Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME

Mathematical simulation models are commonly applied to analyze experimental or environmental data and eventually to acquire predictive capabilities. Typically these models depend on poorly defined, unmeasurable parameters that need to be given a value. Fitting a model to data, so-called inverse modelling, is often the sole way of finding reasonable values for these parameters. There are many challenges involved in inverse model applications, e.g., the existence of non-identifiable parameters, the estimation of parameter uncertainties and the quantification of the implications of these uncertainties on model predictions. The R package FME is a modeling package designed to confront a mathematical model with data. It includes algorithms for sensitivity and Monte Carlo analysis, parameter identifiability, model fitting and provides a Markov-chain based method to estimate parameter confidence intervals. Although its main focus is on mathematical systems that consist of differential equations, FME can deal with other types of models. In this paper, FME is applied to a model describing the dynamics of the HIV virus.

Phytoplankton-bacteria coupling under elevated CO₂ levels: a stable isotope labelling study

The potential impact of rising carbon dioxide (CO2) on carbon transfer from phytoplankton to bacteria was investigated during the 2005 PeECE III mesocosm study in Bergen, Norway. Sets of mesocosms, in which a phytoplankton bloom was induced by nutrient addition, were incubated under 1× (~350 μatm), 2× (~700 μatm), and 3× present day CO2 (~1050 μatm) initial seawater and sustained atmospheric CO2 levels for 3 weeks. 13C labelled bicarbonate was added to all mesocosms to follow the transfer of carbon from dissolved inorganic carbon (DIC) into phytoplankton and subsequently heterotrophic bacteria, and settling particles. Isotope ratios of polar-lipid-derived fatty acids (PLFA) were used to infer the biomass and production of phytoplankton and bacteria. Phytoplankton PLFA were enriched within one day after label addition, whilst it took another 3 days before bacteria showed substantial enrichment. Group-specific primary production measurements revealed that coccolithophores showed higher primary production than green algae and diatoms. Elevated CO2 had a significant positive effect on post-bloom biomass of green algae, diatoms, and bacteria. A simple model based on measured isotope ratios of phytoplankton and bacteria revealed that CO2 had no significant effect on the carbon transfer efficiency from phytoplankton to bacteria during the bloom. There was no indication of CO2 effects on enhanced settling based on isotope mixing models during the phytoplankton bloom, but this could not be determined in the post-bloom phase. Our results suggest that CO2 effects are most pronounced in the post-bloom phase, under nutrient limitation

Simulating algal dynamics within a Bayesian framework to evaluate controls on estuary productivity

The Neuse River Estuary (North Carolina, USA) is a valuable ecosystem that has been affected by the expansion of agricultural and urban watershed activities over the last several decades. Eutrophication, as a consequence of enhanced anthropogenic nutrient loadings, has promoted high phytoplankton biomass, hypoxia, and fish kills. This study compares and contrasts three models to better understand how nutrient loading and other environmental factors control phytoplankton biomass, as chl-a, over time. The first model is purely statistical, while the second model mechanistically simulates both chl-a and nitrogen dynamics, and the third additionally simulates phosphorus. The models are calibrated to a multi-decadal dataset (1997–2018) within a Bayesian framework, which systematically incorporates prior information and accounts for uncertainties. All three models explain over one third of log-transformed chl-a variability, with the mechanistic models additionally explaining the majority of the variability in bioavailable nutrients (R2 > 0.5). By disentangling the influences of riverine nutrient concentrations, flows, and loadings on estuary productivity we find that concentration reductions, rather than total loading reductions, are the key to controlling estuary chl-a levels. The third model indicates that the estuary, even in its upstream portion, is rarely phosphorus limited, and will continue to be mostly nitrogen limited even under a 30% phosphorus reduction scenario. This model also predicts that a 10% change in nitrogen loading (flow held constant) will produce an approximate 4.3% change in estuary chl-a concentration, while the statistical model suggests a larger (10%) effect. Overall, by including a more detailed representation of environmental factors controlling algal growth, the mechanistic models generate chl-a forecasts with less uncertainty across a range of nutrient loading scenarios. Methodologically, this study advances the use of Bayesian methods for modeling the eutrophication dynamics of an estuarine system over a multi-decadal period

