基于负二项和零膨胀负二项回归模型的大兴安岭地区雷击火与气象因素的关系

雷击火的发生与气象因子之间存在着密切的关系。该文选用符合大兴安岭地区林火发生数据结构的负二项(negative binomial,NB)和零膨胀负二项(zero-inflated negative binomial,ZINB)两种模型对大兴安岭林区1980–2005年间雷击火的发生与气象因素间的关系进行建模分析,并与以往研究中所使用的最小二乘(OLS)回归方法相对比。使用SAS和R-Project统计软件进行模型拟合运算,计算得出模型各参数。结果表明,NB和ZINB模型对数据拟合较好,模型内各气象因子显著性水平较高,对雷击火发生次数均具有较好的预测能力。运用AIC和Vuong等检验方法,进一步比较了NB和ZINB模型对数据的拟合水平以及模型预测水平,结果表明ZINB模型无论在数据拟合还是模型预测上都要优于NB模型。提出了大兴安岭地区林火发生与气象因子关系的最优模型。     

不同模型对拟合大兴安岭林火发生与气象因素关系的适用性

选用符合林火发生数据结构的Poisson和零膨胀Poisson(ZIP)模型对大兴安岭林区1980—2005年间林火发生与气象因素关系进行建模分析,并与普通最小二乘回归(ordinary least squares,OLS)方法的结果进行了对比分析.结果表明:OLS模型对研究区域林火发生与气象因素关系的拟合结果较差(R2=0.215);Poisson和ZIP模型的拟合效果较好,具有较好的火灾次数预测能力,且ZIP模型的预测能力高于Poisson模型.运用AIC和Vuong检验方法对Poisson和ZIP模型的拟合水平进行进一步检验,表明ZIP模型的数据拟合度优于Poisson模型.     

我国林火发生预测模型研究进展

通过文献回顾,总结了国内林火发生预测模型的研究现状,并从林火发生驱动因子、林火发生概率预测模型、林火发生频次预测模型和模型检验方法等方面进行归纳分析。得出以下结论: 1)气象、地形、植被、可燃物、人类活动等因素是影响林火发生及模型预测精度的主要驱动因子;2)林火发生概率模型中,地理加权逻辑斯蒂回归模型考虑了变量之间的空间相关性,Gompit回归模型适宜非对称结构的林火数据,随机森林模型不需要多重共线性检验,在避免过度拟合的同时提高了预测精度,是林火发生概率预测模型的优选方法之一;3)林火发生频次模型中,负二项回归模型更适合对过度离散数据进行模拟,零膨胀模型和栅栏模型可以处理林火数据中包含大量零值的问题;4)ROC检验、AIC检验、似然比检验和Wald检验方法是林火概率和频次模型的常用检验方法。林火发生预测模型研究仍是我国当前林火管理工作的重点,预测模型的选择需要依据不同地区林火数据特点。此外,构建林火预测模型时需要考虑更多的影响因素,以提高模型预测精度;未来,需要进一步探索其他数学模型在林火发生预测中的应用,不断提高林火发生预测模型的准确度。     

松栎林天然更新模拟与不确定性分析

森林天然更新的复杂性和不确定性是森林生态系统动态预测中的关键问题。本研究引入贝叶斯技术和全局敏感性分析,构建基于竞争、气候和地形3类因子的秦岭松栎林天然更新模型。备选模型形式以泊松(Poisson)模型、负二项(negative binomial,NB)模型、零膨胀泊松(zero-inflated Poisson,ZIP)模型和零膨胀负二项(zero-inflated negative binomial,ZINB)模型为基础。同时,根据模型参数传递的不确定性量化分析结果,阐释影响森林更新小概率事件的主导因子。结果表明: ZINB模型在油松和锐齿栎更新模拟中均优于其他模型。林分总断面积、光截留、坡位和生长季最低温是影响松栎林中油松天然更新的最关键因子;而林分总断面积、坡向与海拔的组合、年均温和最热季节降水量则是影响松栎林中锐齿栎天然更新的关键因子。油松更新模拟中,各类因子对模型输出的不确定性贡献率从小到大依次为: 竞争因子(25%)＜气候因子(29%)＜地形因子(46%);锐齿栎更新模拟中为: 气候因子(12%)＜竞争因子(24%)＜地形因子(64%)。油松天然更新数量对生长季最低温和最干季节降水量为正响应,对最干季节均温为负响应;锐齿栎天然更新数量对年均温、生长季最低温和最热季节降水量为正响应,对最干季节均温为负响应。基于贝叶斯技术的ZINB模型可以量化森林更新的影响因子,并解释参数传递的不确定性,是预测森林天然更新的有力工具。     

