When two genetically differentiated populations or species come into contact and interbreed, their hybrid offspring will contain a mosaic of the genetic variants characterising the parental lineages, re-arranged into novel combinations. The fitness of these hybrids is central to the evolution of reproductive isolation, but also plays an important role in conservation policy, and in crop and animal breeding.

Fitness landscapes are simple mathematical models that generate a rich variety of context-dependent genetic interactions, making them a useful tool for studying the ways in which these interactions affect hybrid fitness. In this thesis, I will explore a particular fitness landscape model based on Fisher’s geometric model (Fisher, 1930), which provides a flexible yet tractable framework for modelling hybridisation. Throughout, I complement the analytical and simulation results with applications to published empirical data.

First, I explore the fitness of F1 hybrids, and show how phenotypic dominance can generate a diverse range of outcomes. As the dominance effects at different loci are rarely expressed together during divergence, they are unlikely to be co-adapted. I show that, as a consequence, dominance generally reduces F1 fitness, closely resembling the effects of uniparental inheritance, Still, I predict the effects of dominance can also be beneficial, and this may help to explain transgressive hybrids that prosper in extreme environments.

Next, I present results for hybrids of any type, based on a new and more general derivation of the model. I show that predictions can be expressed in terms of two distance measures capturing the net effect and total amount of evolutionary change in terms of additive and dominance effects, as well as their interaction. Each of these terms carries information about the history of divergence, telling us about the type, direction, and subject of selection respectively.

Thinking about the long-term outcomes of hybridisation, I then investigate what we can learn from introgression line studies about coadaptation between alleles and the fixability of heterosis. Consolidating the classical theories of heterosis, I illustrate how this model generates complex genetic architectures characterised by transient overdominance.

Finally, I present an extension of the model to arbitrary ploidy which lets us investigate the effects of dosage on hybrid fitness. Applying these predictions to published data, I show how they can help to explain repeatedly observed differences in patterns of heterosis and inbreeding depression between diploids and tetraploids.