Applied Mathematics for the Life Sciences

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.

Important applications we currently research are

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

Key References:

• Van Lenteren, J.C., Lanzoni, A., Hemerik, L. et al. (2021). The pest kill rate of thirteen natural enemies as aggregate evaluation criterion of their biological control potential of Tutaabsoluta. Scientific Reports 11, 10756, https://doi.org/10.1038/s41598-021-90034-8
• Schneider, R., van’t Klooster, K., Picard, K.L. et al. (2021). Long-term single-cell imaging and simulations of microtubules reveal principles behind wall patterning during proto-xylem development. Nature Communications 12, 669, https://doi.org/10.1038/s41467-021-20894-1
• Li, Y., van Heijster, P., Simpson, M.J. and Wechselberger, M. (2021). Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion. Physica D 423, 132916, https://doi.org/10.1016/j.physd.2021.132916

Faculty: L. Hemerik, E. Deinum, P. van Heijster, E. Siero, P. de Ruiter (emeritus), J. Molenaar (emeritus)

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.

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;

Key references:

• Geelen, C. V. C., Yntema, D. R., Molenaar, J. and Keesman, K. J. (2021). Burst Detection by Water Demand Nowcasting Based on Exogenous Sensors. Water Resources Management, 35, 1183–1196
• Kandemir, M. H., Beelen, M., Wagterveld, R. M., Yntema, D. R. and Keesman, K. J. (2021). Dynamic acoustic fields for size selective particle separation on centimeter scale. Journal of Sound and Vibration 490, 115723
• Roman, M., Roman, P., Verbeke, R., Gutierrez, L., Vanoppen, M., Dickmann, M., Egger, W., Vankelecom, I., Post, J., Cornelissen, E., Keesman, K. and Verliefde, A. (2021). Non-steady diffusion and adsorption of organic micropollutants in ion-exchange membranes: effect of the membrane thickness. iScience 24(2), 102095
• Joubert, D., Stigter, J.D. and Molenaar, J. (2020). An efficient procedure to assist in the re-parametrization of structurally unidentifiable models. Mathematical Biosciences 323, 108328

Faculty: H. Stigter, K. Keesman (emeritus), G. van Willigenburg, J. Molenaar (emeritus)

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 from within and outside Wageningen UR for various applications in the life sciences. We also develop new methodologies for the quantitative analysis of ABMs.

Key references:

• Van Voorn, G., Hengeveld, G. and Verhagen, J. (2020). An agent based model representation to assess resilience and efficiency of food supply chains. Plos one, 15(11), e0242323
• Li, Y., van Heijster, P., Marangell, R. and Simpson, M.J. (2020), Travelling wave solutions in a negative nonlinear diffusion-reaction model. Journal of Mathematical Biology 82 (6), 1495-1522
• Ten Broeke, G., Van Voorn, G. and Ligtenberg, A. (2016). Which sensitivity analysis method should I use for my agent-based model? Journal of Artificial Societies and Social Simulation, 19(1)

Faculty: G. van Voorn, P. van Heijster

Stochastic Differential Equations

Many natural systems, like crops, growing animals, or ecosystems, are affected during their development (e.g., growth or evolution) by exogenous influences, i.e., relevant factors outside of 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 exogenous 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 Ordinary and 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 environmental events on system outcomes, e.g., end-of-season yields.

Key references:

• Tsutsumi-Morita, Y., Heuvelink, E., et al. (2021). Yield dissection models to improve yield; a case study in tomato. In Silico Plants 3(1), diab012.
• Van Voorn, G. A. K., Boer, M. P., et al. (2023). A conceptual framework for the dynamic modeling of time-resolved phenotypes for sets of genotype-environment-management combinations: a model library. Frontiers in Plant Science 14, 1172359.

Faculty: G. van Voorn, P. van Heijster

Courses by Applied Mathematics for the Life Sciences

We include our research experience in our courses, such as

• CSA-34306 Ecological Modelling and Data Analysis in R
• MAT-23306 Multivariate Mathematics Applied
• MAT-24803 Time Dependent Systems
• MAT-26306 Control Engineering
• MAT-31806 System Identification: learning for decision and control
• MAT-32306 Systems and Control Theory
• MAT-34306 Stochastic Differential Equations and Data Assimilation
• SSB-30806 Modelling in Systems Biology

And in PhD courses and summer schools.

For a full list of courses offered by Biometris please check our Education of Biometris page.

We also supervise students at different stages of their academic career. For a list of BSc./MSc./PhD projects check the Biometris thesis page on Brightspace.