Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals

The mark-resight method for estimating the size of a closed population can in many circumstances be a less expensive and less invasive alternative to traditional mark-recapture. Despite its potential advantages, one major drawback of traditional mark-resight methodology is that the number of marked individuals in the population available for resighting needs to be known exactly. In real field studies, this can be quite difficult to accomplish. Here we develop a Bayesian model for estimating abundance when sighting data are acquired from distinct sampling occasions without replacement, but the exact number of marked individuals is unknown. By first augmenting the data with some fixed number of individuals comprising a marked “super population,” the problem may then be reformulated in terms of estimating the proportion of this marked super population that was actually available for resighting. This then allows the data for the marked population available for resighting to be modeled as random realizations from a binomial logit-normal distribution. We demonstrate the use of our model to estimate the New Zealand robin (Petroica australis) population size in a region of Fiordland National Park, New Zealand. We then evaluate the performance of the proposed model relative to other estimators via a series of simulation experiments. We generally found our model to have advantages over other models when sample sizes are smaller with individually heterogeneous resighting probabilities. Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies. WinBUGS and R code to carry out these analyses is available from .     

Software sensor design based on empirical data

Software sensor design consists of building an estimate of some quantity of interest. This estimate can be used either to replace a physical measurement, or to validate an existing one. This paper provides some general guidelines for the design of software sensors based on empirical data. When the model is a priori unknown, the problem can be stated in terms of non-parametric regression or black-box modelling. Complexity control is the main difficulty in this setting. A trade-off must be achieved between two antagonist goals: the model should not be too simple, and model identification should not be too variable. We propose to address this issue by a penalization algorithm, which also estimates the relevance of input features in the identification process. A data-driven software sensor should also provide accuracy and validity indexes of its prediction. We show how these indexes can be estimated for complex non-parametric methods, such as neural networks. An application in environmental monitoring, the design of an ammonia software sensor, illustrates each step of the approach.     

Analyzing longitudinal circular data by projected normal models: a semi-parametric approach based on finite mixture models

The analysis of circular data has been recently the focus of a wide range of literature, with the general objective of providing reliable parameter estimates in the presence of heterogeneity and/or dependence among observations under a longitudinal setting. In this paper, we extend the variance component model approach to the analysis of longitudinal circular data, defining a mixed effects model for radial projections onto the circle and introducing dependence between projections through a set of correlated random coefficients. Estimation is carried out by numerical integration through an expectation-maximization algorithm without parametric assumptions upon the random coefficients distribution. The resulting model is a finite mixture of projected normal distributions. A simulation study has been carried out to investigate the behavior of the proposed model in a series of empirical situations. The proposed model is computationally parsimonious and, when applied to a real dataset on animal orientation, produces novel results.     

Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.     

基于MLP-ANN与Markov Chain的土地利用变化预测方法——以锡林郭勒盟为例

以北方草地典型地区—内蒙古锡林郭勒盟为案例区,在1995年到2000年的土地利用变化与驱动力分析的基础上,利用土地利用转换类型和驱动力模型,采用多层感知人工神经网络模型分析了各种土地利用类型未来的转换潜力;利用马尔可夫链模型,预测了2005和2010年土地利用格局。预测结果显示：高覆盖度草地减少幅度最大,中覆盖度草地减少相对和缓,高、中覆盖度草地的减少造成了未利用地和低覆盖度草地的增加,尤其是前者增加的幅度最大;从空间分布看,高覆盖度草地的减少集中在西北部地区,主要转变为中低覆盖度草地,中覆盖度草地的减少主要集中在西南部地区,其流向主要是以沙化土地为主的未利用地;案例研究表明,多层感知人工神经网络模型与马尔可夫链模型的结合与应用能够在很大程度上预测稳定驱动力作用下的土地利用变化趋势,从而为生态干预提供指导。     

Estimating the footprint of pollution on coral reefs with models of species turnover

Ecological communities typically change along gradients of human impact, although it is difficult to estimate the footprint of impacts for diffuse threats such as pollution. We developed a joint model (i.e., one that includes multiple species and their interactions with each other and environmental covariates) of benthic habitats on lagoonal coral reefs and used it to infer change in benthic composition along a gradient of distance from logging operations. The model estimated both changes in abundances of benthic groups and their compositional turnover, a type of beta diversity. We used the model to predict the footprint of turbidity impacts from past and recent logging. Benthic communities far from logging were dominated by branching corals, whereas communities close to logging had higher cover of dead coral, massive corals, and soft sediment. Recent impacts were predicted to be small relative to the extensive impacts of past logging because recent logging has occurred far from lagoonal reefs. Our model can be used more generally to estimate the footprint of human impacts on ecosystems and evaluate the benefits of conservation actions for ecosystems.     