Modelling the impact of higher temperature on the phytoplankton of a boreal lake

We linked the models PROTECH and MyLake to test potential impacts of climate-changeinduced warming on the phytoplankton community of Pyhäjärvi, a lake in southwest Finland. First, we calibrated the models for the present conditions, which revealed an apparent high significance of internal nutrient loading for Pyhäjärvi. We then estimated the effect of two climate change scenarios on lake water temperatures and ice cover duration with MyLake. Finally, we used those outputs to drive PROTECH to predict the resultant phytoplankton community. It was evident that cyanobacteria will grow significantly better in warmer water, especially in the summer. Even if phosphorus and nitrogen loads to the lake remain the same and there is little change in the total chlorophyll a concentrations, a higher proportion of the phytoplankton community could be dominated by cyanobacteria. The model outputs provided no clear evidence that earlier ice break would advance the timing of the diatom spring bloom.peerReviewe

Bayesian Adaptive Markov Chain Monte Carlo Estimation of Genetic Parameters

Accurate estimation of genetic parameters is crucial for an efficient genetic evaluation system. REML and Bayesian methods are commonly used for the estimation of genetic parameters. In Bayesian approach, the idea is to combine what is known about the parameter which is represented in terms of a prior probability distribution together with the information coming from the data, to obtain a posterior distribution of the parameter of interest. Here a new fast adaptive Markov Chain Monte Carlo (MCMC) sampling algorithm is proposed. It combines both hybrid Gibbs sampler and Metropolis-Hastings (M-H) algorithm, for the estimation of genetic parameters in the linear mixed models with several random effects. The new adaptive MCMC algorithm has two steps: in step 1 the hybrid Gibbs sampler is used to learn an efficient proposal covariance structure for the variance components, and in step 2 the M-H algorithm is used to propose new values based on the learned covariance structure from step 1. Normally the dependencies among the random effects slow down the convergence of the MCMC chain. So in the second step of the algorithm those random effects were marginalized from the likelihood to improve the mixing of the chain. The new algorithm showed good mixing properties and was about twice time faster than the hybrid Gibbs sampling to produce posterior for variance components. Also the new algorithm was able to detect different modes in the posterior distribution. Moreover, the new proposed exponential prior for variance components was able to provide estimated mode of the posterior dominance variance to be zero in case of no dominance. The performance of the method was illustrated with field data and simulated data sets.Eine exakte Schätzung von genetischen Parametern ist entscheidend für ein leistungsfähiges genetisches Evaluierungssystem. Normalerweise werden REML- und Bayes-Verfahren für die Schätzung von genetischen Einflussfaktoren angewendet. Bei der Bayes-Methode werden die Informationen, die über einen Parameter durch A-priori-Wahrscheinlichkeitseinschätzung bekannt sind mit den Daten und Erfahrungen aus aktuellen Studien kombiniert und in eine A-posteriori-Verteilung überführt. In der vorliegenden Arbeit wird ein neuer, schnell anpassungsfähiger Markov Chain Monte Carlo (MCMC) sampling Algorithmus vorgestellt, welcher die Vorteile des Hybrid-Gibbs sampler mit denen des Metropolis-Hastings Algorithmus zur Einschätzung von genetischen Einflussfaktoren in linear mixed models mit mehreren Zufallsvariablen in sich vereinigt. Dieser neue MCMC Algorithmus arbeitet in 2 Stufen: im ersten Schritt wird der Hybrid Gibbs sampler genutzt, um eine effiziente vorgeschlagene Kovarianzstruktur für die Varianzkomponenten zu erlernen, während im zweiten Schritt der M-H Algorithmus zur Aufstellung neuer Werte basierend auf der erlernten Kovarianzstruktur aus Schritt 1 zur Anwendung kommt. Normalerweise verzögern die Abhängigkeiten unter den Zufallsvariablen die Annäherung der Markov-Kette an einen stationären Zustand. Also wurden diese Zufallsvariablen in einem weiteren Schritt von der Wahrscheinlichkeitsschätzung ausgeschlossen, um das Gemisch der Kette zu verbessern. Der neue Algorithmus zeigte gute Mischeigenschaften und war zweimal schneller als der Hybrid-Gibbs sampler, um eine a-posteriori-Verteilung von Varianzkomponenten zu erstellen, außerdem können bei dieser Methode auch mehrere Modes festgestellt werden. Mit der vorgeschlagenen exponentiellen Vorbewertung für Varianzkomponenten ist es weiterhin möglich solche Maximalwerte bei der posterior Verteilung auf den Wert Null zu schätzen im Falle, dass keine Dominanz besteht. Die Durchführung der Methode wurde mit realen und simulierten Datensätzen veranschaulicht

