Ecological footprint (EF): An expanded role in calculating resource productivity (RP) using China and the G20 member countries as examples

As resources become scarcer measuring resource productivity (RP) is more important. Quantifying the value of natural resources is challenging but the ecological footprint (EF) concept provides one method of uniformly describing a variety of natural resources. Current assessments of RP mainly revolve around output efficiency of resources, namely the ratio of GDP to natural resource usage.This paper develops a new method of calculating the RP by using the EF as an indicator of the natural resource input and gross domestic product (GDP) as the output in the equation of RP = GDP/EF. A regression analysis is carried out using GDP per capita and RP of China from 1997 to 2011, and a comparative analysis with the members of the G20 countries according to their RP and per capita GDP in 2008. The results indicate that RP correlates with the per capita GDP, showing that RP is a valid indicator which can be used to measure a country’s level of economic development.     

Adaptive Bayesian sum of trees model for covariate-dependent spectral analysis

This paper introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated nonparametrically using Bayesian penalized linear splines. The trees are considered to be random and fit using a Bayesian backfitting Markov chain Monte Carlo (MCMC) algorithm that sequentially considers tree modifications via reversible-jump MCMC techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior on tree splitting proportions is considered, which provides sparse estimation of covariate effects and efficient variable selection. By averaging over the posterior distribution of trees, the proposed method can recover both smooth and abrupt changes in the power spectrum across multiple covariates. Empirical performance is evaluated via simulations to demonstrate the proposed method's ability to accurately recover complex relationships and interactions. The proposed methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of other covariates.     

Ecological footprint model using the support vector machine technique

The per capita ecological footprint (EF) is one of the most widely recognized measures of environmental sustainability. It aims to quantify the Earth's biological resources required to support human activity. In this paper, we summarize relevant previous literature, and present five factors that influence per capita EF. These factors are: National gross domestic product (GDP), urbanization (independent of economic development), distribution of income (measured by the Gini coefficient), export dependence (measured by the percentage of exports to total GDP), and service intensity (measured by the percentage of service to total GDP). A new ecological footprint model based on a support vector machine (SVM), which is a machine-learning method based on the structural risk minimization principle from statistical learning theory was conducted to calculate the per capita EF of 24 nations using data from 123 nations. The calculation accuracy was measured by average absolute error and average relative error. They were 0.004883 and 0.351078% respectively. Our results demonstrate that the EF model based on SVM has good calculation performance.     

A hierarchical semiparametric regression model for combining HIV-1 phylogenetic analyses using iterative reweighting algorithms

Phylogenetic modeling is computationally challenging and most phylogeny models fit a single phylogeny to a single set of molecular sequences. Individual phylogenetic analyses are typically performed independently using publicly available software that fits a computationally intensive Bayesian model using Markov chain Monte Carlo (MCMC) simulation. We develop a Bayesian hierarchical semiparametric regression model to combine multiple phylogenetic analyses of HIV-1 nucleotide sequences and estimate parameters of interest within and across analyses. We use a mixture of Dirichlet processes as a prior for the parameters to relax inappropriate parametric assumptions and to ensure the prior distribution for the parameters is continuous. We use several reweighting algorithms for combining completed MCMC analyses to shrink parameter estimates while adjusting for data set-specific covariates. This avoids constructing a large complex model involving all the original data, which would be computationally challenging and would require rewriting the existing stand-alone software.     

Bayesian multimodel inference for geostatistical regression models

The problem of simultaneous covariate selection and parameter inference for spatial regression models is considered. Previous research has shown that failure to take spatial correlation into account can influence the outcome of standard model selection methods. A Markov chain Monte Carlo (MCMC) method is investigated for the calculation of parameter estimates and posterior model probabilities for spatial regression models. The method can accommodate normal and non-normal response data and a large number of covariates. Thus the method is very flexible and can be used to fit spatial linear models, spatial linear mixed models, and spatial generalized linear mixed models (GLMMs). The Bayesian MCMC method also allows a priori unequal weighting of covariates, which is not possible with many model selection methods such as Akaike's information criterion (AIC). The proposed method is demonstrated on two data sets. The first is the whiptail lizard data set which has been previously analyzed by other researchers investigating model selection methods. Our results confirmed the previous analysis suggesting that sandy soil and ant abundance were strongly associated with lizard abundance. The second data set concerned pollution tolerant fish abundance in relation to several environmental factors. Results indicate that abundance is positively related to Strahler stream order and a habitat quality index. Abundance is negatively related to percent watershed disturbance.     

