Modeling the presence probability of invasive plant species with nonlocal dispersal

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.     

Tackling the population genetics of clonal and partially clonal organisms

Many clonal organisms experience occasional events of sexual recombination, with profound consequences for their population dynamics and evolutionary trajectories. With the recent development of polymorphic genetic markers and new statistical methods, we now have an unprecedented ability to detect recombination in organisms that are thought to reproduce strictly, or essentially asexually. However, it is not always obvious which methodology to apply. Consequently, biologists might decide how to analyse their data without clear guidelines. Here, we discuss the available methods, focusing on those best suited when working with limited genetic information, such as a few genetic markers or DNA sequences. We conclude by commenting on the prospects offered by some recent conceptual advances and the access to high throughput technologies in an increasing number of model organisms.     

Statistical Analysis of the Recovery of Coliform Organisms on Gelman and Millipore Membrane Filters

The recovery of coliform organisms on Gelman and Millipore membranes was analyzed by using both a model I (which assumes no error in the x variable) and model II (which allows errors in both the variables) regression analysis. The two models afford estimates of the slope which agree within their 95% confidence limits. Using equations derived in this paper, the model II confidence limits on the intercept are obtained. This range does not include the model I intercept limits, thereby demonstrating the differences between results from an incorrect (model I) and correct (model II) approach. In addition, fecal coliform show no differences in response to the two membranes, whereas total coliform exhibit higher recoveries on Gelman membranes.     

Evaluation of HIV-1 kinetic models using quantitative discrimination analysis

MOTIVATION: Since the identification of human immunodeficiency virus (HIV) over twenty years ago, many mathematical models of HIV dynamics have been proposed. The purpose of this study was to evaluate intracellular and intercellular scale HIV models that best described the dynamics of viral and cell titers of a person, where parameters were determined using typically available patient data. In this case, 'best' was defined as the model most capable of describing experimental patient data and was determined by Bayesian-based model discrimination analysis and the ability to provide realistic results. RESULTS: Twenty models of HIV-1 viral dynamics were initially evaluated to determine whether parameters could be obtained from readily available clinical data from established HIV-1 patients with stable disease. Based on this analysis, three models were chosen for further examination and comparison. Parameters were estimated using experimental data from a cohort of 338 people monitored for up to 2484 days. The models were evaluated using a Bayesian technique to determine which model was most probable. The model ultimately selected as most probable was overwhelmingly favored relative to the remaining two models, and it accounted for uninfected cells, infected cells and cytotoxic T lymphocyte dynamics. The authors developed a fourth model for comparison purposes by combining the features of the original three models. Parameters were estimated for the new model and the statistical analysis was repeated for all four models. The model that was initially favored was selected again upon model discrimination analysis. CONTACT: srivasta@engr.uconn.edu.     

Unravelling the dynamics of organisms in a changing world using ecological modelling

Understanding and predicting the dynamics of organisms is a central objective in ecology and conservation biology, and modelling provides a solution to tackling this problem. However, the complex nature of ecological systems means that for a thorough understanding of ecological dynamics at hierarchical scales, a set of modeling approaches need to be adopted. This review illustrates how modelling approaches can be used to understand the dynamics of organisms in applied ecological problems, focussing on mechanistic models at a local scale and statistical models at a broad scale. Mechanistic models incorporate ecological processes explicitly and thus are likely to be robust under novel conditions. Models based on behavioural decisions by individuals represent a typical example of the successful application of mechanistic models to applied problems. Considering the data-hungry nature of such mechanistic models, model complexity and parameterisation need to be explored further for a quick and widespread implementation of this model type. For broad-scale phenomena, statistical models play an important role in dealing with problems that are often inherent in data. Examples include models for quantifying population trends from long-term, large-scale data and those for comparative methods of extinction risk. Novel statistical approaches also allow mechanistic models to be parameterised using readily obtained data at a macro scale. In conclusion, the complementary use and improvement of multiple model types, the increased use of novel model parameterisation, the examination of model transferability and the achievement of wider biodiversity information availability are key challenges for the effective use of modelling in applied ecological problems.     

Unlocking the potential of survival data for model organisms through a new database and online analysis platform: SurvCurv

Lifespan measurements, also called survival records, are a key phenotype in research on aging. If external hazards are excluded, aging alone determines the mortality in a population of model organisms. Understanding the biology of aging is highly desirable because of the benefits for the wide range of aging‐related diseases. However, it is also extremely challenging because of the underlying complexity. Here, we describe SurvCurv, a new database and online resource focused on model organisms collating survival data for storage and analysis. All data in SurvCurv are manually curated and annotated. The database, available at www.ebi.ac.uk/thornton-srv/databases/SurvCurv/ , offers various functions including plotting, Cox proportional hazards analysis, mathematical mortality models and statistical tests. It facilitates reanalysis and allows users to analyse their own data and compare it with the largest repository of model‐organism data from published experiments, thus unlocking the potential of survival data and demographics in model organisms.     

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.     

Novel methods improve prediction of species' distributions from occurrence data

Prediction of species' distributions is central to diverse applications in ecology, evolution and conservation science. There is increasing electronic access to vast sets of occurrence records in museums and herbaria, yet little effective guidance on how best to use this information in the context of numerous approaches for modelling distributions. To meet this need, we compared 16 modelling methods over 226 species from 6 regions of the world, creating the most comprehensive set of model comparisons to date. We used presence-only data to fit models, and independent presence-absence data to evaluate the predictions. Along with well-established modelling methods such as generalised additive models and GARP and BIOCLIM, we explored methods that either have been developed recently or have rarely been applied to modelling species' distributions. These include machine-learning methods and community models, both of which have features that may make them particularly well suited to noisy or sparse information, as is typical of species' occurrence data. Presence-only data were effective for modelling species' distributions for many species and regions. The novel methods consistently outperformed more established methods. The results of our analysis are promising for the use of data from museums and herbaria, especially as methods suited to the noise inherent in such data improve.     

