Testing causal structure in the biogeography of avian extinctions on oceanic islands

In their recent comment in this journal, T. M. Blackburn and colleagues called into question the use of standardized partial regression modelling (also called path analysis and structural equation modelling) when null expectations for regression coefficients are not zero. Here, we answer their critique by showing how randomization can be used to illuminate and interpret causal modelling in analyses that have non-zero expectations. Causal modelling is a powerful tool that can yield novel insights in biogeography when properly interpreted.     

Using path analysis to measure natural selection

We expand current methods for calculating selection coefficients using path analysis and demonstrate how to analyse nonlinear selection. While this incorporation is a straightforward extension of current procedures, the rules for combining these traits to calculate selection coefficients can be complex. We demonstrate our method with an analysis of selection in an experimental population of Arabidopsis thaliana consisting of 289 individuals. Multiple regression analyses found positive directional selection and positive nonlinear selection only for inflorescence height. In contrast, the path analyses also revealed positive directional selection for number of rosette leaves and positive nonlinear selection for leaf number and time of inflorescence initiation. These changes in conclusions came about because indirect selection was converted into direct selection with the change in causal structure. Path analysis has great promise for improving our understanding of natural selection but must be used with caution since coefficient estimates depend on the assumed causal structure.     

Addressing the complexity in non-linear evolution of vegetation phenological change with time-series of remote sensing images

Earth observation based monitoring of change in vegetation phenology and productivity is an important and widely used approach to quantify degradation of ecosystems due to climatic or human influences. Most satellite based studies apply linear or polynomial regression methods for trend detections. In this paper it is argued that natural systems hardly react to human or natural influences in a linear or a polynomial manner. At shorter time-scales of few decades natural systems fluctuate to a certain extent in a non-systematic manner without necessarily changing equilibrium. Finding a systematic model that describes this behavior on large spatial scales is certainly a difficult challenge. Furthermore, the manner vegetation phenology reacts to climate and to socio-economic changes is also dependent on the land cover type and on the bioclimatic region. In addition to this, traditional parametric methods require the fulfillment of several statistical criteria. In case these criteria are violated confidence intervals and significance tests of the models may be biased, even misleading. This paper proposes an alternative approach termed the Steadiness to traditional trend analysis methods. Steadiness combines the direction or tendency of the change and the net change of the time-series over a selected time period. It is a non-parametric approach which can be used without violation of statistical criteria, it can be applied on short time-series as well and results are not dependent on the significance test or on thresholds. To demonstrate differences, a time-series of satellite derived Season Length images for 24 years is analyzed for the entire European continent using linear regression and the Steadiness approach. Spatial and temporal change patterns and sensitivity to pre-processing algorithms are compared between the two methods. We show that linear regression limits the possibilities of assessing fluctuating ecosystem changes whereas the non-parametric Steadiness index more consistently confirms the fluctuating phenological change patterns.     

Meteorological driven factors of population growth in brown planthopper,Nilaparvata lugens Stål (Hemiptera: Delphacidae), in rice paddies

Growth of brown planthopper (BPH) (Nilaparvata lugens Stål) in rice paddies is mainly driven by meteorological factors under similar management practices. By analyzing field investigation and meteorological data collected from 2008 to 2013 in Nanchang, China, we show that BPH population densities and monthly growth rates (BGR) changed greatly from May to October, and these changes were closely associated with meteorological factors. Stepwise regression and path analysis indicated average speed of winds (AW) in June and lowest temperature (LT) in July were the first factors entering analysis, which interpreted 46.20% and 31.90% of their influences on BGR. While highest temperature (HT) in August and average temperature (AT) in September were the most important factors affecting BGR, but their direct path coefficients were all smaller than their corresponding indirect path coefficients. In October, relative humidity (RH), AW and number of raining days (RD) had significant effects on BGR. According to the sum of each meteorological factor entering stepwise regression analysis sequences, we found AW had the utmost effect on BPH growth, followed by AT and RH, but LT and RD least. The work demonstrate dynamic meteorological factors driving BPH growth and outbreak in rice paddies, which would facilitate the development of durable approaches for forecasting and controlling this destructive rice pest.     

