A new procedure to optimize the selection of groups in a classification tree: Applications for ecological data

Agglomerative cluster analyses encompass many techniques, which have been widely used in various fields of science. In biology, and specifically ecology, datasets are generally highly variable and may contain outliers, which increase the difficulty to identify the number of clusters. Here we present a new criterion to determine statistically the optimal level of partition in a classification tree. The criterion robustness is tested against perturbated data (outliers) using an observation or variable with values randomly generated. The technique, called Random Simulation Test (RST), is tested on (1) the well-known Iris dataset [Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugenic. 7, 179–188], (2) simulated data with predetermined numbers of clusters following Milligan and Cooper [Milligan, G.W., Cooper, M.C., 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179] and finally (3) is applied on real copepod communities data previously analyzed in Beaugrand et al. [Beaugrand, G., Ibanez, F., Lindley, J.A., Reid, P.C., 2002. Diversity of calanoid copepods in the North Atlantic and adjacent seas: species associations and biogeography. Mar. Ecol. Prog. Ser. 232, 179–195]. The technique is compared to several standard techniques. RST performed generally better than existing algorithms on simulated data and proved to be especially efficient with highly variable datasets.     

Multivariate analysis of spatial patterns: a unified approach to local and global structures

We propose a new approach to the multivariate analysis of data sets with known sampling site spatial positions. A between-sites neighbouring relationship must be derived from site positions and this relationship is introduced into the multivariate analyses through neighbouring weights (number of neighbours at each site) and through the matrix of the neighbouring graph. Eigenvector analysis methods (e.g. principal component analysis, correspondence analysis) can then be used to detect total, local and global structures. The introduction of the D-centring (centring with respect to the neighbouring weights) allows us to write a total variance decomposition into local and global components, and to propose a unified view of several methods. After a brief review of the matrix approach to this problem, we present the results obtained on both simulated and real data sets, showing how spatial structure can be detected and analysed. Freely available computer programs to perform computations and graphical displays are proposed.     

Monitoring and estimating the flow conditions and fish presence probability under various flow conditions at reach scale using genetic algorithms and kriging methods

The combination of current velocity and water depth influences stream flow conditions, and fish activities prefer particular flow conditions. This study develops a novel optimal flow classification method for identifying types of stream flow based on the current velocity and the water depth using a genetic algorithm. It is applied to the Datuan stream in northern Taiwan. Fish were sampled and their habitat investigated at the study site during the spring, summer, fall and winter of 2008-2009. The current velocity, water depth and maps of the presence probability of fish were estimated by ordinary and indicator kriging. The optimal classification results were compared with the classification results obtained using the Froude number and empirical methods. The flow classification results demonstrate that the proposed optimal flow classification method that considers depth-velocity and optimally identified criteria for classifying flow types, yields a current velocity and water depth of 0.32 (m/s) and 0.29 (m), respectively, and classifies the flow conditions in the study area as pool, run, riffle and slack. The variography results of the current velocity and the water depth data reveal that seasonal flows are not spatially stationary among seasons in the study area. Kriging methods and a two-dimensional hydrodynamic model (River 2D) with empirical and optimal flow classification methods are more effective than the Froude number method in classifying flow conditions in the study area. The flow condition classifications and probability maps were generated by River 2D, ordinary kriging and indicator kriging, to quantify the flow conditions preferred by Sicyopterus japonicus in the study area. However, the proposed optimal classification method with kriging and River 2D is an effective alternative method for mapping flow conditions and determining the relationship between flow and the presence probability of target fish in support of stream restoration.     

Inverse modeling for effective dispersal: Do we need tree size to estimate fecundity?

