**3.1.6.4 Distance decay of similarity**

164 The Dynamical Processes of Biodiversity – Case Studies of Evolution and Spatial Distribution

Fig. 6. The relation between richness (species number inside plots) and

= 0.01) and Bonferroni correction was applied.

fragmentation/disturbance is much less clear when the zones are considered separately: Only fragmentation classes in zone 2 artly show a significance impact on species richness. Note, that here as well the numbers of plots involved in the categories differ considerably. Overall significance was tested with simple anova. Zone 1: fragmentation: F = 1.25ns, disturbance: F = 0.80ns; Zone 2: fragmentation: F = 7.13\*\*\*, disturbance: F = 0.027ns.

Inference regarding the difference between the classes was obtained with pairwise t-Tests (a

There is only relatively slow distance decay of similarity when all data is analyzed together for each zone. However, beta-diversity structure is different for the two zones (Fig. 9). In Zone-1 similarity decreases much faster (-0.00022/km) compared to zone-2 (-0.000088/km). This is more than one order of magnitude and is also reflected in the intercept. The linear regression line of the distance decay relationship intersects the y-axis at a similarity value (Sørensen) of 0.23 for zone-1, whereas the intercept is only 0.11 for zone-2. Not only the distance decay after linear regression but also the spline regression lines show considerable differences between zone-1 and 2. In zone-1 the rate of decay changes heavily and after a rapid decrease from 0 to 100 km distance, the similarity declines much slower. This holds also true when the subsets are further subsetted and e.g. different fragmentation classes are considered (Fig. 12).

Within the zones the slope of the distance decay relationship differs only slightly but significantly between different fragmentation categories (Fig. 12). Only the slopes of the linear regression lines describing the distance decay in the fragmentation classes 1 and 2 of zone-1 are not significantly different (Table 5). The smoothed regression lines cannot be tested in this way but from the illustrations (Fig. 12) it is apparent that there are important differences between the different fragmentation classes.

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 167

Fig. 9. Difference in richness between zones 1 and 2 (Inference obtained with t-Test)

Fragmentation Class

calculated by slnbx – slnby, ρ – p value.

Zone nbx nby dsl ρ

Table 5. Differences in slope of the distance decay relationship between subsets of the data. Each of the subsets comprises all plots that fall into the respective fragmentation class. The

comparison between fragmentation classes 1and 2 in zone 1. Abbreviations: nbx – one of the

The picture does not change much when disturbance classes are considered instead (Table 6). In this case in zone-1 the slope of the linear regression line that describes the distance decay relationship in disturbance class 3 (high) very clearly is significantly steeper compared to the slopes for the classes 1 and 2. The latter two do not differ significantly from each other and the slope is even (very slightly) steeper for disturbance class 2. In zone-2 the slope of class 2 is much steeper than in the disturbance classes 1 and 3 of this zone. This is even apparent in Fig. 13 and as well reflected in the significance tests represented in Table 6.

slopes differ significantly between fragmentation classes with the exception of the

compared subsets, nby – the other of the compared subsets, dsl – difference in slope,

1 1 2 0.0000063 0.405 1 1 3 0.00012 0.001 1 2 3 0.00012 0.001 2 1 2 -0.000019 0.001 2 1 3 0.000027 0.001 2 2 3 0.000046 0.001

Fig. 8. NMDS based on all data, with different coloring regarding the membership of plots to subsets of data. The subsetting factor names each plot. Apparently the plots of the two zones show a clear difference regarding their vegetation composition compared to the plots of zone-1. Such a clear pattern rarely can be achieved. When the coloring is done for the categories of fragmentation, disturbance and richness, it is apparent that these do not impact species composition. NMDS statistic: stress = 36.10.

Fig. 8. NMDS based on all data, with different coloring regarding the membership of plots to subsets of data. The subsetting factor names each plot. Apparently the plots of the two zones show a clear difference regarding their vegetation composition compared to the plots of zone-1. Such a clear pattern rarely can be achieved. When the coloring is done for the categories of fragmentation, disturbance and richness, it is apparent that these do not impact

species composition. NMDS statistic: stress = 36.10.

