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.     

Projecting future expansion of invasive species: comparing and improving methodologies for species distribution modeling

Modeling the distributions of species, especially of invasive species in non‐native ranges, involves multiple challenges. Here, we developed some novel approaches to species distribution modeling aimed at reducing the influences of such challenges and improving the realism of projections. We estimated species–environment relationships for Parthenium hysterophorus L. (Asteraceae) with four modeling methods run with multiple scenarios of (i) sources of occurrences and geographically isolated background ranges for absences, (ii) approaches to drawing background (absence) points, and (iii) alternate sets of predictor variables. We further tested various quantitative metrics of model evaluation against biological insight. Model projections were very sensitive to the choice of training dataset. Model accuracy was much improved using a global dataset for model training, rather than restricting data input to the species’ native range. AUC score was a poor metric for model evaluation and, if used alone, was not a useful criterion for assessing model performance. Projections away from the sampled space (i.e., into areas of potential future invasion) were very different depending on the modeling methods used, raising questions about the reliability of ensemble projections. Generalized linear models gave very unrealistic projections far away from the training region. Models that efficiently fit the dominant pattern, but exclude highly local patterns in the dataset and capture interactions as they appear in data (e.g., boosted regression trees), improved generalization of the models. Biological knowledge of the species and its distribution was important in refining choices about the best set of projections. A post hoc test conducted on a new Parthenium dataset from Nepal validated excellent predictive performance of our ‘best’ model. We showed that vast stretches of currently uninvaded geographic areas on multiple continents harbor highly suitable habitats for parthenium. However, discrepancies between model predictions and parthenium invasion in Australia indicate successful management for this globally significant weed.     

Global simulation of bioenergy crop productivity: analytical framework and case study for switchgrass

A global energy crop productivity model that provides geospatially explicit quantitative details on biomass potential and factors affecting sustainability would be useful, but does not exist now. This study describes a modeling platform capable of meeting many challenges associated with global‐scale agro‐ecosystem modeling. We designed an analytical framework for bioenergy crops consisting of six major components: (i) standardized natural resources datasets, (ii) global field‐trial data and crop management practices, (iii) simulation units and management scenarios, (iv) model calibration and validation, (v) high‐performance computing (HPC) simulation, and (vi) simulation output processing and analysis. The HPC‐Environmental Policy Integrated Climate (HPC‐EPIC) model simulated a perennial bioenergy crop, switchgrass (Panicum virgatum L.), estimating feedstock production potentials and effects across the globe. This modeling platform can assess soil C sequestration, net greenhouse gas (GHG) emissions, nonpoint source pollution (e.g., nutrient and pesticide loss), and energy exchange with the atmosphere. It can be expanded to include additional bioenergy crops (e.g., miscanthus, energy cane, and agave) and food crops under different management scenarios. The platform and switchgrass field‐trial dataset are available to support global analysis of biomass feedstock production potential and corresponding metrics of sustainability.     

Hotspots of uncertainty in land‐use and land‐cover change projections: a global‐scale model comparison

Model‐based global projections of future land‐use and land‐cover (LULC) change are frequently used in environmental assessments to study the impact of LULC change on environmental services and to provide decision support for policy. These projections are characterized by a high uncertainty in terms of quantity and allocation of projected changes, which can severely impact the results of environmental assessments. In this study, we identify hotspots of uncertainty, based on 43 simulations from 11 global‐scale LULC change models representing a wide range of assumptions of future biophysical and socioeconomic conditions. We attribute components of uncertainty to input data, model structure, scenario storyline and a residual term, based on a regression analysis and analysis of variance. From this diverse set of models and scenarios, we find that the uncertainty varies, depending on the region and the LULC type under consideration. Hotspots of uncertainty appear mainly at the edges of globally important biomes (e.g., boreal and tropical forests). Our results indicate that an important source of uncertainty in forest and pasture areas originates from different input data applied in the models. Cropland, in contrast, is more consistent among the starting conditions, while variation in the projections gradually increases over time due to diverse scenario assumptions and different modeling approaches. Comparisons at the grid cell level indicate that disagreement is mainly related to LULC type definitions and the individual model allocation schemes. We conclude that improving the quality and consistency of observational data utilized in the modeling process and improving the allocation mechanisms of LULC change models remain important challenges. Current LULC representation in environmental assessments might miss the uncertainty arising from the diversity of LULC change modeling approaches, and many studies ignore the uncertainty in LULC projections in assessments of LULC change impacts on climate, water resources or biodiversity.     