零膨胀模型在珍稀鱼类资源时空分布预测中的应用——以长江口刀鲚为例

物种分布模型在估计渔业资源栖息分布中已有广泛应用,但在珍稀鱼类资源的时空分布预测方面,数据零值过多的情况是模型选择时应考虑的重要问题,零膨胀模型是解决此类问题的有效手段。根据2009—2016年每个季度在长江口采集的刀鲚资源量与环境调查数据,运用零膨胀泊松(zero-inflated Poisson,ZIP)模型和零膨胀负二项(zero-inflated negative binomial,ZINB)模型建立了长江口刀鲚资源密度与水温等环境因子之间的关系,并运用最优模型对2017年各季节长江口刀鲚资源密度分布进行预测。结果表明:在零膨胀模型结果的第一部分,水温对刀鲚资源密度非零值的发生有显著正向影响;零膨胀模型结果的第二部分显示,经度与刀鲚资源密度的大小呈显著负相关,水温对刀鲚资源密度的大小有显著正向影响;相比最优ZIP模型,最优ZINB模型对数据拟合较好,并具有较好的预测能力;最优模型显示,刀鲚资源密度的预测值在空间上呈现自西向东逐渐减小的趋势,预测结果与实际观测值存在空间分布的一致性;在时间上呈现夏季春季秋季冬季的分布格局,这与水温的季节变化趋势一致。本研究将两种零膨胀模型应用于珍稀鱼类的时空分布预测,可为珍稀鱼类资源与环境之间的关系及其时空分布的研究提供参考。     

基于不同零模型的点格局分析

在种群空间格局研究中,定量分析格局及其形成过程已成为生态学家的主要目标。在量化分析的众多方法中,点格局分析是最常用的方法,而在选择零模型时,完全空间随机模型以外的复杂零模型很少使用,实际上,这些零模型可能有助于认识格局的内在特征。为此,我们在研究实例中,选择完全空间随机模型(complete spatial randomness)、泊松聚块模型(Poisson cluster process)和嵌套双聚块模型(nested double-cluster process)对典型草原处于不同恢复演替阶段的羊草(Leymus chinensis)种群空间格局进行了分析。结果发现:完全空间随机模型仅能检测种群在不同尺度下的格局类型;而通过泊松聚块模型和嵌套双聚块模型检验表明,在恢复演替的初期阶段,羊草种群在小尺度范围内偏离泊松聚块模型,而在整个取样范围内完全符合嵌套双聚块模型;随着恢复演替时间的推移,在恢复演替的后期,在整个取样尺度上,羊草种群与泊松聚块模型相吻合。这是很有意义的生态学现象。这一实例表明在应用点格局分析种群空间格局时,仅通过完全空间随机模型的检验来分析格局特征,或许很难论证复杂的生态过程,而选择一些完全空间随机模型以外的较复杂的零模型,可能发现一些有价值的生态学现象,对揭示格局掩盖下的内在机制有所裨益。     

长白山暗针叶林群落物种多样性维持机制

植物群落物种多样性维持机制一直是生态学研究的热点话题,其中生态位理论和中性理论是被普遍接受的两种理论观点,但是目前关于生态位理论和中性理论在群落物种多样性维持中的相对重要性还没有统一定论。基于长白山暗针叶林群落数据,采用单物种-面积关系模型探究特定树种对邻域物种丰富度的影响,并借助同质性和异质性泊松零模型检验其显著性。(1)群落水平上,在3—15 m空间尺度上,促进种占据优势地位,在>15 m空间尺度上,中性种逐渐取代促进种起主导作用,抑制种比例较低,并且随着空间尺度变化幅度不大。(2)物种水平上,采用同质性泊松零模型检验树种对邻域物种丰富度的影响,臭冷杉、花楷槭、青楷槭在0—20 m空间尺度上对邻域物种丰富度增加起促进作用,黄花落叶松、鱼鳞云杉在0—20 m空间尺度上抑制了邻域物种丰富度增加。花楸树、黑桦和硕桦在全部研究尺度上表现为中性种,髭脉槭、大青杨、红松等在不同研究尺度上表现为不同的作用效果。剔除了生境过滤作用的异质性泊松零模型检验结果与同质性泊松零模型结果差异不显著,表明研究样地内生境过滤作用对多样性格局形成影响不大,各树种间的相互作用对群落物种组成影响较大,进一步证明...     