Urban total ecological footprint forecasting by using radial basis function neural network: A case study of Wuhan city,China

Ecological footprint (EF) forecasting is essential for dynamically evaluating human impact on earth as well as for planning for a sustainable future. In this paper, a radial basis function neural network (RBFNN) model was developed to forecast the total ecological footprint (TEF) from 2006 to 2015. For a case study of Wuhan city, Hubei province in central China, per capita ecological footprint (EF) and biological capacity (BC) were calculated from 1988 to 2005. Partial least square (PLS) was used to select the important impact factors. We put the selected socio-economic factors as input and the TEF as output together to build RBFNN model and predict the development trends of the TEF in the following 10 years. Five-fold cross-validation was conducted to validate the model in the process of input selection and RBFNN model training. From the results, continuous increase of per capita EF (1988–2005) indicated stronger and stronger human effect on the district and Wuhan's ecological state is in the ecological deficit. Up to 2015, the district would have been bearing accumulative TEF of 24.782 million gha, which is near 2.5 times of that in 1988. Although the increase rate of gross domestic product (GDP) would be restricted in a lower level from 2006 to 2015, the urban ecological environmental burden could only respond to the socio-economic circumstances moderately.     

Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

宁夏生态足迹影响因子的偏最小二乘回归分析

生态足迹分析方法是一种度量区域生态可持续程度的有效方法,偏最小二乘回归法(PLS)能有效解决多元回归分析中变量的多重相关性问题,具有容易操作,相关分析精度高等特点。以宁夏为研究区域,在计算了宁夏2001—2010年人均生态足迹的基础上,应用偏最小二乘回归分析法,对影响宁夏生态足迹的各因子的重要程度进行了分析。通过变量投影重要性分析、特异点分析和预测分析,证明所得偏最小二乘回归模型具有较好的精度。研究结果为:2001—2010年,宁夏人均生态足迹由1.818103793 hm2上升至2.894958909 hm2,生态赤字由1.28352051 hm2上升至2.42316627 hm2,生态承载力由0.53458328 hm2下降至0.47179264 hm2;全区GDP、城镇居民人均生活消费支出、第二产业产值和第一产业产值是影响宁夏生态足迹的显著因子。     

Study on mapping Quantitative Trait Loci for animal complex binary traits using Bayesian-Markov chain Monte Carlo approach

It is a challenging issue to map Quantitative Trait Loci (QTL) underlying complex discrete traits,which usually show discontinuous distribution and less information,using conventional statisti-cal methods. Bayesian-Markov chain Monte Carlo (Bayesian-MCMC) approach is the key procedure in mapping QTL for complex binary traits,which provides a complete posterior distribution for QTL parameters using all prior information. As a consequence,Bayesian estimates of all interested vari-ables can be obtained straightforwardly basing on their posterior samples simulated by the MCMC algorithm. In our study,utilities of Bayesian-MCMC are demonstrated using simulated several ani-mal outbred full-sib families with different family structures for a complex binary trait underlied by both a QTL and polygene. Under the Identity-by-Descent-Based variance component random model,three samplers basing on MCMC,including Gibbs sampling,Metropolis algorithm and reversible jump MCMC,were implemented to generate the joint posterior distribution of all unknowns so that the QTL parameters were obtained by Bayesian statistical inferring. The results showed that Bayesian-MCMC approach could work well and robust under different family structures and QTL effects. As family size increases and the number of family decreases,the accuracy of the parameter estimates will be im-proved. When the true QTL has a small effect,using outbred population experiment design with large family size is the optimal mapping strategy.     

