Animals often differ in suites of correlated behaviours, comparable with how humans differ in personality. Constraints on the architecture of behaviour have been invoked to explain why such 'behavioural syndromes' exist. From an adaptationist viewpoint, however, behavioural syndromes should evolve only in those populations where natural selection has favoured such trait covariance, and they should therefore exist only in particular types of population. A comparative approach was used to examine this prediction of the adaptive hypothesis. We measured behavioural correlations in 12 different populations of three-spined stickleback (Gasterosteus aculeatus) and assessed whether they indeed varied consistently according to the selective environment, where population was unit of analysis. For a sample of fry from each population, we measured five different behaviours within the categories of (i) aggression (towards conspecifics); (ii) general activity; and (iii) exploration-avoidance (of novel foods, novel environments and altered environments). We show that behavioural syndromes are not always the same in different types of stickleback population: the often-documented syndrome between aggressiveness, activity and exploratory behaviour existed only in large ponds where piscivorous predators were present. In small ponds where predators were absent, these behaviours were not (or only weakly) associated. Our findings imply that population variation in behavioural syndromes does not result from stochastic evolutionary processes, but may result instead from adaptive evolution of behaviour favouring what should prove to be optimal trait combinations.