基于零模型的宁夏荒漠草原优势种群点格局分析

植物种群空间分布格局是多种生态过程综合作用的结果。明确植物优势种群个体的空间分布格局与形成机制有助于认识种群生态适应对策与群落多样性维持机制。以宁夏荒漠草原优势种群蒙古冰草、短花针茅、牛枝子和牛心朴子为研究对象,采用完全空间随机零模型分析其种群空间分布格局特征,并通过异质泊松零模型与泊松聚块零模型探讨生境异质性、扩散限制等因子在其空间分布格局形成过程中的作用。结果显示:(1)完全空间随机零模型下,4个物种在4 m尺度范围内表现为聚集分布,随尺度增大,逐渐过渡到随机分布和均匀分布。(2)在排除生境异质性的异质泊松零模型下,蒙古冰草种群在整个研究尺度上表现为随机分布;牛枝子、短花针茅和牛心朴子种群仅分别在0—0.2、0.1—0.4 m与0—0.2 m尺度范围内发生偏离,表现为均匀分布与聚集分布,其他尺度均为随机分布。(3)在排除扩散限制的泊松聚块零模型下,所研究种群均表现为随机分布。综上,荒漠草原优势种群在小尺度范围内主要表现为聚集分布;生境异质性与扩散限制均是驱动其空间分布格局形成的重要因子,相对而言,小尺度空间范围内扩散限制的作用更为显著。     

塔里木荒漠河岸林不同生境群落物种多度分布格局

为解释塔里木荒漠河岸林群落构建和物种多度分布格局形成的机理, 本文以塔里木荒漠河岸林2个不同生境(沙地、河漫滩) 4 ha固定监测样地为研究对象, 基于两样地物种调查数据, 采用统计模型(对数级数模型、对数正态模型、泊松对数正态分布模型、Weibull分布模型)、生态位模型(生态位优先占领模型、断棍模型)和中性理论模型(复合群落零和多项式模型、Volkov模型)拟合荒漠河岸林群落物种多度分布, 并用K-S检验与赤池信息准则(AIC)筛选最优拟合模型。结果表明: (1)随生境恶化(土壤水分降低), 植物物种多度分布曲线变化减小, 群落物种多样性、多度和群落盖度降低, 常见种数减少。(2)选用的3类模型均可拟合荒漠河岸林不同生境群落物种多度分布格局, 统计模型和中性理论模型拟合效果均优于生态位模型。复合群落零和多项式模型对远离河岸的干旱沙地生境拟合效果最好; 对数正态模型和泊松对数正态模型对洪水漫溢的河漫滩生境拟合效果最优; 中性理论模型与统计模型无显著差异。初步推断中性过程在荒漠河岸林群落构建中发挥着主导作用, 但模型拟合结果只能作为推断群落构建过程的必要非充分条件, 不能排除生态位过程的潜在作用。     

广东南岭20 hm2样地华南五针松空间分布与生境特征研究

华南五针松(Pinus kwangtungensis)是中国特有种和二级保护植物,因环境变化和人为干扰而导致其生境受损、种群逐渐衰退。为了解华南五针松的种群现状、空间分布格局和生境特征,该研究在广东南岭国家级自然保护区建立了20 hm²的永久监测样地,对样地内胸径≥1 cm的木本植物进行监测,测量土壤、地形等多种环境因子,并采用径级分析预测种群的发展趋势和空间点格局(L function)方法分析个体的空间分布及建立零膨胀泊松(Zero-inflated Poisson,ZIP)回归模型,探讨影响个体分布的重要环境因子。结果表明:(1)华南五针松径级分布近似“钟型”(“bell-shaped”),小径级的个体数量较少,种群更新受限制; 华南五针松偏好海拔较高且地形陡峭的山坡和山脊,呈现较强的生境特异性。(2)空间点格局分析结果显示,个体为显著的聚集分布,其分布格局主要由扩散限制和生境异质性导致。(3)ZIP的结果显示,华南五针松分布的区域(0到1),土壤铵态氮和速效钾含量较高,有机质含量低; 多种环境因子对其多度产生影响(1到N),多度与海拔、物种多样性和平均胸径虽为正相关关系,但与树高、铵态氮、总磷和总钾含量为负相关关系。综上认为,不稳定的径级结构及聚集分布导致的种内竞争将加速其种群的衰退,应重点保护高海拔及土壤养分较低的生境,并减少人为干扰维持其原生生境,该研究结果可用于指导华南五针松的保护和恢复。     

Bootstrap tests for overdispersion in a zero-inflated Poisson regression model

Ridout, Hinde, and Demétrio (2001, Biometrics 57, 219-223) derived a score test for testing a zero-inflated Poisson (ZIP) regression model against zero-inflated negative binomial (ZINB) alternatives. They mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases. To remedy this problem, a parametric bootstrap method is proposed. It is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis.     

The k-ZIG: Flexible Modeling for Zero-Inflated Counts

Summary Many applications involve count data from a process that yields an excess number of zeros. Zero-inflated count models, in particular, zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, along with Poisson hurdle models, are commonly used to address this problem. However, these models struggle to explain extreme incidence of zeros (say more than 80%), especially to find important covariates. In fact, the ZIP may struggle even when the proportion is not extreme. To redress this problem we propose the class of k-ZIG models. These models allow more flexible modeling of both the zero-inflation and the nonzero counts, allowing interplay between these two components. We develop the properties of this new class of models, including reparameterization to a natural link function. The models are straightforwardly fitted within a Bayesian framework. The methodology is illustrated with simulated data examples as well as a forest seedling dataset obtained from the USDA Forest Service's Forest Inventory and Analysis program.     

