Observations from molecular marker studies on recently diverged species indicate that substitution patterns in DNA sequences can often be complex and poorly described by tree-like bifurcating evolutionary models. These observations might result from processes of species diversification and/or processes of sequence evolution that are not tree-like. In these cases, bifurcating tree representations provide poor visualization of phylogenetic signals in sequence data. In this paper, we use median networks to study DNA sequence substitution patterns in plant nuclear and chloroplast markers. We describe how to prune median networks to obtain so called pruned median networks. These simpler networks may help to provide a useful framework for investigating the phylogenetic complexity of recently diverged taxa with hybrid origins.