The shape of phylogenetic trees has been used to make inferences about the evolutionary process by comparing the shapes of actual phylogenies with those expected under simple models of the speciation process. Previous studies have focused on speciation events, but gene duplication is another lineage splitting event, analogous to speciation, and gene loss or deletion is analogous to extinction. Measures of the shape of gene family phylogenies can thus be used to investigate the processes of gene duplication and loss. We make the first systematic attempt to use tree shape to study gene duplication using human gene phylogenies. We find that gene duplication has produced gene family trees significantly less balanced than expected from a simple model of the process, and less balanced than species phylogenies: the opposite to what might be expected under the 2R hypothesis. While other explanations are plausible, we suggest that the greater imbalance of gene family trees than species trees is due to the prevalence of tandem duplications over regional duplications during the evolution of the human genome.