Detecting plant spatial patterns, using multidimensional scaling and cluster analysis, in rural landscapes in Central Iberian Peninsula

Landscape and Urban Planning 95 (2010) 138–150

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Detecting plant spatial patterns, using multidimensional scaling and cluster analysis, in rural landscapes in Central Iberian Peninsula Juan-Javier García-Abad a,∗ , José-Antonio Malpica b , María-Concepción Alonso b a b

Departamento de Geografía, Universidad de Alcalá, 28801 Alcalá de Henares, Spain Departamento de Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain

a r t i c l e

i n f o

Article history: Received 28 July 2009 Received in revised form 30 November 2009 Accepted 4 December 2009 Available online 31 December 2009 Keywords: Floristic data Jaccard similarity Meso-scale Spatial patterns UTM cartographic grid

a b s t r a c t This paper studies perennial and spring-visible plant taxa composition at the small-regional level as a method for determining meso-scale floristic spatial patterns. Vascular plant taxa were inventoried from over 40 universal transversal Mercator (UTM) grid cells of 1 km × 1 km size (Badiel Valley, Central Spain). It has been detected 148 taxa, which allowed for a spatial comparison. Floristic similarity among all grid cells was determined with Jaccard’s index, which allowed us to obtain a symmetrical matrix of similarity values between each pair of grid cells. These grid-cell-based floristic values were subjected to both multidimensional scaling (MDS) and cluster analysis to expose environmental gradients and provide evidence of the incidence in plant distribution particular to the features of a rural landscape. Two main areas have been differentiated by clear environmental behaviour: mesophytic area versus thermic area. The differentiation of these two areas is caused by a strong topographical control that yields the former area with a shady aspect and the latter with a sunny character. Performing a more detailed analysis of clustering levels, other environmental areas have been discerned, all with subtle differences: it has been identified thermo-mesophytic, transitional mesophytic, upper-mesophytic and riparian variant areas. In addition, there are several outstanding outlier cells which reveal special circumstances in the factors’ co-occurrence. The MDS and clustering, collated with simultaneous geographical observations through mapping, showed a strong floristic imbrication, as expected, over the small area studied (40 km2 ). The main valley direction and anthropic effects explain most of the floristic variation. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Floristic and vegetation studies are usually linked to territorial demarcations, with conventional shapes and sizes specified according to different criteria (politics, administration, environmental policy, planning, varied natural lines, etc.). The continuous juxtaposition of those spaces over broad expanses consistently gives rise to large-scale species or vegetation spatial patterns. There is no question that floristic composition may change gradually or suddenly from one space to another. Many discussions have understandably arisen concerning what spatial units could be used to puzzle out plant or vegetation spatial patterns empirically, bearing in mind that the size and shape of those units, as well as the resultant weft, matrix or scale, are key questions (Brown et al., 1996; Dale, 1999; Dungan et al., 2002). Underlying these considerations is the fact that the size of the minimum information spatial unit used to collect floristic data determines the reach and scale of the study. In the same way, the

∗ Corresponding author. Tel.: +34 918854418; fax: +34 918854439. E-mail address: [email protected] (J.-J. García-Abad). 0169-2046/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.landurbplan.2009.12.011

aggregation of area-based information and the thematic resolution of data have effects on landscape pattern analysis (Jelinski and Wu, 1996; Buyantuyev and Wu, 2007). In our work, as a general objective, we measure plant taxa spatial variation at the meso-scale, with the goal of also examining a data structure based on the use of the 1 km × 1 km UTM-grid cartographic system (Datum ED50). Our initial hypothesis is that this size conforms adequately to the scale of order V to VI of the classification of geomorphological features after Tricart (1965), incorporating landform influences in flora and vegetation. This recording unit size had been implemented in Spain since the 1980s as a method of performing plant chorological field scanning, with the objective of gaining better knowledge of plant distribution in small areas (Nuet and Panareda, 1991–1993; González, 1997; Vicedo and Torre, 1997; Escuer, 1998; García-Abad, 2002, 2006). This unit size has been also utilized in some European biogeographical studies (Heikkinen et al., 1998; Kent et al., 1999; Karlsen and Elvebakk, 2003). In these papers a 1 km2 cell is the inventory unit. Although this is a conventional and artificial unit, and the correspondence with natural units is therefore not comparable, it could offer advantages in tracking the variation in species richness and composition among exactly equal space tracts (cells), just as Whittaker et al. (2001) proposed,

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Fig. 1. General map of the study area covering 40 km2 (40 UTM cells) in the middle section of the Badiel Valley.

and in elucidating floristic spatial patterns according to this property. Furthermore, in order to compare species numbers in different sampling plots Wang et al. (2009) has recently stated that they must be of the same size. In this analysis, data are gathered as species presences or absences in each grid cell and arrayed in a cell-taxa matrix. The geographical space is turned into an adequate mathematical space defined by an occurrence matrix. The UTM cartographic system shapes an arrangement in physical space which ensures easy, systematic and exhaustive measurements of spatial pattern diversity on several scales. In contrast, the main drawback is that each unit is not ecologically homogeneous internally and, at the same time, the individual units differ distinctly from each other. If the distribution of flora is gradual and steady, with no discontinuities, then any partitioning of space is necessarily artificial. It is therefore interesting to test whether natural discontinuities do in fact exist. One way to answer this question is to compile a similarity matrix with a regular grid of spatial units (Pielou, 1979). Clustering and multidimensional scaling (MDS) will be used in order to determine the floristic similarity spatial patterns using 1 km × 1 km grid cellbased data. The floristic richness information belonging to each cell can be formalized mathematically by means of a multidimensional space, in which the taxa represent the Cartesian axes and the number of axes the dimensions of the space. In this space, each cell can be represented by a vector or point. It will be necessary to define a metric and a mathematical model which will allow one to find the regularities and structures in the data; these regularities are obscured due to the large amount of information coming from a high number of cells and plants.

