The thesis begins with a general introduction to population genetics in chapter 1. I review the fundamental processes of evolution - mutation, recombination, selection, gene flow and genetic drift - and give an overview of Bayesian inference in statistical population genetics. Later, I introduce the studied species, Alpine ibex (Capra ibex ), and its recent history. This history is intimately linked to the structured population in the Swiss Alps that provides the source of genetic data for this thesis. A particular focus is devoted to approximate Bayesian computation (ABC) in chapter 2, a method of inference that has become important over the last 15 years and is convenient for complex problems of inference. In chapter 3, the biological focus is on estimating the distribution of mutation rates across neutral genetic variation (microsatellites), and on inferring the proportion of male ibex that obtain access to matings each breeding season. The latter is an important determinant of genetic drift. Methodologically, I compare different methods for the choice of summary statistics in ABC. One of the approaches proposed by collaborators and me and based on boosting (a technique developed in machine learning) is found to perform best in this case. Applying that method to microsatellite data from Alpine ibex, I estimate the scaled ancestral mutation rate (THETA anc = 4Neu) to about 1:288, and find that most of the variation across loci of the ancestral mutation rate u is between 7.7*10 -4 and 3.5*10 -3. The proportion of males with access to matings per breeding season is estimated to about 21%. Chapter 4 is devoted to the estimation of migration rates between a large number of pairs of populations. Again, I use ABC for inference. Estimating all rates jointly comes with substantial methodological problems. Therefore, I assess if, by dividing the whole problem into smaller ones and assuming that those are approximately independent, more accuracy may be achieved overall. The net accuracy of the second approach increases with the number of migration rates. Applying that approach to microsatellite data from Alpine ibex, and accounting for the possibility that a model without migration could also explain the data, I find no evidence for substantial gene flow via migration, except for one pair of demes in one direction. While chapters 3 and 4 deal with neutral variation, in chapter 5 I investigate if an allele of the Major Histocompatibility Complex (MHC) has been under selection over the last ten generations. Short- and medium-term methods for detecting signals of selection are combined. For the medium-term analysis, I adapt a matrix iteration approach that allows for joint estimation of the initial allele frequency, the dominance coefficient, and the strength of selection. The focal MHC allele is shared with domestic goat, and an interesting side issue is if this reflects an ancestral polymorphism or is due to recent introgression via hybridization. I find most evidence for asymmetric overdominance (selection coefficient s: 0.974; equilibrium frequency: 0.125) or directional selection against the `goat' allele (s: 0.5) with partial recessivity. Both scenarios suggest a disadvantage of the `goat' homozygote, but differ in the relative fitness of the heterozygotes. Overall, two aspects play a dominating role in this thesis: the biological questions and the process of inference. They are linked, yet while the proximate motivation for the biological component is given by a specific system - the structured population of Alpine ibex in the Swiss Alps - the methods used and advanced here are fairly general and may well be applied in different contexts.

We studied the dynamic of nine populations of Alpine ibex ( Capra ibex ibex ) in five protected areas. We showed a strong effect of age on demographic parameters, with a marked decrease of survival after 10-12 years of age. We also found a high variability of old females' reproduction between populations. Contrary to what is expected for a highly dimorphic species like ibex, males survived as well as females except for old individuals. Winter harshness had a negative impact on survival of old individuals but not on reproduction and survival of young. We conclude that ibex have evolved a highly conservative life-history tactic compared to other ungulates studied to now. From a management viewpoint we also showed that under some circumstances ground counts might provide reliable estimates of ibex population trends.