The estimation of the dispersal kernel for the seedling and sapling stages of the recruitment process was made possible through the application of inverse modeling to dispersal data. This method uses the spatial coordinates of adult trees and the counts of seedlings (or saplings) in small quadrats to estimate the dispersal kernel. The unknown number of recruits produced by an adult tree (the fecundity) is estimated - simultaneously with the dispersal kernel - via an allometric linear model relating the unknown quantity with a (easily) measured characteristic of the adult tree (usually the basal area). However, the allometric relation between tree size and reproductive success in the sapling (or seedling) stage may not be strong enough when numerous, well-documented, post-dispersal processes (such as safe-site limitation for recruitment) cause large post-dispersal seedling mortality, which is usually unrelated to the size of the tree that dispersed them. In this paper we hypothesize that when tree size and reproductive success in the seedling/sapling stage are not well correlated then the use of allometry in inverse modeling is counter-productive and may lead to poor model fits. For these special cases we suggest using a new model for effective dispersal that we term the unrestricted fecundity (UF) model that, contrary to allometric models, makes no assumptions on the fecundities; instead they are allowed to vary freely from one tree to another and even to be zero for trees that are reproductively inactive. Based on this model, we examine the hypothesis that when tree size and reproductive success are weakly correlated and the fecundities are estimated independently of tree size the goodness-of-fit and the ecological meaning of dispersal models (in the seedling or sapling stage) may be enhanced. Parameters of the UF model are estimated through the EM algorithm and their standard errors are approximated via the observed information matrix. We fit the UF model to a dataset from an expanding European beech population of central Spain as well as to a set of simulated dispersal data were the correlation between reproductive success and tree size was moderate. In comparisons with a simple allometric model, the UF model fitted the data better and the parameter estimates were less biased. We suggest using this new approach for modeling dispersal in the seedling and sapling stages when tree size (or other adult-specific covariates) is not deemed to be in strong relation to the reproductive success of adults. Models that use covariates for modeling the fecundity of adults should be preferred when reproductive success and tree size guard a strong relationship.     

Modelling phytoclimatic versatility as a large scale indicator of adaptive capacity to climate change in forest ecosystems

CLIMPAIR is a new phytoclimatic model, correlative and niche-based, which simultaneously assesses non-linear, non-statistical and dual measurements of proximity/potentiality of a site with respect to a number of climatic ranges of species, defined by convex hulls, within a suitability space. This set of phytoclimatic distances makes it possible to evaluate the degree to which each species is suitable for that site. Considering not only the number of species compatible (expected species richness), but also all those compatible covers presenting a high level of suitability evenness and finally applying an indicator derived from Shannon's classic entropy index to the set of standardized phytoclimatic coordinates in the suitability hyperspace, we can evaluate the phytoclimatic entropy which may be considered as a means of estimating the phytoclimatic versatility of the site. A site with high phytoclimatic entropy would promise versatile future behaviour, characterized by a wide range of possibilities of adaptation to climate change, and hence versatility can be used as an index of resilience and ability of a forest ecosystem to adapt to climate change. The model has been applied to peninsular Spain for 18 forest tree species and 12 climatic variables between the current mean climate (period 1951-1999) and a future climatic scenario (period 2040-2069). The results generally point to a significant decrease in the versatility of forest tree formations in the area studied, which is not homogeneous owing to a dual altitudinal/latitudinal decoupling. The decrease in versatility is greater in Mediterranean biogeographical areas than in Euro-Siberian ones, where in some cases it actually increases. In altitudinal terms, areas at elevations of less than 1500 m tend to become less versatile than areas situated at higher elevations, where versatility increases partly as a result of enrichment of alpine conifer forests with broadleaf species.     

判别分析与决策树分析在化学物质生态危害分类中的应用

运用Fisher判别、马氏距离判别和决策树分析3种方法对61种环境优先污染物的生态危害程度进行分类,并比较了各模型的分类正确率.结果显示,决策树分析方法分类正确率最高,为92%;马氏距离判别其次,为87%;Fisher判别最低,为75%.决策树分析方法不仅减少了2项评价指标,而且对61个新数据矩阵的多次分析显示其分类能力非常稳定,正确率基本符合正态分布,且保持在92%左右,为3种方法中最优的分类方法.     

Socially optimal forestry

The Faustmann rule is the major contribution of economic theory to the analysis of forestry management. It is typical to consider the Faustmann rule in the context of a model of a forestry firm in which there is some periodicity in the rate of harvesting over time. This paper on the other hand shows the Faustmann rule to be associated with socially optimal sustained yield or steady-state regimes. In the course of so doing, attention is placed on the role of the shadow price of a tree in the determination of an optimal harvesting policy.     

