Symmetric Bernoulli Distributions and Generalized Binomial Distributions

The generalized binomial distribution is defined as the distribution of a sum of symmetrically distributed Bernoulli random variates. Several two-parameter families of generalized binomial distributions have received attention in the literature, including the Polya urn model, the correlated binomial model and the latent variable model. Some properties and limitations of the three distributions are described. An algorithm for maximum likelihood estimation for two-parameter generalized binomial distributions is proposed. The Polya urn model and the latent variable model were found to provide good fits to sub-binomial data given by Parkes. An extension of the latent variable model to incorporate heterogeneous response probabilities is discussed.     

基于MaxEnt模型预测黄脊竹蝗在中国的适生区

为探明黄脊竹蝗Ceracris kiangsu在我国的潜在适生区,做好早期虫情监测.本研究根据267个黄脊竹蝗物种分布点,结合气候数据,采用最大熵(Maxent)模型和ArcGIS预测黄脊竹蝗在我国的适生区分布.结果表明:影响黄脊竹蝗适生区分布的主要环境变量为最干月降水量和最冷月最低温,次要环境变量为湿季降水量、最热月最高温、降水量季节性变异系数和温度年较差.预测的黄脊竹蝗高适生区、中适生区、低适生区分别占全国陆地总面积的3.0％、5.6％和10.3％,适生区主要分布在江淮流域、长江中下游地区、华南及西南等地.模型预测结果与实际调查一致性较高,能够反映真实分布情况,对科学开展黄脊竹蝗防控具有较高参考价值.     

圆柏大痣小蜂幼虫龄期测定

明确圆柏大痣小蜂Megastigmus sabinae Xu et He（1989）幼虫的最佳分龄指标、幼虫龄数与各虫龄龄期,为探明圆柏大痣小蜂幼虫期的生长规律奠定基础。本研究通过测量圆柏大痣小蜂幼虫上颚关节宽、头宽、体宽和体长4个形态指标,利用频次分布推测幼虫龄数,运用Crosby生长法则和线性回归的方法判断圆柏大痣小蜂幼虫的最佳分龄指标并验证幼虫的龄数。将最佳分龄指标作为龄期判断依据,根据测量结果对其幼虫龄期进行划分。圆柏大痣小蜂幼虫共划分为5个龄期,上颚关节宽为圆柏大痣小蜂幼虫龄期划分的最佳形态指标,各龄幼虫的历期约为30 d、200 d、30 d、30 d、15 d,共305 d,主要以2龄越冬。     

参数仪器变量估计近似分布方差的一种算法

本文对更一般的结构模型给出了参数的一种常用的仪器变量估计近似分布方差的一种算法．并且给出了未知真值x服从指数分布的例子．此算法对生物科学中统计规律的探讨有一定的应用价值．     

石山苣苔属的潜在适生区特征及其环境驱动变量

石山苣苔属(Petrocodon Hance)是著名的观赏花卉之一，但气候动荡和人类活动的强烈干扰，使其绝大部分被评估为极危(CR),至少也是易危(VU)以上。为重建末次间冰期以来石山苣苔属潜在适生区的时空变化，探讨适生区对环境变化的响应关系，为石山苣苔属的起源、地理分化研究和中国特有种质资源保护、园林开发利用提供理论指导，该研究结合120个分布记录和17个环境变量，应用优化的MaxEnt模型和地理信息技术(ArcGIS)对石山苣苔属在中国及中南半岛的适生区及其分布格局进行模拟，并基于逐步多元线性回归分析、冗余分析和蒙特卡洛检验评估影响石山苣苔属当前地理分布的主导变量。结果表明：(1)优化的MaxEnt模型的预测精度高，AUC值大于0.96;石山苣苔属当前适生区从中国西南部连续分布至越南北部，零散分布于中国中部和南部、块状分布于缅甸北部，其中以中国云贵高原南部为最佳适生区。(2)制约石山苣苔属当前地理分布的主导环境变量为最干月降雨量(bio14)、最热季度平均降雨量(bio18)、最湿季降雨量(bio16)、温度变化方差(bio4)、最冷月最低温度(bio6)、海拔(alt)。(3)在...     

On statistical energy functions for biomolecular modeling and design

Statistical energy functions are general models about atomic or residue-level interactions in biomolecules, derived from existing experimental data. They provide quantitative foundations for structural modeling as well as for structure-based protein sequence design. Statistical energy functions can be derived computationally either based on statistical distributions or based on variational assumptions. We present overviews on the theoretical assumptions underlying the various types of approaches. Theoretical considerations underlying important pragmatic choices are discussed.     