Development of biomarkers based on diet-dependent metabolic serotypes: practical issues in development of expert system-based classification models in metabolomic studies

Dietary restriction (DR)-induced changes in the serum metabolome may be biomarkers for physiological status (e.g., relative risk of developing age-related diseases such as cancer). Megavariate analysis (unsupervised hierarchical cluster analysis [HCA]; principal components analysis [PCA]) of serum metabolites reproducibly distinguish DR from ad libitum fed rats. Component-based approaches (i.e., PCA) consistently perform as well as or better than distance-based metrics (i.e., HCA). We therefore tested the following: (A) Do identified subsets of serum metabolites contain sufficient information to construct mathematical models of class membership (i.e., expert systems)? (B) Do component-based metrics out-perform distance-based metrics? Testing was conducted using KNN (k-nearest neighbors, supervised HCA) and SIMCA (soft independent modeling of class analogy, supervised PCA). Models were built with single cohorts, combined cohorts or mixed samples from previously studied cohorts as training sets. Both algorithms over-fit models based on single cohort training sets. KNN models had >85% accuracy within training/test sets, but were unstable (i.e., values of k could not be accurately set in advance). SIMCA models had 100% accuracy within all training sets, 89 % accuracy in test sets, did not appear to over-fit mixed cohort training sets, and did not require post-hoc modeling adjustments. These data indicate that (i) previously defined metabolites are robust enough to construct classification models (expert systems) with SIMCA that can predict unknowns by dietary category; (ii) component-based analyses outperformed distance-based metrics; (iii) use of over-fitting controls is essential; and (iv) subtle inter-cohort variability may be a critical issue for high data density biomarker studies that lack state markers.     

Sensitivity analysis of the tree distribution model Phenofit to climatic input characteristics: implications for climate impact assessment

Species distributions are already affected by climate change. Forecasting their long‐term evolution requires models with thoroughly assessed validation. Our aim here is to demonstrate that the sensitivity of such models to climate input characteristics may complicate their validation and introduce uncertainties in their predictions. In this study, we conducted a sensitivity analysis of a process‐based tree distribution model Phenofit to climate input characteristics. This analysis was conducted for two North American trees which differ greatly in their distribution and eight different types of climate input for the historic period which differ in their spatial (local or gridded data) and temporal (daily vs. monthly) resolution as well as their type (locally recorded, extrapolated or simulated by General Circulation Models). We show that the climate data resolution (spatial and temporal) and their type, highly affect the model predictions. The sensitivity analysis also revealed, the importance, for global climate change impact assessment, of (i) the daily variability of temperatures in modeling the biological processes shaping species distribution, (ii) climate data at high latitudes and elevations and (iii) climate data with high spatial resolution.     

Are the numbers adding up? Exploiting discrepancies among complementary population models

