Beals smoothing revisited

Beals smoothing is a multivariate transformation specially designed for species presence/absence community data containing noise and/or a lot of zeros. This transformation replaces the observed values of the target species by predictions of occurrence on the basis of its co-occurrences with the remaining species. In many applications, the transformed values are used as input for multivariate analyses. As Beals smoothing values provide a sense of “probability of occurrence”, they have also been used for inference. However, this transformation can produce spurious results, and it must be used with caution. Here we study the statistical and ecological bases underlying the Beals smoothing function, and the factors that may affect the reliability of transformed values are explored using simulated data sets. Our simulations demonstrate that Beals predictions are unreliable for target species that are not related to the overall ecological structure. Furthermore, the presence of these “random” species may diminish the quality of Beals smoothing values for the remaining species. A statistical test is proposed to determine when observed values can be replaced with Beals smoothing predictions. Two real-data example applications are presented to illustrate the potentially false predictions of Beals smoothing and the necessary checking step performed by the new test. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Determining alternative models for vegetation response analysis: a non-parametric approach

Abstract. Vegetation models based on multiple logistic regression are of growing interest in environmental studies and decision making. The relatively simple sigmoid Gaussian optimum curves are most common in current vegetation models, although several different other response shapes are known. However, improvements in the technical means for handling statistical data now facilitate fast and interactive calculation of alternative complex, more data-related, non-parametric models. The aim in this study was to determine whether, and if so how often, a complex response shape could be more adequate than a linear or quadratic one. Using the framework of Generalized Additive Models, both parametric (linear and quadratic) and non-parametric (smoothed) stepwise multiple logistic regression techniques were applied to a large data set on wetlands and water plants and to six environmental variables: pH, chloride, orthophosphate, inorganic nitrogen, thickness of the sapropelium layer and depth of the water-body. All models were tested for their goodness-of-fit and significance. Of all 156 generalized additive models calculated, 77 % were found to contain at least one smoothed predictor variable, i.e. an environmental variable with a response better fitted by a complex, non-parametric, than by a linear or quadratic parametric curve. Chloride was the variable with the highest incidence of smoothed responses (48 %). Generally, a smoothed curve was preferable in 23 % of all species-variable correlations calculated, compared to 25 % and 18 % for sigmoid and Gaussian shaped curves, respectively. Regression models of two plant species are presented in detail to illustrate the potential of smoothers to produce good fitting and biologically sound response models in comparison to linear and polynomial regression models. We found Generalized Additive Modelling a useful and practical technique for improving current regression-based vegetation models by allowing for alternative, complex response shapes.     

北美CHIHUAHUAN荒漠啮齿动物群落动态：Ⅲ.变量的频次分布和预测

本文用Ｘ＾２方和柯尔莫哥洛夫检验分析了北美Ｃｈｉｈｕａｈｕａｎ荒漠啮齿动物群落６个生态学变量的频次分布,并用移动平均和指数平滑方法拟合了这些变理的动态变化。结果显示：１）结合种群密度、生物量、物种均匀性和生物量均匀性服从正态分布;２）物种数和物种多样性的频次为向右偏斜的分布,无法用常见的理论分布来近似表示;３）单移动平均和双移动平均分别较好地描述了和的种多样性和物种均匀性;４）其余４个变量可用单指     

Functional mixed effects models

In this article, a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced. The linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects, which are modeled as realizations of zero-mean stochastic processes. The fixed functional effects and the random functional effects are modeled in the same functional space, which guarantee the population-average and subject-specific curves have the same smoothness property. These models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures, can include continuous covariates as well as dummy factors in both the fixed or random design matrices, and include the nested curves models as special cases. Two estimation procedures are proposed. The first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software. The second procedure is a sequential estimation procedure using Kalman filtering. This algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets. A generalized maximum likelihood (GML) ratio test is proposed for inference and model selection. An application to comparison of cortisol profiles is used as an illustration.     

Interspecific variation of body shape and sexual dimorphism in three coexisting species of the genus <Emphasis Type="Italic">Petrotilapia</Emphasis> (Teleostei: Cichlidae) from Lake Malawi

Differences in color patterns have been the most used feature in describing cichlid species belonging to genus Petrotilapia from Lake Malawi. In this study, we quantified morphological variation in body shape within and among three coexisting Petrotilapia species using landmark-based geometric morphometric methods. Statistic analyses revealed significant body shape differences among species but not between sexes. Post hoc multiple comparisons based on Mahalanobis distances revealed that P. nigra was significantly different from P. genalutea and Petrotilapia sp., whereas the latter two were not significantly different. The splines generated showed that the most pronounced variation was in the head region, in which P. nigra had a relatively longer and deeper head than the other two. The most clear-cut distinction was in gape length; P. genalutea had the longest gape, followed by Petrotilapia sp., whereas P. nigra had the shortest gape. Body depth was shallower in P. nigra than the others. When comparing sexes by their centroid size, ANOVA revealed that males were bigger than females. Therefore, we conclude that color is not the only feature that can distinguish these congeners. We discuss the observed sexual dimorphism in terms of sexual selection and relate morphological variation among species to feeding behavior, which may help explain their coexistence in nature.     

Mapping Cancer Risk in Southwestern Ontario with Changing Census Boundaries

Summary Mapping disease risk often involves working with data that have been spatially aggregated to census regions or postal regions, either for administrative reasons or confidentiality. When studying rare diseases, data must be collected over a long time period in order to accumulate a meaningful number of cases. These long time periods can result in spatial boundaries of the census regions changing over time, as is the case with the motivating example of exploring the spatial structure of mesothelioma lung cancer risk in Lambton County and Middlesex County of southwestern Ontario, Canada. This article presents a local‐EM kernel smoothing algorithm that allows for the combining of data from different spatial maps, being capable of modeling risk for spatially aggregated data with time‐varying boundaries. Inference and uncertainty estimates are carried out with parametric bootstrap procedures, and cross‐validation is used for bandwidth selection. Results for the lung cancer study are shown and discussed.