## Over deze cursus

Note that this course can not be combined in an individual programme with FEM-31806 ‘Models for Ecological Systems’.

Systems approaches are widely used in studies of ecological systems for the purpose of increasing our understanding of ecosystems functioning and improving systems management. The application domain ranges from the (sub-)individual level to the (agro-) ecosystem level. Systems approaches represent a scientific concept in which the real world is divided into systems. Depending on the specific objective, these systems are analysed and captured in quantitative simulation models. Studying model behaviour in comparison to real world behaviour allows testing of hypotheses and acquiring a better mechanistic understanding of the study system.

This course introduces the student to the study of the behaviour of complex ecological systems and builds on courses such as EZO-23306 (Biology) and CSA-10806 (Plant Sciences). The course comprises four blocks:

- systems dynamics with examples from population ecology;
- model performance & model evaluation;
- partial differential equations & modelling in space;
- integrating case studies on population dynamics & nutrient dynamics in soil

The first block (chapters 1-6) focuses on conceptual model formulation and quantitative model specification, and refreshes known concepts such as system, model, simulation, state, rate, feedback, time-coefficient, relational diagram, analysis of dimensions or units, numerical integration methods and discontinuities in integral contents. The concepts are explained using examples from population ecology, such as logistic and paralogistic growth of single populations, and the interaction between competing populations. Programming is guided by the use of relational diagrams in the software package Visual Grind.

The second block (chapter 7) focuses on aspects related to model evaluation. Statistical means and inverse modelling are used to assess how well a model describes experimental data. Techniques for parameter estimation and sensitivity analysis are introduced and model outcomes will be discussed critically. Programming will be conducted in in the software package MATLAB, which is more flexible than Visual Grind.

The third block (chapters 8-12) introduces partial differential equations for the simulation of spatial processes in one or two dimensions. We start with simulating heat flow, and mass flow and diffusion of nutrients in soils. Subsequently, several techniques for spatial modelling are studied. Examples are related to population ecology, and include vegetation patterning, and dispersal by organisms, both at the individual and population level.

The fourth block (case studies 1 and 2) will familiarize students with the cycle of systems analysis and programming, which involves the integration of data and systems knowledge in conceptual and mathematical models, model implementation in a program, parameter estimation and model evaluation. Cases will be developed for themes from ecology, crop science and soil science, and management options will be explored.

The course is intended for 2nd or 3rd year university students, in particular for biologists, plant scientists, agro-ecologists, crop protectionists and soil scientists, but the concepts and the simulation techniques are applicable in many different fields of science.

## Leerresultaten

After succesful completion of this course students are expected to be able to:

- apply the cycle of systems analysis and programming for dynamic models;
- analyse systems in terms of states, rates and driving variables on the basis of relational diagrams and unit analysis;
- analyse spatial processes with partial differential equations and their numerical solutions;
- apply individual and population based modelling techniques for dispersal;
- conduct sensitivity analysis, model calibration and model performance evaluation;
- apply systems approaches in ecology, crop science, soil science and in the exploration of management options.

## Voorkennis

Assumed Knowledge:

· Basic mathematical concepts and techniques, including power, exponential and logarithmic functions; calculus: differentiation and integration; vectors and matrices.

· It is assumed that BSc Biology students have followed Modelling Biological Systems, and BSc Plant Sciences students have followed Introduction Quantitative Agroecology.

· Students that do not have this background are urged to read the available background information on Brightspace before the start of the course: a mathematical recap, Chapter 1 and 2 of the syllabus, and the background lectures.

- Code
**PPS20306** - Studiepunten
**ECTS 6** - Email contactpersoon