Consistent micro, macro and state-based population modelling

A population system can be modelled using a micro model focusing on the individual entities, a macro model where the entities are aggregated into compartments, or a state-based model where each possible discrete state in which the system can exist is represented. However, the concepts, building blocks, procedural mechanisms and the time handling for these approaches are very different. For the results and conclusions from studies based on micro, macro and state-based models to be consistent (contradiction-free), a number of modelling issues must be understood and appropriate modelling procedures be applied. This paper presents a uniform approach to micro, macro and state-based population modelling so that these different types of models produce consistent results and conclusions. In particular, we demonstrate the procedures (distribution, attribute and combinatorial expansions) necessary to keep these three types of models consistent. We also show that the different time handling methods usually used in micro, macro and state-based models can be regarded as different integration methods that can be applied to any of these modelling categories. The result is free choice in selecting the modelling approach and the time handling method most appropriate for the study without distorting the results and conclusions.     

Simulation-based estimation of stochastic process parameters in tumor growth

Models are generally developed at the micro level. Data are generally gathered at the macro level. Obtaining the macromodel which is the natural consequence of the underlying micro model is generally not feasible. SIMEST gives a means whereby the micromodel is used to generate, for a given assumed set of parameters, simulated sets of macro data. These data are compared with the actual clinical macro data. The parameters are then adjusted to obtain concordance with the clinical data. In this manner, simulation gives us a means of parameter estimation without the necessity of generating the macro model.     

Hierarchical Bayesian Estimation for the Number of Species

This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian model using the Metropolis algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior distributions with unknown hyperparameters. An empirical Bayes approach is considered and compared with the fully Bayesian approach based on biological data.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.     

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor.     

Flexible dose-response models for Japanese atomic bomb survivor data: Bayesian estimation and prediction of cancer risk

Generalised absolute risk models were fitted to the latest Japanese atomic bomb survivor cancer incidence data using Bayesian Markov Chain Monte Carlo methods, taking account of random errors in the DS86 dose estimates. The resulting uncertainty distributions in the relative risk model parameters were used to derive uncertainties in population cancer risks for a current UK population. Because of evidence for irregularities in the low-dose dose response, flexible dose-response models were used, consisting of a linear-quadratic-exponential model, used to model the high-dose part of the dose response, together with piecewise-linear adjustments for the two lowest dose groups. Following an assumed administered dose of 0.001 Sv, lifetime leukaemia radiation-induced incidence risks were estimated to be 1.11 x 10(-2) Sv(-1) (95% Bayesian CI -0.61, 2.38) using this model. Following an assumed administered dose of 0.001 Sv, lifetime solid cancer radiation-induced incidence risks were calculated to be 7.28 x 10(-2) Sv(-1) (95% Bayesian CI -10.63, 22.10) using this model. Overall, cancer incidence risks predicted by Bayesian Markov Chain Monte Carlo methods are similar to those derived by classical likelihood-based methods and which form the basis of established estimates of radiation-induced cancer risk.     

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

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

A bayesian approach to the multistate Jolly-Seber capture-recapture model

This article considers a Bayesian approach to the multistate extension of the Jolly-Seber model commonly used to estimate population abundance in capture-recapture studies. It extends the work of George and Robert (1992, Biometrika79, 677-683), which dealt with the Bayesian estimation of a closed population with only a single state for all animals. A super-population is introduced to model new entrants in the population. Bayesian estimates of abundance are obtained by implementing a Gibbs sampling algorithm based on data augmentation of the missing data in the capture histories when the state of the animal is unknown. Moreover, a partitioning of the missing data is adopted to ensure the convergence of the Gibbs sampling algorithm even in the presence of impossible transitions between some states. Lastly, we apply our methodology to a population of fish to estimate abundance and movement.     

