Crisp & Chandler, Paraphyletic species 
831 
from higher taxa. Such a property exists: it is their position at the base of the 
phylogenetic system. All higher taxa consist of at least two terminals (species) which 
share one or more apomorphies. (Monotypic higher taxa have only one species, 
which should have an autapomorphy.) However species, being basal in the system, 
are the generators of apomorphies. If speciation is the point at which apomorphies 
appear (= fixation of a new character), then this event irreversibly transforms the 
ancestral species from an autapomorphic (monophyletic) entity to a symplesiomorphic 
(metaphyletic) one. If species are the generators of new species, then they cannot be 
simultaneously monophyletic. Species are temporarily monophyletic if they have 
not yet spawned a daughter species. They are permanently monophyletic only if 
they have become extinct without leaving a descendant. A corollary of this special 
view of species is the notion that when species are conceived as part of lineages, 
speciation is not coincident with the splitting of lineages. It is the point at which 
autapomorphies evolve. Thus the appropriate model of speciation is an asymmetric 
one of branching off, not a symmetric one of splitting (Kornet 1993b). 
How frequent are paraphyletic species? 
From the discussion above it is clear that most species concepts predict a high 
frequency of paraspecies and metaspecies (except the monophyletic species concept, 
which evades the problem). Suppose that we segregate as a species any 
autapomorphic set of populations and segregate as another species the set of 
populations that is diagnosed only by lacking the autapomorphy. This procedure 
would be consistent with both the phylogenetic species concept and the composite 
species concept. It reflects the asymmetric model of speciation presented above. 
Both species are uniquely diagnosable but the first species would be monophyletic 
and the second either paraphyletic or metaphyletic. If this simple protocol worked 
in all cases, at least 50% of all species would be either paraphyletic or metaphyletic. 
However it is possible that two diagnosable sister-groups would each show a 
(different) autapomorphy. Both would be treated as species and both would be 
monophyletic. Such occurrences would lower the overall proportion of non- 
monophyletic species. This scenario does not require symmetrical splitting of lineages, 
since it may be assumed that there is some delay between lineage splitting and 
character fixation (Nixon & Wheeler 1992; Kornet 1993b). If this delay is very different 
in the two daughter lineages, then observation of both at the same time is likely to 
show one species to be autapomorphic and its sister group to be metaphyletic. 
However, even if there is such a difference, both lineages may be sufficiently old to 
have acquired an autapomorphy (i.e., speciated) when observed. (This assumes that 
neither lineage has split again in the meantime.) Thus the frequency of symmetrical 
versus asymmetrical speciation will depend partly on the probability of lineages 
splitting, relative to the probability of character fixation. If this ratio were high, then 
speciation would appear asymmetrical in most cases, and the proportion of non- 
monophyletic species could be well above 50%. If the ratio were low, then 
autapomorphic species pairs would be more common and the proportion of non- 
monophyletic species would lie closer to 0%. Note that if two allopatric populations 
have split permanently (cf. evolutionary species concept) but neither has yet acquired 
an autapomorphy, then we have no evidence for treating them as distinct species. 
For this reason, we would never expect 100% non-monophyletic species. 
In this paper we have presented several empirical examples of paraspecies and 
metaspecies. All these examples are plants, but animal examples arising from 
phylogenetic analysis at the population level exist too (Green & Borkin 1993; Melnick 
& Hoelzer 1993; Melnick et al. 1993; Hoelzer & Melnick 1994; Patton & Smith 1994). 
However, these are selected examples and give no clue to the frequency of non- 