Fig. 9. Difference in richness between zones 1 and 2 (Inference obtained with t-Test)


Table 5. Differences in slope of the distance decay relationship between subsets of the data. Each of the subsets comprises all plots that fall into the respective fragmentation class. The slopes differ significantly between fragmentation classes with the exception of the comparison between fragmentation classes 1and 2 in zone 1. Abbreviations: nbx – one of the compared subsets, nby – the other of the compared subsets, dsl – difference in slope, calculated by slnbx – slnby, ρ – p value.

The picture does not change much when disturbance classes are considered instead (Table 6). In this case in zone-1 the slope of the linear regression line that describes the distance decay relationship in disturbance class 3 (high) very clearly is significantly steeper compared to the slopes for the classes 1 and 2. The latter two do not differ significantly from each other and the slope is even (very slightly) steeper for disturbance class 2. In zone-2 the slope of class 2 is much steeper than in the disturbance classes 1 and 3 of this zone. This is even apparent in Fig. 13 and as well reflected in the significance tests represented in Table 6.

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 169

Zone nbx nby dsl ρ

Table 6. Differences in slope of the distance decay relationship between subsets of the data. Each of the subsets comprises all plots that fall into the respective disturbance class. The slopes differ significantly between disturbance classes with the exception of the comparison between disturbance classes 1 and 2 in zone 1 and the comparison between classes 1 and 3 in zone 2. Abbreviations: nbx - one of the compared subsets, nby - the other of the compared

Fig. 11. 3d-plot of disturbance (x-axis), fragmentation (y-axis), and richness (z-axis). The latter is a continuous variable whereas the other two are factor variables. There is no joint

relation between these three

subsets, dsl - difference in slope, calculated by slnbx – slnby, ρ - p-value.

Disturbance Class

1 1 2 -0.000018 0.236 1 1 3 0.000079 0.004 1 2 3 0.000096 0.007 2 1 2 0.000032 0.001 2 1 3 0.0000025 0.328 2 2 3 -0.000029 0.026

Fig. 10. NMDS based on all data, with different coloring regarding the membership of plots to subsets of data. The subsetting factor names each plot. Apparently the plots of the two zones show a clear difference regarding their vegetation composition compared to the plots of zone-1. Such a clear pattern rarely can be achieved. When the coloring is done for the categories of fragmentation, disturbance and richness, it is apparent that these do not impact species composition. NMDS statistic: stress = 36.10.

Fig. 10. NMDS based on all data, with different coloring regarding the membership of plots to subsets of data. The subsetting factor names each plot. Apparently the plots of the two zones show a clear difference regarding their vegetation composition compared to the plots of zone-1. Such a clear pattern rarely can be achieved. When the coloring is done for the categories of fragmentation, disturbance and richness, it is apparent that these do not impact

species composition. NMDS statistic: stress = 36.10.


Table 6. Differences in slope of the distance decay relationship between subsets of the data. Each of the subsets comprises all plots that fall into the respective disturbance class. The slopes differ significantly between disturbance classes with the exception of the comparison between disturbance classes 1 and 2 in zone 1 and the comparison between classes 1 and 3 in zone 2. Abbreviations: nbx - one of the compared subsets, nby - the other of the compared subsets, dsl - difference in slope, calculated by slnbx – slnby, ρ - p-value.

Fig. 11. 3d-plot of disturbance (x-axis), fragmentation (y-axis), and richness (z-axis). The latter is a continuous variable whereas the other two are factor variables. There is no joint relation between these three

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 171

Slope and aspect show no influence on species composition. The similarity in species composition has been regressed against the dissimilarity regarding slope and aspect. No correlation (Mantel) has been found neither for zone-1(r = -0.0068) nor for zone-2 (r = 0.01). This holds even when we controlled for the influence of altitude on this relation (partial Mantel test). In the latter case Mantel correlation values amount to r = -0.019 (zone-1) and

The vegetation composition of the 6 sites show considerable differences. This is clearly apparent in the DCA drawn from the data in Fig. 14 (a & b). Because there are very few species shared between plots (see Fig. 15 for more detail regarding this issue) and because there are much more species than plots (when each of the 6 sites is considered as a single sample) the metaMDS algorithm very fast finds a stable solution. After 2 runs a very low

Fig. 14. a and b: Ordination plots of the 6-sites data. The six transects vary considerable in their species composition. Both methods come to comparable results. Sites 3 and 4 are highly dissimilar. Sites 2, 5, and 6 build something like a cluster (but is relatively vague), whereas Site 1 is far from 3 and 4 and closer to the other three but at the same time relatively distinct

**3.1.6.5 The influence of slope and aspect on similarity and distance decay** 

r = 0.01341 (zone-2) respectively.

from all other Sites.

