Aneuploidy is a feature of many cancers. Recent studies demonstrate that in the hematopoietic stem and progenitor cell (HSPC) compartment aneuploid cells have reduced fitness and are efficiently purged from the bone marrow. However, early phases of hematopoietic reconstitution following bone marrow transplantation provide a window of opportunity whereby aneuploid cells rise in frequency, only to decline to basal levels thereafter. Here we demonstrate by Monte carlo modeling that two mechanisms could underlie this aneuploidy peak: rapid expansion of the engrafted HSpc population and bone marrow microenvironment degradation caused by pre-transplantation radiation treatment. Both mechanisms reduce the strength of purifying selection acting in early post-transplantation bone marrow. We explore the contribution of other factors such as alterations in cell division rates that affect the strength of purifying selection, the balance of drift and selection imposed by the HSPC population size, and the mutation-selection balance dependent on the rate of aneuploidy generation per cell division. We propose a somatic evolutionary model for the dynamics of cells with aneuploidy or other fitness-reducing mutations during hematopoietic reconstitution following bone marrow transplantation. Similar alterations in the strength of purifying selection during cancer development could help explain the paradox of aneuploidy abundance in tumors despite somatic fitness costs. Aneuploidy, or deviation of the chromosome number from the normal karyotype (resulting from chromosome mis-segregation), is associated with many cancers, being prevalent in both solid cancers and leukemia 1-4. The effects of aneuploidy vary, with some cellular phenotypes dependent on what specific chromosome(s) is lost or gained, and other phenotypes arising from a general stress response to aneuploidy 5. Consequently, associations of aneuploidy with cancers range widely, from a few percent, such as the loss of chromosome 1 or gain of chromosome 5 in kidney adenocarcinoma, to 50%, such as the loss of chromosome 3 in melanoma, and even 70% for the loss of chromosome 22 in meningiomas 2. In total, almost 90% of cancers exhibit gains or losses of at least one chromosome arm, with patterns specific to particular tumor types 4. For example, squamous cell cancers originating in multiple organs exhibit a common pattern of chromosome arm 3p loss and 3q gain. Aneuploid cells have been shown to drive adaptation in yeast 6-8. This evidence has led to speculations that by conferring greater adaptability, variability of chromosomal ploidy in a cell population might lead to the expansion of aneuploid clones in human tissues, fueling further accumulation of oncogenic alterations in cells and progression to cancer 9-11. However, aneuploidy has been shown to more commonly reduce the fitness of animal