Shallow environmental gradients put inland species at risk: Insights and implications from predicting future distributions of Eucalyptus species in South Western Australia

As climate changes, tree decline in Mediterranean‐type ecosystems is increasing worldwide, often due to decreased effective precipitation and increased drought and heat stress, and has recently been observed in coastal species of the iconic Eucalyptus (Myrtaceae) genus in the biodiversity hotspot of south‐west Western Australia. To investigate how this drought‐related decline is likely to continue in the future, we used species distribution modelling techniques to generate broad‐scale predictions of future distribution patterns under three distinct projected climate change scenarios. In a moderate climate change scenario, suitable habitat for all species was predicted to decrease by, on average, 73% by the year 2100, with most receding into southern areas of their current distribution. Although the most severe Eucalyptus declines in south‐west Western Australia have been observed in near‐coastal regions, our predictions suggest that inland species are at greater risk from climate change, with six inland species predicted to lose 95% of their suitable habitat in a moderate change scenario. This is due to the shallow environmental gradients of inland regions causing larger spatial shifts of environmental envelopes, which is likely to be relevant in many regions of the world. The knowledge gained suggests that future research and conservation efforts in south‐west Western Australia and elsewhere should avoid focussing disproportionately on coastal regions for reasons of convenience and proximity to population centres, and properly address the inland region where the biggest future impacts may occur.     

揭示群落结构及其环境响应的联合物种分布模型的研究进展

物种分布模型通常用于基础生态和应用生态研究,用来确定影响生物分布和物种丰富度的因素,量化物种与非生物条件的关系,预测物种对土地利用和气候变化的反应,并确定潜在的保护区.在传统的物种分布模型中,生物的相互作用很少被纳入,而联合物种分布模型(JSDMs)作为近年提出的一种新的可行方法,可以同时考虑环境因素和生物交互作用,因而成为分析生物群落结构和种间相互作用过程的有力工具.JSDMs以物种分布模型(SDMs)为基础,通常采用广义线性回归模型建立物种对环境变量的多变量响应,以随机效应的形式获取物种间的关联,同时结合隐变量模型(LVMs),并基于Laplace近似和马尔科夫蒙脱卡罗模拟的最大似然估计或贝叶斯方法来估算模型参数.本文对JSDMs的产生及理论基础进行归纳总结,重点介绍了不同类型JSDMs的特点及其在现代生态学中的应用,阐述了JSDMs的应用前景、使用过程中存在的问题及发展方向.随着对环境因素与多物种种间关系研究的深入,JSDMs将是今后物种分布模型研究的重点.     

The MIAmaxent R package: Variable transformation and model selection for species distribution models

The widely used “Maxent” software for modeling species distributions from presence‐only data (Phillips et al., Ecological Modelling, 190, 2006, 231) tends to produce models with high‐predictive performance but low‐ecological interpretability, and implications of Maxent's statistical approach to variable transformation, model fitting, and model selection remain underappreciated. In particular, Maxent's approach to model selection through lasso regularization has been shown to give less parsimonious distribution models—that is, models which are more complex but not necessarily predictively better—than subset selection. In this paper, we introduce the MIAmaxent R package, which provides a statistical approach to modeling species distributions similar to Maxent's, but with subset selection instead of lasso regularization. The simpler models typically produced by subset selection are ecologically more interpretable, and making distribution models more grounded in ecological theory is a fundamental motivation for using MIAmaxent. To that end, the package executes variable transformation based on expected occurrence–environment relationships and contains tools for exploring data and interrogating models in light of knowledge of the modeled system. Additionally, MIAmaxent implements two different kinds of model fitting: maximum entropy fitting for presence‐only data and logistic regression (GLM) for presence–absence data. Unlike Maxent, MIAmaxent decouples variable transformation, model fitting, and model selection, which facilitates methodological comparisons and gives the modeler greater flexibility when choosing a statistical approach to a given distribution modeling problem.     

随机森林算法基本思想及其在生态学中的应用——以云南松分布模拟为例

通常来讲,生态学者对于解释生态关系、描述格局和过程、进行空间或时间预测比较感兴趣。这些工作可以通过模拟输出值(响应)与一些特征值(即解释变量)的关系来实现。然而,生态数据模拟遇到了挑战,这是因为响应变量和预测变量可能是连续变量或离散变量。需要解释的生态关系通常是非线性的,并且解释变量之间具有复杂的相互作用关系。响应变量和解释变量存在缺失值并不是不常有的现象,奇异值也经常出现在生态数据中。此外,生态学者通常希望生态模型即要易于建立又易要于解释。通常是利用多种统计方法来分析处理各种各样情景中出现的独特的生态问题,这些模型包括(多元)逻辑回归、线性模型、生存模型、方差分析等等。随机森林是一个可以处理所有这些问题的有效方法。随机森林可以用来做分类、聚类、回归和生存分析、评估变量的重要性、检测数据中的奇异值、对缺失数据进行插补等。鉴于随机森林本身在算法上的优势,将就随机森林在生态学中的应用进行总结,对建模过程进行概述,并以云南松分布模拟研究为例,对其主要功能特点进行案例展示。通过对随机森林的一般术语、概念和建模思想进行介绍,有利于读者掌握本方法的应用本质,可以预见随机森林在生态学研究中将得到更多的应用和发展。     

