A Note on Binary Contingency Tables

This paper considers contingency tables in which the marginal frequencies for one variable are all 1. This could occur with two-category binary data or when a continuous variable is treated in categorical fashion. Some results concerning the expectation of goodness-of-fit statistics are reported. In particular it is noted that the expectation of the Pearson statistic is independent of the model being fitted.     

Use of the Score Statistic for Testing Goodness-of-Fit of Some Generalised Distributions

The use of the score statistic to test whether a generalised distribution gives an improved fit over a non-generalised distribution is recommended. The score statistic for a generalised exponential family is derived. Several specific examples are given.     

利用GARP生态位模型预测桔小实蝇（Bactrocera dorsalis）在中国的适生区域

桔小实蝇Bactrocera dorsalis (Hendel)是一种多食性害虫,明确其可能适生的区域对该虫的科学监测及防治意义重大。利用桔小实蝇在我国的已知分布点数据和亚洲地区的14个环境地理变量图层,运用GARP生态位模型结合GIS空间分析模块预测了该虫在亚洲的地理分布。结果表明桔小实蝇可分布在中国、日本、菲律宾、马来西亚、泰国北部、越南、柬埔寨、老挝、缅甸、尼泊尔、巴基斯坦、孟加拉国和斯里兰卡,这与EPPO报道的分布区域一致。将拟合过程中获得的生态位运算法则投影到我国,并考虑模型间的一致性,预测桔小实蝇在我国各省及市县范围的分布：云南大部、四川南部和东部、贵州大部、重庆大部、广西、广东、台湾、香港、澳门、海南、福建、江西、浙江大部、湖南大部、湖北大部、上海、江苏南部、河南局部及安徽部分地区为桔小实蝇的适生区。次适生区沿适生区周围分布,为四川、贵州、重庆、湖北北部、河南南部和江苏南部的一些零星地区。适生区和次适生区大多有较高密度的寄主果树,为桔小实蝇的生存提供了条件。预测结果经独立验证数据的适合性测验表明,选择的最优模型具有显著的统计学意义,显示了很好的预测能力。GARP生态位模型可以解决生态学、生物地理学和环境保护方面的一系列问题,具有广泛的应用前景,为物种已知基础分布点资料的综合分析以及有害生物的适生性分析、监测和防治提供了技术平台。     

The performance of models relating species geographical distributions to climate is independent of trophic level

Species–climate ‘envelope’ models are widely used to evaluate potential climate change impacts upon species and biodiversity. Previous studies have used a variety of methods to fit models making it difficult to assess relative model performance for different taxonomic groups, life forms or trophic levels. Here we use the same climatic data and modelling approach for 306 European species representing three major taxa (higher plants, insects and birds), and including species of different life form and from four trophic levels. Goodness‐of‐fit measures showed that useful models were fitted for >96% of species, and that model performance was related neither to major taxonomic group nor to trophic level. These results confirm that such climate envelope models provide the best approach currently available for evaluating reliably the potential impacts of future climate change upon biodiversity.     

Which function describes the species–area relationship best? A review and empirical evaluation