**3.1.6.6 Continuous plots for the six sites** 

stress value of 3.21 results (see also Figure 14a).

Fig. 12. Slopes of the distance decay relationship for subsets of the data. Each of the subsets comprises all comparisons between the plots of one zone and one fragmentation class therein. Besides the fact that similarity decreases much faster with distance in zone-1; there are apparent differences between fragmentation classes. The spline regression was obtained with a lowess smoothing algorithm as offered by the function lowess() with f=0.2 of the R package stats.

Fig. 13. Slopes of the distance decay relationship for subsets of the data. Each of the subsets comprises all comparisons between the plots of one zone and one disturbance class therein. Besides the fact, that similarity decreases much faster with distance in zone-1; there are apparent differences between disturbance classes. The spline regression was obtained with a lowess smoothing algorithm as offered by the function lowess() with f=0.2 of the R package stats.

#### **3.1.6.5 The influence of slope and aspect on similarity and distance decay**

Slope and aspect show no influence on species composition. The similarity in species composition has been regressed against the dissimilarity regarding slope and aspect. No correlation (Mantel) has been found neither for zone-1(r = -0.0068) nor for zone-2 (r = 0.01). This holds even when we controlled for the influence of altitude on this relation (partial Mantel test). In the latter case Mantel correlation values amount to r = -0.019 (zone-1) and r = 0.01341 (zone-2) respectively.

#### **3.1.6.6 Continuous plots for the six sites**

170 The Dynamical Processes of Biodiversity – Case Studies of Evolution and Spatial Distribution

Fig. 12. Slopes of the distance decay relationship for subsets of the data. Each of the subsets comprises all comparisons between the plots of one zone and one fragmentation class therein. Besides the fact that similarity decreases much faster with distance in zone-1; there are apparent differences between fragmentation classes. The spline regression was obtained with a lowess smoothing algorithm as offered by the function lowess() with f=0.2 of the R

Fig. 13. Slopes of the distance decay relationship for subsets of the data. Each of the subsets comprises all comparisons between the plots of one zone and one disturbance class therein. Besides the fact, that similarity decreases much faster with distance in zone-1; there are apparent differences between disturbance classes. The spline regression was obtained with a lowess smoothing algorithm as offered by the function lowess() with f=0.2 of the R package

package stats.

stats.

The vegetation composition of the 6 sites show considerable differences. This is clearly apparent in the DCA drawn from the data in Fig. 14 (a & b). Because there are very few species shared between plots (see Fig. 15 for more detail regarding this issue) and because there are much more species than plots (when each of the 6 sites is considered as a single sample) the metaMDS algorithm very fast finds a stable solution. After 2 runs a very low stress value of 3.21 results (see also Figure 14a).

Fig. 14. a and b: Ordination plots of the 6-sites data. The six transects vary considerable in their species composition. Both methods come to comparable results. Sites 3 and 4 are highly dissimilar. Sites 2, 5, and 6 build something like a cluster (but is relatively vague), whereas Site 1 is far from 3 and 4 and closer to the other three but at the same time relatively distinct from all other Sites.

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 173

Fig. 16. NMDS plot of the 6-sites data. Colors represent the different sites as indicated in the legend. Sites are relatively clearly separated. Especially sites 3 and 4 show almost no species overlap. The sites of zone 2 (4, 5, and 6) clump much closer together (compared to the sites of zone 1 (1, 2, and 3). Furthermore interesting is the very clear separation of some quadrats in sites 1 and 2 (on the right hand side of the figure) because it occurs within the sites. The

Fig. 17. Comparison of similarity between the 6 sites. The letters above the boxes connects sites not significantly different in mean similarity. Medians are often very low (sites 1, 3, 4) because a lot of quadrats inside do not share any species at all (so similarity is zero)

stress value 49.16 is rather high which indicates a not so good final solution.

