Abstract: Introduction Clusters of subclonal mutations attributed to subclonal expansions have been observed across most cancer types. To date it is not clear what fraction of these expansions can be ascribed to selective sweeps or genetic drifts. The widely held theory states that tumour expansion arises from a series of selective sweeps. However, Williams et al. (Nat. Genet. 48:238–224, 2016) recently claimed to have identified neutral tumour evolution in one third of 904 samples from The Cancer Genome Atlas (TCGA). Material and methods First, using the same equations we simulated data of tumour undergoing selective sweeps. Second, we simulated data using branching processes, i.e. more realistic models. Third, we analysed the mutations from \textasciitilde 1600 exomes and \textasciitilde 1500,whole genomes of real tumours from TCGA and the International Cancer Genome Consortium, respectively. We grouped them into neutral and non-neutral tumours according to the rationale described by Williams et al. We then applied dN/dS, an orthogonal widely used approach to detect selection in non-synonymous mutations of coding regions. Finally, we ran dN/dS on subclonal mutations within individual cancer types. Results and discussions Application of the method described by Williams et al. led to over-calling of neutrality and led to random predictions (area under the curve\textasciitilde =50%) in simulations based on the deterministic or stochastic models, respectively. dN/dS analyses revealed significant and widespread positive selection in clonal and subclonal mutations within both neutral and non-neutral groups. Despite power limits, the subclonal mutations of many individual cancer types displayed dN/dS{$>$}1, evidence for positive selection. Conclusion Altogether, our results point to the lack of evidence for neutral tumour evolution and uncovered strong positive selection within subclonal mutations across cancers.