Thomas Petzoldt

Challenges and Opportunities for Integrating Lake Ecosystem Modelling Approaches

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.

A community-based framework for aquatic ecosystem models

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.

Identifying cardinal dates in phytoplankton time series to enable the analysis of long-term trends

Phenology and seasonal succession in aquatic ecosystems are strongly dependent on physical factors. In order to promote investigations into this coupling, methods of characterising annual time series of phytoplankton were derived and applied to a 31-year data set from Saidenbach Reservoir (Saxony, Germany). Field data are often scarce and irregularly sampled, particularly in the transition period from winter to spring, so reliable methods of determining cardinal dates in the time series are necessary. The proposed methods were used to determine the beginning, maximum and end of the spring mass development of phytoplankton by estimating the inflexion points (A), fitting a Weibull-type function (B) and fitting linear segments to the logarithmic values (C). For the data set from Saidenbach Reservoir, all three methods proved to be relevant to the analysis of long-term trends. Differences between the maxima determined by the different methods seemed small, but there were deviations when the maximum was related to physical factors such as ice-out. The Weibull-type fit gave the most reliable and comprehensible results and is recommended for trend analyses. For all methods, long-term analysis of the duration of the spring mass development and the duration of the spring full circulation revealed a period of consistently low values (1975–1990) followed by a period of higher values (1990–2005). These periods were also identified for the date of ice-out, although in this case there was a period of high values followed by a period of low values. A sensitivity analysis that compared results from subsampled time series with increasing time intervals indicated that a minimum of one sample every three weeks is needed to obtain reliable results.

Impact of inorganic carbon availability on microcystin production by Microcystis aeruginosa PCC 7806.

ABSTRACT Batch culture experiments with the cyanobacterium Microcystis aeruginosa PCC 7806 were performed in order to test the hypothesis that microcystins (MCYSTs) are produced in response to a relative deficiency of intracellular inorganic carbon (Ci,i). In the first experiment, MCYST production was studied under increased Ci,i deficiency conditions, achieved by restricting sodium-dependent bicarbonate uptake through replacement of sodium bicarbonate in the medium with its potassium analog. The same experimental approach was used in a second experiment to compare the response of the wild-type strain M. aeruginosa PCC 7806 with its mcyB mutant, which lacks the ability to produce MCYSTs. In a third experiment, the impact of varying the Ci,i status on MCYST production was examined without suppressing the sodium-dependent bicarbonate transporter; instead, a detailed investigation of a dark-light cycle was performed. In all experiments, a relative Ci,i deficiency was indicated by an elevated variable fluorescence signal and led to enhanced phycocyanin cell quotas. Higher MCYST cell quotas (in the first and third experiments) and increased total (intracellular plus extracellular) MCYST production (in the first experiment) were detected with increased Ci,i deficiency. Furthermore, the MCYST-producing wild-type strain and its mcyB mutant showed basically the same response to restrained inorganic carbon uptake, with elevated variable fluorescence and phycocyanin cell quotas with increased Ci,i deficiency. The response of the wild type, however, was distinctly stronger and also included elevated chlorophyll a cell quotas. These differences indicate the limited ability of the mutant to adapt to low-Ci,i conditions. We concluded that MCYSTs may be involved in enhancing the efficiency of the adaptation of the photosynthetic apparatus to fluctuating inorganic carbon conditions in cyanobacterial cells.

Hybrid expert system DELAQUA — a toolkit for water quality control of lakes and reservoirs

Abstract An expert system to be used for assisting in control of water quality of lakes and reservoirs is presented. Its character is hybrid with regard to structure and function. Shell NEXPERT OBJECT serves as platform for the implementation, while the hypertext system ToolBook has been used to develop the user interface which consists of three levels: (1) an object-oriented geographic interface with maps of the country, region and catchment area of waters under consideration, (2) an intelligent front-end to support the handling of the simulation model SALMO and the historical data base HIDA, and (3) a user interface to consult knowledge bases of three water quality problems (eutrophication, algal blooms and pathogens). The deterministic model SALMO, empirical models of the Vollenweider-type and a fuzzy model are accessible from the knowledge bases for eutrophication and algal blooms.