When the quadrats (that make up the sites) are considered separately, it is not possible to calculate a NMDS with the metaMDS algorithm because a majority of the compared quadrats have no species in common. Nevertheless, this means that overall beta-diversity in trees is very high. A solution can be achieved with the slightly less robust isoMDS[MASS] function. It accepts any distance matrix achieved in advance (rather than calculating a distance matrix during the process) and does not feature several random starts with different starting configurations but only a simple iteration algorithm. The result is displayed in Fig. 16. The sites are relatively clearly separated, which indicates that the similarity among quadrats of a site is much higher than similarity across sites. This can be tested with the mrpp() function of package vegan for R (see above). Applied to the data the function returns the following statistics: A = 0.11\*\*\*, delta\_obs = 0.83, delta\_exp = 0.94. This indicates that the groups are distinct in their species composition

Fig. 15. Pairwise comparison of shared, not shared, and unshared species for all possible pairs of sites from the 6-sites data. Explanation: shared species occur on both of the compared sites, not shared species occur on only one of the compared sites, unshared species do not occur on both the compared sites. Note, that the fraction of shared species is always relatively small

When the quadrats (that make up the sites) are considered separately, it is not possible to calculate a NMDS with the metaMDS algorithm because a majority of the compared quadrats have no species in common. Nevertheless, this means that overall beta-diversity in trees is very high. A solution can be achieved with the slightly less robust isoMDS[MASS] function. It accepts any distance matrix achieved in advance (rather than calculating a distance matrix during the process) and does not feature several random starts with different starting configurations but only a simple iteration algorithm. The result is displayed in Fig. 16. The sites are relatively clearly separated, which indicates that the similarity among quadrats of a site is much higher than similarity across sites. This can be tested with the mrpp() function of package vegan for R (see above). Applied to the data the function returns the following statistics: A = 0.11\*\*\*, delta\_obs = 0.83, delta\_exp = 0.94. This

Fig. 15. Pairwise comparison of shared, not shared, and unshared species for all possible pairs of sites from the 6-sites data. Explanation: shared species occur on both of the compared sites, not shared species occur on only one of the compared sites, unshared species do not occur on both the compared sites. Note, that the fraction of shared species is

always relatively small

indicates that the groups are distinct in their species composition

Fig. 16. NMDS plot of the 6-sites data. Colors represent the different sites as indicated in the legend. Sites are relatively clearly separated. Especially sites 3 and 4 show almost no species overlap. The sites of zone 2 (4, 5, and 6) clump much closer together (compared to the sites of zone 1 (1, 2, and 3). Furthermore interesting is the very clear separation of some quadrats in sites 1 and 2 (on the right hand side of the figure) because it occurs within the sites. The stress value 49.16 is rather high which indicates a not so good final solution.

Fig. 17. Comparison of similarity between the 6 sites. The letters above the boxes connects sites not significantly different in mean similarity. Medians are often very low (sites 1, 3, 4) because a lot of quadrats inside do not share any species at all (so similarity is zero)

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 175

1995), 420 to 777 stems ha-1 in Brazil (Campbell *et al.,* 1992) and 639 to 713 stems ha-1 in

