T. Dobzhansky (1938) - The largest and most inclusive reproductive community of sexual and cross-fertilizing individuals which share a common gene pool.
Ernst Mayr (1940) - A species consists of a group of populations which replace each other geographically or ecologically and of which the neighboring ones intergrade or interbreed wherever they are in contact or which are potentially capable of doing so (with one or more of the populations) in those cases where contact is prevented by geographical or ecological barriers.
Julian Huxley (in "Evolution, The Modern Synthesis", 1942) - There is some reasonable measure of agreement among competent systematists as to the criteria they adopt for classifying organisms as different species. There are first, visible (morphological) resemblance between members of a group, of such a nature as to be consonant with the view that the group is actually or potentially an interbreeding one; secondly, lack of intergrading with other groups; thirdly, a geographical area of distribution consonant with the idea of a common ancestry for the group; and fourthly, where data are available, infertility on crossing with related forms.
G.G. Simpson (1961) - A lineage of populations evolving with time, separately from others, with its own unique evolutionary role and tendencies. (The Evolutionary Concept)
E.O. Wiley (1981) - An evolutionary species is a single lineage of ancestor-descendent populations which maintains its identity from other such lineages and which has its own evolutionary tendencies and historical fate.
S. Wright (1968) - A species in time and space is composed of numerous local populations, each one intercommunicating and intergrading with others.
H.H. Ross - The different kinds of living things.
C.L. Prosser (1986) - Biological species are populations of like organisms which exchange genes.
M. Ghiselin (1974) - The most extensive units in the natural economy, such that reproductive competition occurs among their parts.
L. Van Valen (1976) - A lineage or closely related set of lineages which occupies an adaptive zone minimally different from that of any other lineages in its range, and which evolves separately from all other lineages outside its range.
C.D. Michener - A species is a group of organisms not itself divisible by phenetic gaps resulting from concordant differences in character states (except for morphs - such as sex, age, or caste), but separated by such phenetic gaps from other such units.
J.B.S. Haldane - I object to the term "species concept", which I think is misleading. A species in my opinion is a name given to a group of organisms for convenience, and indeed of necessity. The only objective facts are the differences which exist between all members of two groups of organisms in which, in fact, all members doation of individual biparental organisms which share a common fertilization system.biparental organisms which share a common fertilization system.
Various authors - A paleospecies is a segment of an evolving lineage and obviously has no sharp borders in time.
J. Cracraft - An irreducible (basal) cluster of organisms diagnosably distinct from other clusters, and within which there is a parental pattern of ancestry and descent. (Phylogenetic Concept)
A.G. Kluge - The species category is the smallest historical individual within which there is a parental pattern of ancestry and descent.
A.R. Templeton - The most inclusive population of individuals having the potential for phenotypic cohesion through intrinsic cohesion mechanisms. (Cohesion Concept) [Table 1.]
Table. Classification of cohesion mechanisms (from A.R. Templeton 1989. The meaning of species and speciation: a genetic perspective. Pp. 3-27 in D. Otte and J. A. Endler (eds.), Speciation and its Consequences. Sinauer, Sunderland).