Over the last few decades the Biological Species Concept (BSC)
has become predominately the dominant species definition used.
This concept defines a species as a reproductive community.
This though has had much refinement through the years. The
earliest precursor to the concept is in Du Rietz (1930), then
later Dobzhansky added  to this definition in 1937.But even after
this the definition was highly restrictive. The definition of a
species that is  accepted as the Biological species concept was
founded by Ernst Mayr (1942);

..groups of actually or potentially interbreeding  natural
populations which are reproductively isolated from other such
groups

However, this is a definition on what happens in nature. Mayr
later amended this definition to include an ecological component;

..a reproductive community of populations (reproductively
isolated from others) that occupies a specific niche in nature

The BSC is greatly accepted amongst vertebrate zoologists &
entomologists. Two reasons account for this .Firstly these are
the groups that the authors of the BSC worked with. (Mayr is an
ornithologist & Dobzhansky has worked mainly with Drosophila).
More  importantly Sexual reproduction is the predominate form of
reproduction in these groups. It is not coincidental that the BSC
is less widely used amongst botanists.  Terrestrial plants
exhibit much more greater diversity in their mode of reproduction
than  vertebrates and insects.

There has been many criticisms of the BSC in its theoretical
validity and practical utility. For example, the application of
the BSC to a number of groups is problematic because of
interspecific hybridisation between clearly delimited
species.(Skelton).

It cant be applied to species that reproduce asexually ( e.g
Bdelloid rotifers,eugelenoid flagellates ).Asexual forms of
normally sexual organisms are also known. Prokaryotes are also
left out by the concept because sexuality as defined in the
eukaryotes  is unknown.

The Biological species concept is also questionable in those
land plants that primarily self-pollinate.(Cronquist 1988).
Practically the BSC has its limitations in the most obvious form
of fossils.-It cant be applied to this evolutionary distinct
group because they no longer mate.( Do homo Erectus and homo
sapiens represent the same or different species?)
It  also has limitations when practically applied to delimit
species. The BSC suggests breeding experiments as the test of
whether a n organism is a distinct species. But this is a test
rarely made, as the number of crosses needed to delimit a species
can be massive. So the time, effort and money needed to carry out
such tests is prohibitive. Not only this but the experiment
carried out are often inconclusive.

In practice even strong believers of the BSC use phenetic
similarities and discontinuties for delimiting species.
Although more widely known ,several alternatives to the
biological species concept exist.
The Phenetic (or Morphological / Recognition) Species Concept
proposes an alternative to the BSC (Cronquist) that has been
called a “renewed practical species definition”. This  defines
species as;

“… the smallest groups that are consistently and
persistently distinct and distinguishable by ordinary means.”

Problems with this definition can be seen ,once again depending
on the background of the user.  For example “ordinary means”
includes any techniques that are widely available, cheap and
relatively easy to apply. These means will differ among different
groups of organisms. For example, to a botanist working with
angiosperms ordinary means might mean a hand lens; to an
entomologist working with beetles it might mean a dissecting
microscope; to a phycologist working with diatoms it might mean a
scanning electron microscope. What means are ordinary are
determined by what is needed to examine the organisms in
question.  So once again we see that it is a Subjective view
depending on how the biologist wants to read the definition. It
also has similar difficulties to the BSC in defining between
asexual species and existence of hybrids.

There are several phylogenetic species definitions. All of them
suggest hat classifications should reflect the best supported
hypotheses of the phylogeny of the organisms. Baum (1992)
describes two types of phylogenetic species concepts, one of thes
is that A species must be monophyletic and share one or more
derived character. There are two meanings to monophyletic (Nelson
1989). The first defines a monophyletic group as all the
descendants of a common ancestor and the ancestor. The second
defines a monophyletic group as a group of organisms that
are more closely related to each  other than to any other
organisms.

So really, the species concepts are only theoretical and by no
means no standard as to which species should be grouped. However
it can be argued that without a more stuructured approached
proper discussion can not occur due to conflicting species names.
And so, if there are quite large problems with all of the
species concepts, the question about what is used in practicehas
to be asked. Most taxonomists use on or  more of four main
criteria; (Stace 1990)

1.The individuals should bear a close resemblance to one another
such that they are always   readily recognisable as members
of that  group
2.There are gaps between  the spectra of variation exhibite by
related species; if there are no   such gaps then there is a
case for amalgamating the taxtas a single species.
3.Each species occupies a definable geographical area (wide or
narrow) and is demonstrably suited to the environmental
conditions which it encounters.
4.In sexual taxa, the individuals should be capable of
interbreeding with little or no loss of fertility, and there
are should be some reduction in the levelll or success
(measured in terms of  hybrid fetility or competitiveness of
crossing with other species.

Of course, as has been seen, no one of these criteria is
absolute and it is more often left to the taxonomists own
judgement.
Quite frequently a classification system is brought about from
the wrong reasons. Between two taxa similarities and differences
can be found which have to be consisdered ,and it is simply up to
the taxonomists discretion as to which differences or simila
rities should be empahasised. So differences are naturally going
to arise between taxonomists.The system used  can be brought
about for convienience, from historical  aspects and to save
argument. – It may be a lot easier to stick with a current
concept, although requiring radical changes, because of the
upheaval and confusion that may be caused.

As seen much has been written on the different concepts and
improvements to these concepts but  these amount to little more
than personal judgements aimed at producing a workable
classification (Stace).In general most Biologists adopt the
definition of species that is most suited to the type of animal
or plant that they are working with at the time and use their own
judgement as to what that means. It is common practice amongst
most taxonomists to look for discontinuities in variation which
can be used to delimit the kingdoms,divisions etc.. Between a
group of closley related taxa it can be useful, although highly
subjective, to use the crtieria of equivalence or comparibility.
Usually however, the criteria of discontinuity is more accurate
than comparibility ,even if the taxa are widely different.

References
Mayr, Ernst, 1904-/Systematics and the origin of species : from
the viewpoint of a zoologist/1942/QH 366

Cronquist, Arthur / The evolution and classification of flowering
plants/1968/QK 980

Stace, Clive A., Clive Anthony, 1938-/ Plant taxonomy and
biosystematics/1991/QK 990

Stuessy, Tod F / Plant taxonomy : the systematic evaluation of
comparative data/1990/QK 95

Evolution : a biological and palaeontological approach / editor
[for the Course Team] Peter Skelton/1993/QH 366

http://wfscnet.tamu.edu/courses/wfsc403/ch_7.htm  – Interspecific
Competition

http://sevilleta.unm.edu/lruedas/systmat.html  – Phylogenetic