The basal area for both the zones is ranging from 2.89 and 40.95 m2ha-1 for ≥30 cm girth threshold. Thorn forest of the zone-1 had least basal area and high basal area was observed in the semi-evergreen forest of northern Eastern Ghats (40.95 m2ha-1). The mean basal area value of the present study is also lesser than the values for the comparable girth threshold of ≥30cm gbh of several other tropical forests: 28.1 and 30.8 m2ha-1 respectively of dry evergreen forest sites of Kuzhanthaikuppam and Thirumanikkuzhi (Parthasarathy & Karthikeyan, 1997b) Puthupet (Parthasarathy & Sethi, 1997) on the Coromandel coast of south India; 24.2 m2ha-1 of Malaysia (Poore, 1968), 27.6 to 32.0 m2ha-1 and 25.5 to 27.0 m2ha-1 of Brazilian Amazon (Campbell *et al.,* 1986, 1992); 27.8 and 41.67 m2ha-1 of Costa Rica (Lieberman & Lieberman, 1987; Watternberg & Breckle, 1995); 32.8 to 40.2 m2ha-1 of Central Amazonian upland forest (Ferreira & Prance, 1998); 42.6 m2ha-1 of Courtallam reserve forest in the Indian Western Ghats (Parthasarathy & Karthikeyan, 1997a); 39.7 m2ha-1 of Uppangala forests, central Western Ghats, India (Pascal & Pelissier, 1996); and 25.91 to 47.75 m2ha-1 in the 30 ha of Varagalaiar, Anamalais, southern Western Ghats (Ayyappan & Parthasarathy, 1999). But a value of present study is lesser than: 53.3 to 94.6 m2ha-1 and 55.3 to 78.3 m2ha-1 of Kalakad, southern Western Ghats, India (Parthasarathy 1999; Parthasarathy, 2001) and the values of a couple of other tropical forests: 47 (for alluvium) to 49.5 m2ha-1 (for slope forest) of New Caledonia (Jaffre & Veillon, 1990), and 62 m2ha-1 of

In both the zones, family-wise five predominant families explain the dominance of the forests which includes Combretaceae, Mimosaceae, Euphorbiaceae, Caesalpiniaceae and Rubiaceae. It contributes 39% of the family dominance which characterize the tree community pattern and in close range with other tropical forests regions (Gordon *et al.*, 2004; Linares-Palomino & Ponce-Alvarez, 2005) while the other Indian Eastern Ghats site, where the family Oleaceae (26.6%) dominated (Kadavul & Parthasarathy, 1999a) and in dry evergreen forests in south India, where the Melastomataceae and Rubiaceae with 56%

The trend of decreasing diversity and density with increasing girth class is in conformity with the studies of Chittibabu & Parthasarathy (2000); Jeffre & Veillon (1990); Kadavul & Parthasarathy (1999a, b); Newbery *et al.,* (1992) and Paijmans (1970). Both the zones had typical reverse J-shaped structure for girth frequency (Fig. 4o). Northern region of the Andhra Pradesh explains mature stands in all the girth-class with good regeneration were in close conformity with other tropical forests around the world (Chittibabu & Parthasarathy, 2000; Kadavul & Parthasarathy, 1999a, b; Manokaran & Kochummen, 1987; Nadkarni *et al.*,

A total of 197 species, 139 genera and 57 families (Table 3) were stated from six transects covering thee-ha of the tropical forests in Northern and Southern Andhra Pradesh, Eastern Ghats. Species richness (43-72 species ha-1) and species diversity 2.9-3.6 H') are comparable with the other sites in the Eastern Ghats. The mean value of 60 species ha-1 recorded in the present study is higher than that of 43 species ha-1 in Shervarayan hills (Kadavul & Parthasarathy, 1999a), 57 species ha-1 in Mylodai forest of Courtallum (Parthasarathy & Karthikeyan, 1997b). In Mudumalai tropical forest, Western Ghats, the 12 most common

Central Amazonia (Ferreira & Prance, 1998).

Monteverde, Costa Rica (Nadkarni *et al.,* 1995).

dominated (Parthasarathy & Karthikeyan, 1997b).

1995; Sukumar *et al.,* 1992).

**4.1.2 Continuous plots for the six sites** 

Also beta-diversity (expressed by compositional similarity) differs significantly between sites (Fig. 17). Only the sites 4 and 5 do not significantly differ in their similarity structure. However they have also been quite similar in species composition (as seen in the NMDS plot in Fig. 16) with site 5 being clearly positioned between site 3 and 4. All of the above can partly be grasped also from the species matrix, wherein - even without ordering - it is obvious that only few species occur on more than one or on even more sites.

A moderate percentage of quadrats (47%) are clustered into the "right" cluster when site membership is (very simplistically) compared to cluster membership. This was obtained by computing a simple Wards clustering with hclust[stats] followed by the application of cutree[stats] which simply cuts the resulting dendogram tree to obtain group (or cluster-) memberships for all tested objects (the quadrats in our case) when the number of groups has been specified.
