Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

Stability of Adult Emergence and Activity/Rest Rhythms in Fruit Flies Drosophila melanogaster under Semi-Natural Condition

Here we report the results of a study aimed at examining stability of adult emergence and activity/rest rhythms under seminatural conditions (henceforth SN), in four large outbred fruit fly Drosophila melanogaster populations, selected for emergence in a narrow window of time under laboratory (henceforth LAB) light/dark (LD) cycles. When assessed under LAB, selected flies display enhanced stability in terms of higher amplitude, synchrony and accuracy in emergence and activity rhythms compared to controls. The present study was conducted to assess whether such differences in stability between selected and control populations, persist under SN where several gradually changing time-cues are present in their strongest form. The study revealed that under SN, emergence waveform of selected flies was modified, with even more enhanced peak and narrower gate-width compared to those observed in the LAB and compared to control populations in SN. Furthermore, flies from selected populations continued to exhibit enhanced synchrony and accuracy in their emergence and activity rhythms under SN compared to controls. Further analysis of zeitgeber effects revealed that enhanced stability in the rhythmicity of selected flies under SN was primarily due to increased sensitivity to light because emergence and activity rhythms of selected flies were as stable as controls under temperature cycles. These results thus suggest that stability of circadian rhythms in fruit flies D. melanogaster, which evolved as a consequence of selection for emergence in a narrow window of time under weak zeitgeber condition of LAB, persists robustly in the face of day-to-day variations in cycling environmental factors of nature.

Efficient Management of Fruit Pests by Pheromone Nanogels

Environment-friendly management of fruit flies involving pheromones is useful in reducing the undesirable pest populations responsible for decreasing the yield and the crop quality. A nanogel has been prepared from a pheromone, methyl eugenol (ME) using a low-molecular mass gelator. This was very stable at open ambient conditions and slowed down the evaporation of pheromone significantly. This enabled its easy handling and transportation without refrigeration, and reduction in the frequency of pheromone recharging in the orchard. Notably the involvement of the nano-gelled pheromone brought about an effective management of Bactrocera dorsalis, a prevalent harmful pest for a number of fruits including guava. Thus a simple, practical and low cost green chemical approach is developed that has a significant potential for crop protection, long lasting residual activity, excellent efficacy and favorable safety profiles. This makes the present invention well-suited for pest management in a variety of crops.

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.

On the SIG-dimension of trees under the L (a)-metric

Let where be a set of points in d-dimensional space with a given metric rho. For a point let r (p) be the distance of p with respect to rho from its nearest neighbor in Let B(p,r (p) ) be the open ball with respect to rho centered at p and having the radius r (p) . We define the sphere-of-influence graph (SIG) of as the intersection graph of the family of sets Given a graph G, a set of points in d-dimensional space with the metric rho is called a d-dimensional SIG-representation of G, if G is isomorphic to the SIG of It is known that the absence of isolated vertices is a necessary and sufficient condition for a graph to have a SIG-representation under the L (a)-metric in some space of finite dimension. The SIG-dimension under the L (a)-metric of a graph G without isolated vertices is defined to be the minimum positive integer d such that G has a d-dimensional SIG-representation under the L (a)-metric. It is denoted by SIG (a)(G). We study the SIG-dimension of trees under the L (a)-metric and almost completely answer an open problem posed by Michael and Quint (Discrete Appl Math 127:447-460, 2003). Let T be a tree with at least two vertices. For each let leaf-degree(v) denote the number of neighbors of v that are leaves. We define the maximum leaf-degree as leaf-degree(x). Let leaf-degree{(v) = alpha}. If |S| = 1, we define beta(T) = alpha(T) - 1. Otherwise define beta(T) = alpha(T). We show that for a tree where beta = beta (T), provided beta is not of the form 2 (k) - 1, for some positive integer k a parts per thousand yen 1. If beta = 2 (k) - 1, then We show that both values are possible.