Intertype mark correlation function: A new tool for the analysis of species interactions

The spatial pattern of the different species in complex ecosystems reflects the underlying ecological processes. In this paper a second order moment function is proposed and tested to analyse the spatial distribution of a mark, which could be a tree characteristic such as diameter or height, between two different types of points, which could be two different tree species. The proposed function was a conditional density function based on the intertype K_rs(d) function, incorporating as test function the correlation of the marks between pairs composed of points of different types. The results obtained in simulated and real plots prove that the function is capable of revealing the scale at which spatial correlation of the mark between two types of points exists. The proposed function allows the spatial association between individuals of different species at different life stages to be identified. This analysis may reveal information on species ecology and interspecific interactions in forest ecosystems.     

A Landscape Approach to Biodiversity Conservation of Sacred Groves in the Western Ghats of India

Abstract:  Although sacred groves are important for conservation in India, the landscape that surrounds them has a vital influence on biodiversity within them. Research has focused on tree diversity inside these forest patches. In a coffee-growing region of the Western Ghats, however, landscape outside sacred groves is also tree covered because planters have retained native trees to provide shade for coffee plants. We examined the diversity of trees, birds, and macrofungi at 58 sites—10 forest-reserve sites, 25 sacred groves, and 23 coffee plantations— in Kodagu district. We measured landscape composition and configuration around each site with a geographic information system. To identify factors associated with diversity we constructed multivariate models by using a decision-tree technique. The conventional measures of landscape fragmentation such as patch size did not influence species richness. Distance of sacred groves from the forest reserve had a weak influence. The measures of landscape structure (e.g., tree cover in the surroundings) and stand structure (e.g., variability in canopy height) contributed to the variation in species richness explained by multivariate models. We suggest that biodiversity present within sacred groves has been influenced by native tree cover in the surrounding landscape. To conserve this biodiversity the integrity of the tree-covered landscape matrix will need to be conserved.     

Constrained additive ordination

For several decades now, ecologists have sought to determine the shape of species' response curves and how they are distributed along unknown underlying gradients, environmental latent variables, or ordination axes. Its determination has important implications for both continuum theory and community analysis because many theories and models in community ecology assume that responses are symmetric and unimodal. This article proposes a major new technique called constrained additive ordination (CAO) that solves this problem by computing the optimal gradients and flexible response curves. It allows ecologists to see the response curves as they really are, against the dominant gradients. With one gradient, CAO is a generalization of constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO). It supplants symmetric bell-shaped response curves in CQO with completely flexible smooth curves. The curves are estimated using smoothers such as the smoothing spline. Loosely speaking, CAO models are generalized additive models (GAMs) fitted to a very small number of latent variables. Being data driven rather than model driven, CAO allows the data to "speak for itself" and does not make any of the assumptions made by canonical correspondence analysis. The new methodology is illustrated with a hunting spider data set and a New Zealand tree species data set.     

Determination of metallic cobalt in the atmosphere

Due to the fact that, among the different chemical species, metallic cobalt is characterized by the highest toxicity, in this paper is proposed a procedure for its determination in the atmospheric paniculate. The air is filtered on a cellulose or glass fiber membrane, to collect the paniculate containing among the other species, metallic cobalt: the determination is based on a selective dissolution of the metallic cobalt possibly present followed by its determination by atomic absorption spectroscopy. The typical interferences that can be present in the matrix are discussed and suggestions for their minimisation are proposed. By the following procedure is also possible to determine separately the sum of the insoluble and water soluble cobalt compounds.     

Effects of sample survey design on the accuracy of classification tree models in species distribution models

We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by resubstitution rates were similar for each lichen species irrespective of the underlying sample survey form. Cross-validation estimates of prediction accuracies were lower than resubstitution accuracies for all species and both design types, and in all cases were closer to the true prediction accuracies based on the EVALUATION data set. We argue that greater emphasis should be placed on calculating and reporting cross-validation accuracy rates rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE tree models on the EVALUATION data set shows significantly lower prediction accuracy for the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic sample surveys may generate models with limited predictive capability. These differences were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in accuracy were as large as 50%. The classification tree structures also differed considerably both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on non-probabilistic sample surveys.     