Mathematical determination of coiled shell volumes and surface areas

Mathematical models of shells enable researchers to estimate the maximum possible sizes of organisms that once occupied fossil shells. In this study, a whorl-by-whorl method of determining coiled shell volumes and surface areas is introduced. The whorl-by-whorl analysis yielded results that were more accurate than those obtained from a model that assumes isometric growth, when both were used to calculate volumes of gastropod shells. The whorl-by-whorl method is more laborious, but it is better suited for the analysis of shells exhibiting allometric variation than are methods that use models of isometric growth.     

SelSim: a program to simulate population genetic data with natural selection and recombination

SUMMARY: SelSim is a program for Monte Carlo simulation of DNA polymorphism data for a recombining region within which a single bi-allelic site has experienced natural selection. SelSim allows simulation from either a fully stochastic model of, or deterministic approximations to, natural selection within a coalescent framework. A number of different mutation models are available for simulating surrounding neutral variation. The package enables a detailed exploration of the effects of different models and strengths of selection on patterns of diversity. This provides a tool for the statistical analysis of both empirical data and methods designed to detect natural selection. AVAILABILITY: http://www.stats.ox.ac.uk/mathgen/software.html. SUPPLEMENTARY INFORMATION: http://www.stats.ox.ac.uk/mathgen/software.html.     

Interpreting Statistical Evidence with Empirical Likelihood Functions

There has been growing interest in the likelihood paradigm of statistics, where statistical evidence is represented by the likelihood function and its strength is measured by likelihood ratios. The available literature in this area has so far focused on parametric likelihood functions, though in some cases a parametric likelihood can be robustified. This focused discussion on parametric models, while insightful and productive, may have left the impression that the likelihood paradigm is best suited to parametric situations. This article discusses the use of empirical likelihood functions, a well‐developed methodology in the frequentist paradigm, to interpret statistical evidence in nonparametric and semiparametric situations. A comparative review of literature shows that, while an empirical likelihood is not a true probability density, it has the essential properties, namely consistency and local asymptotic normality that unify and justify the various parametric likelihood methods for evidential analysis. Real examples are presented to illustrate and compare the empirical likelihood method and the parametric likelihood methods. These methods are also compared in terms of asymptotic efficiency by combining relevant results from different areas. It is seen that a parametric likelihood based on a correctly specified model is generally more efficient than an empirical likelihood for the same parameter. However, when the working model fails, a parametric likelihood either breaks down or, if a robust version exists, becomes less efficient than the corresponding empirical likelihood.     

All your base: a fast and accurate probabilistic approach to base calling

The accuracy of base calls produced by Illumina sequencers is adversely affected by several processes, with laser cross-talk and cluster phasing being prominent. We introduce an explicit statistical model of the sequencing process that generalizes current models of phasing and cross-talk and forms the basis of a base calling method which improves on the best existing base callers, especially when comparing the number of error-free reads. The novel algorithms implemented in All Your Base (AYB) are comparable in speed to other competitive base-calling methods, do not require training data and are designed to be robust to gross errors, producing sensible results where other techniques struggle. AYB is available at http://www.ebi.ac.uk/goldman-srv/AYB/.     

Statistical analyses of repeated measures in physiological research: a tutorial

Experimental designs involving repeated measurements on experimental units are widely used in physiological research. Often, relatively many consecutive observations on each experimental unit are involved and the data may be quite nonlinear. Yet evidently, one of the most commonly used statistical methods for dealing with such data sets in physiological research is the repeated-measurements ANOVA model. The problem herewith is that it is not well suited for data sets with many consecutive measurements; it does not deal with nonlinear features of the data, and the interpretability of the model may be low. The use of inappropriate statistical models increases the likelihood of drawing wrong conclusions. The aim of this article is to illustrate, for a reasonably typical repeated-measurements data set, how fundamental assumptions of the repeated-measurements ANOVA model are inappropriate and how researchers may benefit from adopting different modeling approaches using a variety of different kinds of models. We emphasize intuitive ideas rather than mathematical rigor. We illustrate how such models represent alternatives that 1) can have much higher interpretability, 2) are more likely to meet underlying assumptions, 3) provide better fitted models, and 4) are readily implemented in widely distributed software products.     

Efficient exact maximum a posteriori computation for bayesian SNP genotyping in polyploids

The problem of genotyping polyploids is extremely important for the creation of genetic maps and assembly of complex plant genomes. Despite its significance, polyploid genotyping still remains largely unsolved and suffers from a lack of statistical formality. In this paper a graphical bayesian model for SNP genotyping data is introduced. This model can infer genotypes even when the ploidy of the population is unknown. We also introduce an algorithm for finding the exact maximum a posteriori genotype configuration with this model. This algorithm is implemented in a freely available web-based software package SuperMASSA. We demonstrate the utility, efficiency, and flexibility of the model and algorithm by applying them to two different platforms, each of which is applied to a polyploid data set: Illumina GoldenGate data from potato and Sequenom MassARRAY data from sugarcane. Our method achieves state-of-the-art performance on both data sets and can be trivially adapted to use models that utilize prior information about any platform or species.     

应用神经网络和多元回归技术预测森林产量

应用传统统计技术常会因样本小和测量数据不符某种分布而受到限制。本文评价一种前馈型神经网络算法以预测落叶阔叶林产量。另外,还介绍一种由定性变为定量的数据变换方法,以用相对小的样本建立多元回归预测模型。数据变换方法有助于改善多元回归模型的预测效果。在本实验的条件下,研究结果表明神经网络技术能够产生最好的预测效果.