A perplexing new question that has emerged from the recent surge of interest in behavioural syndromes or animal personalities is--why do individual animals behave consistently when behavioural flexibility is advantageous? If individuals have a tendency to be generally aggressive, then a relatively aggressive individual might be overly aggressive towards offspring, mates or even predators. Despite these costs, studies in several taxa have shown that individuals that are more aggressive are also relatively bold. However, the behavioural correlation is not universal; even within a species, population comparisons have shown that boldness and aggressiveness are correlated in populations of sticklebacks that are under strong predation pressure, but not in low predation populations. Here, we provide the first demonstration that an environmental factor can induce a correlation between boldness and aggressiveness. Boldness under predation risk and aggressiveness towards a conspecific were measured before and after sticklebacks were exposed to predation by trout, which predated half the sticklebacks. Exposure to predation generated the boldness-aggressiveness behavioural correlation. The behavioural correlation was produced by both selection by predators and behavioural plasticity. These results support the hypothesis that certain correlations between behaviours might be adaptive in some environments.