The repeatability observed across cancers arising in the same tissue can help understand the evolutionary process of tumour initiation. We recently developed a framework to quantify the local malignant adaptation of genetic clones in tissue-specific environments. In this Commentary, we argue that such a 1-dimensional model can be improved by separating its 2 components to obtain a dual scale: local adaptation, dictating proliferation rates in the local environment, and malignant adaptation, influencing the likelihood that a clone becomes cancerous and invasive. Such a change could strengthen our understanding of the population dynamics underlying cancer initiation and assess different evolutionary scenarios.