SUBJECT

Ecological modelling I

lecture

master

Faculty of Science

Biology MSc

2

Semesters 1-4

Autumn/Spring semester

1. Population dynamics, density independent models. The basic problems, and the basic equations. The exponential processes.

2. Population dynamics, discrete density dependent models I. Modelling of the density dependency. The linear stability analysis. The canonical form of the logistic model, and the linear stability of it.

3. Population dynamics, discrete density dependent models II. Web diagrams and the stability analysis. Bifurcation, classificatio of the simeple bifurcatiuons. When the period-two emerges in the logistic model?

4. Population dynamics, discrete density dependent models III. Contest and scramble competition. The Ricker and the Beverton-Holt models.

5. Chaos in population dynamics I. The characteristics of chaos. Period doubling, as a route to chaos. The notion of Ljapunov exponent. Calculation of Ljapunov exponent in one dimensional systems.

6. Chaos in population dynamics II. detecting chaos in population time series. The parameter fitting method. Takens embedding theorem, and its consequence in the tiem seriesd analysis.

7. Chaos in the population dynamics III. The population dynamics of the Tribolium castaneum. The LPA model and its characteristics. The LPA model and the experimental results on Tribolium castaneum.

8. Continuous population dynamical models. Linear stability analysis in the continuous model. The continuous logistic model. The dynamical consequences of the Allee effect.

9. Population dynamics and selection. The dynamics of allele frequency haploid and diploid populations. The equlibrium allele frequency, Fisher's theorem. Density dependent selection. Rougharden's model for the r and K selection. Selection if population moves along a limit cycle.

10. Dynamics of structured populations I. The basic assumptions in the models. Matrix algebra: eigenvalue, eigenvector, baze, baze transformation. The nice nature of diagonal matrices.

11. Dynamics of structured populations II. The strong ergodicity theorem of the demography. Stable cohort distribution and the reproductive value. The Frobenius theorem, and the growth of the population. Elasticity and sensitivity.

12. Dynamics of structured populations III. The nature of Leslie matrices. Deduction of the Euler-Lotka equation. The stable cohort distribution and the reproductive value in the Leslie model. Other demographic parameters in the Leslie model.

13. Dynamics of structured populations IV. Density dependent Leslie models. Selection in the Leslie model. Where an optimal individual invests the energy?

14. Metapopulations. The basic assumptions of the spatially explicit models. Assumptions of the metapopulation modelling. The Levins' model, and its behaviour. The variations of the Levins' model: source-sink model, Allee effect, disappearing patches. Finite stochastic metapopulations, and the expeccted time of extinction. *

• Case, T. J. An illustrated giude to theoretical ecology. Oxford Univ. press. 2000.

• Gurney, W. S. C. and Nisbet, R. M. Ecological dynamics. Oxford Univ. press 1998 *