Solving Differential Equations in R

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Thermal performance curves of Paramecium caudatum: A model selection approach

The ongoing climate change has motivated numerous studies investigating the temperature response of various organisms, especially that of ectotherms. To correctly describe the thermal performance of these organisms, functions are needed which sufficiently fit to the complete optimum curve. Surprisingly, model-comparisons for the temperature-dependence of population growth rates of an important ectothermic group, the protozoa, are still missing. In this study, temperature reaction norms of natural isolates of the freshwater protist Paramecium caudatum were investigated, considering nearly the entire temperature range. These reaction norms were used to estimate thermal performance curves by applying a set of commonly used model functions. An information theory approach was used to compare models and to identify the best ones for describing these data. Our results indicate that the models which can describe negative growth at the high- and low-temperature branch of an optimum curve are preferable. This is a prerequisite for accurately calculating the critical upper and lower thermal limits. While we detected a temperature optimum of around 29 °C for all investigated clonal strains, the critical thermal limits were considerably different between individual clones. Here, the tropical clone showed the narrowest thermal tolerance, with a shift of its critical thermal limits to higher temperatures.

Modelling the effects of temperature and food on individual growth and reproduction of Daphnia and their consequences on the population level

Abstract Individual based simulations of population dynamics require the availability of growth models with adequate complexity. For this purpose a simple-to-use model (non-linear multiple regression approach) is presented describing somatic growth and reproduction of Daphnia as a function of time, temperature and food quantity. The model showed a good agreement with published observations of somatic growth (r 2 = 0.954, n = 88) and egg production (r 2 = 0.898, n = 35). Temperature is the main determinant of initial somatic growth and food concentration is the main determinant of maximal body length and clutch size. An individual based simulation was used to demonstrate the simultaneous effects of food and temperature on the population level. Evidently, both temperature and food supply affected the population growth rate but at food concentrations above approximately 0.4 mg Cl −1 Scenedesmus acutus temperature appeared as the main determinant of population growth. Four simulation examples are given to show the wide applicability of the model: (1) analysis of the correlation between population birth rate and somatic growth rate, (2) contribution of egg development time and delayed somatic growth to temperature-effects on population growth, (3) comparison of population birth rate in simulations with constant vs. decreasing size at maturity with declining food concentrations and (4) costs of diel vertical migration. Due to its plausible behaviour over a broad range of temperature (2–20 °C) and food conditions (0.1–4 mg Cl −1 ) the model can be used as a module for more detailed simulations of Daphnia population dynamics under realistic environmental conditions.

Coping with Temperature at the Warm Edge – Patterns of Thermal Adaptation in the Microbial Eukaryote Paramecium caudatum

Background Ectothermic organisms are thought to be severely affected by global warming since their physiological performance is directly dependent on temperature. Latitudinal and temporal variations in mean temperatures force ectotherms to adapt to these complex environmental conditions. Studies investigating current patterns of thermal adaptation among populations of different latitudes allow a prediction of the potential impact of prospective increases in environmental temperatures on their fitness. Methodology/Principal Findings In this study, temperature reaction norms were ascertained among 18 genetically defined, natural clones of the microbial eukaryote Paramecium caudatum. These different clones have been isolated from 12 freshwater habitats along a latitudinal transect in Europe and from 3 tropical habitats (Indonesia). The sensitivity to increasing temperatures was estimated through the analysis of clone specific thermal tolerances and by relating those to current and predicted temperature data of their natural habitats. All investigated European clones seem to be thermal generalists with a broad thermal tolerance and similar optimum temperatures. The weak or missing co-variation of thermal tolerance with latitude does not imply local adaptation to thermal gradients; it rather suggests adaptive phenotypic plasticity among the whole European subpopulation. The tested Indonesian clones appear to be locally adapted to the less variable, tropical temperature regime and show higher tolerance limits, but lower tolerance breadths. Conclusions/Significance Due to the lack of local temperature adaptation within the European subpopulation, P. caudatum genotypes at the most southern edge of their geographic range seem to suffer from the predicted increase in magnitude and frequency of summer heat waves caused by climate change.

Extending one-dimensional models for deep lakes to simulate the impact of submerged macrophytes on water quality

Submerged macrophytes can stabilise clear water conditions in shallow lakes. However, many existing models for deep lakes neglect their impact. Here, we tested the hypothesis that submerged macrophytes can affect the water clarity in deep lakes. A one-dimensional, vertically resolved macrophyte model was developed based on PCLake and coupled to SALMO-1D and GOTM hydrophysics and validated against field data. Validation showed good coherence in dynamic growth patterns and colonisation depths. In our simulations the presence of submerged macrophytes resulted in up to 50% less phytoplankton biomass in the shallowest simulated lake (11?m) and still 15% less phytoplankton was predicted in 100?m deep oligotrophic lakes. Nutrient loading, lake depth, and lake shape had a strong influence on macrophyte effects. Nutrient competition was found to be the strongest biological interaction. Despite a number of limitations, the derived dynamic lake model suggests significant effects of submerged macrophytes on deep lake water quality. Existing models were innovatively combined to study macrophyte effects in deep lakes.Submerged macrophytes can significantly affect the water clarity in deep lakes.This effect depends on lake geometry, depth, and nutrient loading.