2. Methods 2.1. Study area and landscape features The Badiel Valley is located in the Central Iberian Peninsula (Spain), corresponding to a temperate latitude and Mediterranean climate. The study area (Fig. 1) covers exactly 40 km2 , since it is fitted into 40 UTM cartographic system grid cells of 1 km × 1 km (Datum ED50). The cells cover roughly the middle section of the val-

ley, with the same orientation NE-SW; in this section of the valley, there is an enlargement down-river (western sector) and a narrowing up-river (eastern sector), with corresponding detailed and local variations in environmental factors regarding vegetation. The whole territory belongs to the natural region named La Alcarria, which in turn is part of the Tajo basin. The Tajo basin (ca. 15.000 km2 ) consists of a tertiary sedimentation basin that contains sediments with little or no Alpine deformation and that, as the intracratonic depocentre, is bounded by mountain ranges. Their deposits present a succession of Neogene terrestrial sediments, such as a mosaic of continental environments ranging from alluvial fan to evaporite lakes, cropping out of three Miocene units (lower, intermediate and upper units) and a thin Pliocene stratigraphic unit (Alonso-Zarza and Calvo, 2002). La Alcarria (ca. 5.300 km2 ) basically coincides with outcroppings of the upper Miocene unit, where these are not overlain by the Pliocene unit. The “alcarrian” landscape pattern consists of discontinuous calcareous tableland (termed “alcarrias” or “páramos”) or uplands separated by narrow valleys, and intermediate outcroppings corresponding to intermediate and lower geological units, which appear in valley slopes. In the Badiel River area, the unique outcropping that occurs is an Intermediate unit consisting of strong terrigenous deposits of sandstone, sand, silt and clay. Other landscape elements complete the area: there are heterometric and heterogeneous colluviums in the slopes falling abruptly to lower land, especially in shady exposures. In addition, there are alluvial plains and floodplains on the valley floors (termed “vegas”), with gravel, sand and silt. The climate is typically Mediterranean with light continental influence, and has transitional subhumid–semiarid traits: the annual rainfall is 500–600 mm with a dry season in summer; the annual average maximum temperature is 19–21 ◦ C, and the minimum is 3–6 ◦ C; the annual average temperature is 12.0–13.5 ◦ C. The annual potential evapotranspiration is 680–750 mm; the actual evapotranspiration is 425–475, and the water balance thus shows a low total runoff of 25–100 mm. The main land uses are forestry (48.4%) and intensive agriculture (47.9%), with the remaining inhabited areas reduced to 3.7%. Within forestry lands, the following Mediterranean vegetation types can be distinguished: grasslands and scrub (18.2%);

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evergreen micro-mesoforests of Quercus ilex L. (13.8%); deciduous micro-mesoforests of Quercus faginea Lam. and mixed (8.2%); pine reforestations (7%); and reedbed communities coupled with river lowlands and relicts of seminatural riparian forests (1.2%). The landscape units are evident: (a) the páramos, with the top at 1030 m above sea level, separated by the main valley (Badiel River) and two other secondary valleys (Valdeprisco Brook in the NW, with an analogous orientation; and Valdeiruega Brook in the N, with a nearly N–S orientation); (b) the relatively symmetrical slopes where the elevation range varies between 170 and 200 m; (c) some vegas levelled by agricultural activity; and (d) some disturbed riversides fitted tightly to quasi- and non-permanent water streams. Overall, the main factors explaining differential plant establishment are: (a) the existence of slope-contrasted exposures (this can be observed in Fig. 1); and (b) diverse land uses (agricultural and pastoral activities, afforestation, human residences, and main road). When the 1 km × 1 km UTM grid is superimposed on this geographical setting, the result shows conventional units wellorganized in shape and cartographic extent, but not necessarily environmentally homogeneous. At each 1 km2 unit the gathering landscape elements are varied; some are usually held to be prevailing, however, which allows for defined particular characterizations. For instance, upland (with agricultural use) characterizes some grid cells (0115, 0217, 0220, 0318, 0321, 0422, 0519, 0620, 0723, 0823, 0921 and 0924), but each one in turn involves another peculiar landscape element or factor: some also have important north slopes (0115, 0217, 0318, 0519, 0721, 0821), others mix solely with south slopes (0823, 0924), and others coexist with both alternatives (0120, 0220, 0321, 0620). Consequently, the cell running in spatial juxtaposition along the valley would allow one part of the existing ecological and environmental variations to be discerned: exactly those corresponding to the scale imposed by the cell size. 2.2. The 1 × 1 km UTM-grid cells plant survey: method and preliminary results As a pilot study, the 1 × 1 km grid scanning method is applied to this area of 40 km2 , in order to create the conditions of a smallregional level of analysis within a larger-scale chorological project (several hundreds of square kilometres). In this context, a 1 km2 cell is too large for fine and micro-scale ecological studies, but may be an acceptable unit in filling the chorological gaps. Consequently, as a compromise solution, we have designed a method that could be effective in meso-scale ecological analysis, without unduly delaying the chorological advance. We have renounced the attempt to attain a complete inventory from each 1 km2 grid cell (absolute total species richness), since not all species can be detected within a time frame reasonable for fulfilling the objectives of chorological coverage. For this reason, we have recorded only that part of the flora (we will employ the term “partial richness” from now on) which permits a reliable spatial comparison (perennial plants, considered here as permanently visible plants). Moreover, we will record plants which also can be sighted in the time period in which the survey is performed (the spring). Of these plants, only native vascular plants occurring spontaneously were included. Plant presence/absence data were collected in a floristic field survey conducted from April to June of 2000. Subspecies level was utilized. Taxonomic nomenclature follows Castroviejo (1986–2005), who has published volumes covering approximately 40% of the Iberian and Balearic flora. For the taxa not included in this reference book, we follow Rivas-Martínez et al. (2002) and, finally, Bolòs and Vigo, 1984–2001. We made a list of plant taxa which, because of their phenological behaviour and/or their perennial character, should be sighted in the spring period without present-