Minimizing the cost of translocation failure with decision‐tree models that predict species’ behavioral response in translocation sites

The high number of failures is one reason why translocation is often not recommended. Considering how behavior changes during translocations may improve translocation success. To derive decision‐tree models for species’ translocation, we used data on the short‐term responses of an endangered Australian skink in 5 simulated translocations with different release conditions. We used 4 different decision‐tree algorithms (decision tree, decision‐tree parallel, decision stump, and random forest) with 4 different criteria (gain ratio, information gain, gini index, and accuracy) to investigate how environmental and behavioral parameters may affect the success of a translocation. We assumed behavioral changes that increased dispersal away from a release site would reduce translocation success. The trees became more complex when we included all behavioral parameters as attributes, but these trees yielded more detailed information about why and how dispersal occurred. According to these complex trees, there were positive associations between some behavioral parameters, such as fight and dispersal, that showed there was a higher chance, for example, of dispersal among lizards that fought than among those that did not fight. Decision trees based on parameters related to release conditions were easier to understand and could be used by managers to make translocation decisions under different circumstances. Minimizar el Costo del Fracaso de la Reubicación con Modelos de Árboles de Decisión que Predigan la Respuesta Conductual de la Especie en los Sitios de Reubicación     

Dynamic reserve site selection under contagion risk of deforestation

Recently, dynamic reserve site selection models based on stochastic dynamic programming (SDP) have been proposed. The models consider a random development pattern in which the probability that a site will be developed is independent of the development status of other sites. However, development often takes the form of a contagion process in which the sites most likely to be developed are near sites that already have been developed. To consider site selections in such cases, we propose improved algorithms that make use of a graph representation of the sites network. The first formulation is an exact, dynamic programming algorithm, with which theoretical and experimental complexities are evaluated. The exact method can be applied only to small problems (less than 10 sites), but real-world problems may have hundreds or thousands of sites, implying that heuristic selection methods must be used. We provide a general framework for describing such heuristic solution methods, and propose a new heuristic method based on a parameterised reinforcement learning algorithm. The method allows us to compute a heuristic function by performing and exploiting many simulations of the deforestation process. We show that the method can be applied to problems with hundreds of sites, and demonstrate experimentally that it outperforms previously proposed heuristic methods in terms of the average number of species conserved.     

Quantifying the Indicator Power of an Indicator Species

Abstract:  Biodiversity indicator species are needed for classifying biotopes and sites for conservation, and a number of methods have been developed for determining indicator species for this purpose. Nevertheless, in addition to site classification, there is sometimes a need to define an indicator species that indicates the occurrence of another species. For example, when a species of interest (target species) is difficult to detect or identify, a reliable indicator species can function as a tool that saves time and money. We derived a method that provides a quantitative measure of the indicator power (IP) of an indicator species for the target species or any species assemblage. We calculated the measure of IP from a presence–absence matrix that covered several sites. The method provided a list of indicator species, the presence of which reliably indicated the presence of another species (e.g., a threatened or rare species in a given area). The IP of the species was highest when the number of shared occurrences between the indicator species and the target species was high and, simultaneously, when the indicator species and the target species occurred separately in only a few cases. The IP was also positively influenced by the number of sites with no occurrences of either the indicator or the target species. Our method can also be used to quantify different types of species occurrence indications. We refer to these types as presence–presence, presence–absence, absence–presence, and absence–absence indications. To clarify the use of the method, we examined the situation with red-listed polypores in White-backed Woodpecker (Dendrocopos leucotos) habitats in Fennoscandia and found some suitable indicator species. Our method provides a new, objective way to evaluate the IP of an indicator species.     