Using spotlight observations to predict resource selection and abundance for white-tailed deer

Spotlight surveys for white-tailed deer (Odocoileus virginianus) can yield large presence-only datasets applicable to a variety of resource selection modeling procedures. By understanding how populations distribute according to a given resource for a reference area, density and abundance can be predicted across new areas assuming the relationship between habitat quality (measured by an index of selection) and species distribution are equivalent. Habitat-based density estimators have been applied to wildlife species and are useful for addressing conservation and management concerns. Although achieving reliable population estimates is a primary goal for spotlighting studies, presence-only models have yet to be applied to spotlight data for estimating habitat selection and abundance for deer. From 2012 to 2017, we conducted spring spotlight surveys in each of 99 counties in Iowa, USA, and collected spatial locations for 20,149 groups of deer (n = 71,323 individuals). We used a resource selection function (RSF) based on deer locations to predict the relative probability of use for deer at the population level and to estimate statewide abundance. The number of deer observed statewide increased significantly with increasing RSF value for all years and the mean RSF value along survey transects explained 59% of the variability in county-level deer counts, indicating that a functional response between habitat quality and deer distribution existed at landscape scales. We applied our RSF to a habitat-based density estimator (extrapolation) and zero-inflated Poisson (ZIP) and negative binomial (ZINB) count models to predict statewide abundance from spotlight counts. Population estimates for 2012 were variable, indicating that atypical weather conditions may affect spotlight counts and population estimates in some years. For 2013–2017, we predicted a mean population of 439,129 (95% CI ∼ ± 55,926), 440,360 (∼ ± 43,676), and 465,959 (∼ ± 51,242) deer across years for extrapolation, ZIP, and ZINB models, respectively. Estimates from all models were not significantly different than estimates from an existing deer population accounting model in Iowa for 2013 and 2016, and differed by <76,000 deer for all models from 2013–2017. Extrapolation and ZIP models performed similarly and differed by <2,897 deer across all years, whereas ZINB models showed inconsistencies in model convergence and precision of estimates. Our results indicate that presence-only models are capable of producing reliable and precise estimates of resource selection and abundance for deer at broad landscape scales in Iowa and provide a tool for estimating deer abundance in a spatially explicit manner. © 2019 The Wildlife Society.     

Modeling Forest Fire Occurrences Using Count-Data Mixed Models in Qiannan Autonomous Prefecture of Guizhou Province in China

Forest fires can cause catastrophic damage on natural resources. In the meantime, it can also bring serious economic and social impacts. Meteorological factors play a critical role in establishing conditions favorable for a forest fire. Effective prediction of forest fire occurrences could prevent or minimize losses. This paper uses count data models to analyze fire occurrence data which is likely to be dispersed and frequently contain an excess of zero counts (no fire occurrence). Such data have commonly been analyzed using count data models such as a Poisson model, negative binomial model (NB), zero-inflated models, and hurdle models. Data we used in this paper is collected from Qiannan autonomous prefecture of Guizhou province in China. Using the fire occurrence data from January to April (spring fire season) for the years 1996 through 2007, we introduced random effects to the count data models. In this study, the results indicated that the prediction achieved through NB model provided a more compelling and credible inferential basis for fitting actual forest fire occurrence, and mixed-effects model performed better than corresponding fixed-effects model in forest fire forecasting. Besides, among all meteorological factors, we found that relative humidity and wind speed is highly correlated with fire occurrence.     

Zero-inflated Poisson and binomial regression with random effects: a case study

In a 1992 Technometrics paper, Lambert (1992, 34, 1-14) described zero-inflated Poisson (ZIP) regression, a class of models for count data with excess zeros. In a ZIP model, a count response variable is assumed to be distributed as a mixture of a Poisson(lambda) distribution and a distribution with point mass of one at zero, with mixing probability p. Both p and lambda are allowed to depend on covariates through canonical link generalized linear models. In this paper, we adapt Lambert's methodology to an upper bounded count situation, thereby obtaining a zero-inflated binomial (ZIB) model. In addition, we add to the flexibility of these fixed effects models by incorporating random effects so that, e.g., the within-subject correlation and between-subject heterogeneity typical of repeated measures data can be accommodated. We motivate, develop, and illustrate the methods described here with an example from horticulture, where both upper bounded count (binomial-type) and unbounded count (Poisson-type) data with excess zeros were collected in a repeated measures designed experiment.