 individuals (sensu Soulé 1980) infragments of the median size we documentedfor Los Tuxtlas. Moreover, according to thiscomparison even the largest forest fragment inour study area (9.356 ha) would be insufficientto support such minimum populations of twofelids (jaguar and puma) and the tapir.Empirical support for these expectations isprovided by field studies that have documented

a contemporary impoverishment of the non-volant mammalian fauna in our study area,particularly the medium/large animals whosehabitat-area requirements are larger (Dirzo &Miranda 1991b, Estrada et al. 1994).

An additional factor that may exacerbatebiological impoverishment in forest fragmentsin Los Tuxtlas is isolation by distance tosources of inmigrants. Its is known that severalgroups of forest organisms are reluctant tocross open areas as short as 100 m, includingeuglossine bees, understory birds and dungbeetles (Powell & Powell 1987, Klein 1989,Bierregaard & Dale 1996). In Los Tuxtlas it hasbeen documented that forest fragments inwhich monkeys are present have a meandistance to other forested sites of 166 m, whilefragments in which monkeys are absent have amean distance of 462 m (Estrada et al. 1999).Our documented negative correlation betweendistance to the largest fragment and averagefragment area may exacerbate isolation andtherefore the vulnerability of populations ofseveral species inhabiting such fragments. Inaddition, the predominant grassland matrixwhere most of the fragments are immerseappears to determine the movement of speciesof dung beetles and non-volant mammals, assuggested by the consistent poor representationof these animals in pastures (Estrada et al 1994,Estrada et al. 1999). In comparison, otheranimals such as bats show a more similarspecies composition and abundance betweenlarge and small forest fragments (Estrada &Coates-Estrada 2002) suggesting that they areless susceptible to fragmentation. Evidently,attributes such as mobility, home range andtolerance to contrasting physical environmentsdetermine the vulnerability of animals tofragmentation (Estrada & Coates-Estrada2002).

From a botanical standpoint, while studiesin some tropical forests indicate that smallforest remnants may retain a considerableproportion of their original number of plantspecies for some time (Turner et al. 1994),evidence indicates that, in the long run, most ofthe plant communities in small forest fragments(~ 1 ha) tend to become impoverished due tothe over-dominance of a subset of their species(Leigh et al. 1993, Turner et al. 1996, Asquithet al. 1997). The ecological consequences offragmentation on plants is an aspect that

464 MENDOZA ET AL.

currently is being investigated at Los Tuxtlas.The effects of fragmentation may be

exacerbated by a series of edge-related effects.Depending on the distance of penetration of therelevant variables, incorporation of such effectswill, in the first place, reduce “effective”fragment size and number and, consequently,overall habitat area and distribution. In ourcase, this situation is illustrated by the dramaticreduction in the number of fragments (from1005 to 597) and an increase of the Ginicoefficient (from 0.928 to 0.978) resulting fromthe application of the estimated penetrationdistance, 30 m, of microclimatic disruption.Nevertheless, penetration distances will varydepending on the variables of interest.Laurance (2002) indicates that penetrationdistances in Amazonia range from 10 m to 400m and thus fragment effective size, G, andspatial distribution will vary too. Our exerciseapplication with penetration distances of 60 mas is the case of edge effects on lower canopy-foliage density, or 100 m, as is the case ofeffects on abundance and diversity of leaf-litterinvertebrates (Laurance 2002) yielded evenmore dramatic changes in the number ofeffective fragments and fragmentationparameters. Thus, the ecological effects of edgewill depend on the variable of interest. In LosTuxtlas, for example, a 30-m edge effectsignificantly affect the rates of leaf pathogenicinfection by fungi (R. Dirzo, unpublished.data), as such fungi are highly susceptible tochanges in temperature and humidity.According to the literature, ecological effectson variables such as foliage density, or on leaf-litter invertebrates are to be expected bypenetration distances of 60 and 100 m,respectively. Furthermore, in our case even thelargest fragments are l ikely to remainsusceptible to some edge effects, given theconsiderable departure from the circular shapewe detected in such fragments in this site.

