A strictly cladistic classification could theoretically have an impractically large number of levels

If we could count all the branch points between the earliest common ancestor of all modern species and the present, the number would be ludicrously high, requiring far more levels than the existing Linnaean system.

There are two things to say in the defence of cladism on this point:

1. The problem is not acute in practice since we know very little about the phylogenetic relations of living things. Only in extreme circumstances, such as the Hawaiian fruitflies, do we know enough for extra levels to be needed.

2. When we do know the fine branching of phylogeny, it is perfectly possible to devise a classificatory scheme to represent it. Hennig, in his final work on the phylogeny of the insects, represented the phylogeny by a numerical scheme shown in the figure.

Linnaeus devised his system for approximately 10 000 - 20 000 named species. About a million species have been named now and the expansion of our knowledge requires an expanded classificatory scheme to accommodate it.

Figure: part of Hennig's (1981) classification of the insects. The state of phylogenetic theory for the insects is too advanced for the limited number of Linnaean terms so Hennig instead classified each group by a series of numbers. The order of splitting can be traced back through the series of numbers.