1. Cladistics: This school focuses solely on evolutionary branching patterns (cladogenesis) to create phylogenetic trees (cladograms). It emphasizes shared derived characteristics (synapomorphies) to group organisms, ignoring similarities that may have arisen through convergent evolution or that are ancestral (plesiomorphic). The resulting classifications are strictly hierarchical and reflect evolutionary relationships based on common ancestry.
2. Evolutionary Systematics (also called traditional systematics): This approach considers both branching patterns and the degree of evolutionary change (anagenesis) when constructing classifications. It incorporates both shared derived and shared ancestral characteristics in its analysis, leading to classifications that reflect both evolutionary history and overall similarity. This method can lead to paraphyletic groups (groups that don't include all descendants of a common ancestor).
3. Phenetics (Numerical Taxonomy): This approach emphasizes overall similarity between organisms, regardless of their evolutionary history. It uses numerical methods to analyze a large number of observable characteristics (phenotypic traits) to construct classifications based on similarity indices. While it's less widely used now compared to cladistics and evolutionary systematics, it can be a useful supplementary tool.
It's important to note that these schools are not mutually exclusive, and many systematists integrate aspects of multiple approaches in their work. Cladistics has become the dominant approach in recent decades, but evolutionary systematics remains influential, and phenetic methods are still applied in specific contexts.