通径分析理论与实践中的几个问题

本文讨论了通径分析理论与应用中常见的几个问题．分析了剩余效应对结果的决定系数的理论组成,和剩余效应与观测的自变量间存在相关时对通径分析结果的影响．     

凡纳对虾形态性状对体重的影响效果分析

选择 6月龄凡纳对虾 176只 ,测定了体长、头胸甲长、胸宽、胸高、额剑上刺数、额剑下刺数、尾长和上市体重共 8个性状 ,采用相关分析和通径分析方法 ,剔除了与体长及头胸甲长有共线性的自变量尾长 ,计算了以形态性状为自变量对体重作依变量的相关系数、通径系数、决定系数及相关指数 ,定量地分析了形态性状对体重的影响效果。结果表明 ,凡纳对虾 5个形态性状与体重的相关系数达到极显著水平 (P<0 .0 1) ;通径分析揭示了多元分析中多个自变量与依变量的真实关系 ,体长、头胸甲长、胸宽、额剑下缘刺数目对体重的通经系数达到显著水平 ,它们是直接影响体重的重要指标 ,其中体长对体重的直接影响(0 .4 2 8* * )最大 ,是影响体重的最主要因素 ,其次为头胸甲长 (0 .2 90 * * )和胸宽 (0 .2 4 5 * * ) ,额剑下缘刺数对体重的直接影响(0 .0 70 * )较小 ;胸高与体重的相关程度很大 (0 .792 3) ,但它与额剑上缘刺数对体重的直接影响都非常小 ,主要通过其他性状间接影响活体重 ,是影响体重的次要因素 ,均被剔除 ;决定系数分析结果与通径分析结果有一致的变化趋势 ;所选形态性状与体重的复相关指数为 R2 =0 .92 13,说明影响体重的主要自变量指标已经找到 ;多元回归分析建立了体长 (X1 )、头胸甲长 (X2 )、胸宽(X3)、     

Improving gene network inference by comparing expression time-series across species, developmental stages or tissues

We present a method for gene network inference and revision based on time-series data. Gene networks are modeled using linear differential equations and a generalized stepwise multiple linear regression procedure is used to recover the interaction coefficients. Our system is designed for the recovery of gene interactions concurrently in many gene regulatory networks related by a tree or a more general graph. We show how this comparative framework can facilitate the recovery of the networks and improve the quality of the solutions inferred.     

Identifying environmental signals from population abundance data using multivariate time-series analysis

Individual organisms are affected by various natural and anthropogenic environmental factors throughout their life history. This is reflected in the way population abundance fluctuates. Consequently, observed population dynamics are often produced by the superimposition of multiple environmental signals. This complicates the analysis of population time-series. Here, a multivariate time-series method called maximum autocorrelation factor analysis (MAFA) was used to extract underlying signals from multiple population time series data. The extracted signals were compared with environmental variables that were suspected to affect the populations. Finally, a simple multiple regression analysis was applied to the same data set, and the results from the regression analysis were compared with those from MAFA. The extracted signals with MAFA were strongly associated with the environmental variables, suggesting that they represent environmental factors. On the other hand, with the multiple regression analysis, one of the important signals was not identifiable, revealing the shortcoming of the conventional approach. MAFA summarizes data based on their lag-one autocorrelation. This allows the identification of underlying signals with a small effect size on population abundance during the observation. It also uses multiple time series collected in parallel; this enables us to effectively analyze short time series. In this study, annual spawning adult counts of Chinook salmon at various locations within the Klamath Basin, California, were analyzed.     

Unbalanced Repeated Measures with Random Coefficients

In a random coefficient repeated measures model, the regression coefficients relating the observations to some underlying variable, such as time, are themselves taken to be random distributed over experimental units. In this paper, a general approach to repeated measures analysis is extended to this wider model. In the model three specific error structures for the random regression coefficients have been studied, viz, the random coefficients variance matrix is considered to be (i) diagonal, (ii) proportional to the identity matrix and (iii) completely general. An example will be analyzed to illustrate the procedure.     