A model of surface fire,climate and forest pattern in the Sierra Nevada,California

A spatially explicit forest gap model was developed for the Sierra Nevada, California, and is the first of its kind because it integrates climate, fire and forest pattern. The model simulates a forest stand as a grid of 15×15 m forest plots and simulates the growth of individual trees within each plot. Fuel inputs are generated from each individual tree according to tree size and species. Fuel moisture varies both temporally and spatially with the local site water balance and forest condition, thus linking climate with the fire regime. Fires occur as a function of the simulated fuel loads and fuel moisture, and the burnable area is simulated as a result of the spatially heterogeneous fuel bed conditions. We demonstrate the model’s ability to couple the fire regime to both climate and forest pattern. In addition, we use the model to investigate the importance of climate and forest pattern as controls on the fire regime. Comparison of model results with independent data indicate that the model performs well in several areas. Patterns of fuel accumulation, climatic control of fire frequency and the influence of fuel loads on the spatial extent of fires in the model are particularly well-supported by data. This model can be used to examine the complex interactions among climate, fire and forest pattern across a wide range of environmental conditions and vegetation types. Our results suggest that, in the Sierra Nevada, fuel moisture can exert an important control on fire frequency and this control is especially pronounced at sites where most of the annual precipitation is in the form of snow. Fuel loads, on the other hand, may limit the spatial extent of fire, especially at elevations below 1500 m. Above this elevation, fuel moisture may play an increasingly important role in limiting the area burned.     

Finding all optimal solutions to the reserve site selection problem: formulation and computational analysis

The problem of selecting nature reserves has received increased attention in the literature during the past decade, and a variety of approaches have been promoted for selecting those sites to include in a reserve network. One set of techniques employs heuristic algorithms and thus provides possibly sub-optimal solutions. Another set of models and accompanying algorithms uses an integer programming formulation of the problem, resulting in an optimization problem known as the Maximal Covering Problem, or MCP. Solution of the MCP provides an optimal solution to the reserve site selection problem, and while various algorithms can be employed for solving the MCP they all suffer from the disadvantage of providing a single optimal solution dictating the selection of areas for conservation. In order to provide complete information to decision makers, the determination of all alternate optimal solutions is necessary. This paper explores two procedures for finding all such solutions. We describe the formulation and motivation of each method. A computational analysis on a data set describing native terrestrial vertebrates in the state of Oregon illustrates the effectiveness of each approach.     

Herbivores and variation in the composition of specific phenolics of boreal coniferous trees: a search for patterns

Coniferous trees of different species, or of the same species growing at different locations, vary in the extent to which they are attacked by various herbivores and pathogens. Plant secondary metabolites might be a key to understanding some of this variation. At the site level, we investigated if there was an intra- or interspecies pattern for individual compounds (or for groups of compounds) and their relationship to indices of plant nitrogen and plant productivity. For example, do plants exhibit similar covariance in defence compounds when evaluated across a number of sites varying in productivity? Here, we concentrated on the phenolic profile of Pinus sylvestris, Picea abies, Juniperus communis and Pinus contorta. Our results indicate striking differences in secondary chemistry profiles of the twigs including needles of the trees and in the inter-relationships amongst individual compounds and groups of compounds. Flavonols occurred in high variety in P. sylvestris and were highly correlated with each other, differing from P. contorta. But the results of the factor analyses indicate an underlying pattern for flavonols of the coumaroyl type for P. contorta. In contrast, the compounds of the other tree species showed a low degree of inter-correlation. Co-occurring phenolics of different tree species were not correlated. Overall, our analysis of site indices indicated that plant productivity was not a useful predictor for the concentration of specific phenolics. The relationship amongst plant nitrogen and specific phenolics might be the result of two defence strategies (one related and the other not related to nitrogen content). This might enable the plant to shift its defences against attacks with a high degree of flexibility.     

A spatial clustering perspective on autocorrelation and regionalization

We revisit one of the classical problems in geography and cartography where multiple observations on a lattice (N) need to be grouped into many fewer regions (G), especially when this number of desired regions is unknown a priori. Since an optimization through all possible aggregations is not feasible, a hierarchical classification scheme is proposed with an objective function sensitive to spatial pattern. The objective function to be minimized during the assignment of observations to regions (classification) consists of two terms: the first characterizes accuracy and the second, model complexity. For the latter, we introduce a spatial measure that characterizes the number of homogeneous patches rather than the usual number of classes. A simulation study shows that such a classification procedure is less sensitive to random and spatially correlated error (noise) than non-spatial classification. We also show that for conditional autoregressive error (noise) fields the optimal partitioning is the one that has the highest within-units generalized Moran coefficient. The classifier is implemented in ArcView to demonstrate both a socio-economic and an environmental application to illustrate some potential applications.