Estimating parameters of neutral communities: from one single large to several small samples

The neutral theory of S. P. Hubbell postulates a two-scale hierarchical framework consisting of a metacommunity following the speciation-drift equilibrium characterized by the "biodiversity number" theta, and local communities following the migration-drift equilibrium characterized by the "migration rate" m (or the "fundamental dispersal number" I). While Etienne's sampling formula allows simultaneous estimation of theta and m from a single sample of a local community, its applicability to a network of (rather small) samples is questionable. We define here an alternative two-stage approach estimating theta from an adequate subset of the individuals sampled in the field (using Ewens' sampling formula) and m from community samples (using Etienne's sampling formula). We compare its results with the simultaneous estimation of theta and m (one-stage estimation), for simulated neutral samples and for 50 1-ha plots of evergreen forest in South India. The one-stage approach exhibits problems of bias and of poor differentiability between high-theta, low-m and low-theta, high-m solution domains. Conversely, the two-stage approach yielded reasonable estimates and is to be preferred when several small, scattered plots are available instead of a single large one.     

Nonparametric analysis of directional data based on data depth

Data depth is a statistical method whose primary aim is to order data of a reference space according to centrality. This is particularly appealing for directional data because no standard ordering is available, not even in the circular case. Moreover, the depth approach deals in a natural way with the peculiar aspects of directional data, i.e., the lack of a zero-direction and the wrap-around effect. The paper reviews the data depth program concentrating on typical applications to directional distributions and data. Two geometrical depth functions, simplicial depth and Tukey’s depth, are considered. Several depth-based summaries, including angular medians, depth regions and dispersion parameters are illustrated, the latter with some novel results. Examples cover symmetric and asymmetric distributions as well as real-data applications.     

Effects of sample survey design on the accuracy of classification tree models in species distribution models

We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by resubstitution rates were similar for each lichen species irrespective of the underlying sample survey form. Cross-validation estimates of prediction accuracies were lower than resubstitution accuracies for all species and both design types, and in all cases were closer to the true prediction accuracies based on the EVALUATION data set. We argue that greater emphasis should be placed on calculating and reporting cross-validation accuracy rates rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE tree models on the EVALUATION data set shows significantly lower prediction accuracy for the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic sample surveys may generate models with limited predictive capability. These differences were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in accuracy were as large as 50%. The classification tree structures also differed considerably both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on non-probabilistic sample surveys.     

Estimating preferences for outdoor recreation:: a comparison of continuous and count data demand system frameworks

Continuous and count data demand system models have emerged as attractive alternatives to the discrete choice random utility maximization models (RUMs) that currently dominate the seasonal, multi-site recreation demand literature. This paper compares the frameworks conceptually and investigates their empirical performance with a common data set. Although the two modeling approaches employ substantially different behavioral and econometric assumptions, results from a recreation application based on the 1997 Iowa Wetlands Survey suggest that qualitatively similar policy inferences arise from the competing structures.     

Colony choice in birds: models based on temporally invariant site quality

We propose two stochastic models to explain how birds choose colonies. In the resource choice model, birds settle at each site at a rate proportional to the total resources the site contains. In the reduced resource choice model, a smaller cohort of birds enters sites at a rate determined by the total resources at each, and the remaining individuals enter sites at a rate that is linearly proportional to the total number of birds already nesting at each site. Thus, a fraction of birds chooses sites based on the resources present, and the remainder are attracted to a site by the presence of other birds. Colony site quality is assumed not to vary between years. Both models result, on average, in an ideal free distribution of colony sizes if the birds' settlement rate is linearly related to the resources in a site, if resources are distributed equally among individuals within sites, and if individuals with equal resources have equal fitness. We applied these models to long-term data on colony sizes and site usage of cliff swallows in south-western Nebraska. A test of the resource choice model suggested that the swallow population as a whole did not choose sites based strictly on site quality or the total resources contained at each site. However, a test of the reduced resource choice model suggested that a smaller fraction of the individuals in each colony may have based their choice of site on local resource availability, with the remaining birds aggregating at those sites based on the number of birds already settled there. Tests of these models may provide insight into how individuals choose colony sites and why colonies vary in size.     