Test of validity of a dynamic soil carbon model using data from leaf litter decomposition in a West African tropical forest

Abstract. We evaluated the applicability of the dynamic soil carbon model Yasso07 in tropical conditions in West Africa by simulating the litter decomposition process using as required input into the model litter mass, litter quality, temperature and precipitation collected during a litterbag experiment. The experiment was conducted over a six-month period on leaf litter of five dominant tree species, namely Afzelia africana, Anogeissus leiocarpa, Ceiba pentandra, Dialium guineense and Diospyros mespiliformis in a semi-deciduous vertisol forest in Southern Benin. Since the predictions of Yasso07 were not consistent with the observations on mass loss and chemical composition of litter, Yasso07 was fitted to the dataset composed of global data and the new experimental data from Benin. The re-parameterized versions of Yasso07 had a good predictive ability and refined the applicability of the model in Benin to estimate soil carbon stocks, its changes and CO2 emissions from heterotrophic respiration as main outputs of the model. The findings of this research support the hypothesis that the high variation of litter quality observed in the tropics is a major driver of the decomposition and needs to be accounted in the model parameterization. </jats:p

A trial for theoretical prediction of microalgae growth for parallel flow

Many models established for solving the problem of the prediction of microalgae growth. However, the models are semi-empirical or considerable fitting coefficients exist in the theoretical model. Therefore, the prediction ability of the model is reduced by the fitting coefficients. The growth mechanism of microalgae is not clearly understood until now, and the growth state is related to the microalgae strains. The above reasons conducted the problem of microalgae growth is much difficult in theoretical prediction. Furthermore, the predicted results of the established models are dependent on the size of the photobioreactor (PBR), light intensity, flow field, and concentration field. Therefore, the growth rate of the dependent variable is the function of independent variables including nutrients concentration, light intensity, flow field, PBR size, temperature, pH. The experimental works are 106 for each independent variable selects 10 values of 6 variables which can not be accomplished. The dimensionless method maybe provide a way to solve the problem. In this paper, the analytical solution of the growth rate was obtained for the parallel flow. The dimensionless growth rate expressed as function of Reynolds number and Schmidt number, which can be used for arbitrary parallel flow due to the parameters are expressed as dimensionless quantity. The solution of growth rate was used to predict the experimentally measured data. The results show that the theoretically predicted growth rate is consistent with the experimentally measured growth rate of microalgae on the order of magnitude. These results will be useful in the design and operation of PBRs for biofuel production.Comment: 23 pages, 4 figures, 1 tabl

A multi-dating approach to age-modelling long continental records: The 135 ka El Cañizar de Villarquemado sequence (NE Spain)

Under embargo until: 2021-06-23We present a multidisciplinary dating approach - including radiocarbon, Uranium/Thorium series (U/Th), paleomagnetism, single-grain optically stimulated luminescence (OSL), polymineral fine-grain infrared stimulated luminescence (IRSL) and tephrochronology - used for the development of an age model for the Cañizar de Villarquemado sequence (VIL) for the last ca. 135 ka. We describe the protocols used for each technique and discuss the positive and negative results, as well as their implications for interpreting the VIL sequence and for dating similar terrestrial records. In spite of the negative results of some techniques, particularly due to the absence of adequate sample material or insufficient analytical precision, the multi-technique strategy employed here is essential to maximize the chances of obtaining robust age models in terrestrial sequences. The final Bayesian age model for VIL sequence includes 16 AMS 14C ages, 9 single-grain quartz OSL ages and 5 previously published polymineral fine-grain IRSL ages, and the accuracy and resolution of the model are improved by incorporating information related to changes in accumulation rate, as revealed by detailed sedimentological analyses. The main paleohydrological and vegetation changes in the sequence are coherent with global Marine Isotope Stage (MIS) 6 to 1 transitions since the penultimate Termination, although some regional idiosyncrasies are evident, such as higher moisture variability than expected, an abrupt inception of the last glacial cycle and a resilient response of vegetation in Mediterranean continental Iberia in both Terminations.acceptedVersio