Aim The aims of this study are to resolve terminological confusion around different types of species–area relationships (SARs) and their delimitation from species sampling relationships (SSRs), to provide a comprehensive overview of models and analytical methods for SARs, to evaluate these theoretically and empirically, and to suggest a more consistent approach for the treatment of species–area data. Location Curonian Spit in north‐west Russia and archipelagos world‐wide. Methods First, I review various typologies for SARs and SSRs as well as mathematical models, fitting procedures and goodness‐of‐fit measures applied to SARs. This results in a list of 23 function types, which are applicable both for untransformed (S) and for log‐transformed (log S) species richness. Then, example data sets for nested plots in continuous vegetation (n = 14) and islands (n = 6) are fitted to a selection of 12 function types (linear, power, logarithmic, saturation, sigmoid) both for S and for log S. The suitability of these models is assessed with Akaike’s information criterion for S and log S, and with a newly proposed metric that addresses extrapolation capability. Results SARs, which provide species numbers for different areas and have no upper asymptote, must be distinguished from SSRs, which approach the species richness of one single area asymptotically. Among SARs, nested plots in continuous ecosystems, non‐nested plots in continuous ecosystems, and isolates can be distinguished. For the SARs of the empirical data sets, the normal and quadratic power functions as well as two of the sigmoid functions (Lomolino, cumulative beta‐P) generally performed well. The normal power function (fitted for S) was particularly suitable for predicting richness values over ten‐fold increases in area. Linear, logarithmic, convex saturation and logistic functions generally were inappropriate. However, the two sigmoid models produced unstable results with arbitrary parameter estimates, and the quadratic power function resulted in decreasing richness values for large areas. Main conclusions Based on theoretical considerations and empirical results, I suggest that the power law should be used to describe and compare any type of SAR while at the same time testing whether the exponent z changes with spatial scale. In addition, one should be aware that power‐law parameters are significantly influenced by methodology.     

Seasonal Habitat Associations of the Wolverine in Central Idaho

ABSTRACT Although understanding habitat relationships remains fundamental to guiding wildlife management, these basic prerequisites remain vague and largely unstudied for the wolverine. Currently, a study of wolverine ecology conducted in Montana, USA, in the 1970s is the sole source of information on habitat requirements of wolverines in the conterminous United States. The Montana study and studies conducted in Canada and Alaska report varying degrees of seasonal differences in wolverine habitat use. This article provides an empirical assessment of seasonal wolverine habitat use by 15 wolverines (Gulo gulo) radiotracked in central Idaho, USA, in 1992–1996. We controlled for radiotelemetry error by describing the probability of each location being in a habitat cover type, producing a vector of cover type probabilities suited for resource selection analysis within a logistic regression framework. We identified variables that were important to presence of wolverines based on their strength (significance) and consistency (variability in coeff. sign) across all possible logistic regression models containing 9 habitat cover types and 3 topographic variables. We selected seasonal habitat models that incorporated those variables that were strong and consistent, producing a subset of potential models. We then ranked the models in this subset based on Akaike's Information Criterion and goodness-of-fit. Wolverines used modestly higher elevations in summer versus winter, and they shifted use of cover types from whitebark pine (Pinus albicaulis) in summer to lower elevation Douglas fir (Pseudotsuga menziezii) and lodgepole pine (Pinus contorta) communities in winter. Elevation explained use of habitat better than any other variable in both summer and winter. Grass and shrub habitats and slope also had explanatory power. Wolverines preferred northerly aspects, had no attraction to or avoidance of trails during summer, and avoided roads and ungulate winter range. These findings improve our understanding of wolverine presence by demonstrating the importance of high-elevation subalpine habitats to central Idaho wolverines.     

Novel two-phase sampling designs for studying binary outcomes

In biomedical cohort studies for assessing the association between an outcome variable and a set of covariates, usually, some covariates can only be measured on a subgroup of study subjects. An important design question is—which subjects to select into the subgroup to increase statistical efficiency. When the outcome is binary, one may adopt a case-control sampling design or a balanced case-control design where cases and controls are further matched on a small number of complete discrete covariates. While the latter achieves success in estimating odds ratio (OR) parameters for the matching covariates, similar two-phase design options have not been explored for the remaining covariates, especially the incompletely collected ones. This is of great importance in studies where the covariates of interest cannot be completely collected. To this end, assuming that an external model is available to relate the outcome and complete covariates, we propose a novel sampling scheme that oversamples cases and controls with worse goodness-of-fit based on the external model and further matches them on complete covariates similarly to the balanced design. We develop a pseudolikelihood method for estimating OR parameters. Through simulation studies and explorations in a real-cohort study, we find that our design generally leads to reduced asymptotic variances of the OR estimates and the reduction for the matching covariates is comparable to that of the balanced design.