Table 1 Abbreviations (A) for ecological groups (EG) and concerned plant taxa number (N). A

EG

N

sdS ceW up sfS snS pmG pxG rdW deW wgV rcV ssW

Seral dwarf scrub Coniferous and evergreen woodland Unclassified plants (tolerant and others) Seral forest mantle deciduous shrub Subnitrophilous dwarf scrub Perennial mesophytic grassland Perennial xerophytic grassland Riparian wet deciduous woodland Deciduous woodland Tall fresh water graminoids vegetation Rock crevice chasmophyte vegetation Semi-shaded perennial herb of fringe woodland

45 21 17 14 11 10 10 10 4 3 2 1

ing problems of absence (plants visible year round and spring plants visible all season) or taxonomic discrimination. In summary, the study is based on those plants with major phytomass and permanence. A total of 148 plants were inventoried for the list. These plants can be associated into several ecological groups according to RivasMartínez et al. (2002). Table 1 shows these ecological species groups and the number of characteristic plants for each. Table 2 shows the considered plants. The group prevalence corresponds to that of dwarf scrubs (sdS and snS) followed by the climatophylous woodlands (ceW and deW) and mantle formations (sfS and ssW). The climatophylous grasslands (pmG and pxG) are frequent, but cover small areas or are mixed with shrubs and dwarf scrubs. The riparian vegetation and reedbeds (rdW and wgV) are in a minority. 2.3. Jaccard distance and statistical methods The objective will be to find cell groups which exhibit significant differences from each other and which suggest plausible geographic or environmental interpretations, since clustering delimits discrete units within a homogeneous taxa pool on the basis of floristic similarities. The presence–absence data have been successfully employed to observe the plant species response to the environment (Oksanen and Minchin, 2002; Damgaard, 2006). Once it is known which plants are in each cell, the similarity between pair of cells will be calculated. Using the list of plants and the inventory of territorial units, the data are to be distributed in a matrix of 40 cells × 148 plants, wherein the plants variable is binary (1 represents presence and 0 absence). The Jaccard (ı) distance (Jaccard, 1901) was chosen due to its effectiveness in showing the floristic composition coincidence, its simplicity, its widespread use and its reliance on presence/absence data, as stated by Poulin (2003). We define Jaccard’s similarity index of  ij between cells i and j; let the table of association for cells i, j be represented by xi

xj

Presence (1) Absence (0)

Presence (1)

Absence (0)

a c

b d

where a is the number of plant taxa found in both grid cells i and j (coincidences), b is the number of plant taxa in cell i but not in j, c is the number of plant taxa in cell j, but not in i, and, finally, d is the number of plant taxa absent from cells i and j but present in others. Matrices for values a, b, a + b + c have been obtained for the purpose of analyzing and obtaining some insight into the data. From these parameters Jaccard’s index is defined as ij =

a , a+b+c

J.-J. García-Abad et al. / Landscape and Urban Planning 95 (2010) 138–150 Table 2 Plant taxa, ecological group (EG: see Table 1 for abbreviations) and 1 × 1 km grid cell number where is present (N). Plant taxa

EG

N

Brachypodium retusum (Pers.) P. Beauv. Crataegus monogyna Jacq. Genista scorpius (L.) DC. Helianthemum cinereum (Cav.) Pers. Lavandula latifolia (L.) Medik. Lithodora fruticosa (L.) Griseb. Phlomis lychnitis L. Quercus ilex L. Quercus faginea Lam. Rubia peregrina L. Santolina chamaecyparissus L. Thymus vulgaris L.

pxG sfS sdS sdS sdS sdS pxG ceW deW ceW snS sdS

40 40 40 40 40 40 40 40 40 40 40 40

Euphorbia nicaeensis All. Euphorbia serrata L. Helichrysum stoechas (L.) Moench Rosa micrantha Borrer ex Sm. Teucrium chamaedrys L. Teucrium gnaphalodes L’Hér.

sdS up snS sfS ceW snS

39 39 39 39 39 39

Linum suffruticosum L. Staehelina dubia L. Thymus sylvestris Hoffmanns. & Link

sdS sdS sdS

38 38 38

Fumana ericifolia Wallr. Helianthemum hirtum (L.) Mill. Lonicera etrusca Santi Rubus ulmifolius Schott Salvia lavandulifolia Vahl

sdS sdS ceW sfS sdS

37 37 37 37 37

Cephalaria leucantha (L.) Roem. & Schult. Sanguisorba verrucosa (Link ex G. Don) Ces.

sdS pmG

36 36

Coronilla minima L. subsp. lotoides (W.D.J. Koch) Nyman Globularia vulgaris L. Koeleria vallesiana (Honck.) Gaudin Rosmarinus officinalis L.

sdS sdS up sdS

35 35 35 35

Bupleurum rigidum L. Erucastrum nasturtiifolium (Poir.) O.E. Schulz Helianthemum asperum Lag. ex Dunal Jasminum fruticans L.

ceW up sdS ceW

34 34 34 34

Coris monspeliensis L. Dactylis hispanica Roth Dorycnium pentaphyllum Scop. Linum narbonense L. Sideritis incana L.

sdS pxG sdS pxG sdS

33 33 33 33 33

Aphyllanthes monspeliensis L. Argyrolobium zanonii (Turra) P.W. Ball

sdS sdS

31 31

Phlomis herba-venti L. Thesium humifusum DC.

up sdS

30 30

Aristolochia pistolochia L. Hedysarum boveanum Bunge ex Basiner

sdS sdS

29 29

Rhamnus saxatilis Jacq.

sfS

28

Alyssum serpyllifolium Desf.