Study on mapping Quantitative Trait Loci for animal complex binary traits using Bayesian-Markov chain Monte Carlo approach

It is a challenging issue to map Quantitative Trait Loci (QTL) underlying complex discrete traits, which usually show discontinuous distribution and less information, using conventional statistical methods. Bayesian-Markov chain Monte Carlo (Bayesian-MCMC) approach is the key procedure in mapping QTL for complex binary traits, which provides a complete posterior distribution for QTL parameters using all prior information. As a consequence, Bayesian estimates of all interested variables can be obtained straightforwardly basing on their posterior samples simulated by the MCMC algorithm. In our study, utilities of Bayesian-MCMC are demonstrated using simulated several animal outbred full-sib families with different family structures for a complex binary trait underlied by both a QTL and polygene. Under the Identity-by-Descent-Based variance component random model, three samplers basing on MCMC, including Gibbs sampling, Metropolis algorithm and reversible jump MCMC, were implemented to generate the joint posterior distribution of all unknowns so that the QTL parameters were obtained by Bayesian statistical inferring. The results showed that Bayesian-MCMC approach could work well and robust under different family structures and QTL effects. As family size increases and the number of family decreases, the accuracy of the parameter estimates will be improved. When the true QTL has a small effect, using outbred population experiment design with large family size is the optimal mapping strategy.     

基于生态足迹模型的城市可持续发展定量评估与预测

生态足迹理论对城市生态系统研究、生态城市建设具有重要的指导意义.以广州市为案例,计算并分析了2001～2005年间广州生态足迹动态变化过程,结果表明2005年人均生态需求为3.95527hm²·人^-1,远大于供给,其中人们对化石燃料土地的生态需求占主要部分(72.67%).五年间人均生态足迹逐渐上升,GDP生态足迹则基本呈逐年下降趋势.用STELLA软件对人均生态足迹需求的变化进行了相关预测.结果显示:2001～2025年广州市人均生态需求呈上升趋势,且上升速度较为迅速,其原因是化石燃料土地的生态足迹需求上升较快而造成的.由此可见,化石燃料生态足迹的人均需求是影响人均生态足迹需求上升的一个关键因素.     

A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity.     

A fast algorithm for Bayesian multi-locus model in genome-wide association studies

Genome-wide association studies (GWAS) have identified a large amount of single-nucleotide polymorphisms (SNPs) associated with complex traits. A recently developed linear mixed model for estimating heritability by simultaneously fitting all SNPs suggests that common variants can explain a substantial fraction of heritability, which hints at the low power of single variant analysis typically used in GWAS. Consequently, many multi-locus shrinkage models have been proposed under a Bayesian framework. However, most use Markov Chain Monte Carlo (MCMC) algorithm, which are time-consuming and challenging to apply to GWAS data. Here, we propose a fast algorithm of Bayesian adaptive lasso using variational inference (BAL-VI). Extensive simulations and real data analysis indicate that our model outperforms the well-known Bayesian lasso and Bayesian adaptive lasso models in accuracy and speed. BAL-VI can complete a simultaneous analysis of a lung cancer GWAS data with ~3400 subjects and ~570,000 SNPs in about half a day.     

The relative performance of Bayesian and parsimony approaches when sampling characters evolving under homogeneous and heterogeneous sets of parameters

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.
© The Willi Hennig Society 2006.     

A Bayesian Approach to Detect Quantitative Trait Loci Using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) techniques are applied to simultaneously identify multiple quantitative trait loci (QTL) and the magnitude of their effects. Using a Bayesian approach a multi-locus model is fit to quantitative trait and molecular marker data, instead of fitting one locus at a time. The phenotypic trait is modeled as a linear function of the additive and dominance effects of the unknown QTL genotypes. Inference summaries for the locations of the QTL and their effects are derived from the corresponding marginal posterior densities obtained by integrating the likelihood, rather than by optimizing the joint likelihood surface. This is done using MCMC by treating the unknown QTL genotypes, and any missing marker genotypes, as augmented data and then by including these unknowns in the Markov chain cycle along with the unknown parameters. Parameter estimates are obtained as means of the corresponding marginal posterior densities. High posterior density regions of the marginal densities are obtained as confidence regions. We examine flowering time data from double haploid progeny of Brassica napus to illustrate the proposed method.     

