Conditionally autoregressive models improve occupancy analyses of autocorrelated data: An example with environmental DNA

Site occupancy‐detection models (SODMs) are statistical models widely used for biodiversity surveys where imperfect detection of species occurs. For instance, SODMs are increasingly used to analyse environmental DNA (eDNA) data, taking into account the occurrence of both false‐positive and false‐negative errors. However, species occurrence data are often characterized by spatial and temporal autocorrelation, which might challenge the use of standard SODMs. Here we reviewed the literature of eDNA biodiversity surveys and found that most of studies do not take into account spatial or temporal autocorrelation. We then demonstrated how the analysis of data with spatial or temporal autocorrelation can be improved by using a conditionally autoregressive SODM, and show its application to environmental DNA data. We tested the autoregressive model on both simulated and real data sets, including chronosequences with different degrees of autocorrelation, and a spatial data set on a virtual landscape. Analyses of simulated data showed that autoregressive SODMs perform better than traditional SODMs in the estimation of key parameters such as true‐/false‐positive rates and show a better discrimination capacity (e.g., higher true skill statistics). The usefulness of autoregressive SODMs was particularly high in data sets with strong autocorrelation. When applied to real eDNA data sets (eDNA from lake sediment cores and freshwater), autoregressive SODM provided more precise estimation of true‐/false‐positive rates, resulting in more reasonable inference of occupancy states. Our results suggest that analyses of occurrence data, such as many applications of eDNA, can be largely improved by applying conditionally autoregressive specifications to SODMs.     

An Inverse Gaussian Model for Divorce by Marriage Cohort

A model to predict the cumulative divorce trajectories of a marriage cohort is presented. It implies a defective inverse, Gaussian distribution for the lengths of exposure to marriage, of a marriage cohort. The model was fitted to published data of cohort divorce trajectories with encouraging results. The model's contribution to our understanding of marriage variables is discussed and is shown that it provides a useful basis for formulating and testing hypotheses about marriage divorce phenomena. Although the primary emphasis is on the statistical aspects of the subject, some practical implications for the marriage dissolution are considered.     

A comparison of simultaneous autoregressive and generalized least squares models for dealing with spatial autocorrelation

Aim  In their recent paper, Kissling & Carl (2008 ) recommended the spatial error simultaneous autoregressive model (SAR_err) over ordinary least squares (OLS) for modelling species distribution. We compared these models with the generalized least squares model (GLS) and a variant of SAR (SAR_vario). GLS and SAR_vario are superior to standard implementations of SAR because the spatial covariance structure is described by a semivariogram model.
Innovation  We used the complete datasets employed by Kissling & Carl (2008 ), with strong spatial autocorrelation, and two datasets in which the spatial structure was degraded by sample reduction and grid coarsening. GLS performed consistently better than OLS, SAR_err and SAR_vario in all datasets, especially in terms of goodness of fit. SAR_vario was marginally better than SAR_err in the degraded datasets.
Main conclusions  GLS was more reliable than SAR-based models, so its use is recommended when dealing with spatially autocorrelated data.     

Analyzing species distributions among temporary ponds with a permutation test approach to the join-count statistic

The Bluff Springs Sand Ponds (BSSPs) are a set of closely-spaced temporary ponds of varying hydroperiod, depth and surface area. We sampled crustacean communities of 15 ponds throughout hydroperiods in 1996 to examine species distributions among ponds. Although ponds were closely spaced (within ca. 16 ha), most species were present in subsets of the 15 ponds. We then analyzed spatial patterns of 12 crustacean species for complete spatial randomness (CSR) using join-count statistics. However, the join-count was designed for large-samples (n>50), so we further analyzed (by simulation) the join-count and a variation of the join-count (Cliff & Ord, 1981) for small-scale reliability. Simulation results revealed that neither testing distribution was reliable for n<30. We then used a permutation test to analyze species distributions and concluded that some species were distributed non-randomly. Therefore, further investigations of mechanisms causing species distributions (e.g., hydroperiod, physical/chemical conditions, biotic interactions) are clearly prescribed. The permutation test should be useful for studies of species distribution patterns among other temporary waters, and can help focus studies on causal mechanisms of distributions among small numbers of temporary aquatic habitats.     