State-space model combining local camera data and regional administration data reveals population dynamics of wild boar

Recent increases in wildlife cause negative impacts on humans through both economic and ecological damage, as well as the spread of pathogens. Understanding the population dynamics of wildlife is crucial to develop effective management strategies. However, it is difficult to estimate accurate and precise population size over large spatial and temporal scales because of the limited data availability. We addressed these issues by first fitting a random encounter and staying time (REST) model based on camera trap data to construct an informative prior distribution for a capture rate parameter in a harvest-based Bayesian state-space model. We constructed a Bayesian state-space model that integrated administration data on the number of captured wild boar with the prior distribution of capture efficiency estimated by camera trap data. The model with informative prior distribution from the REST model successfully estimated population dynamics, whereas the model using only the administration data did not, owing to a lack of parameter convergence. We identified areas where (1) wild boars exhibit a high potential population growth rate and a high carrying capacity, (2) current trapping efforts are effectively suppressing local populations, and (3) trapping reinforcement is required to control populations in the whole region. The model could be used to predict future trends in populations under the assumptions of ongoing trapping pressure. This will help identify spatially explicit trapping efforts to achieve target population levels.     

Modeling and Design of H-Infinity Controller for Piezoelectric Actuator LIPCA

<正> We proposed a dynamic model identification and design of an H-Infinity (i.e.H_∞) controller using a LightweightPiezo-Composite Actuator (LIPCA).A second-order dynamic model was obtained by using input and output data, and applyingan identification algorithm.The identified model coincides well with the real LIPCA.To reduce the resonating mode that istypical of piezoelectric actuators, a notch filter was used.A feedback controller using the H_∞ control scheme was designed basedon the identified dynamic model; thus, the LIPCA can be easily used as an actuator for biomemetic applications such as artificialmuscles or macro/micro positioning in bioengineering.The control algorithm was implemented using a microprocessor, analogfilters, and power amplifying drivers.Our simulation and experimental results demonstrate that the proposed control algorithmworks well in real environment, providing robust performance and stability with uncertain disturbances.     

A dedicated target capture approach reveals variable genetic markers across micro‐ and macro‐evolutionary time scales in palms

Understanding the genetics of biological diversification across micro‐ and macro‐evolutionary time scales is a vibrant field of research for molecular ecologists as rapid advances in sequencing technologies promise to overcome former limitations. In palms, an emblematic, economically and ecologically important plant family with high diversity in the tropics, studies of diversification at the population and species levels are still hampered by a lack of genomic markers suitable for the genotyping of large numbers of recently diverged taxa. To fill this gap, we used a whole genome sequencing approach to develop target sequencing for molecular markers in 4,184 genome regions, including 4,051 genes and 133 non‐genic putatively neutral regions. These markers were chosen to cover a wide range of evolutionary rates allowing future studies at the family, genus, species and population levels. Special emphasis was given to the avoidance of copy number variation during marker selection. In addition, a set of 149 well‐known sequence regions previously used as phylogenetic markers by the palm biological research community were included in the target regions, to open the possibility to combine and jointly analyse already available data sets with genomic data to be produced with this new toolkit. The bait set was effective for species belonging to all three palm sub‐families tested (Arecoideae, Ceroxyloideae and Coryphoideae), with high mapping rates, specificity and efficiency. The number of high‐quality single nucleotide polymorphisms (SNPs) detected at both the sub‐family and population levels facilitates efficient analyses of genomic diversity across micro‐ and macro‐evolutionary time scales.     

Coalescent-based DNA barcoding: multilocus analysis and robustness

DNA barcoding is the assignment of individuals to species using standardized mitochondrial sequences. Nuclear data are sometimes added to the mitochondrial data to increase power. A barcoding method for analysing mitochondrial and nuclear data is developed. It is a Bayesian method based on the coalescent model. Then this method is assessed using simulated and real data. It is found that adding nuclear data can reduce the number of ambiguous assignments. Finally, the robustness of coalescent-based barcoding to departures from model assumptions is studied using simulations. This method is found to be robust to past population size variations, to within-species population structures, and to designs that poorly sample populations within species. Supplementary Material is available online at www.liebertonline.com/cmb.     

Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model

In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.     