Large carnivores are difficult to monitor because they tend to be sparsely distributed, sensitive to human activity, and associated with complex life histories. Consequently, understanding population trend and viability requires conservationists to cope with uncertainty and bias in population data. Joint analysis of combined data sets using multiple models (i.e., integrated population model) can improve inference about mechanisms (e.g., habitat heterogeneity and food distribution) affecting population dynamics. However, unobserved or unobservable processes can also introduce bias and can be difficult to quantify. We developed a Bayesian hierarchical modeling approach for inference on an integrated population model that reconciles annual population counts with recruitment and survival data (i.e., demographic processes). Our modeling framework is flexible and enables a realistic form of population dynamics by fitting separate density-dependent responses for each demographic process. Discrepancies estimated from shared parameters among different model components represent unobserved additions (i.e., recruitment or immigration) or removals (i.e., death or emigration) when annual population counts are reliable. In a case study of gray wolves in Wisconsin (1980–2011), concordant with policy changes, we estimated that a discrepancy of 0% (1980–1995), −2% (1996–2002), and 4% (2003–2011) in the annual mortality rate was needed to explain annual growth rate. Additional mortality in 2003–2011 may reflect density-dependent mechanisms, changes in illegal killing with shifts in wolf management, and nonindependent censoring in survival data. Integrated population models provide insights into unobserved or unobservable processes by quantifying discrepancies among data sets. Our modeling approach is generalizable to many population analysis needs and allows for identifying dynamic differences due to external drivers, such as management or policy changes.     

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

This work is in line with an on-going effort tending toward a computational (quantitative and refutable) understanding of human neuro-cognitive processes. Many sophisticated models for behavioural and neurobiological data have flourished during the past decade. Most of these models are partly unspecified (i.e. they have unknown parameters) and nonlinear. This makes them difficult to peer with a formal statistical data analysis framework. In turn, this compromises the reproducibility of model-based empirical studies. This work exposes a software toolbox that provides generic, efficient and robust probabilistic solutions to the three problems of model-based analysis of empirical data: (i) data simulation, (ii) parameter estimation/model selection, and (iii) experimental design optimization.

This is a PLOS Computational Biology Software Article

     

Critical review of activated sludge modeling: State of process knowledge,modeling concepts,and limitations

This work critically reviews modeling concepts for standard activated sludge wastewater treatment processes (e.g., hydrolysis, growth and decay of organisms, etc.) for some of the most commonly used models. Based on a short overview on the theoretical biochemistry knowledge this review should help model users to better understand (i) the model concepts used; (ii) the differences between models, and (iii) the limits of the models. The seven analyzed models are: (1) ASM1; (2) ASM2d; (3) ASM3; (4) ASM3 + BioP; (5) ASM2d + TUD; (6) Barker & Dold model; and (7) UCTPHO+. Nine standard processes are distinguished and discussed in the present work: hydrolysis; fermentation; ordinary heterotrophic organisms (OHO) growth; autotrophic nitrifying organisms (ANO) growth; OHO & ANO decay; poly‐hydroxyalkanoates (PHA) storage; polyphosphate (polyP) storage; phosphorus accumulating organisms PAO) growth; and PAO decay. For a structured comparison, a new schematic representation of these processes is proposed. Each process is represented as a reaction with consumed components on the left of the figure and produced components on the right. Standardized icons, based on shapes and color codes, enable the representation of the stoichiometric modeling concepts and kinetics. This representation allows highlighting the conceptual differences of the models, and the level of simplification between the concepts and the theoretical knowledge. The model selection depending on their theoretical limitations and the main research needs to increase the model quality are finally discussed. Biotechnol. Bioeng. 2013; 110: 24–46. © 2012 Wiley Periodicals, Inc.     

A reinforcement learning-based hybrid modeling framework for bioprocess kinetics identification

Constructing predictive models to simulate complex bioprocess dynamics, particularly time-varying (i.e., parameters varying over time) and history-dependent (i.e., current kinetics dependent on historical culture conditions) behavior, has been a longstanding research challenge. Current advances in hybrid modeling offer a solution to this by integrating kinetic models with data-driven techniques. This article proposes a novel two-step framework: first (i) speculate and combine several possible kinetic model structures sourced from process and phenomenological knowledge, then (ii) identify the most likely kinetic model structure and its parameter values using model-free Reinforcement Learning (RL). Specifically, Step 1 collates feasible history-dependent model structures, then Step 2 uses RL to simultaneously identify the correct model structure and the time-varying parameter trajectories. To demonstrate the performance of this framework, a range of in-silico case studies were carried out. The results show that the proposed framework can efficiently construct high-fidelity models to quantify both time-varying and history-dependent kinetic behaviors while minimizing the risks of over-parametrization and over-fitting. Finally, the primary advantages of the proposed framework and its limitation were thoroughly discussed in comparison to other existing hybrid modeling and model structure identification techniques, highlighting the potential of this framework for general bioprocess modeling.     