pmG

27

Carex halleriana Asso Hippocrepis commutata Pau

ceW sdS

26 26

Bryonia dioica Jacq. Matthiola fruticulosa (Loefl. ex L.) Maire Phragmites australis (Cav.) Steudel

up up wgV

25 25 25

Bituminaria bituminosa (L.) C.H. Stirt. Coronilla minima L. subsp. minima Digitalis obscura L. Leuzea conifera (L.) DC. Sideritis hirsuta L. Teucrium capitatum L. Thymelaea pubescens (L.) Meisn.

pxG pmG sdS pxG snS sdS sdS

24 24 24 24 24 24 24

Sedum sediforme (Jacq.) Pau

pxG

23

Astragalus monspessulanus L. Cistus laurifolius L. Satureja intricata Lange

sdS sdS sdS

22 22 22

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Table 2 ( Continued ) Plant taxa

EG

N

Ulmus minor Mill.

rdW

22

Populus nigra L. Quercus coccifera L. Retama sphaerocarpa (L.) Boiss.

rdW ceW sdS

21 21 21

Astragalus incanus L.

pmG

20

Cistus albidus L. Fumana thymifolia (L.) Spach ex Webb Juniperus oxycedrus L. subsp. oxycedrus

sdS sdS ceW

18 18 18

Ligustrum vulgare L. Rhamnus alaternus L.

sfS ceW

17 17

Ficus carica L. Prunus spinosa L. Rosa canina L. (s.l.)

rcV sfS sfS

16 16 16

Clematis vitalba L. Colutea hispanica Talavera & Arista

sfS ceW

15 15

Centaurea toletana Boiss. & Reut. Moricandia moricandioides (Boiss.) Heywood

up up

13 13

Convolvulus lineatus L. Ruta angustifolia Pers.

pmG snS

12 12

Amelanchier ovalis Medik. Asparagus acutifolius L. Euphorbia minuta Loscos & J. Pardo Helianthemum apenninum (L.) Mill. Onobrychis saxatilis (L.) Lam.

sfS ceW sdS up up

11 11 11 11 11

Hedera helix L. Thapsia villosa L.

deW pmG

10 10

Asphodelus ramosus L. Erysimum mediohispanicum Polatschek Genista pumila (Debeaux & É. Rev. ex Hervier) Vierh. Hormatophylla lapeyrousiana (Jord.) P. Küpfer Plantago albicans L. Populus alba L. Rhamnus lycioides L. Salix alba L

pxG sdS sdS up pmG rdW ceW rdW

9 9 9 9 9 9 9 9

Juniperus communis L. subsp. hemisphaerica (C.Presl) Nyman

ceW

8

Arctostaphyllos uva-ursi (L.) Spreng. Fumana procumbens (Dunal) Gren. & Godr. Plantago sempervirens Crantz Ruta montana L. Viburnum lantana L.

sdS pmG snS snS sfS

7 7 7 7 7

Agrimonia eupatoria L. Brachypodium sylvaticum (Huds.) P. Beauv. Cotoneaster tomentosus (Aiton) Lindl.

ssW rdW sfS

6 6 6

Antirrhinum graniticum Rothm. Atractylis humilis L. Helianthemum oelandicum (L.) Dum. Cours. Iris pseudacorus L. Lonicera periclymenum L. Pinus halepensis Mill. Sambucus nigra L.

up sdS pmG wgV sfS ceW sfS

5 5 5 5 5 5 5

Acer monspessulanum L. Astragalus alopecuroides L. Daphne gnidium L. Lavandula pedunculata (Mill.) Cav. Paeonia officinalis L.

deW sdS ceW sdS up

4 4 4 4 4

Corylus avellana L. Jasonia saxatilis (Lam.) Guss. Ononis tridentata L. Thymus zygis L. Typha angustifolia L.

deW rcV sdS up wgV

3 3 3 3 3

Carduncellus monspelliensium All. Fraxinus angustifolia Vahl Hyssopus officinalis L. Juniperus thurifera L. Lycium europaeum L. Mercurialis tomentosa L.

pmG rdW up ceW snS snS

2 2 2 2 2 2

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Table 2 ( Continued ). Plant taxa

EG

N

Sedum album L. Thymus mastichina L.

pxG snS

2 2

Bassia prostrata (L.) G. Beck Halimium umbellatum (L.) Spach Cistus salviifolius L. Cornus sanguinea L. Juniperus communis L. subsp. communis Juniperus oxycedrus L. subsp. badia (H. Gay) Debeaux Juniperus phoenicea L. Malus sylvestris (L.) Mill. Ononis fruticosa L. Ononis rotundifolia L. Ruscus aculeatus L. Salix atrocinerea Brot. Salix purpurea L. Salix triandra L. Stipa tenacissima L.

snS sdS sdS sfS up ceW ceW rdW up ceW ceW rdW rdW rdW pxG

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

␥ij approaches 1 when plant taxa composition is identical between grid cells, and 0 when two grid cells have no species in common. For the mathematical model that will be used here, a distance will be preferable to an index, as the distance will reveal the likeness or similarity; small values of distance between two points correspond to a high degree of likeness or similarity. The relation between index and distance is obtained by subtracting from the unit, and is given, for the Jaccard case, by the equation: ıij = d(xi , xj ) = 1 − ij = 1 −

a b+c = . a+b+c a+b+c

Therefore, ıij will be known as the Jaccard distance and represent the likeness between the points or cells i and j. The Jaccard distance was calculated and produced a symmetrical matrix of similarity values between each pair in the 40 UTM-grid cells of 1 km2 , which was subjected to statistical analysis. It will be useful to determine, later, the average similarity of each cell of 1 km × 1 km, which will provide a map (shown afterwards) that will show which areas contain a better or worse representation of the flora with respect to the whole territory, due to a co-occurrence of environments favourable to the landscape configuration.

