Spatial analysis of two-species interactions

Summary In this paper, I present and discuss some methods for the analysis of univariate and bivariate spatial point pattern data. Examples of such data in ecology include x-y coordinates of organisms in mapped field plots. I illustrate the methods with analyses of data from mapped field plots on Mount St. Helens, Washington state, USA. The statistical methods I emphasize are graphical methods that rely on analysis of distances between organisms. Hypothesis testing for methods like these is easily done using Monte Carlo methods, which I also discuss. For both univariate and bivariate analyses, I find that second-order methods such as K-function plots are often preferable to first-order methods (i.e., QQ-plots). However, for multivariate analyses, these second-order methods are more sensitive to small sample sizes than first-order analyses.     

Comparing trends in cancer rates across overlapping regions

Monitoring and comparing trends in cancer rates across geographic regions or over different time periods have been major tasks of the National Cancer Institute's (NCI) Surveillance, Epidemiology, and End Results (SEER) Program as it profiles healthcare quality as well as decides healthcare resource allocations within a spatial-temporal framework. A fundamental difficulty, however, arises when such comparisons have to be made for regions or time intervals that overlap, for example, comparing the change in trends of mortality rates in a local area (e.g., the mortality rate of breast cancer in California) with a more global level (i.e., the national mortality rate of breast cancer). In view of sparsity of available methodologies, this article develops a simple corrected Z-test that accounts for such overlapping. The performance of the proposed test over the two-sample "pooled"t-test that assumes independence across comparison groups is assessed via the Pitman asymptotic relative efficiency as well as Monte Carlo simulations and applications to the SEER cancer data. The proposed test will be important for the SEER * STAT software, maintained by the NCI, for the analysis of the SEER data.     

Bayesian models and Markov chain Monte Carlo methods for protein motifs with the secondary characteristics.

Statistical methods have been developed for finding local patterns, also called motifs, in multiple protein sequences. The aligned segments may imply functional or structural core regions. However, the existing methods often have difficulties in aligning multiple proteins when sequence residue identities are low (e.g., less than 25%). In this article, we develop a Bayesian model and Markov chain Monte Carlo (MCMC) methods for identifying subtle motifs in protein sequences. Specifically, a motif is defined not only in terms of specific sites characterized by amino acid frequency vectors, but also as a combination of secondary characteristics such as hydrophobicity, polarity, etc. Markov chain Monte Carlo methods are proposed to search for a motif pattern with high posterior probability under the new model. A special MCMC algorithm is developed, involving transitions between state spaces of different dimensions. The proposed methods were supported by a simulated study. It was then tested by two real datasets, including a group of helix-turn-helix proteins, and one set from the CATH Protein Structure Classification Database. Statistical comparisons showed that the new approach worked better than a typical Gibbs sampling approach which is based only on an amino acid model.     

A Thurstonian model for quantitative genetic analysis of ranks: a Bayesian approach

A fully Bayesian method for quantitative genetic analysis of data consisting of ranks of, e.g., genotypes, scored at a series of events or experiments is presented. The model postulates a latent structure, with an underlying variable realized for each genotype or individual involved in the event. The rank observed is assumed to reflect the order of the values of the unobserved variables, i.e., the classical Thurstonian model of psychometrics. Parameters driving the Bayesian hierarchical model include effects of covariates, additive genetic effects, permanent environmental deviations, and components of variance. A Markov chain Monte Carlo implementation based on the Gibbs sampler is described, and procedures for inferring the probability of yet to be observed future rankings are outlined. Part of the model is rendered nonparametric by introducing a Dirichlet process prior for the distribution of permanent environmental effects. This can lead to potential identification of clusters of such effects, which, in some competitions such as horse races, may reflect forms of undeclared preferential treatment.     

Extending Tests of Random Effects to Assess for Measurement Invariance in Factor Models

Factor analysis models are widely used in health research to summarize hard-to-measure predictor or outcome variable constructs. For example, in the ELEMENT study, factor models are used to summarize lead exposure biomarkers which are thought to indirectly measure prenatal exposure to lead. Classic latent factor models are fitted assuming that factor loadings are constant across all covariate levels (e.g., maternal age in ELEMENT); that is, measurement invariance (MI) is assumed. When the MI is not met, measurement bias is introduced. Traditionally, MI is examined by defining subgroups of the data based on covariates, fitting multi-group factor analysis, and testing differences in factor loadings across covariate groups. In this paper, we develop novel tests of measurement invariance by modeling the factor loadings as varying coefficients, i.e., letting the factor loading vary across continuous covariate values instead of groups. These varying coefficients are estimated using penalized splines, where spline coefficients are penalized by treating them as random coefficients. The test of MI is then carried out by conducting a likelihood ratio test for the null hypothesis that the variance of the random spline coefficients equals zero. We use a Monte Carlo EM algorithm for estimation, and obtain the likelihood using Monte Carlo integration. Using simulations, we compare the Type I error and power of our testing approach and the multi-group testing method. We apply the proposed methods to summarize data on prenatal biomarkers of lead exposure from the ELEMENT study and find violations of MI due to maternal age.     