气候变化下寒露林蛙在中国的潜在地理分布

近几十年来,全球变暖对全球生物多样性及其地理分布产生了重要影响,特别是对气候变化敏感的两栖动物。寒露林蛙(Rana hanluica)是中国特有种,但在濒危物种红色名录中处于无危状态。为了评估寒露林蛙种群的生存现状,掌握该物种在中国的潜在分布区,以及在未来气候变化条件下适宜生境区的变化,本研究利用最大熵(MaxEnt)生态位模型和地理信息系统,对中国未来气候变化情景下(2050和2070年)寒露林蛙的适宜生境区进行识别。基于47个寒露林蛙分布位点和20个典型环境因子,建立了寒露林蛙在当前和未来气候条件下的适宜生境模型,并分析了相关的环境影响因子。结果表明: MaxEnt模型的预测准确度较高,受试者工作曲线面积值达0.993;寒露林蛙在当前气候条件下的潜在适宜生境面积为36.36万km²,潜在地理分布区域主要位于湖南省和贵州省;影响潜在地理分布的主要环境因子为最干月降水量和海拔。在未来2种典型浓度路径的气候情景下(SSP1-2.5和SSP5-8.5),寒露林蛙适宜生境区均出现不同程度的缩减,导致总适宜生境面积呈减少趋势;其高适宜生境向高纬度地区转移,其核心分布区仍以湖南省为主。     

Testing the ability of species distribution models to infer variable importance

Models of species’ distributions and niches are frequently used to infer the importance of range- and niche-defining variables. However, the degree to which these models can reliably identify important variables and quantify their influence remains unknown. Here we use a series of simulations to explore how well models can 1) discriminate between variables with different influence and 2) calibrate the magnitude of influence relative to an ‘omniscient’ model. To quantify variable importance, we trained generalized additive models (GAMs), Maxent and boosted regression trees (BRTs) on simulated data and tested their sensitivity to permutations in each predictor. Importance was inferred by calculating the correlation between permuted and unpermuted predictions, and by comparing predictive accuracy of permuted and unpermuted predictions using AUC and the continuous Boyce index. In scenarios with one influential and one uninfluential variable, models failed to discriminate reliably between variables when training occurrences were < 8–64, prevalence was > 0.5, spatial extent was small, environmental data had coarse resolution and spatial autocorrelation was low, or when pairwise correlation between environmental variables was |r| > 0.7. When two variables influenced the distribution equally, importance was underestimated when species had narrow or intermediate niche breadth. Interactions between variables in how they shaped the niche did not affect inferences about their importance. When variables acted unequally, the effect of the stronger variable was overestimated. GAMs and Maxent discriminated between variables more reliably than BRTs, but no algorithm was consistently well-calibrated vis-à-vis the omniscient model. Algorithm-specific measures of importance like Maxent's change-in-gain metric were less robust than the permutation test. Overall, high predictive accuracy did not connote robust inferential capacity. As a result, requirements for reliably measuring variable importance are likely more stringent than for creating models with high predictive accuracy.     

Current and future distribution of the deciduous shrub Hydrangea macrophylla in China estimated by MaxEnt

Climate change has a significant impact on the growth and distribution of vegetation worldwide. Hydrangea macrophylla is widely distributed and considered a model species for studying the distribution and responses of shrub plants under climate change. These results can inform decision‐making regarding shrub plant protection, management, and introduction of germplasm resources, and are of great importance for formulating ecological countermeasures to climate change in the future. We used the maximum entropy model to predict the change, scope expansion/reduction, centroid movement, and dominant climate factors that restrict the growth and distribution of H. macrophylla in China under current and future climate change scenarios. It was found that both precipitation and temperature affect the distribution of suitable habitat for H. macrophylla. Akaike information criterion (AICc) was used to select the feature combination (FC) and the regularization multiplier (RM). After the establishment of the optimal model (FC = QP, RM = 0.5), the complexity and over‐fitting degree of the model were low (delta AICc = 0, omission rate = 0.026, difference between training and testing area under the curve values = 0.0009), indicating that it had high accuracy in predicting the potential geographical distribution of H. macrophylla (area under the curve = 0.979). Overall, from the current period to future, the potential suitable habitat of this species in China expanded to the north. The greenhouse effect caused by an increase in CO₂ emissions would not only increase the area of high‐suitability habitat in Central China, but also expand the area of total suitable habitat in the north. Under the maximum greenhouse gas emission scenario (RCP8.5), the migration distance of the centroid was the longest (e.g., By 2070s, the centroids of total and highly suitable areas have shifted 186.15 km and 89.84 km, respectively).