Cluster analysis is used to define plant taxa assemblages, and is more widely employed in similarity analysis (Kent, 2006). Generally speaking, clustering techniques provide a description of the data as a function of a group of cells with strong internal similarity. To group the cells, a metric is necessary in order to quantify the similarity or affinity between them. Among the different possibilities for defining the variables, we will consider binary variables of the presence-and-absence type, depending on whether or not a plant has been found in a certain cell. There are many similarity measurements for binary variables; some reviews on this theme include Real and Vargas (1996) and Finch (2005). An important issue is the choice of method used to reduce the dimensionality of the data; the measurement method will explain the spatial patterns that produce the floristic composition of the territory. It is important that the mathematical model fits well with the real model and provides meaningful spatial structures. We have chosen MDS as the dimensional reduction method due to its intuitiveness. This method allows for the exploration of the underlying complex relationship structure among cells projecting the data in a two- or three-dimensional space. In order to cluster the cells in relation to their floristic affinity we used two methods: (1) a non-metric MDS, because it provides a graphical representation of cells which allows for the examination of the floristic richness relationship among cells; we agree with McCune and Grace (2002) that MDS could be considered to be the most effective ordination method of ecological community data; and (2) a clustering technique, based on the average linkage within groups method of clustering, in which clusters are combined in such a way that the average distance between all cells in the resulting cluster is minimized. This technique complements the MDS analysis. 3. Results 3.1. One-dimensional statistical analysis For the 148 plant taxa concerned, the average number in each cell was 69.3, with a standard deviation of 11.1; the cell with the maximum richness value had 92 (0320) and that with the minimum value had 34 (0921). In Fig. 2 it can be observed the partial

Fig. 2. Cartographic sketch of partial plant taxa richness.

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143

Fig. 3. Average similarity cartographic sketch. The value of each cell is calculated as the average of the values of similarity between the actual cell and each of the remaining 39 cells.

floristic richness distribution. It is recommended to compare this figure with the landscape units appearing in the map in Fig. 1. A higher number of plants were found in those cells in which páramos, north-facing slopes, south-facing slopes and riversides also occurred (0923, 0822). The high richness of the 0320 cell is explained by its location on the border between two different floristic zones, as verified below. Conversely, lower richness values occur in cells where intensive agriculture (corresponding usually with páramos and vegas: 0921, 0622, 0118, 0321, 0519, 0620 and 0115), pine forestation (Pinus halepensis and P. nigra: 0621 and 0220), and, finally, abrupt rocky outcroppings and erosive scars (0621, 0622 and 0220) occur. The similarity matrix has 780 values, ranging from a minimum of 0.33 to a maximum of 0.80, with a mean central tendency of 0.57 and a median of 0.58; its dispersion from the mean given by the standard deviation is 0.08; its lower quartile is 0.51 and its upper quartile is 0.62; in addition, it has a skewed shape, leaning toward the left with a value of standardized skewedness of −4.11 and a higher pointed bell shape than in a normal distribution due to its standardized kurtosis of 1.61. In the distribution obtained with Jaccard’s similarity a nonnormality of the data was found significant due to skewedness toward the left, since the values go below the central tendency. Each cell has an average similarity value. Fig. 3 shows the average similarity spatial distribution. From these values a unique mean value for the whole study area is calculated, 0.57, with a frequency of 40, a standard deviation of 0.045, a maximum value of 0.62 and a minimum of 0.38.

Fig. 4 shows a broad central agglomeration of cells, with the exception of some atypical outlier cells (0921, 0621, 0622, 0220, 0321 and 0118) isolated far from the centre and the surrounding the central cloud. These individual cells are located in different positions in the valley and have low richness and average similarity values (as can be seen in Figs. 2 and 3). This double property can be explained by these cells’ tendency away from natural environmental guidelines, particularly those subject to higher human impact and the occurrence or co-occurrence of rocky outcroppings. Notice also in Fig. 4 how the central agglomeration can be divided into two detached groups, one on the left and the other on the right, separated by a central corridor running close to the second diagonal. These groups correspond to two differentiated environmental areas, as we will describe below. To complement the MDS results, a clustering statistical technique was applied. The resultant dendrogram is presented as Fig. 5. In this work we decided, as per conventional criteria, to divide the dendrogram at the level necessary to isolate most of the atypical cells. For the sake of avoiding excessive geographical fragmenta-

3.2. Multidimensional statistical analysis To group the grid cells according to floristic idiosyncrasy, we first applied the MDS. The resulting stress was 0.071 and the square correlation in distance was 0.929, which resulted in a well-fitted model (Kruskal, 1964). Fig. 4 shows the projection of the cells’ distribution in two dimensions. The distance between cells in the diagram indicates a high or low degree of similarity; here, one must bear in mind that this is not a representative measure of individual cell differences, but a global measurement of all of them. The farther the cells are from the centre (0.0), the more dissimilar they are.

Fig. 4. A two-dimensional representation of cells produced by multidimensional scaling.

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Fig. 5. Dendrogram (average linkage method, within group). The numbers in circles illustrate the areas and outlier cells discriminated in each cluster level. For the sake of clarity only results down to the fifth level are included.

tion, only results down to the fifth level are shown and discussed here (see Fig. 5). Observation of Figs. 4 and 5 shows that the results are similar, to a certain degree, if the following two points are considered: (a) the dendrogram gives almost the same outlier cells (0622, 0621, 0921, 0118 and 0321), and (b) if these outliers are removed, it becomes

apparent that a large number of cells were differentiated into two groups representing two broad geographical sectors. Coincidentally, the isolated outlier cells can be observed in Fig. 4 as the ones farthest away from the centre of the MDS graph. Cell 0220 was not considered in the dendrogram (Fig. 5) and is the MDS outlier case most proximal to the central cloud (Fig. 4); the cells belonging to

