It is well known that animals that are hybrids of parents with differing genetic makeup tend to be more vigorous and productive than their parents: they are not simply the parental average. This phenomenon of hybrid vigor is variously described as non-additive, heterotic, transgressive or dominant, depending on the exact behaviour of the trait in question. Hybrid vigour is very important in animal breeding, but its causes are poorly understood at the level of the genome. It is also accepted that physical traits are often under the control of many genes, and that the expression of these genes individually tend to behave additively. There is thus a gap in our understanding - how do we explain hybrid vigour if most genes behave additively? In this project we aim to answer this question. In preparatory work leading up to this project we have examined aspects of of non-additive traits in populations of pigs, mice and rats. We find that non-additive effects on traits are surprisingly common. Second, when we attempt to identify the genes that are causal for these effects we noticed that often a genetic variant with non-addivive effects on both a physical trait and the expression of a gene have the remarkable property that the affected gene is often on a different chromosome. Thus long-range effects on the expression of a gene tend to be non-additive, in contrast to short-range effects which are additive, and which do not play a role in hybrid vigour. Up to now research has focused on these short-range effects, but our data suggest that it is the long-range effects that are the most relevant to non-additive effects.We have also found that sometimes the effect of a gene depends on whether it is inherited from the mother or father, adding an additional level of non-additive complexity. Yet another source of non-linearity is that genomes may be re-arranged, moving the locations of genes and sometimes silencing them. In our proposal we will analyse genetic data in population of pigs, mice and rats on which we also have extensive data on growth and other traits, to seek patterns that are predictive of non-additive phenomena. By looking across many data sets we can be sure that our conclusions are robust and are likely to generalise to other mammals.