Variation and diversity are key concepts in the biological sciences. Much of the variation found in nature is the result of stochastic processes like mutation, recombination, genetic drift, and environmental or demographic stochasticity. However, at all levels of biological organisation part of the variation is structured in a systematic way. Most probably, much of this patterned variation results from directional processes like competition or selection. It is one of our core aims to investigate how such ‘adaptive variation’ does arise and how it is maintained on an ecological or evolutionary time scale.

At the behavioural level, we are interested in the evolution of ‘animal personalities’, the phenomenon that individuals differ systematically in whole suites of behavioural tendencies, and that, moreover, these tendencies are stable in time and correlated across contexts. How can various behavioural types coexist; why isn’t there a single type of highest fitness that outcompetes all other types? And why are behavioural tendencies stable in time and consistent across contexts; shouldn’t one expect a more flexible structure of behaviour?

At the life-history level, we are interested in the evolution of alternative phenotypes, like the differentiation of a primordially homogeneous population into distinct morphs, distinct mating types or distinct castes of workers. Under which circumstances should one expect the evolution of coexisting specialist phenotypes, rather than a single generalist phenotype? Why, for example, is the evolutionary transition from a state where all individuals are simultaneous hermaphrodites to a population with two separate sexes common in animals, but rare in plants? What are the evolutionary and ecological consequences of morph differentiation? What are, for example, the evolutionary and ecological implications of the interplay between natural and sexual selection?

At the population level, we are interested in the emergence of new species. To what extent can speciation be viewed as an adaptive process? Can we predict speciation on the basis of intraspecific and environmental factors? How can our understanding of speciation be used to explain global biodiversity patterns?

At the community level, we are interested in species coexistence and the interaction of ecology and evolution in shaping community patterns. Why can hundreds of algal species coexist in a droplet of water while the ‘principle of competitive exclusion’ predicts that the number of coexisting species will not exceed the number of limiting resources? To what extent are the structure of a food web and the energy flow pattern within a food web the result of adaptive evolution?

Interestingly, the answer to one type of question at one level of organisation is often of a similar structure as the answer to a quite different question at a different level of organisation. Indeed, many explanations of adaptive variation can be traced back to two basic principles: evolutionary branching resulting from architectural constraints and non-equilibrium dynamics caused by non-transitive interactions as in the Rock-Scissors-Paper game. Based on this general insight, there is hope that the detailed study of seemingly diverse examples of adaptive variation may in the end result in a general theory for the emergence and stability of biodiversity patterns.