## M7116 Structured population models

Faculty of Science
Spring 2021
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: k (colloquium). Other types of completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Guaranteed by
prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Mon 9:00–10:50 online_M3
• Timetable of Seminar Groups:
M7116/01: Mon 1. 3. to Fri 14. 5. Mon 11:00–11:50 online_M3, Z. Pospíšil
Prerequisites
any linear algebra, any calculus
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Structured population models, i.e. discrete dynamical models with discrete (matrix) or continuous (integral) operator represent one of basic theoretical tools for population ecology and demography. The aim of the subject is to teach students to construct models of evolution of population that is structured to certain classes (the word "population" is meant in a very broad sense) and subsequently to analyze models with constant matrix in details (both transient and asymptotic dynamics) and to inform them with methods to analyze models with time or frequency dependent operators.
Learning outcomes
At the end of this course students should be able to: Construct the models (in collaboration with ecologists or demographers); analyse the model mathematically; interpret the results of analysis.
Syllabus
• 1. Age and stage structured models 2. Leslie and projction matrices 3. Steady states, their existence and stability. Perron-Frobenius theorem 4. Parameters identification from observed data 5. Density-dependent models 6. Two-sex models 7. Models with external variability
Literature
recommended literature
• CASWELL, Hal. Matrix population models :construction, analysis, and interpretation. 2nd ed. Sunderland, Mass.: Sinauer Associates, 2001. xvi, 722 s. ISBN 0-87893-096-5. info
not specified
• Ellner, P.E., Childs, D.Z., Rees, M. Data-driven Modelling of Structured Populations, Springer 2016, ISBN 978-3-319-28891-8
Teaching methods
Lecture with class discussion focused on general questions, seminar talks over particular models. The political-epidemiological cicumstances cause replacing of teaching by an asynchronous distant form.
Assessment methods
Colloquium should demonstrate the ability of students to understand the studied problems by elaborating a group project.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2004, Autumn 2006, Autumn 2008, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Spring 2015, Spring 2017, Spring 2019.
• Enrolment Statistics (recent)