Using bivariate models to understand between- and within-cluster regression coefficients, with application to twin data

In the regression analysis of clustered data it is important to allow for the possibility of distinct between- and within-cluster exposure effects on the outcome measure, represented, respectively, by regression coefficients for the cluster mean and the deviation of the individual-level exposure value from this mean. In twin data, the within-pair regression effect represents association conditional on exposures shared within pairs, including any common genetic or environmental influences on the outcome measure. It has therefore been proposed that a comparison of the within-pair regression effects between monozygous (MZ) and dizygous (DZ) twins can be used to examine whether the association between exposure and outcome has a genetic origin. We address this issue by proposing a bivariate model for exposure and outcome measurements in twin-pair data. The between- and within-pair regression coefficients are shown to be weighted averages of ratios of the exposure and outcome variances and covariances, from which it is straightforward to determine the conditions under which the within-pair regression effect in MZ pairs will be different from that in DZ pairs. In particular, we show that a correlation structure in twin pairs for exposure and outcome that appears to be due to genetic factors will not necessarily be reflected in distinct MZ and DZ values for the within-pair regression coefficients. We illustrate these results in a study of female twin pairs from Australia and North America relating mammographic breast density to weight and body mass index.     

Grouped generalized estimating equations for longitudinal data analysis

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real data set.     

Autoregressive models for capture-recapture data: a Bayesian approach

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.     

A Procedure of Multiple Period Searching in Unequally Spaced Time-Series with the Lomb-Scargle Method

Periodogram analysis of unequally spaced time-series, as part of many biological rhythm investigations, is complicated. The mathematical frameworkis scattered over the literature, and the interpretation of results is often debatable. In this paper, we show that the Lomb-Scargle method is the appropriate tool for periodogram analysis of unequally spaced data. A unique procedure of multiple period searching is derived, facilitating the assessment of the various rhythms that may be present in a time-series. All relevant mathematical and statistical aspects are considered in detail, and much attention is given to the correct interpretation of results. The use of the procedure is illustrated by examples, and problems that may be encountered are discussed. It is argued that, when following the procedure of multiple period searching, we can even benefit from the unequal spacing of a time-series in biological rhythm research.     

Estimating brain functional connectivity with sparse multivariate autoregression

There is much current interest in identifying the anatomical and functional circuits that are the basis of the brain's computations, with hope that functional neuroimaging techniques will allow the in vivo study of these neural processes through the statistical analysis of the time-series they produce. Ideally, the use of techniques such as multivariate autoregressive (MAR) modelling should allow the identification of effective connectivity by combining graphical modelling methods with the concept of Granger causality. Unfortunately, current time-series methods perform well only for the case that the length of the time-series Nt is much larger than p, the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging for which relatively short time-series are measured over thousands of voxels. Methods are introduced for dealing with this situation by using sparse MAR models. These can be estimated in a two-stage process involving (i) penalized regression and (ii) pruning of unlikely connections by means of the local false discovery rate developed by Efron. Extensive simulations were performed with idealized cortical networks having small world topologies and stable dynamics. These show that the detection efficiency of connections of the proposed procedure is quite high. Application of the method to real data was illustrated by the identification of neural circuitry related to emotional processing as measured by BOLD.     

A Procedure of Multiple Period Searching in Unequally Spaced Time-Series with the Lomb–Scargle Method

Periodogram analysis of unequally spaced time-series, as part of many biological rhythm investigations, is complicated. The mathematical frameworkis scattered over the literature, and the interpretation of results is often debatable. In this paper, we show that the Lomb–Scargle method is the appropriate tool for periodogram analysis of unequally spaced data. A unique procedure of multiple period searching is derived, facilitating the assessment of the various rhythms that may be present in a time-series. All relevant mathematical and statistical aspects are considered in detail, and much attention is given to the correct interpretation of results. The use of the procedure is illustrated by examples, and problems that may be encountered are discussed. It is argued that, when following the procedure of multiple period searching, we can even benefit from the unequal spacing of a time-series in biological rhythm research.     