Bayesian Inference for Generalized Linear Mixed Model Based on the Multivariate t Distribution in Population Pharmacokinetic Study

This article provides a fully Bayesian approach for modeling of single-dose and complete pharmacokinetic data in a population pharmacokinetic (PK) model. To overcome the impact of outliers and the difficulty of computation, a generalized linear model is chosen with the hypothesis that the errors follow a multivariate Student t distribution which is a heavy-tailed distribution. The aim of this study is to investigate and implement the performance of the multivariate t distribution to analyze population pharmacokinetic data. Bayesian predictive inferences and the Metropolis-Hastings algorithm schemes are used to process the intractable posterior integration. The precision and accuracy of the proposed model are illustrated by the simulating data and a real example of theophylline data.     

The combination of population pharmacokinetic studies

Pharmacokinetic data consist of drug concentrations with associated known sampling times and are collected following the administration of known dosage regimens. Population pharmacokinetic data consist of such data on a number of individuals, possibly along with individual-specific characteristics. During drug development, a number of population pharmacokinetic studies are typically carried out and the combination of such studies is of great importance for characterizing the drug and, in particular, for the design of future studies. In this paper, we describe a model that may be used to combine population pharmacokinetic data. The model is illustrated using six phase I studies of the antiasthmatic drug fluticasone propionate. Our approach is Bayesian and computation is carried out using Markov chain Monte Carlo. We provide a number of simplifications to the model that may be made in order to ease simulation from the posterior distribution.     

Matrix heterogeneity affects population size of the harvest mice: Bayesian estimation of matrix resistance and model validation

It has been increasingly recognized that landscape matrices are an important factor determining patch connectivity and hence the population size of organisms living in highly fragmented landscapes. However, most previous studies estimated the effect of matrix heterogeneity using prior information regarding dispersal or habitat preferences of a focal organism. Here we estimated matrix resistance of harvest mice in agricultural landscapes using a novel pattern‐oriented modeling with Bayesian estimation and no prior information, and then conducted model validation using data sets independent from those used for model construction. First, we investigated the distribution patterns of harvest mice for approximately 400 habitat patches, and estimated matrix resistance for different matrix types using statistical models incorporating patch size, patch environment, and patch connectivity. We used Bayesian estimation with a Markov chain Monte Carlo algorithm, and searched for appropriate matrix resistance that best explained the distribution pattern. Patch connectivity as well as patch quality was an important determinant of local population size for the harvest mice. Moreover, matrix resistance was far from uniform, with rice and crop fields exhibiting low resistance and forests, creeks, roads and residential areas showing much higher resistance. The deviance explained by this model (heterogeneous matrix model) was much larger than that obtained by the model with no consideration of matrix heterogeneity (homogeneous matrix model). Second, we obtained distribution data from five additional landscapes that were more fragmented than that used for model construction, and used them for model validation. The heterogeneous matrix model well predicted the population size for four out of five landscapes. In contrast, the homogeneous model considerably overestimated population sizes in all cases. Our approach is widely applicable to species living in fragmented landscapes, especially those for which prior information regarding movement or dispersal is difficult to obtain.     

fastruct: model‐based clustering made faster

Bayesian model‐based clustering programs have gained increased popularity in studies of population structure since the publication of the software structure . These programs are generally acknowledged as performing well, but their running‐time may be prohibitive. fastruct is a non‐Bayesian implementation of the classical model with no‐admixture uncorrelated allele frequencies. This new program relies on the expectation–maximization principle, and produces assignment rivalling other model‐based clustering programs. In addition, it can be manyfold faster than Bayesian implementations. The software consists of a command‐line engine, which is suitable for batch analysis of data, and a graphical interface, which is convenient for exploring data.     

Recommendations for estimating mark rate of cetaceans in photo-ID research: A critique of field sampling protocols and variance estimation

Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS-Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS-Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.     

Experimentelle Untersuchung,Modellierung und optimale Berechnung eines mehrstufigen Säulenfermentors II. Experimentelle Bestimmung der Parameter und Koeffizienten des mathematischen Modells

Using a system analysis for the investigation of all processes which occur in a biochemical reactor on the micro and macro level, a mathematical model was worked out. It characterizes the model of the kinetics and stoichiometry of the growth of microorganisms and the rules of hydrodynamics and mass transfer in form of blocks. Relating to the discussed mathematical total model [11], experimental data on which the calculation of the model parameters is based are described in this second part of the paper. They were determined not only directly from the cultivation process, but also from experiments with model media.