Copy number variants (CNVs) are a pervasive, but understudied source of genetic variation and evolutionary potential. Long-term evolution experiments in chemostats provide an ideal system for studying the molecular processes underlying CNV formation and the temporal dynamics of de novo CNVs. Here, we developed a fluorescent reporter to monitor gene amplifications and deletions at a specific locus with single-cell resolution. Using a CNV reporter in nitrogen-limited chemostats, we find that GAP1 CNVs are repeatedly generated and selected during the early stages of adaptive evolution resulting in predictable dynamics of CNV selection. However, subsequent diversification of populations defines a second phase of evolutionary dynamics that cannot be predicted. Using whole genome sequencing, we identified a variety of GAP1 CNVs that vary in size and copy number. Despite GAP1's proximity to tandem repeats that facilitate intrachromosomal recombination, we find that non-allelic homologous recombination (NAHR) between flanking tandem repeats occurs infrequently. Rather, breakpoint characterization revealed that for at least 50% of GAP1 CNVs, origin-dependent inverted-repeat amplification (ODIRA), a DNA replication mediated process, is the likely mechanism. We also find evidence that ODIRA generates DUR3 CNVs, indicating that it may be a common mechanism of gene amplification. We combined the CNV reporter with barcode lineage tracking and found that 10^3-10^4 independent CNV-containing lineages initially compete within populations, which results in extreme clonal interference. Our study introduces a novel means of studying CNVs in heterogeneous cell populations and provides insight into the underlying dynamics of CNVs in evolution.