A divisive scheme for constructing minimal spanning trees in coordinate space

An algorithm to generate a minimal spanning tree is presented when the nodes with their coordinates in some m-dimensional Euclidean space and the corresponding metric are given. This algorithm is tested on manually generated data sets. The worst case time complexity of this algorithm is O(n log2n) for a collection of n data samples.

Multispecies coexistence of trees in tropical forests: spatial signals of topographic niche differentiation increase with environmental heterogeneity

Neutral and niche theories give contrasting explanations for the maintenance of tropical tree species diversity. Both have some empirical support, but methods to disentangle their effects have not yet been developed. We applied a statistical measure of spatial structure to data from 14 large tropical forest plots to test a prediction of niche theory that is incompatible with neutral theory: that species in heterogeneous environments should separate out in space according to their niche preferences. We chose plots across a range of topographic heterogeneity, and tested whether pairwise spatial associations among species were more variable in more heterogeneous sites. We found strong support for this prediction, based on a strong positive relationship between variance in the spatial structure of species pairs and topographic heterogeneity across sites. We interpret this pattern as evidence of pervasive niche differentiation, which increases in importance with increasing environmental heterogeneity.

Socio-cultural protection of endemic trees in humanised landscape

Culturally protected forest patches or sacred groves have been the integral part of many traditional societies. This age old tradition is a classic instance of community driven nature conservation sheltering native biodiversity and supporting various ecosystem functions particularly hydrology. The current work in Central Western Ghats of Karnataka, India, highlights that even small sacred groves amidst humanised landscapes serve as tiny islands of biodiversity, especially of rare and endemic species. Temporal analysis of landuse dynamics reveals the changing pattern of the studied landscape. There is fast reduction of forest cover (15.14-11.02 %) in last 20 years to meet up the demand of agricultural land and plantation programs. A thorough survey and assessment of woody endemic species distribution in the 25 km(2) study area documented presence of 19 endemic species. The distribution of these species is highly skewed towards the culturally protected patches in comparison to other land use elements. It is found that, among the 19 woody endemic species, those with greater ecological amplitude are widely distributed in the studied landscape in groves as well as other land use forms whereas, natural population of the sensitive endemics are very much restricted in the sacred grove fragments. The recent degradation in the sacred grove system is perhaps, due to weakening of traditional belief systems and associated laxity in grove protection leading to biotic disturbances. Revitalisation of traditional practices related to conservation of sacred groves can go a long way in strengthening natural ecological systems of fragile humid tropical landscape.

On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.

Reducing the babel in plant volatile communication: using the forest to see the trees

While plants of a single species emit a diversity of volatile organic compounds (VOCs) to attract or repel interacting organisms, these specific messages may be lost in the midst of the hundreds of VOCs produced by sympatric plants of different species, many of which may have no signal content. Receivers must be able to reduce the babel or noise in these VOCs in order to correctly identify the message. For chemical ecologists faced with vast amounts of data on volatile signatures of plants in different ecological contexts, it is imperative to employ accurate methods of classifying messages, so that suitable bioassays may then be designed to understand message content. We demonstrate the utility of `Random Forests' (RF), a machine-learning algorithm, for the task of classifying volatile signatures and choosing the minimum set of volatiles for accurate discrimination, using datam from sympatric Ficus species as a case study. We demonstrate the advantages of RF over conventional classification methods such as principal component analysis (PCA), as well as data-mining algorithms such as support vector machines (SVM), diagonal linear discriminant analysis (DLDA) and k-nearest neighbour (KNN) analysis. We show why a tree-building method such as RF, which is increasingly being used by the bioinformatics, food technology and medical community, is particularly advantageous for the study of plant communication using volatiles, dealing, as it must, with abundant noise.

In the elephant's seed shadow: the prospects of domestic bovids as replacement dispersers of three tropical Asian trees

As populations of the world's largest animal species decline, it is unclear how ecosystems will react to their local extirpation. Due to the unique ecological characteristics of megaherbivores such as elephants, seed dispersal is one ecosystem process that may be affected as populations of large animals are decimated. In typically disturbed South Asian ecosystems, domestic bovids (cattle, Bos primigenius, and buffalo, Bubalus bubalis) may often be the species most available to replace Asian elephants (Elephas maximus) as endozoochorous dispersers of large-fruited mammal-dispersed species. We use feeding trials, germination trials, and movement data from the tropical moist forests of Buxa Tiger Reserve (India) to examine whether domestic bovids are viable replacements for elephants in the dispersal of three largefruited species: Dillenia indica, Artocarpus chaplasha, and Careya arborea. We find that (1) once consumed, seeds are between 2.5 (C. arborea) and 26.5 (D. indica) times more likely to pass undigested into elephant dung than domestic bovid dung; and (2) seeds from elephant dung germinated as well as or better than seeds taken from bovid dung for all plant species, with D. indica seeds from elephant dung 1.5 times more likely to germinate. Furthermore, since wild elephants have less constrained movements than even free-roaming domestic bovids, we calculate that maximum dispersal by elephants is between 9.5 and 11.2 times farther than that of domestic bovids, with about 20% of elephant-dispersed seeds being moved farther than the maximum distance seeds are moved by bovids. Our findings suggest that, while bovids are able to disperse substantial numbers of seeds over moderate distances for two of the three study species, domestic bovids will be unable to routinely emulate the reliable, long-distance dispersal of seeds executed by elephants in this tropical moist forest. Thus while domestic bovids can attenuate the effects of losing elephants as dispersers, they may not be able to prevent the decline of various mammal-dispersed fruiting species in the face of overhunting, habitat fragmentation, and climate change.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)