Can we quickly check if one family tree fits inside another?

Evolutionary biologists use networks to represent complex relationships that simple trees can't capture, but need to verify when a given tree actually appears within a network. Van Iersel and colleagues developed an algorithm solving this problem faster on "tree-like" networks, then proved they've hit the speed limit: no fundamentally faster solution exists. This matters because phylogenetic networks are increasingly common in studying reticulate evolution (hybridization, gene flow), making this containment check essential.