Aneuploidy plays critical roles in genome evolution.Alleles, whose dosages affect the fitness of an ancestor, will have altered frequencies in the descendant populations upon perturbation.Single-cell sequencing enables comprehensive genome-wide copy number profiling of thousands of cells at various evolutionary stage and lineage. That makes it possible to discover dosage effects invisible at tissue level, provided that the cell lineages can be accurately reconstructed.Here, we present a Minimal Event Distance Aneuploidy Lineage Tree (MEDALT) algorithm that infers the evolution history of a cell population based on single-cell copy number (SCCN) profiles. We also present a statistical routine named lineage speciation analysis (LSA), which facilitates discovery of fitness-associated alterations and genes from SCCN lineage trees.We assessed our approaches using a variety of single-cell datasets. Overall, MEDALT appeared more accurate than phylogenetics approaches in reconstructing copy number lineage.From the single-cell DNA-sequencing data of 20 triple-negative breast cancer patients, our approaches effectively prioritized genes that are essential for breast cancer cell fitness and are predictive of patient survival, including those implicating convergent evolution. Similar benefits Recent advances in single-cell DNA sequencing (e.g., tagmentation based approach 15 and single-cell CNV solution by the 10X Genomics) have enabled large-scale acquisition of singlecell copy number (SCCN) profiles in tens of thousands of cells at around 100 kb resolution (~0.1X sequencing coverage per cell) [16][17][18][19] . Other platforms such as single-cell RNA-sequencing 20, 21 and single-cell ATAC-sequencing 22 have also been utilized for SCCN profiling.These SCCN profiles not only present a rich pool of genetic perturbations that are invisible at tissue level, but also potentiate reconstruction of cellular lineage, based on which the impact of an allele on cellular fitness can be measured. Thus, statistical approaches that integrate cellular lineage tracing with population genetic analysis 23 can enable discovery of novel disease genes and mechanisms of disease progression.So far, studies performing retrospective lineage tracing from single-cell data have largely been utilizing phylogenetics approaches designed to model species evolution, which is quite different from cellular evolution in terms of duration, scale, genetics and dynamics 24, 25 . Many existing phylogenetics approaches assume that genomic sites evolve independently and follow the socalled infinite site assumption (ISA) 26 . But in the context of aneuploidy, a genome site can often be altered repeatedly by different CNAs, due partly to constraints on genome and chromatin structures, properties of DNA replication/repairing 27 and functional selection. To apply conventional maximum parsimony approaches on SCCN data, one has to over-segment genomic regions and represent copy numbers as characters in disjoint intervals, which illrepresents the properties of DNAs and dis...