Spatially correlated disturbances in a locally dispersing population model

The basic contact process in continuous time is studied, where instead of single occupied sites becoming empty independently, larger-scale disturbance events simultaneously remove the population from contiguous blocks of sites. Stochastic spatial simulations and pair approximations were used to investigate the model. Increasing the spatial scale of disturbance events increases spatial clustering of the population and variability in growth rates within localized regions, reduces the effective overall population density, and increases the critical reproductive rate necessary for the population to persist. Pair approximations yield a closed-form analytic expression for equilibrium population density and the critical value necessary for persistence.     

Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis

We developed a Kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis. Kalman smoothing estimates are based on complete marker trajectories. This is an improvement over other techniques, such as the global optimisation method (GOM), Kalman filtering, and local marker estimation (LME), where the estimate at each time instant is only based on part of the marker trajectories. We applied GOM, Kalman filtering, LME, and Kalman smoothing to marker trajectories from both simulated and experimental gait motion, to estimate the joint kinematics of a ten segment biomechanical model, with 21 degrees of freedom. Three simulated marker trajectories were studied: without errors, with instrumental errors, and with soft tissue artefacts (STA). Two modelling errors were studied: increased thigh length and hip centre dislocation. We calculated estimation errors from the known joint kinematics in the simulation study. Compared with other techniques, Kalman smoothing reduced the estimation errors for the joint positions, by more than 50% for the simulated marker trajectories without errors and with instrumental errors. Compared with GOM, Kalman smoothing reduced the estimation errors for the joint moments by more than 35%. Compared with Kalman filtering and LME, Kalman smoothing reduced the estimation errors for the joint accelerations by at least 50%. Our simulation results show that the use of Kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques (GOM, Kalman filtering, and LME) for both simulated, with and without modelling errors, and experimentally measured gait motion.     

四种结构类型的蛋白质设计方法

给出了以疏水一亲水模型为基础的蛋白质设计方法,该方法以物理学原理为基础,以相对熵作为优化的目标函数。对四种不同结构类型的天然结构的真实蛋白质进行了检测,分析了影响检测成功率的主要因素,结果表明,该方法是普适的,可用于对不同结构类型的蛋白质设计序列。     

Bayesian analysis of crossclassified spatial data with autocorrelation

Summary .   We address the development of methods for analyzing crossclassified categorical data that are spatially autocorrelated. We first extend the autologistic model to accommodate two variables. Two bivariate autologistic models are constructed, namely a two-step model and a symmetric model. Importance sampling is used to approximate the complex normalizing factors that arise in these models, and Markov chain Monte Carlo techniques are used to generate simulations of posterior distributions. The resulting models then are expanded to accommodate trend surfaces and directional effects. Simulation studies and real data are used to illustrate this method.     

Local environmental effects and spatial effects in macroecological studies using mapped abundance classes: the case of the rook Corvus frugilegus in Scotland

1. The study of the spatial pattern of species abundance is complicated by statistical problems, such as spatial autocorrelation of the abundance data, which lead to the confusion of environmental effects and dispersal. 2. Atlas-derived data for the rook in Scotland are used as a case study to propose an approach for assessing the likely contribution of dispersal and local environmental effects, based on a Bayesian Conditional Autoregressive (CAR) approach. 3. The availability of moist grasslands is a key factor explaining the spatial pattern of abundance. This is influenced by a combination of climatic and soil-related factors. A direct link to soil properties is for the first time reported for the wide-scale distribution of a bird species. In addition, for this species, dispersal seems to contribute significantly to the spatial pattern and produces a smoother than expected decline in abundance at the north-western edge of its distribution range. Areas where dispersal is most likely to be important are highlighted. 4. The approach described can help ecologists make more efficient use of atlas data for the investigation of the structure of species abundance, and can highlight potential sink areas at the landscape and regional scale. 5. Bayesian spatial models can deal with data autocorrelation in atlas-type data, while clearly communicating uncertainty through the estimation of the full posterior probability distribution of all parameters.     

Inverse Problem in Materials Science

Abstract

The importance of the inverse problem in materials science, that is, the determination of unknown parameters in the physico-chemical models from the experimental values is emphasized. The main attention is given to the problem of how to take into account experimental systematic errors during the inverse problem.