The formal processes of alpha-taxonomy ensure that species have unique names and can be
identified. No similar process is mandatory for infraspecific variation, so the species
is a uniquely important practical term. At present, there is little agreement of the
definition of a species. In the last 30 years, numerous concepts have been proposed. The
nature of fish species is reviewed. Clonal inheritance of nuclear genes occurs in several
lineages. Hybridization is frequent, often leading to introgression, which may lead to
extinction of species. Species may have hybrid origins. There is good evidence for parallel
speciation in similar habitats. There are clearly exceptions to the cladistic assumption
of dichotomous branching during speciation. Sibling species may exist with no discernible
niche differentiation. Basic assumptions are violated for the recognition, phylogenetic,
ecological and some formulations of the evolutionary species concepts. The most satisfactory
definitions are two of the earliest proposed in the light of evolutionary theory. The
Darwinian view is that species are recognizable entities which are not qualitatively
distinct from varieties. A restatement of this concept in genetic terms provides a means
of dealing with all forms of species known in present-day fishes. This modified Darwinian
concept is operated through the application of fuzzy logic rather than rigid definition.
This involves a search for discontinuities between species, rather than an a priori
definition of how boundaries are to be determined. A subset of Darwinian species are
Mayrian or `biological species', which are characterized by their demonstrable reproductive
isolation from other species. The status of a population as a Mayrian species is a testable
hypothesis. Molecular techniques allow this hypothesis to be tested more easily than
previously, at least when dealing with sympatric populations.