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the detailed differences of presence data. More than two thirds of these plants (69.4%) correspond to taxa characteristic of the M area. Consequently, this can be considered a floristic refuge for wood plants that are less drought resistant. Therefore, taxa sfS (see Tables 1 and 2) such as Ligustrum vulgare, Amelanchier ovalis, Clematis vitalba, Rosa canina (s.l.) and Rhamnus saxatilis and shaded taxa, such as Hedera helix, together with Salix alba, Populus nigra, Brachypodium sylvaticum and Phragmites australis, form a relatively closed broad meso-hygrophyte group. On the other hand, such elements as Digitalis obscura or Satureja intricata clearly indicate ecological differences between the meso-like scrubs and others that endure thermic conditions, such as Cistus albidus or Retama sphaerocarpa. This occurs equally frequently among plants typical of evergreen woodland (for instance, Jasminum fruticans and Juniperus communis subsp. hemisphaerica versus Quercus coccifera and Daphne gnidium). 3.4. Second cluster level

Fig. 6. MDS diagram. Two main groups were exhibited: one for the thermic area (Th) and a second for the mesophytic area (M). Also note that six isolated cells were located at a distance from the center of the diagram, and corresponded to outliers.

each sector are the same in the MDS and the dendrogram, except for two cells (0219 and 0320). The plants’ spatial patterns can be arranged in two ways: (a) the MDS shows two large geographical sectors and six outlier cells (Figs. 6 and 7a), and (b) the dendrogram shows six differentiated plant areas (Fig. 7b–f) at five successive cluster levels (represented by the vertical lines in Fig. 5, clusters 3, 4, 8, 9 and 11), if the outliers are removed. 3.3. First level of analysis In light of the major landscape features of each cell, we interpret the results of floristic composition while observing the geographical distributions issuing from the mapping of each case. Fig. 7a and b exhibits cartographic sketches for the MDS and first level of cluster analysis, respectively. Two large plant areas are apparent, with an evident geographical contiguity. On the one hand, the Southern and Eastern area is characterized by having all the landscape units (páramos, slopes, vegas and riverside), although with a low incidence of south-facing slopes. Considering this feature, there is a high influence of north-facing slopes, and occurrence of main fluvial environments and topographically sheltered sites. For this reason, this area will be named the mesophytic area (M area). On the other hand, the alternative north and north-western area or thermic area (Th area) embraces the secondary valleys (Valdeprisco and Valdeiruega), the discontinued south-facing hillsides and the less narrow part of the valley. The geographical features thus contrast with those of the M area. As stated above, in these two areas the cells 0219 and 0320 represent the only divergence between the MDS and cluster analyses. At this stage, we will follow the cluster analysis because it provides other, more detailed levels. The first level yielded three divisions: the two broad general groups and an outlier cell. The M area, constituting 23 cells (57.5% of the total), contains almost all of the plant taxa concerned (142, the 96%). The Th area consists of 16 cells (40%) and has 123 plant taxa (83%). The outlier cell (0921) has the lowest richness and average similarity values; at the same time, it is the most distant cell in Fig. 4 from the centre, on account of the reduced spontaneous vegetation area brought about by crops, main roads and urban areas. Tables 3 and 4 show the 36 plants (almost a quarter), discriminating between both areas with an ad hoc criterion, and specifying

The Th area remained consistent, but the original M area was fragmented into two: one S–SW area versus another E–S area (Fig. 7c). Practically speaking, these three areas do not lose geographical continuity, except for 0521, and the grid cells remain contiguous. This configuration still reflects an environmental pattern maintenance, which is shaped in the landscape as a floristic linkage of geographical contiguity and nearness. Curiously, this cluster level distributes the partial richness in the three demarcated areas fairly well: the Th area contains 123 taxa, the S–SW area 127 and the E–S area 126. This geographical partitioning implies the exposure of a new area characterized by continued north-facing slopes in the less narrow part of valley, with strong incidence of riverside environments, but attenuated in respect to the southern aspects (S–SW area). The E–S area, on the contrary, maintains strong incidence of shaded environments, but in the narrower part of the valley. This feature could counteract somewhat the effects of southern aspects when they occur. Riverside is also present in this area, but very disturbed. The autoecological trends of the indicator plants listed in Appendix A reveal that it is reasonable to attribute thermo-mesophytic mixed conditions (thermo-mesophytic area or ThM area) to the first area, implying an environmental transition between two differentiated areas into the first cluster level. The alternative area would have a strict mesophytic character; hence, we continue referring to this as a mesophytic area (M-2 area). Most of the plants indicated in each area have ecological trends with clearly differentiated meanings (see Appendix A). For instance, Coronilla lotoides, Dorycnium pentaphyllum, Hedysarum europaeum, Plantago sempervirens and Dactylis hispanica are thermic plants that endure xeric conditions, grow in perturbed and scarce deep soils, and feature low leaching of bases. Conversely, Cistus laurifolius and Lavandula pedunculata tolerate basic shores a little or not at all, a property that would be diminished where the percolation water from precipitation is more effective or where the bases rise by evapotranspiration somewhat less effectively. Weak endorreic páramos sites, or those where forest protection favours a higher efficiency in percolation, could cause the establishment of those two plants. Cotoneaster tomentosus demands an accurately shaded environment. Ruta angustifolia (Th area indicator plant) and R. montana almost overlap ecologically, but the latter represents a somewhatreduced thermic stage, as its specific name suggests. The Carex halleriana case could be explained by the more efficient sheltering role of the forest and understory cover in the M-2 area. 3.5. Third cluster level On the one hand, this cluster detaches three outlier grid cells: 0621 and 0622, belonging to Th area in the previous cluster, and

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Fig. 7. Floristic sketches of the central section of the Badiel Valley (Central Spain) UTM-grid zone designation 30 TWL: (a) resultant area sketch for the MDS diagram (see Fig. 6); resultant area sketch for clustering at the (b) first, (c) second, (d) third, (e) fourth, and (f) fifth cluster levels. The symbols stand for: M, M-2, M-3, M-4, mesophytic areas; Ou, outlier grid cells; RV, thermo-mesophytic area-riparian variant; Th, Th-2, Th-3, thermic areas; ThM, ThM-2, ThM-3, thermo-mesophytic areas; TM, transitional mesophytic area; UM, upper-mesophytic area.

