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Species is one of the concepts used in taxonomy to classify organisms. The word species is difficult to define exactly, as there a number of different methods of determining an organism's species, and different definitions may be more appropriate for different types of organisms. Nonetheless, it is generally agreed that the species is the only "real" taxon (i.e., occurring in nature) in the Linnean hierarchy.
Species used to be classified as morphological species, with animals which looked similar being placed as members of the same species. This method is very problematic, however, and a number of alternative methods have been proposed:
One of the standard definitions in use is the Biological Species Concept, or Mayrian Species Concept in honor of its principal architect, Ernst Mayr, which states that if two creatures can produce viable offspring, they are the same species. While this definition works well for most of the life forms we humans are familiar with in everyday life, it unfortunately doesn't apply to critters that reproduce asexually (such as bacteria). And this is not just a problem with the BSC: For every species definition yet proposed, there is at least one known life form to which that definition does not apply!
Though the BSC is very popular with most biologists and has exerted significant influence on most classifications, there are substantial problems with this definition besides its lack of applicability to agamospecies. The BSC is not sufficent for delineating species boundaries amongst extinct taxa, as we quite simply can never determine if two fossil forms that are possibly synonymous (e.g., Sinornis santensis and Cathayornis yandica) were reproductively isolated. One of the most intuitively uncomfortable results of strict application of the BSC is the combination into hybrid taxa of distinctly different species, a problem which has received a great deal of attention in Ornithology. For example, under the aegis of the BSC, Icterus bullocki and Icterus galbula were placed together within a single species, referred to as the "Northern Oriole," and yet genetic data have since challenged this reclassification by demonstrating that these two species are in fact more closely related to other taxa within Icteridae.
In light of these difficulties, Niles Eldredge & Joel Cracraft proposed in 1980 a Phylogenetic Species Concept (sometimes referred to as a Hennigian Species Concept), which differs substantially from the BSC in that seeks to define species as the smallest populational aggregate or lineage that can be diagnosed upon the basis of synapomorphic characters. The PSC has come into vogue with many researchers (e.g., Mary McKitrick and Robert Zink) and is equally applicable to agamospecies. It is contrasted with the variety of evolutionary species concepts which seek to define species as the largest population or lineage which can be delimited on the basis of synapomorphic characters. A logical criticism advanced by adherents of the BSC is that the PSC is merely a more rigorous reiteration of the Mayrian model, after all, how else are unqiue character states formed and subsequently retained if not by reproductive isolation? As it were, the debate is not likely to end anytime soon.
One might think that the lack of an overall, universally applicable species definition would be a serious problem for biologists. In practice, it isn't; very few biologists are interested in all aspects of the organisms they study, so in reality, any given biologist will choose which species definition covers the points they're interested in, and will also make it clear to other biologists that they're using Species Definition X rather than Species Definitions Y or Z.
For a thorough critique of the BSC, PSC, and other species concepts, see Speciation (J. A. Coyne and H. A. Orr, 2004).
See also: Speciation.