Testing hotspot models of lek evolution: data from three species of ungulates

Summary Hotspot models propose that leks have evolved because certain sites are associated with extremely high female encounter rates. In this paper we test five predictions of hotspot models, using data from studies of three species of lekking ungulates. As predicted, we found that lekking species generally had large female home ranges. However, in contrast to other predictions of hotspot models, ungulate leks did not occur at sites of maximum adult female density, lekking was not associated with low overall female density, and the adult sex ratio and the proportion of females that were in oestrus both differed substantially between leks and off-lek areas. Our empirical results therefore confirm recent theoretical assessments of the hotspot process, suggesting that while hotspots may help explain broad patterns of male dispersion, further mechanisms are needed to generate the extent of territory clustering seen at leks. Correspondence to: A. Balmford     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Time: a hidden constraint on the behavioural ecology of baboons

Summary Data from wild populations of baboons are used to derive functional equations relating time budget components, day journey length and group size to environmental variables. This set of equations predicts both time budgets in an independent sample of populations and the geographical distribution of baboon populations extremely well. I then use these equations to examine the maximum ecologically tolerable group size for baboons occupying different habitats. Groups which exceed this value exhibit signs of ecological stress: they spend less time resting and in social activity than would be expected for their size and environment, they are more likely to fragment during foraging and they travel faster. Populations living in poor quality (low rainfall) habitats are more likely to live in groups that are stressed in this way.     

基于生态系统管理的湿地概念生态模型研究

湿地是地球上的一种重要生态系统,基于生态系统管理理念,进行湿地保护与管理,既是湿地科学发展的必然结果.也是当前湿地保护与管理的客观需求.湿地生态模型是以湿地生态系统作为研究对象的模型,是对湿地生态系统组成、结构、过程和功能进行简化、类比或抽象,是用来反映湿地生态系统各种过程和关系的定性或定量化工具.湿地概念生态模型是各类湿地生态模型中最基本的类型,是对湿地生态系统组成及其相互关系的一种简约的定性表达,特别是指人类活动影响下湿地生态系统因子变化及其相互关系的概念性表达.湿地概念生态模型构建的主要目的是旨在识别人类活动对湿地生态系统的驱动与胁迫,这些驱动与胁迫产生的一系列生态效应,以及湿地生态系统对此所表现出来的特征.湿地生态系统是一个多层次、多因子组成的,结构复杂、功能多样、具有多向反馈和调节机制的复杂大系统或巨系统.影响系统状态或驱动系统变化的因子众多,既有来自系统内部的、也有来自系统外部的,它们对系统造成的影响往往具有联动关系和因果效应.湿地概念生态模型就是在生态系统管理理论指导下,将这些系统因子及其关系抽象并提取出来,以"驱动-胁迫-效应-表征"为主线,判断系统变化与演化背后存在的因果关系,构建能够反映系统变化与演化特征和规律的结构性关系网络模型.湿地概念生态模型研究的意义在于在科学与决策之间架起一座桥梁,为实施湿地生态保护与管理提供指导,同时为建立湿地数量化模型奠定基础.     

Exploring land use determinants in Italian municipalities: comparison of spatial econometric models

Environmental and Ecological Statistics - This study sets up a spatial econometric framework to explore the factors that best describe land consumption in Italy at the municipal level. By modelling...     

Biosecurity threats: the design of surveillance systems,based on power and risk

We consider the problem of designing a surveillance system to detect a broad range of invasive species across a heterogeneous sampling frame. We present a model to detect a range of invertebrate invasives whilst addressing the challenges of multiple data sources, stratifying for differential risk, managing labour costs and providing sufficient power of detection. We determine the number of detection devices required and their allocation across the landscape within limiting resource constraints. The resulting plan will lead to reduced financial and ecological costs and an optimal surveillance system.     

Correction to: Exploring land use determinants in Italian municipalities: comparison of spatial econometric models

Environmental and Ecological Statistics -     

Estimation of thermodynamic parameters of the biosphere, based on remote sensing

A method that allows the estimation of the thermodynamic parameters of the biosphere has been developed. It results in the subdivision of the following four phase states of the biosphere: three equilibrium states: “white planet” with high albedo and low entropy; temperate forest in winter with high entropy; and desert with high entropy; and one nonequilibrium state: the “active forests” with low entropy, high information gain and the highest exergy values. The phase shift to a nonequilibrium state happens when albedo is less than 0.2.