Rapid determination of main constituents of packed juices by reverse phase-high performance liquid chromatography: an insight in to commercial fruit drinks

The present work reports the compositional analysis of thirteen different packed fruit juices using high performance liquid chromatography (HPLC). Vitamin C, organic acids (citric and malic) and sugars (fructose, glucose and sucrose) were separated, analyzed and quantified using different reverse phase methods. A new rapid reverse phase HPLC method was developed for routine analysis of vitamin C in fruit juices. The precision results of the methods showed that the relative standard deviations of the repeatability and reproducibility were < 0.05 and < 0.1 respectively. Correlation coefficient of the calibration models developed was found to be higher than 0.99 in each case. It has been found that the content of Vitamin C was less variable amongst different varieties involved in the study. It is also observed that in comparison to fresh juices, the packed juices contain lesser amounts of vitamin C. Citric acid was found as the major organic acids present in packed juices while maximum portion of sugars was of sucrose. Comparison of the amount of vitamin C, organic acids and sugars in same fruit juice of different commercial brands is also reported.

Rhythmic egg-laying behaviour in virgin females of fruit flies Drosophila melanogaster

Fruit fly Drosophila melanogaster females display rhythmic egg-laying under 12: 12 h light/dark (LD) cycles which persists with near 24 h periodicity under constant darkness (DD). We have shown previously that persistence of this rhythm does not require the neurons expressing pigment dispersing factor (PDF), thought to be the canonical circadian pacemakers, and proposed that it could be controlled by peripheral clocks or regulated/triggered by the act of mating. We assayed egg-laying behaviour of wild-type Canton S (CS) females under LD, DD and constant light (LL) conditions in three different physiological states; as virgins, as females allowed to mate with males for 1 day and as females allowed to mate for the entire duration of the assay. Here, we report the presence of a circadian rhythm in egg-laying in virgin D. melanogaster females. We also found that egg-laying behaviour of 70 and 90% females from all the three male presence/absence protocols follows circadian rhythmicity under DD and LL, with periods ranging between 18 and 30 h. The egg-laying rhythm of all virgin females synchronized to LD cycles with a peak occurring soon after lights-off. The rhythm in virgins was remarkably robust with maximum number of eggs deposited immediately after lights-off in contrast to mated females which show higher egg-laying during the day. These results suggest that the egg-laying rhythm of D. melanogaster is endogenously driven and is neither regulated nor triggered by the act of mating; instead, the presence of males results in reduction in entrainment to LD cycles.

Forest area estimation and reporting: implications for conservation, management and REDD

Periodic estimation, monitoring and reporting on area under forest and plantation types and afforestation rates are critical to forest and biodiversity conservation, sustainable forest management and for meeting international commitments. This article is aimed at assessing the adequacy of the current monitoring and reporting approach adopted in India in the context of new challenges of conservation and reporting to international conventions and agencies. The analysis shows that the current mode of monitoring and reporting of forest area is inadequate to meet the national and international requirements. India could be potentially over-reporting the area under forests by including many non-forest tree categories such as commercial plantations of coconut, cashew, coffee and rubber, and fruit orchards. India may also be under-reporting deforestation by reporting only gross forest area at the state and national levels. There is a need for monitoring and reporting of forest cover, deforestation and afforestation rates according to categories such as (i) natural/primary forest, (ii) secondary/degraded forests, (iii) forest plantations, (iv) commercial plantations, (v) fruit orchards and (vi) scattered trees.

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.

Parasites exert conflicting selection pressures to affect reproductive asynchrony of their host plant in an obligate pollination mutualism