Estimating carbon fixation of plant organs for afforestation monitoring using a process‐based ecosystem model and ecophysiological parameter optimization

Afforestation projects for mitigating CO₂ emissions require to monitor the carbon fixation and plant growth as key indicators. We proposed a monitoring method for predicting carbon fixation in afforestation projects, combining a process‐based ecosystem model and field data and addressed the uncertainty of predicted carbon fixation and ecophysiological characteristics with plant growth. Carbon pools were simulated using the Biome‐BGC model tuned by parameter optimization using measured carbon density of biomass pools on an 11‐year‐old Eucommia ulmoides plantation on Loess Plateau, China. The allocation parameters fine root carbon to leaf carbon (FRC:LC) and stem carbon to leaf carbon (SC:LC), along with specific leaf area (SLA) and maximum stomatal conductance (g_smax) strongly affected aboveground woody (AC) and leaf carbon (LC) density in sensitivity analysis and were selected as adjusting parameters. We assessed the uncertainty of carbon fixation and plant growth predictions by modeling three growth phases with corresponding parameters: (i) before afforestation using default parameters, (ii) early monitoring using parameters optimized with data from years 1 to 5, and (iii) updated monitoring at year 11 using parameters optimized with 11‐year data. The predicted carbon fixation and optimized parameters differed in the three phases. Overall, 30‐year average carbon fixation rate in plantation (AC, LC, belowground woody parts and soil pools) was ranged 0.14–0.35 kg‐C m^?2 y^?1 in simulations using parameters of phases (i)–(iii). Updating parameters by periodic field surveys reduced the uncertainty and revealed changes in ecophysiological characteristics with plant growth. This monitoring method should support management of afforestation projects by carbon fixation estimation adapting to observation gap, noncommon species and variable growing conditions such as climate change, land use change.     

A note on MAR, identifying restrictions, model comparison, and sensitivity analysis in pattern mixture models with and without covariates for incomplete data

Summary Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions is one approach to mixture model identification ( Little, 1995 , Journal of the American Statistical Association 90 , 1112–1121; Little and Wang, 1996 , Biometrics 52 , 98–111; Thijs et al., 2002 , Biostatistics 3 , 245–265; Kenward, Molenberghs, and Thijs, 2003 , Biometrika 90 , 53–71; Daniels and Hogan, 2008 , in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis) and is a natural starting point for missing not at random sensitivity analysis ( Thijs et al., 2002 , Biostatistics 3 , 245–265; Daniels and Hogan, 2008 , in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random (MAR) may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g., baseline covariates with time‐invariant coefficients). In this article, we explore conditions necessary for identifying restrictions that result in MAR to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time‐invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.     

Models for Bounded Systems with Continuous Dynamics

Summary .  Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty (e.g., measurement error, model choice, and inherent stochasticity of process parameters). In addition to continuity, natural processes are often bounded; specifically, they tend to have nonnegative support. Various techniques have been implemented to accommodate nonnegative processes, but such techniques are often limited or overly compromising. This article offers an alternative to common differential modeling practices by using a bias-corrected truncated normal distribution to model the observations and latent process, both having bounded support. Parameters of an underlying continuous process are characterized in a Bayesian hierarchical context, utilizing a fourth-order Runge–Kutta approximation.     