0118, belonging to the ThM area in the previous cluster. On the other hand, it separates a small area with only two grid cells (0520 and 0620) from the previous M-2 area. They are located precisely between the current M-3 area and ThM-2 (Fig. 7d). The transitional character of areas seems obvious; hence, we call this the transitional mesophytic area (TM area). The configuration that can be seen in the sketch in Fig. 7d suffers from some slight disjunctions in the Th-2 and M-3 areas,

where the geographical continuity is interrupted. Although both the ThM-2 (10 cells) and M-3 (9 cells) areas have reduced cell grid numbers in respect to the original M area, they maintain a higher partial richness (125 and 124 taxa, respectively) than Th-2 (121 taxa in 14 cells), despite its small surface. The TM area’s separation from the previous M-2 area is due primarily to the low richness of both cells in the grid involved (63 taxa each, and 75 in all), and secondly to their geographical neigh-

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Table 3 Plant taxa characterising mesophytic area (23 grid cells) opposite thermic area (16). Number of 1 km × 1 km grid cells where the plant is present (N). Grid cells percentage in relation to all of the area (%). Plant taxa whose presence difference () is ≥25% in M area with regard to Th area are related. Taxa appear ordered from higher to lower . Plant taxa

Mesophytic area

Satureja intricata Ligustrum vulgare Sideritis hirsuta Amelanchier ovalis Digitalis obscura Clematis vitalba Bryonia dioica Teucrium capitatum Hedera helix Rosa canina (s.l.) Helianthemum apenninum Centaurea toletana Juniperus communis subsp. hemisphaerica Phragmites australis Ficus carica Rhamnus saxatilis Astragalus monspessulanus Aristolochia pistolochia Convolvulus lineatus Fumana procumbens Salix alba Populus nigra Jasminum fruticans Asparagus acutifolius Brachypodium sylvaticum

Thermic area

N

%

19 15 19 11 18 13 18 18 9 13 10 11 8 18 12 19 16 20 10 7 8 15 22 9 6

82.6 65.2 82.6 47.8 78.3 56.5 78.3 78.3 39.1 56.5 43.5 47.8 34.8 78.3 52.2 82.6 70.0 87.0 43.5 30.4 34.8 65.2 95.7 39.1 26.1

bourhood and concrete internal floristic composition, making them alike. In this way, the difference between the current M-3 and the TM areas consists particularly of the absence of a certain amount of taxa in the latter, with standout absences including some clearly mesophytic plants such as Ulmus minor, Viburnum lantana, Paeonia officinalis or Sambucus nigra (see Appendix A), and others with unconcerned or dissimilar ecological values. Some taxa, such as Erysimum mediohispanicum and Genista pumila, imprint certain cohesive effects on the TM area relative to others in which their presence is trivial. Other taxa such as Fumana thymifolia, Thymelaea pubescens and Matthiola fruticulosa provide indicator values that are relatively more thermic in relation to the M-3 area. In any case, the TM area’s small size and border position do not allow, on this scale, an adequately ecological assignation. 3.6. Fourth cluster level In this cluster, the preceding M-3 area is divided into two others, with positions plainly contrasted, one to the North, and the other to the South (Fig. 7e). The southern area takes up a topo-

N 2 2 5 0 5 2 6 6 0 3 1 2 0 7 3 8 6 9 2 0 1 6 11 2 0

 % 12.5 12.5 31.3 0 31.3 12.5 37.5 37.5 0 18.8 6.3 12.5 0 43.8 18.8 50.0 37.5 56.3 12.5 0 6.3 37.5 68.8 12.5 0

70.1 52.7 51.3 47.8 47.0 44.0 40.8 40.8 39.1 37.7 37.2 35.3 34.8 34.5 33.4 32.6 32.5 30.7 31.0 30.4 28.5 27.7 26.9 26.6 26.1

graphical location markedly shadier than the other areas (so we will name this the upper-mesophytic or UM area). Besides such strictly mesophytic taxa as Prunus spinosa and Coronilla minima, which appear in Appendix A, others such as Paeonia officinalis (sciophyte) and Sambucus nigra (deciduous forest mantle plant) contribute to delineating the UM area, and from this follows the naming of the mesophytic area (M-4 area). However, this northern area, having southern aspects, includes as differential indicators thermic (Rhamnus alaternus), xerothermic (Sedum sediforme) and heliophyte (Rosmarinus officinalis). 3.7. Fifth cluster level Finally, this last cluster isolates another outlier cell (0321) before being incorporated to the Th-2 area, and also fragments the previous ThM-2 area into two (Fig. 7f). All in all, the 40 original grid cells are subdivided into eleven partitions (six areas and five isolated cells). That last sharing-out is due to the weight of riparian environments in sites where riverside is somewhat conserved. Hence, we will call this the riparian variant (RV), in the thermomesophytic area (ThM-3), to that area where riverine taxa (Populus

Table 4 Plant taxa characterizing thermic area (16 grid cells) opposite mesophytic area (23). Number of 1 km × 1 km grid cells where the plant is present (N). Grid cells percentage in relation to all of the area (%). Here the used criteria is the opposite of that in Table 3, i.e.: plant taxa whose presence difference () is ≥25% in Th area with regard to M area are related. Taxa appear ordered from higher to lower . Plant taxa

Cistus albidus Ruta angustifolia Juniperus oxycedrus Alyssum serpyllifolium Hormatophylla lapeyroussiana Arctostaphyllos uva-ursi Thapsia villosa Astragalus incanus Quercus coccifera Retama sphaerocarpa Daphne gnidium

