A practical guide for optimal designs of experiments in the Monod model

The Monod model is a classical microbiological model much used in microbiology, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was shown theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources (Dette et al., 2003). The purpose of this paper is to provide this method as a computational ?tool? such that it can be used by practitioners-without strong mathematical and statistical backgroundfor the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a computer program for practical optimal design calculations in Mathematica 5.0 software. In addition, analogous programs in Matlab software will be soon available at www.optimal-design.org. --Monod model,microbial growth,biodegradation kinetics,optimal experimental design,D-optimality

Design of experiments for microbiological models

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Efficient three-dimensional reconstruction of aquatic vegetation geometry: Estimating morphological parameters influencing hydrodynamic drag

Aquatic vegetation can shelter coastlines from energetic waves and tidal currents, sometimes enabling accretion of fine sediments. Simulation of flow and sediment transport within submerged canopies requires quantification of vegetation geometry. However, field surveys used to determine vegetation geometry can be limited by the time required to obtain conventional caliper and ruler measurements. Building on recent progress in photogrammetry and computer vision, we present a method for reconstructing three-dimensional canopy geometry. The method was used to survey a dense canopy of aerial mangrove roots, called pneumatophores, in Vietnam’s Mekong River Delta. Photogrammetric estimation of geometry required 1) taking numerous photographs at low tide from multiple viewpoints around 1 m2 quadrats, 2) computing relative camera locations and orientations by triangulation of key features present in multiple images and reconstructing a dense 3D point cloud, and 3) extracting pneumatophore locations and diameters from the point cloud data. Step 3) was accomplished by a new ‘sector-slice’ algorithm, yielding geometric parameters every 5 mm along a vertical profile. Photogrammetric analysis was compared with manual caliper measurements. In all 5 quadrats considered, agreement was found between manual and photogrammetric estimates of stem number, and of number × mean diameter, which is a key parameter appearing in hydrodynamic models. In two quadrats, pneumatophores were encrusted with numerous barnacles, generating a complex geometry not resolved by hand measurements. In remaining cases, moderate agreement between manual and photogrammetric estimates of stem diameter and solid volume fraction was found. By substantially reducing measurement time in the field while capturing in greater detail the 3D structure, photogrammetry has potential to improve input to hydrodynamic models, particularly for simulations of flow through large-scale, heterogenous canopies

Data-Driven Analysis of Forest–Climate Interactions in the Conterminous United States

A predictive understanding of interactions between vegetation and climate has been a grand challenge in terrestrial ecology for over 200 years. Developed in recent decades, continental-scale monitoring of climate and forest dynamics enables quantitative examination of vegetation–climate relationships through a data-driven paradigm. Here, we apply a data-intensive approach to investigate forest–climate interactions across the conterminous USA. We apply multivariate statistical methods (stepwise regression, principal component analysis) including machine learning to infer significant climatic drivers of standing forest basal area. We focus our analysis on the ecoregional scale. For most ecoregions analyzed, both stepwise regression and random forests indicate that factors related to precipitation are the most significant predictors of forest basal area. In almost half of US ecoregions, precipitation of the coldest quarter is the single most important driver of basal area. The demonstrated data-driven approach may be used to inform forest-climate envelope modeling and the forecasting of large-scale forest dynamics under climate change scenarios. These results have important implications for climate, biodiversity, industrial forestry, and indigenous communities in a changing world

A Forest Model Intercomparison Framework and Application at Two Temperate Forests Along the East Coast of the United States