A PATH-ANALYTIC MODEL FOR THE MEASUREMENT OF SELECTION ON MORPHOLOGY

This paper describes a path model for the analysis of phenotypic selection upon continuous morphological characters. The path-analysis model assumes that selection occurs on unmeasured general size and shape allometry factors that summarize linear relations among sets of ontogenetically, phylogenetically, or functionally related traits. An unmeasured factor for general size is considered the only aspect of morphometric covariance matrices for which there is an a priori biological explanation. Consequently, selection coefficients are derived for each measured character by holding constant only a general size factor, rather than by using multiple regression to adjust for the full covariance matrix. Fitness is treated as an unmeasured factor with loadings, representing directional selection coefficients, computed as the covariances of the size-adjusted characters with the measured fitness indicator. The magnitudes and signs of the selection coefficients, combined with biological insight, may suggest hypotheses of selection on one or more shape allometry factors. Hypotheses of selection on general size and shape allometry factors are evaluated through cycles of measurement, analysis, and experimentation, designed to refine the path diagram depicting the covariances among the measured characters, the measured indicator of fitness, and unmeasured factors for morphology and fitness. The path-analysis and multiple-regression models were applied to data from remeasurement of Lande and Arnold's (1983) pentatomid bugs and to Bumpus's (1899) data on house sparrows. The path analysis suggested the hypothesis that variation in bug survivorship was an expression of directional selection on wing loading. Bumpus's data are consistent with a hypothesis of stabilizing selection on general size in females and directional selection for small wing size relative to body size in males.     

Estimation of 2Nes from temporal allele frequency data

We develop a new method for estimating effective population sizes, Ne, and selection coefficients, s, from time-series data of allele frequencies sampled from a single diallelic locus. The method is based on calculating transition probabilities, using a numerical solution of the diffusion process, and assuming independent binomial sampling from this diffusion process at each time point. We apply the method in two example applications. First, we estimate selection coefficients acting on the CCR5-delta 32 mutation on the basis of published samples of contemporary and ancient human DNA. We show that the data are compatible with the assumption of s = 0, although moderate amounts of selection acting on this mutation cannot be excluded. In our second example, we estimate the selection coefficient acting on a mutation segregating in an experimental phage population. We show that the selection coefficient acting on this mutation is approximately 0.43.     

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

Background  

We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks.     

Detection of Deregulated Modules Using Deregulatory Linked Path

The identification of deregulated modules (such as induced by oncogenes) is a crucial step for exploring the pathogenic process of complex diseases. Most of the existing methods focus on deregulation of genes rather than the links of the path among them. In this study, we emphasize on the detection of deregulated links, and develop a novel and effective regulatory path-based approach in finding deregulated modules. Observing that a regulatory pathway between two genes might involve in multiple rather than a single path, we identify condition-specific core regulatory path (CCRP) to detect the significant deregulation of regulatory links. Using time-series gene expression, we define the regulatory strength within each gene pair based on statistical dependence analysis. The CCRPs in regulatory networks can then be identified using the shortest path algorithm. Finally, we derive the deregulated modules by integrating the differential edges (as deregulated links) of the CCRPs between the case and the control group. To demonstrate the effectiveness of our approach, we apply the method to expression data associated with different states of Human Epidermal Growth Factor Receptor 2 (HER2). The experimental results show that the genes as well as the links in the deregulated modules are significantly enriched in multiple KEGG pathways and GO biological processes, most of which can be validated to suffer from impact of this oncogene based on previous studies. Additionally, we find the regulatory mechanism associated with the crucial gene SNAI1 significantly deregulated resulting from the activation of HER2. Hence, our method provides not only a strategy for detecting the deregulated links in regulatory networks, but also a way to identify concerning deregulated modules, thus contributing to the target selection of edgetic drugs.