Thermic area

Mesophytic area



N

%

N

%

13 10 11 14 7 6 7 11 11 11 4

81.3 62.5 68.8 87.5 43.8 37.5 43.8 68.8 68.8 68.8 25

5 2 7 12 2 1 3 9 10 10 0

21.7 8.7 30.4 52.2 8.7 4.3 13.0 39.1 43.5 43.5 0

59.6 53.8 38.4 35.3 35.1 33.2 30.8 29.7 25.3 25.3 25.0

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alba, Iris pseudacorus, Corylus avellana) or a semi-shaded perennial herb (Agrimonia eupatoria) are frequently present as emerging indicators. Other riverine taxa are also commonly present (Salix alba and Ulmus minor), as well as lianas typical of the mesophytic forest mantle (Clematis vitalba and Bryonia dioica). Against these taxa, the ThM-3 area still includes xerothermic taxa (Argyrolobium zanonii) and plants enduring in scarcely deep or almost-bare soils (Atractylus humilis, Helianthemum oelandicum and Moricandia moricandioides). 4. Discussion and conclusions An evaluation of ecological phenomena can be obtained by a linear method (Waller et al., 2007). Since nature is the product of a complex combination of processes a non-linear method could be applied; to quote a recent case, Lipkovich et al. (2008) develop a general algorithm based in cluster analysis. With the data represented in a two- or three-dimensional space in the current study, the MDS results in an efficient tool to be used as a means of simple visual inspection of this structure. MDS is basically used herein to reduce the information in a multidimensional space to a low dimensional degree; generally two or three dimensions. The cells’ agglomeration displayed by the MDS showed a strong floristic imbrication. This could be anticipated in a continuous area where the prevailing environmental factors on a regional scale do not undergo appreciable discontinuities. It can also be expected of a space so reduced as the analyzed here, circumscribed inside a rectangle of 10 km × 9 km. In this study, the MDS and the cluster analysis provide quite similar results. In fact, the difference between the two methods is only apparent in two cells; note that these are precisely situated in the M and Th border, which reveals such an imbrication. The systematic inventory method based on UTM grids of 1 km × 1 km allows for, among other uses, the establishment of an arrangement of plants based on their rare or frequent appearance in these basic units of floristic information (Table 2), and therefore also based on a degree of participation in the flora of a territory. It is thus not only possible to establish typologies from the maximum frequency to the maximum rareness, but also to establish the number of plants that contribute to the differentiation of areas according to their clustering levels. In this work it was observed that, in the five analyzed successive levels and according to the established criteria of relevance, there have been 85 plants with this property, i.e. 57.4% of the total (see Appendix A). These indicator taxa are, logically, within those of medium frequency (neither very high nor very low). This territory shows a spatial pattern with a common floristic amount of plants (30% of the concerned plants appear in more than 75% of the grid cells) and other less common plants which provide their own environmental specificity. Most of the time, the particular spatial distributions (for each plant) reveal lax guidelines of ecological transition; however, they sometimes display discontinuities which would require a more detailed study for explanation. When the landscape elements are not extremely atomized, the 1 km2 size is appropriated to unmask ecotones, discontinuities, evident disturbance areas, and mixed cases. Basically, in this part of the valley, on the meso-scale, the landscape factors operate as a system with several ways: topography shapes micro-climate, micro-climate shapes topography, and, in

turn, topography shapes vegetation. More subtly, vegetation could shape topography. Consequently, our results show that the UTM 1 km2 cell fits in with the Tricart’ order V to VI scales, according to phytogeomorphological joint relationships. Although this unit is conventional and artificial, and the correspondence with natural units is therefore not comparable, it offers advantages in tracking the variation in species richness and composition among exactly equal space tracts (cells), and in elucidating floristic spatial patterns according to this property. The last explanation for this imbricate composition must be sought not only in the natural factors, but also in the co-occurring anthropic factors that have sometimes substantially transformed the landscape, with non-natural fragments and severe perturbations. Alard and Poudevigne (1999), and Wania et al. (2006), among others, have highlighted those factors for rural landscapes. This strong human influence blurs the natural trace in territories that, like the Iberian Peninsula, have a long history of human intervention (three to four thousand years B.P.), generally in non-mountainous spaces and close to water streams. In these conditions, any detailed environmental analysis must always consider this in attempting to understand discontinuities, abrupt ruptures and existing atypical spaces. The main achievement of this study is the detection of the spatial structure of the flora using just the degree of similarity between 1 km2 grid cells, and the consideration of the presence/absence of certain plant taxa. In this way, due to the main valley direction, two main areas have been differentiated with clear environmental behaviour (M area versus Th area), one area with a shady aspect and other with a sunny aspect. Furthermore, the Th area remains fairly homogeneous throughout the successive cluster levels, unlike the M area, since factors in that area begin operating on a local scale. Aside from the described areas, the detection of outlier cells with the MDS and clustering technique in relation to the flora is significant. These outliers basically correspond to spaces where stress and disturbance have altered the space along with the biotic and abiotic factors of co-occurrence in the distribution of the plants. The applied method provides an examination of the spatial diversity and variation of plant taxa, and demonstrates how it is possible to determine meso-scale patterns with MDS. The method makes this aim compatible with adequate chorological advance. This implies a field scanning method that is systematic only for a subset of the floristic range (perennial and spring-visible vascular taxa). This type of floristic analysis has presented a good treatment for woodland and climatophylous scrubland, but another type of data collection should be implemented in the future with respect to grasslands. In any case, both plant types are relevant because they occupy most of the plant landscape and the larger phytomass. We feel the chosen methodological strategy using MDS and clustering is effective and the results obtained are worthwhile. Appendix A. Indicator taxa for each group in the hierarchical structure of the cluster analysis. It shows characteristic plant taxa discriminating environmental areas whose presence difference is ≥25% in left area with regard to right area and vice versa. Taxa appear ordered from higher to lower value. The pertinent grid cell number of each area is given within parentheses.

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