Systems Analysis and Modelling

Note that this course can not be combined in an individual programme with FEM31806 '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 EZO23306 (Biology) and CSA10806 (Plant Sciences). The course comprises four blocks:

1. systems dynamics with examples from population ecology;
2. model performance & model evaluation;
3. partial differential equations & modelling in space;
4. 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

• 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

• Mandatory attendance (%) Students are expected to be present during computer practicals and case study work
• Assignment other (20%) During the course two case studies will be conducted in which students will apply systems approaches to concrete questions of ecology, crop science and soil science, with the aim to explore and evaluate system management options. Students will work on the case studies in groups of two and hand in a power point report not later than 17.00 on the Friday before the case study presentations. Each slide of the power point has to provide a complete answer to one question. On Thursday of week 3 and 6, the case studies will be presented and discussed. Each group will present 1-3 questions. The reports are graded based on the answers provided in the powerpoint. The average grade of the two case reports forms 20% of the overall grade. The presentation itself is not graded, but presence is obligatory to get the grade.
• Written test with open questions (80%) 80% of the grade is formed by a three-hour, written, closed-Syllabus exam with open questions, which is aimed at testing the gained insights and knowledge, related to learning outcomes 1-6. The exam contains three main questions, each consisting of several sub-questions, and dealing with separate main themes of the course. Both in the case studies and in the written exam the students have to show their knowledge on the basic concepts used in systems analysis and their ability to formulate a quantitative simulation model based on information provided on a certain (eco)system.

· 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.

• A reader will be available at https://wurreadershop.proefschriftmaken.nl/shop/wur. The reader contains all the reading material, and many exercises that enable the student to apply concepts and tools. If you have any questions, contact your course coordinator.