Population Genetic Models of Genomic Imprinting

The phenomenon of genomic imprinting has recently excited much interest among experimental biologists. The population genetic consequences of imprinting, however, have remained largely unexplored. Several population genetic models are presented and the following conclusions drawn: (i) systems with genomic imprinting need not behave similarly to otherwise identical systems without imprinting; (ii) nevertheless, many of the models investigated can be shown to be formally equivalent to models without imprinting; (iii) consequently, imprinting often cannot be discovered by following allele frequency changes or examining equilibrium values; (iv) the formal equivalences fail to preserve some well known properties. For example, for populations incorporating genomic imprinting, parameter values exist that cause these populations to behave like populations without imprinting, but with heterozygote advantage, even though no such advantage is present in these imprinting populations. We call this last phenomenon "pseudoheterosis." The imprinting systems that fail to be formally equivalent to nonimprinting systems are those in which males and females are not equivalent, i.e., two-sex viability systems and sex-chromosome inactivation.     

Model‐based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio‐ethanol production

In this work, a methodology for the model‐based identifiable parameter determination (MBIPD) is presented. This systematic approach is proposed to be used for structure and parameter identification of nonlinear models of biological reaction networks. Usually, this kind of problems are over‐parameterized with large correlations between parameters. Hence, the related inverse problems for parameter determination and analysis are mathematically ill‐posed and numerically difficult to solve. The proposed MBIPD methodology comprises several tasks: (i) model selection, (ii) tracking of an adequate initial guess, and (iii) an iterative parameter estimation step which includes an identifiable parameter subset selection (SsS) algorithm and accuracy analysis of the estimated parameters. The SsS algorithm is based on the analysis of the sensitivity matrix by rank revealing factorization methods. Using this, a reduction of the parameter search space to a reasonable subset, which can be reliably and efficiently estimated from available measurements, is achieved. The simultaneous saccharification and fermentation (SSF) process for bio‐ethanol production from cellulosic material is used as case study for testing the methodology. The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space. It is shown by a cross‐validation that using the identified parameters (even though the reduction of the search space), the model is still able to predict the experimental data properly. Moreover, it is shown that the model is easily and efficiently adapted to new process conditions by solving reduced and well conditioned problems. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1064–1082, 2013     

FATE‐HD: a spatially and temporally explicit integrated model for predicting vegetation structure and diversity at regional scale

During the last decade, despite strenuous efforts to develop new models and compare different approaches, few conclusions have been drawn on their ability to provide robust biodiversity projections in an environmental change context. The recurring suggestions are that models should explicitly (i) include spatiotemporal dynamics; (ii) consider multiple species in interactions and (iii) account for the processes shaping biodiversity distribution. This article presents a biodiversity model (FATE‐HD) that meets this challenge at regional scale by combining phenomenological and process‐based approaches and using well‐defined plant functional groups. FATE‐HD has been tested and validated in a French National Park, demonstrating its ability to simulate vegetation dynamics, structure and diversity in response to disturbances and climate change. The analysis demonstrated the importance of considering biotic interactions, spatio‐temporal dynamics and disturbances in addition to abiotic drivers to simulate vegetation dynamics. The distribution of pioneer trees was particularly improved, as were all undergrowth functional groups.     

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log‐normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero‐vectors; (ii) The multivariate zero‐inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero‐truncated/deflated count data and it is difficult to apply to high‐dimensional cases; (iii) The Type I multivariate zero‐adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.     

Models of maximum stress and strain of zebrafish embryos under indentation

Micro-injection of zebrafish embryo is widely applied in biology for the analysis of early developmental processes. The success of a micro-injection to a large extent depends on the mechanical interaction between the micro-pipette and the membrane of the zebrafish embryo. In this paper, we present the development of (i) a maximum stress model of the deformed membrane with respect to the depth of indentation, (ii) a family-of-conics elongation model to determine the length of the deformed membrane for the estimation of the maximum strain at a given indentation depth, and (iii) an experimental system to generate the required data for these two models. The significance of these results is that the estimated maximum stress provides a performance target for the penetration process, while the estimated corresponding maximum strain serves as an indicator of the extent of deformation sustained by the embryo prior to penetration. Implications of these modeling and experimental results are discussed in the context of optimizing the process of micro-injection.     

Tests for independence between marks and points of a marked point process

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.