Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

Predicting tree distributions in an East African biodiversity hotspot: model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix.     

Analyzing spatial count data,with an application to weed counts

Count data on a lattice may arise in observational studies of ecological phenomena. In this paper a hierarchical spatial model is used to analyze weed counts. Anisotropy is introduced, and a bivariate extension of the model is presented.     

Extending null scenarios with Faddy distributions in a probabilistic randomization protocol for presence-absence data

Environmental and Ecological Statistics - Navarro and Manly (Popul Ecol 51:505–512, 2009) (NM) have proposed a randomization protocol for null model analysis of species occurrences at...     

Functional ANOVA starting from discrete data: an application to air quality data

A nonparametric functional approach is proposed to compare the mean functions of $k$ k samples of curves. In practice, curves data are usually collected in a discrete form and hence they must be pre-processed to use purely functional techniques. However, in the context of $k$ k -sample tests, the pre-processing step can have effects in terms of power reduction. Hall and Van Keilegom (Stat Sin 17:1511–1531, 2007) proposed a methodology to minimizing these effects in the context of tests for the equality of two distribution functions. Their procedure is here extended to the case of $k$ k -sample hypothesis tests. The asymptotic validity of the procedure is established and its finite sample performance is analyzed through Monte Carlo experiments. As an illustration, the method is applied to air quality data collected from several monitoring stations placed at different geographical locations at the center of Spain.     

温带阔叶红松林中不同树种和倒木对土壤性质的影响

以长白山温带阔叶红松林为研究对象,通过野外采集土壤样品,综合研究老龄树及倒木对周边表层土壤性质的影响。研究结果显示,在本研究样地条件下,不同树种周边的表层土壤性质存在显著性差异,红松（Pinus koraiensis）周边土壤中水溶性有机碳WSOC的质量分数和特征吸光系数SUVA254值都高于紫椴（乃砌amurensis）和水曲柳（Fraxinus mandshurica）,但是土壤水溶性总氮WSTN和交换性无机氮的质量分数却是红松低于紫椴和水曲柳。对倒木影响的森林表层土壤性质的研究结果显示,倒木下方森林表层土壤中WSOC、WSTN以及交换性矿质氮的质量分数都明显地高于林间土壤,说明在小尺度空间区域内,倒木可能是森林表层土壤活性碳、氮库的重要输入源。此外,本研究还利用主成分分析探讨了受树种影响的森林表层土壤不同性质之间的关联性,并对树种和倒木影响周边土壤性质的可能性机制进行分析。     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.     

Indirect benefits of symbiotic coccoids for an ant-defended myrmecophytic tree

The net benefits of mutualism depend directly on the costs and effectiveness of mutualistic services and indirectly on the interactions that affect those services. We examined interactions among Cordia alliodora myrmecophytic trees, their symbiotic ants Azteca pittieri, coccoid hemipterans, and foliar herbivores in two Neotropical dry forests. The tree makes two investments in symbiotic ants: it supplies nesting space, as domatia, and it provides phloem to coccoids, which then produce honeydew that is consumed by ants. Although higher densities of coccoids should have higher direct costs for trees, we asked whether higher densities of coccoids can also have higher indirect benefits for trees by increasing the effectiveness of ant defense against foliar herbivores. We found that trees benefited from ant defense against herbivores. Ants defended trees effectively only when colonies reached high densities within trees, and ant and coccoid densities within trees were strongly positively correlated. The benefits of reduced foliar herbivory by larger ant colonies were therefore indirectly controlled by the number of coccoids. Coccoid honeydew supply also affected per capita ant aggression against tree herbivores. Ants experimentally fed a carbohydrate-rich diet, analogous to sugar obtained from coccoids, were more aggressive against caterpillars per capita than ants fed a carbohydrate-poor diet. Ant defense was more effective on more valuable and vulnerable young leaves than on older leaves. Young domatia, associated with young leaves, contained higher coccoid densities than older domatia, which suggests that coccoids may also drive spatially favorable ant defense of the tree. If higher investments by one mutualistic partner are tied to higher benefits received from the other, there may be positive feedback between partners that will stabilize the mutualism. These results suggest that higher investment by trees in coccoids leads to more effective defense by ants against the tree's foliar herbivores.     

A diagnostic test for autocorrelation in increment-averaged data with application to soil sampling

Motivated by the problem of detecting spatial autocorrelation in increment- averaged data from soil core samples, we use the Cholesky decomposition of the inverse of an autocovariance matrix to derive a parametric linear regression model for autocovariances. In the absence of autocorrelation, the off-diagonal terms in the lower triangular matrix from the Cholesky decomposition should be identically zero, and so the regression coefficients should be identically zero. The standard F-test of this hypothesis and two bootstrapped versions of the test are evaluated as autocorrelation diagnostics via simulation. Size is assessed for a variety of heteroskedastic null hypotheses. Power is evaluated against autocorrelated alternatives, including increment-averaged Ornstein-Uhlenbeck and Matérn processes. The bootstrapped tests maintain approximately the correct size and have good power against moderately autocorrelated alternatives. The methods are applied to data from a study of carbon sequestration in agricultural soils.     

A new probability model with application to heavy-tailed hydrological data

Environmental and Ecological Statistics - Because of the dramatic changes that are being observed in the climatic conditions of the world, such as excess of rains, drought and huge floods, we...     

Prediction of potential areas of species distributions based on presence-only data

We introduce a methodology to infer zones of high potential for the habitat of a species, useful for management of biodiversity, conservation, biogeography, ecology, or sustainable use. Inference is based on a set of sites where the presence of the species has been reported. Each site is associated with covariate values, measured on discrete scales. We compute the predictive probability that the species is present at each node of a regular grid. Possible spatial bias for sites of presence is accounted for. Since the resulting posterior distribution does not have a closed form, a Markov chain Monte Carlo (MCMC) algorithm is implemented. However, we also describe an approximation to the posterior distribution, which avoids MCMC. Relevant features of the approach are that specific notions of data acquisition such as sampling intensity and detectability are accounted for, and that available a priori information regarding areas of distribution of the species is incorporated in a clear-cut way. These concepts, arising in the presence-only context, are not addressed in alternative methods. We also consider an uncertainty map, which measures the variability for the predictive probability at each node on the grid. A simulation study is carried out to test and compare our approach with other standard methods. Two case studies are also presented.     

Hierarchical modeling of count data with application to nuclear fall-out

We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R². We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998).     

A test for space limitation with an application to recently settled lobsters

Space limitation in larval settlement can play an important role in the population dynamics of marine species. A novel statistical test for space limitation based on quadrat counts of individuals is described. The test is based on identifying a significant relationship between the relative dispersion of quadrat counts and overall mean density. An application to a time series of quadrat counts of recently settled American lobsters Homarus americanus covering the period 1993–2007 in Casco Bay, Maine, USA (43°45′N; 69°58′W), is presented. For this data set, the null hypothesis that space is not limiting could not be rejected (P = 0.10).     

CircSiZer: an exploratory tool for circular data

Smoothing methods and SiZer (SIgnificant ZERo crossing of the derivatives) are useful tools for exploring significant underlying structures in data samples. An extension of SiZer to circular data, namely CircSiZer, is introduced. Based on scale-space ideas, CircSiZer presents a graphical device to assess which observed features are statistically significant, both for density and regression analysis with circular data. The method is intended for analyzing the behavior of wind direction in the atlantic coast of Galicia (NW Spain) and how it has an influence over wind speed. The performance of CircSiZer is also checked with some simulated examples.