Light regime in relation to plant population geometry

A beam-emission experiment using a Monte Carlo technqiue was attempted in a computer model for the random distribution (RD) of foliage. The RD foliage consisted of 500 leaves of the same size, their individual areas being just 1/100 of the unit land area; i.e., a leaf area index (LAI) of RD foliage was equal to 5. Satisfactory agreement of light transmission under a uniform overcast sky was obtained between the observed values in the RD foliage and theoretical anticipations for any leaf inclination angle and/or leaf area density. This result demonstrated the usefulness of the Monte Carlo technique adopted in this experiment. The Monte Carlo experiment was also applied to a patch-like population. For such a foliage, additional effect of lateral incidence were worth noting in contrast with the microclimates in the corresponding infinite foliage. For every leaf inclination angle the mean light flux density below the middle stratum within a patch-like population was not further attenuate with increasing LAI.     

Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Summary Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time‐varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi‐Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi‐Markovian manner. The underlying semi‐Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi‐Markov chain represent—in the corresponding growth phase—both the influence of time‐varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi‐Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation–maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.     

The frequency of cyclic processes in biological multistate systems

Summary Cyclic processes in stochastic models of macromolecular biological systems are considered. The diagram solution of the model equations (master equation) gives rise to special functions of the rate constants, called the circuit (or one-way cycle) fluxes. As Hill has shown, these functions are the fundamental theoretical components of the operational fluxes, i.e., of the rates of reaction, of transport, of energy conversion, etc. Evidence recently has been found by Monte Carlo simulations that the circuit fluxes can be interpreted as the frequencies of circuit completions. Making use of the theory of graphs, we prove that this physical interpretation of the circuit fluxes is generally valid.     

Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics

A formal partially dynamical approach to ergodic sampling, hybrid Monte Carlo, has been adapted for the first time from its proven application in quantum chromodynamics to realistic molecular systems. A series of simulations of pancreatic trypsin inhibitor were run using temperature-rescaled molecular dynamics and hybrid Monte Carlo. It was found that simulations run using hybrid Monte Carlo equilibrated an order of magnitude faster than those run using temperature-rescaled molecular dynamics. Certain aspects of improved performance obtained using hybrid Monte Carlo are probably due to the increased efficiency with which this algorithm explores phase space. To discuss this we introduce the notion of “trajectory stiffness”. © 1993 John Wiley & Sons, Inc.     

STACRP: a secure trusted auction oriented clustering based routing protocol for MANET

In mobile ad hoc network?(MANET) nodes have a tendency to drop others’ packet to conserve its own energy. If most of the nodes in a network start to behave in this way, either a portion of the network would be isolated or total network functionality would be hampered. This behavior is known as selfishness. Therefore, selfishness mitigation and enforcing cooperation between nodes is very important to increase the availability of nodes and overall throughput and to achieve the robustness of the network. Both credit and reputation based mechanisms are used to attract nodes to forward others’ packets. In light of this, we propose a game theoretic routing model, Secure Trusted Auction oriented Clustering based Routing Protocol (STACRP), to provide trusted framework for MANET. Two auction mechanisms procurement and Dutch are used to determine the forwarding cost-per-hop for intermediate nodes. Our model is lightweight in terms of computational and communication requirements, yet powerful in terms of flexibility in managing trust between nodes of heterogeneous deployments. It manages trust locally with minimal overhead in terms of extra messages. STACRP organizes the network into 1-hop disjoint clusters and elects the most qualified and trustworthy nodes as Clusterhead. The trust is quantified with carefully chosen parameters having deep impact on network functionality. The trust model is analyzed using Markov chain and is proven as continuous time Markov chain. The security analysis of the model is analyzed to guarantee that the proposed approach achieves a secure reliable routing solution for MANETs. The proposed model have been evaluated with a set of simulations that show STACRP detects selfish nodes and enforces cooperation between nodes and achieves better throughput and packet delivery ratio with lees routing overhead compare to AODV.     

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.     