1. Plant reproductive phenology is generally viewed as an individual's strategy to maximize gamete exchange and propagule dispersal and is often considered largely dependent on patterns of floral initiation. Reproductive phenology, however, can be affected by proximate responses to pollinators, parasites and herbivores which could influence floral longevity or fruit development time. 2. We examined the influence of insect interactants on within-plant reproductive phenology in the fig-fig wasp nursery pollination mutualism in Ficus racemosa (Moraceae). Most figs support a wasp community comprised of a mutualistic pollinator, with several host-plant-specific non-pollinating herbivorous gallers and parasitoids. These wasps reproduce within enclosed inflorescences called syconia, which develop into fruit after pollination. While different wasp species oviposit into syconia at varying times during its ontogeny, all wasp progeny are constrained to exit syconia simultaneously just prior to fruit ripening. Developing larvae of early-ovipositing wasps may hasten syconium ontogeny through formation of earlier and larger nutrient sinks, whereas larvae of late-arriving parasites may lengthen syconium ontogeny to complete their development successfully. Seeds are also important nutrient sinks. The number of seeds and the type and number of developing wasps may therefore be expected to influence syconium development times, thereby affecting the reproductive synchrony of syconia on a plant. 3. Observations on naturally pollinated and parasitized syconia indicated that their seed and wasp content affected syconium development time. Experimental manipulations of syconia to produce only seeds or various combinations of wasps confirmed this finding. Early-ovipositing galler progeny reduced syconium development times, while gallers ovipositing concurrently with pollinators had no effect on syconium development. Late-ovipositing parasitoid progeny, the presence of only seeds within the syconium, or delayed pollination increased syconium development time. The differential development of syconia, which was influenced by mutualistic or parasitic progeny, accordingly contributed to within-tree reproductive asynchrony. 4. Synthesis. Individual reproductive units in fig trees called syconia, which also function as brood sites for pollinating and parasitic fig wasps, have plastic development durations dependent on pollination timing and species of wasps developing within them. Syconium development times are a likely compromise between conflicting demands from developing seeds and different wasp species.

Fruit and Seed Volatiles: Multiple Stage Settings, Actors and Props in an Evolutionary Play

Plants emit volatile organic compounds (VOCs) from most parts of their anatomy. Conventionally, the volatiles of leaves, flowers, fruits and seeds have been investigated separately. This review presents an integrated perspective of volatiles produced by fruits and seeds in the context of selection on the whole plant. It suggests that fruit and seed volatiles may only be understood in the light of the chemistry of the whole plant. Fleshy fruit may be viewed as an ecological arena within which several evolutionary games are being played involving fruit VOCs. Fruit odour and colour may be correlated and interact via multimodal signalling in influencing visits by frugivores. The hypothesis of volatile crypsis in the evolution of hard seeds as protection against volatile diffusion and perception by seed predators is reviewed. Current views on the role of volatiles in ant dispersal of seeds or myrmecochory are summarised, especially the suggestion that ants are being manipulated by plants in the form of a sensory trap while providing this service. Plant VOC production is presented as an emergent phenotype that could result from multiple selection pressures acting on various plant parts; the ``plant'' phenotype and VOC profile may receive significant contributions from symbionts within the plant. Viewing the plant as a holobiont would benefit an understanding of the emergent plant phenotype.

Directed Nonabelian Sandpile Models on Trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

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.

The Asian elephant is amongst the top three frugivores of two tree species with easily edible fruit

Large animal species are prone to local extirpation, but ecologists cannot yet predict how the loss of megaherbivores affects ecosystem processes such as seed dispersal. Few studies have compared the quantity and quality of seed dispersal by megaherbivores versus alternative frugivores in the wild, particularly for plant species with fruit easily consumed by many frugivorous species. In a disturbed tropical moist forest in India, we examine whether megaherbivores are a major frugivore of two tree species with easily edible, mammal-dispersed fruit. We quantify the relative fruit removal rates of Artocarpus chaplasha and Careya arborea, by the Asian elephant (Elephas maximus) and alternative dispersers. Through focal watches and camera trapping, we found the elephant to be amongst the top three frugivores for each tree species. Furthermore, seed transects under A. chaplasha show that arboreal frugivores discard seeds only a short distance from the parental tree, underscoring the elephant's role as a long-distance disperser. Our data provide unprecedented support for an old notion: megaherbivores may be key dispersers for a broad set of mammal-dispersed fruiting species, and not just fruit inaccessible to smaller frugivores. As such, the elephant may be particularly important for the functional ecology of the disturbed forests it still inhabits across tropical Asia.