A salient aspect revealed by the spatialconfiguration of remnant forest in the studyarea is that the intensive habitat transformationthat this region has experienced has notproceeded with a homogeneous pacethroughout the landscape. Instead, it has had aparticularly strong impact on the lowlands,confining most of the forest remnants to thehilltops. Thus, the remaining vegetation doesnot constitute a representative sample of the

original diversity of habitat types. Even whenthis is a logical, expected result, the magnitudeof such conservational bias, and the detailedquantification of the spatial reconfiguration offorests are aspects that may provide usefulinsights in the case of topographically complexareas. For example, our expectation thatfragment size inequality would monotonicallydecrease with elevation was not supported bythe data. Instead, we found an increasing trendfollowed by a dramatic fall only in the highestelevation. The values of the Gini coefficient atthe lowland sites (0-330) and at theintermediate elevation (331-660) were ratherhigh (0.739 and 0.797, respectively), reflectinga considerable fragmentation of the area atthese elevations. On the other hand, the highestG value at the elevation 991-1,320 m, wherethe number of fragments is small (27), isexplained by the fact that there is a single largefragment that dramatically contrasts with thefew, very small, vegetation patches also presentat this elevation. In contrast, the lowestinequality value (0.469) observed at the highestelevation, arises from the fact thatfragmentation is minimal in a very inaccessiblearea that, albeit of small size (ca. 0.87 % of thetotal study area), retains a very highproportional forest coverage. Yet the existenceof one single small fragment adjacent to thecontinuous forest here makes the inequalityvalue to be of relatively intermediatemagnitude (0.469). If such a fragment (whichaccounts for only 3 % of the forest area at thiselevation) were removed from the analysis thenfragmentation would be absent here, thussupporting our initial expectation of a negativerelationship between site accessibility andfragmentation.

Our evaluation of remnant forestdistribution as a function of elevation has thecaveat that the altitudinal belts were chosenarbitrarily and this may lead to the generationof artificial fragmentation patterns. However,the observed distribution of remaining forestand its fragmentation in relation to elevationreflects the existence of a considerabledisruption in the availability of habitat types.The consequences of such ecological biaswarrant further investigation in this and othertropical sites with comparable topographiccomplexity. Nevertheless, one can anticipatethat the seasonal, altitudinal migrations known

465PATTERNS OF FOREST FRAGMENTATION IN LOS TUXTLAS

in some tropical forests birds and Lepidoptera(see González et al. 1997) are likely to betruncated in Los Tuxtlas and other sites withsimilar patterns of fragmentation.

Our analysis of forest coverage and thequantitative description of fragmentation in LosTuxtlas provide some baselines forconservation and restoration planning, as wellas the subsequent monitoring of the effects ofsuch activities. In addition to the obviousconservation of the remaining vegetation,restoration activities, especially in thelowlands, should be undertaken as soon aspossible. In particular, restoration effortsshould be directed to reestablish forestcontinuity along the lowlands in a south-easterly direction (see Fig. 2). This is necessaryin order to favor connectivity of the largestforest tract of our study area with the otherlarge tract of remaining forest in the region, theSanta Marta volcano (see description of Studyarea). Furthermore, our digital map (Fig. 2)suggests the specific remnants that would haveto be connected to provide the greatest effect ofcontinuity, as assessed by the greatest reductionin the Gini coefficient. Such exercises may beundertaken first by computer simulations todefine the greatest impacts on G and then,followed by on-site programs of substitution ofcurrent activities (cattle grazing) by fencing ofcorridors and/or replacement by agroforestrypractices that provide a more suitable habitatfor native plants and animals. The benefits of aprogram like this can be compared with othertargeted efforts using the fragmentationparameters we proposed here as guidelines. Ingeneral, once the on-site programs areundertaken, the fragmentation parameters canbe used in the assessment and monitoring of theeffectiveness of the deployed efforts.

In a larger context, the extensivefragmentation we observed at Los Tuxtlasresults of global relevance, given the fact thatthis area constitutes the extreme northerlydistribution of tropical rain forest in theAmericas (Dirzo & Miranda 1991a). Our studyprovides a diagnostic analysis that makes itevident that, in addition to the dramatic loss offorest area (see Dirzo & García 1992),fragmentation has affected the region to aconsiderable extent. This calls for urgentconservation and restoration measures to betaken if we are to prevent a geographic

contraction of the natural distribution of thisecosystem on the continent.

Finally, by taking advantage of theincreasing accessibili ty to remote senseimagery and of the availability of tools toanalyze it , and including fragmentationparameters like the ones we employed in thisstudy, we may gain a more realistic perception(i.e. , beyond the mere estimates ofdeforestation rates) of the current threats totropical and global biodiversity.

ACKNOWLEDGEMENTS

We thank Fernando Rosas and ArmandoAguirre for their assistance in the field.William Laurance read a previous draft andoffered valuable comments. Martin Rickerallowed us to use his digital aerial photographsfrom Los Tuxtlas. EM was supported by adoctoral fellowship from CONACyT andDGEP-UNAM. A research period at the CCB-Stanford for EM was made possible by the helpof Carol L. Boggs and the financial supportfrom the Packard Foundation. Support to RDfor field work was also provided by thePackard Foundation and by CONACYT.

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Associate Editor: Juan ArmestoReceived June 29, 2004; accepted March 8, 2005