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Avian influenza viruses (AIVs) periodically cross species barriers and infect humans. The likelihood that an AIV will evolve mammalian transmissibility depends on acquiring and selecting mutations during spillover, but data from natural infection is limited. We analyze deep sequencing data from infected humans and domestic ducks in Cambodia to examine how H5N1 viruses evolve during spillover. Overall, viral populations in both species are predominated by low-frequency (<10%) variation shaped by purifying selection and genetic drift, and half of the variants detected within-host are never detected on the H5N1 virus phylogeny. However, we do detect a subset of mutations linked to human receptor binding and replication (PB2 E627K, HA A150V, and HA Q238L) that arose in multiple, independent humans. PB2 E627K and HA A150V were also enriched along phylogenetic branches leading to human infections, suggesting that they are likely human-adaptive. Our data show that H5N1 viruses generate putative human-adapting mutations during natural spillover infection, many of which are detected at >5% frequency within-host. However, short infection times, genetic drift, and purifying selection likely restrict their ability to evolve extensively during a single infection. Applying evolutionary methods to sequence data, we reveal a detailed view of H5N1 virus adaptive potential, and develop a foundation for studying host-adaptation in other zoonotic viruses. Author summary: H5N1 avian influenza viruses can cross species barriers and cause severe disease in humans. H5N1 viruses currently cannot replicate and transmit efficiently among humans, but animal infection studies and modeling experiments have suggested that human adaptation may require only a few mutations. However, data from natural spillover infection has been limited, posing a challenge for risk assessment. Here, we analyze a unique dataset of deep sequence data from H5N1 virus-infected humans and domestic ducks in Cambodia. We find that well-known markers of human receptor binding and replication arise in multiple, independent humans. We also find that 3 mutations detected within-host are enriched along phylogenetic branches leading to human infections, suggesting that they are likely human-adapting. However, we also show that within-host evolution in both humans and ducks are shaped heavily by purifying selection and genetic drift, and that a large fraction of within-host variation is never detected on the H5N1 phylogeny. Taken together, our data show that H5N1 viruses do generate human-adapting mutations during natural infection. However, short infection times, purifying selection, and genetic drift may severely limit how much H5N1 viruses can evolve during the course of a single infection. [ABSTRACT FROM AUTHOR]