Applied mathematics for life sciences

Biometris focuses on quantitative descriptions for a range of important life sciences applications aimed at improving the quality of life. This inlcudes modelling of cellular processes, crop growth, agents, populations, patterns, ecosystems, social-ecological and socio-technical systems, and various engineered and controlled environments. For this, we use different model approaches such as mathematics, software, and statistics.

Theoretical Biology

Theoretical biology covers the full spectrum of theoretical investigation of the living world, ranging from philosophy of biology to mathematical biology, and bio-informatics. Biometris looks at theoretical biology for applications aimed at improving quality of life, in which ordinary differential equations or partial differential equations are used for, e.g., the quantitative description of pattern formation or population dynamics.

Applications 

Important applications we currently research are:

• Quantitative descriptions of biological control
• Food webs
• Socio-economic systems
• Pattern formation in vegetation, plants, cells, and animals

Dynamic Systems, Signals, and Control

We often encounter non-linear process behaviour in the life sciences and the challenge is to identify non-linear models that describe these processes on the basis of knowledge (summarized in a set of ordinary differential equations) and corresponding data. Dynamic system identification and control theory are applied in the Wageningen setting, meaning that practical examples are always motivating and leading in the analysis, while real-time processing of large amounts of data are often part of this analysis. Once an initial version of a model has been identified, model-based controller design is carried out and optimal input signals that yield desired system behaviour are computed. The modelling and control of a dynamic system is an iterative process and the loop is repeated several times before a satisfactory performance is achieved. Developing a good model prediction and a reliable dynamic model is a highly relevant skill that can be applied in a wide range of exciting fields.

Applications

Important applications we currently research are:

• The dynamic optimization and control of processes in innovative greenhouses based on climate and plant models;
• Extended Kalman filters for state- and parameter reconstruction in technical and biological systems;
• Non-linear parameter estimation and input in reactor systems and networks;
• Structural identifiability and structural controllability for non-linear systems;
• Food engineering applications;
• Ecosystem management based on, for example, water infiltration models;

Agent Based Models

Socio-technical systems (STS) and socio-ecological systems (SES) are dominated by interactions between autonomous decision makers and action takers (usually human agents) and their natural or technical environment. Examples of STS/SES are agricultural landscapes, managed ecosystems, fisheries, cities, and many more, in which the effects of actions by individuals on system outcomes can neither be trivially aggregated nor ignored. This is the result of the diversity in human agents who are involved, and who differ in, for instance, the decisions they make and their access to resources. Agent Based Models (ABMs) are a tool for the quantitative representation of STS/SES, involving an explicit description of the decision making and action taking processes of relevant agents and the interactions of these agents with each other and their surroundings. ABMs are commonly used for the exploration of the effects of alternative policies for STS/SES management, and as boundary objects in serious gaming with stakeholders to collectively learn about the possible effects of interventions. At Biometris we develop ABMs in collaboration with fellow researchers form within and outside Wageningen UR for various applications in the life sciences. We also develop new methodologies for the quantitative analysis of ABMs.

Stochastic Differential Equations

Many natural systems, like crops, growing animals, or ecosystems, are affected during their development (e.g., growth or evolution) by exogeneous influences, i.e., relevant factors outside our control, such as (extreme) weather, diseases, and environmental conditions. The combination of the background of the system (e.g., genetics or species assemblage) and the stochastic nature of exogeneous influences leads to uncertainty surrounding the prediction of how the system will develop in time, potentially invalidating outcome predictions such as yield predictions of new genotypes in new environments or evolutionary (drift) patterns. This uncertainty can be reduced by combining proper modelling techniques with frequent on-the-fly measurements (e.g., by satellites, drones, and smart sensors) that are currently becoming more and more available. At Biometris we develop models of Stochastic Differential Equations (SDEs) in collaboration with our statistics colleagues and fellow researchers from within and outside Wageningen UR for the quantification of the effects of stochastic events on system outcomes, e.g., end-of-season yields.