A Variational Bayes Approach to the Analysis of Occupancy Models

Detection-nondetection data are often used to investigate species range dynamics using Bayesian occupancy models which rely on the use of Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the parameters of the model. In this article we develop two Variational Bayes (VB) approximations to the posterior distribution of the parameters of a single-season site occupancy model which uses logistic link functions to model the probability of species occurrence at sites and of species detection probabilities. This task is accomplished through the development of iterative algorithms that do not use MCMC methods. Simulations and small practical examples demonstrate the effectiveness of the proposed technique. We specifically show that (under certain circumstances) the variational distributions can provide accurate approximations to the true posterior distributions of the parameters of the model when the number of visits per site (K) are as low as three and that the accuracy of the approximations improves as K increases. We also show that the methodology can be used to obtain the posterior distribution of the predictive distribution of the proportion of sites occupied (PAO).     

The historical ecological footprint: From over-population to over-consumption

The ecological risk from over-population has been recognized since Malthus (1798). GDP growth per capita in agriculture disproved his pessimism but, since the Club of Rome and its case on Limits to Growth more recently there has been concern that there is a parallel risk from such growth in terms of ecological footprints (EF). Authors have developed a GDP/EF correlation function and calculated the ecological footprint (EF) from 10,000 B.C. till 1960, using historical statistics, with the method of backcasting (Brandes and Brooks, 2005).¹ In all major indicators growth patterns have been dominating, not only since the industrial revolution, but in the known history of mankind. From data since 1961, we calculate the correlation between GDP and the ecological footprint and have been able to determine long time data series of population, GDP, biocapacity and EF. Our findings are first: the main driver of growth and environmental degradation is not population per se, but consumption patterns and levels multiplied by the number of consumers, especially in developed economies, as the I = PAT equation recognized (Ehrlich and Holdren, 1971). In fact, as we approach to today, population, which used to be the key driver to growth and environmental degradation, becomes the least important driver, especially in the last two decades. Second: change is not incremental or linear as assumed in much mainstream economics: in line with Schumpeter's bunching and swarming and it jumps and leaps asymmetrically, as in our finding of such a leap (the 7th) between the 1930s and 1970s. Third: the dominant paradigm legitimizing growth (from the late 18th century) while already challenged by many since the Club of Rome and other reports should be revisited in terms of the concept of ‘fullness’ in the sense that while the earth in 1776 was roughly 10 per cent full, by 2008 this figure was over 150 per cent.     

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.     

基于不同需求层次的中国城镇居民消费隐含碳排放时空演变机制

正确认识不同需求水平下人均隐含碳排放量的变化,对实现低碳经济及低碳生活具有重要的参考价值。基于居民消费需求层次建立不同需求层次与隐含碳排放的对应关系,将人均隐含碳排放分解为生存型、发展型、奢侈型三类,并运用投入产出法进行核算,在对不同需求层次人均隐含碳排放的空间格局演变分析的基础上采用空间面板方法对其驱动机制进行甄别。结果显示,在全国层面,各需求层次人均隐含碳排放均呈现上升趋势,空间分布不均衡性主要体现在南北差异上,北部地区始终是各需求层次人均隐含碳排放的主要空间载体,其中多数省分生存型人均隐含碳排放上升势头较强,发展型和奢侈型的高值区在省份数量上分别呈现先减后增与逐渐增加的变化趋势;不同需求层次人均隐含碳排放水平相似的地区在空间上呈集聚分布,具有较强的"马太效应";空间面板模型结果显示技术减排是降低不同需求层次人均隐含碳排放的重要举措,而人口规模在各需求层次上的负向减排作用远小于正向的人口结构效应,宏观经济因素主要表现为增排效应,而居民消费因素的作用通道存在差异。此外,部分因素在各需求层次上存在显著空间外溢效应,应重视区域间的横向联动减排效应,做好隐含碳减排的统筹协调工作。     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.