Historical Linguistics and Language Families 6, Exercise 1: tree and wave

Tree model: assumes languages change only through social splitting and
divergence. It explains descent and subgroups. It struggles to explain some
shared features, especially in the Germanic languages (Wikipedia, Wave
model).

Wave model: an innovation starts in one area and spreads speaker to speaker
and dialect to dialect, like waves on water. It adds a way to show
innovations that overlap in intersecting patterns, which the tree cannot
easily represent.

The page says the wave model improves but does not supersede the tree; use
the tree for descent and the waves for spread (the last point is my gloss).