Solving Differential Equations in R: Package deSolve

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

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.

Here, we present a community perspective on how to explore, exploit and evolve the diversity in aquatic ecosystem models. These models play an important role in understanding the functioning of aquatic ecosystems, filling in observation gaps and developing effective strategies for water quality management. In this spirit, numerous models have been developed since the 1970s. We set off to explore model diversity by making an inventory among 42 aquatic ecosystem modellers, by categorizing the resulting set of models and by analysing them for diversity. We then focus on how to exploit model diversity by comparing and combining different aspects of existing models. Finally, we discuss how model diversity came about in the past and could evolve in the future. Throughout our study, we use analogies from biodiversity research to analyse and interpret model diversity. We recommend to make models publicly available through open-source policies, to standardize documentation and technical implementation of models, and to compare models through ensemble modelling and interdisciplinary approaches. We end with our perspective on how the field of aquatic ecosystem modelling might develop in the next 5–10 years. To strive for clarity and to improve readability for non-modellers, we include a glossary.

Statistical Methods for the Qualitative Assessment of Dynamic Models with Time Delay (R Package qualV)