Bayesian inference for genomic imprinting underlying developmental characteristics

The identification of imprinted genes is becoming a standard procedure in searching for quantitative trait loci (QTL) underlying complex traits. When a developmental characteristic such as growth or drug response is observed at multiple time points, understanding the dynamics of gene function governing the underlying feature should provide more biological information regarding the genetic control of an organism. Recognizing that differential imprinting can be development-specific, mapping imprinted genes considering the dynamic imprinting effect can provide additional biological insights into the epigenetic control of a complex trait. In this study, we proposed a Bayesian imprinted QTL (iQTL) mapping framework considering the dynamics of imprinting effects and model multiple iQTLs with an efficient Bayesian model selection procedure. The method overcomes the limitation of likelihood-based mapping procedure, and can simultaneously identify multiple iQTLs with different gene action modes across the whole genome with high computational efficiency. An inference procedure using Bayes factors to distinguish different imprinting patterns of iQTL was proposed. Monte Carlo simulations were conducted to evaluate the performance of the method. The utility of the approach was illustrated through an analysis of a body weight growth data set in an F(2) family derived from LG/J and SM/J mouse stains. The proposed Bayesian mapping method provides an efficient and computationally feasible framework for genome-wide multiple iQTL inference with complex developmental traits.     

Binding of ligands to a one-dimensional heterogeneous lattice. I. General model for the calculation of binding isotherms by a Monte Carlo approach

A Monte Carlo method is presented to calculate equilibria for the binding of ligands to one-dimensional heteropolymers. Equivalency with other methods suitable for particular cases was verified (i.e., matrix and combinatorial methods). The principal interest of this Monte Carlo method is in its facility for adaptation to any physically conceivable binding model and that it gives access to the parameters accounting for partial binding to each different type of site. General properties of binding isotherms with excluded-site effects and relations between partial binding ratios and partial free site ratios are discussed. An effective calculation is presented for illustration of the method.     

A rigorous mathematical treatment for the excluded volume effect in Monte Carlo simulations of polymeric chains

In Monte Carlo simulations of polymeric chains, the chains are most often represented as spheres, or cylinders with flat ends. In this methodological paper, we adopt a representation of the chains as spherocylinders (continuous cylinders ending in semispheres). With such a representation the testing for chain overlap, which is the crucial step for the inclusion of the excluded volume effect in the simulations, can be defined in a rigorous geometrical framework. The treatment we then derive fulfills the following features: it allows a very simple, automatic, and exhaustive classification of all the possible configurations; and it provides a physical representation for steric hindrance effects more natural than the flat-ended cylinders. Notably, this representation avoids the introduction of artificial anisotropies in the treatments. This spherocylindrical representation is also well suited for several types of calculations that can be involved in elaborate Monte Carlo simulations.     

Markov Chain Monte Carlo Algorithm based metabolic flux distribution analysis on Corynebacterium glutamicum

MOTIVATION: Metabolic flux analysis via a (13)C tracer experiment has been achieved using a Monte Carlo method with the assumption of system noise as Gaussian noise. However, an unbiased flux analysis requires the estimation of fluxes and metabolites jointly without the restriction on the assumption of Gaussian noise. The flux distributions under such a framework can be freely obtained with various system noise and uncertainty models. RESULTS: In this paper, a stochastic generative model of the metabolic system is developed. Following this, the Markov Chain Monte Carlo (MCMC) approach is applied to flux distribution analysis. The disturbances and uncertainties in the system are simplified as truncated Gaussian multiplicative models. The performance in a real metabolic system is illustrated by the application to the central metabolism of Corynebacterium glutamicum. The flux distributions are illustrated and analyzed in order to understand the underlying flux activities in the system. AVAILABILITY: Algorithms are available upon request.     

Untangling the Tangled Bank: A Novel Method for Partitioning the Effects of Phylogenies and Traits on Ecological Networks

Understanding how evolutionary and ecological processes shape species interaction networks remains as one of the main challenges in eco-evolutionary studies. Here, we present an integrative analytical framework to partition the effects of phylogenies and functional traits on the structure of ecological networks. The method combines fuzzy set theory and matrix correlation, implemented under a Monte Carlo framework. We designed a simulation study in order to estimate the accuracy of the methods proposed here, measuring Type I Error rates. The simulation study shows that the method is accurate, i.e., incorrectly rejecting a true null hypothesis in ~5% of the cases and falling within the confidence interval. We illustrate our framework using data from a seed dispersal network from southern Brazil. Our analyses suggest that birds must have specific traits in order to consume their plant resources, and that phylogenetic resemblance has no explanatory power for species traits and species interactions in this seed-dispersal network.     