State-of-the-art forest models are often complex, analytically intractable, and computationally expensive, due to the explicit representation of detailed biogeochemical and ecological processes. Different models often produce distinct results while predictions from the same model vary with parameter values. In this project, we developed a rigorous quantitative approach for conducting model intercomparisons and assessing model performance. We have applied our original methodology to compare two forest biogeochemistry models, the Perfect Plasticity Approximation with Simple Biogeochemistry (PPA-SiBGC) and Landscape Disturbance and Succession with Net Ecosystem Carbon and Nitrogen (LANDIS-II NECN). We simulated past-decade conditions at flux tower sites located within Harvard Forest, MA, USA (HF-EMS) and Jones Ecological Research Center, GA, USA (JERC-RD). We mined field data available from both sites to perform model parameterization, validation, and intercomparison. We assessed model performance using the following time-series metrics: Net ecosystem exchange, aboveground net primary production, aboveground biomass, C, and N, belowground biomass, C, and N, soil respiration, and species total biomass and relative abundance. We also assessed static observations of soil organic C and N, and concluded with an assessment of general model usability, performance, and transferability. Despite substantial differences in design, both models achieved good accuracy across the range of pool metrics. While LANDIS-II NECN showed better fidelity to interannual NEE fluxes, PPA-SiBGC indicated better overall performance for both sites across the 11 temporal and two static metrics tested (HF-EMS R 2 ¯ = 0.73 , + 0.07 , R M S E ¯ = 4.68 , − 9.96 ; JERC-RD R 2 ¯ = 0.73 , + 0.01 , R M S E ¯ = 2.18 , − 1.64 ). To facilitate further testing of forest models at the two sites, we provide pre-processed datasets and original software written in the R language of statistical computing. In addition to model intercomparisons, our approach may be employed to test modifications to forest models and their sensitivity to different parameterizations

Autoregressive Modeling of Forest Dynamics

In this work, we employ autoregressive models developed in financial engineering for modeling of forest dynamics. Autoregressive models have some theoretical advantage over currently employed forest modeling approaches such as Markov chains and individual-based models, as autoregressive models are both analytically tractable and operate with continuous state space. We performed a time series statistical analysis of forest biomass and basal areas recorded in Quebec provincial forest inventories from 1970 to 2007. The geometric random walk model adequately describes the yearly average dynamics. For individual patches, we fit an autoregressive process (AR) of order 1 capable to model negative feedback (mean-reversion). Overall, the best fit also turned out to be geometric random walk; however, the normality tests for residuals failed. In contrast, yearly means were adequately described by normal fluctuations, with annual growth on average of 2.3%, but with a standard deviation of order of 40%. We used a Bayesian analysis to account for the uneven number of observations per year. This work demonstrates that autoregressive models represent a valuable tool for the modeling of forest dynamics. In particular, they quantify the stochastic effects of environmental disturbances and develop predictive empirical models on short and intermediate temporal scales

Data from: Intercomparison of photogrammetry software for 3D vegetation modeling

Photogrammetry-based 3D reconstruction of objects is becoming increasingly appealing in research areas unrelated to computer vision. It has the potential to facilitate the assessment of forest inventory-related parameters by enabling or expediting resource measurements in the field. We hereby compare several implementations of photogrammetric algorithms (CMVS/PMVS, CMPMVS, MVE, OpenMVS, SURE, and Agisoft PhotoScan) with respect to their performance in vegetation assessment. The evaluation is based on (a) a virtual scene where the precise location and dimensionality of objects is known a priori and is thus conducive to a quantitative comparison, and (b) using series of in-situ acquired photographs of vegetation with overlapping field of view where the photogrammetric outcomes are compared quantitatively. Performance is quantified by computing ROC curves that summarize the type-I and type-II errors between the reference and reconstructed tree models. Similar artifacts are observed in synthetic- and in-situ- based reconstructions

Time Series Analysis of Forest Dynamics at the Ecoregion Level

Forecasting of forest dynamics at a large scale is essential for land use management, global climate change and biogeochemistry modeling. We develop time series models of the forest dynamics in the conterminous United States based on forest inventory data collected by the US Forest Service over several decades. We fulfilled autoregressive analysis of the basal forest area at the level of US ecological regions. In each USA ecological region, we modeled basal area dynamics on individual forest inventory pots and performed analysis of its yearly averages. The last task involved Bayesian techniques to treat irregular data. In the absolute majority of ecological regions, basal area yearly averages behave as geometric random walk with normal increments. In California Coastal Province, geometric random walk with normal increments adequately describes dynamics of both basal area yearly averages and basal area on individual forest plots. Regarding all the rest of the USA’s ecological regions, basal areas on individual forest patches behave as random walks with heavy tails. The Bayesian approach allowed us to evaluate forest growth rate within each USA ecological region. We have also implemented time series ARIMA models for annual averages basal area in every USA ecological region. The developed models account for stochastic effects of environmental disturbances and allow one to forecast forest dynamics