Abstract (eng)
In this diploma thesis, the implementation of a software package is presented, which facilitates the simulation and analysis of multilocus migration-selection models. The deterministic, discrete simulation iterates the underlying difference equation to find the equilibria of the dynamical system. As an application, the equilibrium structure of a population under quadratic stabilizing selection is investigated.
First, we state the biological assumptions and introduce the mathematical model. We define the investigated dynamical system and introduce fitness functions, recombination, and migration models. Furthermore, we define important quantities to measure properties of the genetic composition and of differentiation at equilibrium.
Then, we review related work concerning forward-time simulations and quadratic stabilizing selection. Moreover, we discuss the limiting case of strong migration.
This is followed by a discussion of the implementation of the developed software. This comprises the object model, the database architecture, and a discussion of algorithmic issues.
Finally, the results obtained by the application of the program to the case of quadratic stabilizing selection are presented. First, the case of a diallelic two-locus panmictic population is investigated, allowing for arbitrary optimum position. Then, two demes are considered, displacing the optima symmetrically within the demes, and assuming the Deakin migration model.