Any group of organisms are related by descent from a common ancestor, 2. There is a bifurcating pattern of cladogenesis, 3. Change in characteristics occurs in lineages over time. This is the most important and the least controversial assumption. Hierarchic order in nature is manifested in the distribution of characters shared among organisms.
Common ancestry is worked out from the number of synapomorphies among taxa.
For any three taxa, two taxa are more closely related to each other if they share a more recent common ancestor relative to a third. A single ancestral lineage split to give rise to two descendants. These are unrealistic assumptions of cladistics which are violated in real life. The hypothesis of a fossil species being a direct ancestor may be rejected if it possesses autapomorphies. Outgroup comparisons 3.