There is fundamental doubt about whether the natural unit of measurement for temperament and personality corresponds to single traits or to multi-trait profiles that describe the functioning of a whole person. Biogenetic researchers of temperament usually assume they need to focus on individual traits that differ between individuals. Recent research indicates that a shift of emphasis to understand processes within the individual is crucial for identifying the natural building blocks of temperament. Evolution and development operate on adaptation of whole organisms or persons, not on individual traits or categories. Adaptive functioning generally depends on feedback among many variable processes in ways that are characteristic of complex adaptive systems, not machines with separate parts. Advanced methods of unsupervised machine learning can now be applied to genome-wide association studies and brain imaging in order to uncover the genotypic–phenotypic architecture of traits like temperament, which are strongly influenced by complex interactions, such as genetic epistasis, pleiotropy and gene–environment interactions. We have found that the heritability of temperament can be nearly fully explained by a large number of genetic variants that are unique for multi-trait profiles, not single traits. The implications of this finding for research design and precision medicine are discussed. This article is part of the theme issue ‘Diverse perspectives on diversity: multi-disciplinary approaches to taxonomies of individual differences'.