Thomas Petzoldt

Bio: Thomas Petzoldt is an academic researcher from Dresden University of Technology. The author has contributed to research in topics: Population & Climate change. The author has an hindex of 27, co-authored 62 publications receiving 3523 citations.

Solving Differential Equations in R: Package deSolve

Abstract: In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR), DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1) to demonstrate the potential of using R for dynamic modeling, (2) to highlight typical uses of the different methods implemented and (3) to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in the future; it is free software and distributed under the GNU General Public License, as part of the R software project.

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

Abstract: 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.

Challenges and opportunities for integrating lake ecosystem modelling approaches

Abstract: A large number and wide variety of lake ecosystem models have been developed and published during the past four decades. We identify two challenges for making further progress in this field. One such challenge is to avoid developing more models largely following the concept of others (‘reinventing the wheel’). The other challenge is to avoid focusing on only one type of model, while ignoring new and diverse approaches that have become available (‘having tunnel vision’). In this paper, we aim at improving the awareness of existing models and knowledge of concurrent approaches in lake ecosystem modelling, without covering all possible model tools and avenues. First, we present a broad variety of modelling approaches. To illustrate these approaches, we give brief descriptions of rather arbitrarily selected sets of specific models. We deal with static models (steady state and regression models), complex dynamic models (CAEDYM, CE-QUAL-W2, Delft 3D-ECO, LakeMab, LakeWeb, MyLake, PCLake, PROTECH, SALMO), structurally dynamic models and minimal dynamic models. We also discuss a group of approaches that could all be classified as individual based: super-individual models (Piscator, Charisma), physiologically structured models, stage-structured models and trait-based models. We briefly mention genetic algorithms, neural networks, Kalman filters and fuzzy logic. Thereafter, we zoom in, as an in-depth example, on the multi-decadal development and application of the lake ecosystem model PCLake and related models (PCLake Metamodel, Lake Shira Model, IPH-TRIM3D-PCLake). In the discussion, we argue that while the historical development of each approach and model is understandable given its ‘leading principle’, there are many opportunities for combining approaches. We take the point of view that a single ‘right’ approach does not exist and should not be strived for. Instead, multiple modelling approaches, applied concurrently to a given problem, can help develop an integrative view on the functioning of lake ecosystems. We end with a set of specific recommendations that may be of help in the further development of lake ecosystem models.

Solving Differential Equations in R

Abstract: The open‐source software R has become one of the most widely used systems for statistical data analysis and for making graphs, but it is also well suited for other disciplines in scientific computing. One of the fields where considerable progress has been made is the solution of differential equations. Here we first give an overview of the types of differential equations that R can solve, and then demonstrate how to use R for solving a 2‐Dimensional partial differential equation.

A community-based framework for aquatic ecosystem models

Abstract: Here, we communicate a point of departure in the development of aquatic ecosystem models, namely a new community-based framework, which supports an enhanced and transparent union between the collective expertise that exists in the communities of traditional ecologists and model developers. Through a literature survey, we document the growing importance of numerical aquatic ecosystem models while also noting the difficulties, up until now, of the aquatic scientific community to make significant advances in these models during the past two decades. Through a common forum for aquatic ecosystem modellers we aim to (i) advance collaboration within the aquatic ecosystem modelling community, (ii) enable increased use of models for research, policy and ecosystem-based management, (iii) facilitate a collective framework using common (standardised) code to ensure that model development is incremental, (iv) increase the transparency of model structure, assumptions and techniques, (v) achieve a greater understanding of aquatic ecosystem functioning, (vi) increase the reliability of predictions by aquatic ecosystem models, (vii) stimulate model inter-comparisons including differing model approaches, and (viii) avoid ‘re-inventing the wheel’, thus accelerating improvements to aquatic ecosystem models. We intend to achieve this as a community that fosters interactions amongst ecologists and model developers. Further, we outline scientific topics recently articulated by the scientific community, which lend themselves well to being addressed by integrative modelling approaches and serve to motivate the progress and implementation of an open source model framework.

The Theory of Island Biogeography

Abstract: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

Modern Applied Statistics With S

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Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period.

Abstract: It is urgent to understand the future of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) transmission. We used estimates of seasonality, immunity, and cross-immunity for human coronavirus OC43 (HCoV-OC43) and HCoV-HKU1 using time-series data from the United States to inform a model of SARS-CoV-2 transmission. We projected that recurrent wintertime outbreaks of SARS-CoV-2 will probably occur after the initial, most severe pandemic wave. Absent other interventions, a key metric for the success of social distancing is whether critical care capacities are exceeded. To avoid this, prolonged or intermittent social distancing may be necessary into 2022. Additional interventions, including expanded critical care capacity and an effective therapeutic, would improve the success of intermittent distancing and hasten the acquisition of herd immunity. Longitudinal serological studies are urgently needed to determine the extent and duration of immunity to SARS-CoV-2. Even in the event of apparent elimination, SARS-CoV-2 surveillance should be maintained because a resurgence in contagion could be possible as late as 2024.