CORRELATIONS between different characters measured on individuals of a population have both genetic and environmental causes. In an extensive genetic analysis of the open-field behaviour of mice, which is a widely used index of “emotionality”, we have found that genetic and corresponding environmental patterns of association among pairs of characters are similar. We suggest that this relationship may frequently occur in nature and may account for the failure of recent attempts to obtain maximally and minimally heritable factor scores by multi-variate analysis.