T suppressor efferent circuit which affects contact sensitivity to picryl chloride: the late-acting, second nonspecific T suppressor factor bears I-A determinants which are responsible for the I-A genetic restriction in its interaction with its target cell

The T suppressor efferent circuit in the picryl (TNP) system, which inhibits the passive transfer of contact sensitivity, involves at least two antigen-nonspecific factors. The second nonspecific T suppressor factor (ns-2) bears I-A determinants of both the alpha and the beta chain as shown by affinity chromatography on immobilized anti-I-A monoclonal antibodies. Sequential absorption shows that the determinants of the alpha and beta chain occur on the same molecular complex. No absorption was obtained with anti-I-E antibody. There are two genetic restrictions associated with ns-2--the first is in its release from the second T suppressor efferent cell (on exposure to antigen) and the second is in its inhibitory interaction with its target cell. Both are MHC restricted and matching in I-A (but not I-E, or I-J) is sufficient. The question was asked whether the I-A of the ns-2 was directly responsible for the I-A genetic restriction in its action. F1 TsF was made in (H-2k X H-2b)F1 mice by injecting picrylated parental cells intravenously and triggering the release of ns-2 with the corresponding picrylated parental cells. Both I-Ak- and I-Ab-positive ns-2 were produced and were separated by affinity chromatography on immobilized anti-I-A monoclonal antibody. The I-A phenotype of these separated ns-2 of F1 origin determines the genetic restriction in their action; i.e., I-Ak+ ns-2 only inhibits passive transfer by H-2k cells and I-Ab+ ns-2 only acts on H-2b cells. In contrast, the I-A haplotype of the picrylated cell used to induce the Ts cell which makes ns-2 is unimportant. It was concluded that the I-A on the ns-2, and not a possible recognition site for I-A, serves as a restriction element. This finding suggests that ns-2 may act directly on the I-A-restricted T cell which mediates contact sensitivity.     

Metabolic engineering under uncertainty. I: framework development

Standard bioprocess conditions have been widely applied for the microbial conversion of raw material to essential industrial products. Successful metabolic engineering (ME) strategies require a comprehensive framework to manage the complexity embedded in cellular metabolism, to explore the impacts of bioprocess conditions on the cellular responses, and to deal with the uncertainty of the physiochemical parameters. We have recently developed a computational and statistical framework that is based on Metabolic Control Analysis and uses a Monte Carlo method to simulate the uncertainty in the values of the system parameters [Wang, L., Birol, I., Hatzimanikatis, V., 2004. Metabolic control analysis under uncertainty: framework development and case studies. Biophys. J. 87(6), 3750-3763]. In this work, we generalize this framework to incorporate the central cellular processes, such as cell growth, and different bioprocess conditions, such as different types of bioreactors. The framework provides the mathematical basis for the quantification of the interactions between intracellular metabolism and extracellular conditions, and it is readily applicable to the identification of optimal ME targets for the improvement of industrial processes [Wang, L., Hatzimanikatis, V., 2005. Metabolic engineering under uncertainty. II: analysis of yeast metabolism. Submitted].     

Dosimetric characterization of an 192Ir brachytherapy source with the Monte Carlo code PENELOPE

Monte Carlo calculations are highly spread and settled practice to calculate brachytherapy sources dosimetric parameters. In this study, recommendations of the AAPM TG-43U1 report have been followed to characterize the Varisource VS2000 ¹⁹²Ir high dose rate source, provided by Varian Oncology Systems.In order to obtain dosimetric parameters for this source, Monte Carlo calculations with PENELOPE code have been carried out. TG-43 formalism parameters have been presented, i.e., air kerma strength, dose rate constant, radial dose function and anisotropy function. Besides, a 2D Cartesian coordinates dose rate in water table has been calculated. These quantities are compared to this source reference data, finding results in good agreement with them.The data in the present study complement published data in the next aspects: (i) TG-43U1 recommendations are followed regarding to phantom ambient conditions and to uncertainty analysis, including statistical (type A) and systematic (type B) contributions; (ii) PENELOPE code is benchmarked for this source; (iii) Monte Carlo calculation methodology differs from that usually published in the way to estimate absorbed dose, leaving out the track-length estimator; (iv) the results of the present work comply with the most recent AAPM and ESTRO physics committee recommendations about Monte Carlo techniques, in regards to dose rate uncertainty values and established differences between our results and reference data.The results stated in this paper provide a complete parameter collection, which can be used for dosimetric calculations as well as a means of comparison with other datasets from this source.