Starting from a "Biological" definition of species, one soon is convinced that the species idea in itself is flawed. Here I have collected some links and excerpts on this topic. Notes for a digression on species and speciation. These are frequent topics for classroom digressions.

I found an article on line. For the criminally insane price of US$55.87 I could get a copy of this from the cartel at http://www.ingentaconnect.com/:

Márquez L.M.; Van Oppen M.J.H.; Willis B.L.¹; Reyes A.²; Miller D.J.². 2002. The highly cross-fertile coral species, Acropora hyacinthus and Acropora cytherea, constitute statistically distinguishable lineages. Molecular Ecology, Volume 11, Number 8, August 2002 , pp. 1339-1349(11).

Here are some other links:

From Wikipedia article, Definitions of "Species"

Definitions of species

The question of how best to define "species" is one that has occupied biologists for centuries, and the debate itself has become known as the species problem. One definition that is widely used is that a species is a group of actually or potentially interbreeding populations that are reproductively isolated from other such groups.

The definition of a species given above is derived from the behavioral biologist Ernst Mayr, and is somewhat idealistic . Since it assumes sexual reproduction, it leaves the term undefined for a large class of organisms that reproduce asexually. Biologists frequently do not know whether two morphologically similar groups of organisms are "potentially" capable of interbreeding. Further, there is considerable variation in the degree to which hybridization may succeed under natural and experimental conditions, or even in the degree to which some organisms use sexual reproduction between individuals to breed. Consequently, several lines of thought in the definition of species exist:

Typological species
A group of organisms in which individuals are members of the species if they sufficiently conform to certain fixed properties. The clusters of variations or phenotypes within specimens (i.e. longer and shorter tails) would differentiate the species. This method was used as a "classical" method of determining species, such as with Linnaeus early in evolutionary theory. However, we now know that different phenotypes do not always constitute different species (e.g.: a 4-winged Drosophila born to a 2-winged mother is not a different species). Species named in this manner are called morphospecies.

Morphological species
A population or group of populations that differs morphologically from other populations. For example, we can distinguish between a chicken and a duck because they have different shaped bills and the duck has webbed feet. Species have been defined in this way since well before the beginning of recorded history. This species concept is much criticised because more recent genetic data reveal that genetically distinct populations may look very similar and, contrarily, large morphological differences sometimes exist between very closely-related populations. Nonetheless, most species known have been described solely from morphology.

Biological / Isolation species
A set of actually or potentially interbreeding populations. This is generally a useful formulation for scientists working with living examples of the higher taxa like mammals, fish, and birds, but meaningless for organisms that do not reproduce sexually. It does not distinguish between the theoretical possibility of interbreeding and the actual likelihood of gene flow between populations and is thus impractical in instances of allopatric (geographically isolated) populations. The results of breeding experiments done in artificial conditions may or may not reflect what would happen if the same organisms encountered each other in the wild, making it difficult to gauge whether or not the results of such experiments are meaningful in reference to natural populations.

Biological / reproductive species
Two organisms that are able to reproduce naturally to produce fertile offspring. Organisms that can reproduce to almost always make infertile hybrids, such as a mule or hinny, are not considered to be the same species.

Mate-recognition species
A group of organisms that are known to recognize one another as potential mates. Like the isolation species concept above, it applies only to organisms that reproduce sexually. Unlike the isolation species concept, it focuses specifically on pre-mating reproductive isolation.

Phylogenetic (Cladistic)/ Evolutionary / Darwinian species^{[verification needed]}
A group of organisms that shares an ancestor; a lineage that maintains its integrity with respect to other lineages through both time and space. At some point in the progress of such a group, members may diverge from one another: when such a divergence becomes sufficiently clear, the two populations are regarded as separate species. Subspecies as such are not recognized under this approach; either a population is a phylogenetic species or it is not taxonomically distinguishable.

Ecological species
A set of organisms adapted to a particular set of resources, called a niche, in the environment. According to this concept, populations form the discrete phenetic clusters that we recognize as species because the ecological and evolutionary processes controlling how resources are divided up tend to produce those clusters

Genetic species
based on similarity of DNA of individuals or populations. Techniques to compare similarity of DNA include DNA-DNA hybridization, and genetic fingerprinting (or DNA barcoding).

Phenetic species
based on phenotypes

Recognition species
based on behavioral interactions

Microspecies
Species that reproduce without meiosis or fertilization so that each generation is genetically identical to the previous generation. See also apomixis.

Cohesion species
Most inclusive population of individuals having the potential for phenotypic cohesion through intrinsic cohesion mechanisms. This is an expansion of the mate-recognition species concept to allow for post-mating isolation mechanisms; no matter whether populations can hybridize successfully, they are still distinct cohesion species if the amount of hybridization is insufficient to completely mix their respective gene pools.

Evolutionarily Significant Unit (ESU)
An evolutionarily significant unit is a population of organisms that is considered distinct for purposes of conservation. Often referred to as a species or a wildlife species, an ESU also has several possible definitions, which coincide with definitions of species.

In practice, these definitions often coincide, and the differences between them are more a matter of emphasis than of outright contradiction. Nevertheless, no species concept yet proposed is entirely objective, or can be applied in all cases without resorting to judgement. Given the complexity of life, some have argued that such an objective definition is in all likelihood impossible, and biologists should settle for the most practical definition. For most vertebrates, this is the biological species concept (BSC), and to a lesser extent (or for different purposes) the phylogenetic species concept (PSC). Many BSC subspecies are considered species under the PSC; the difference between the BSC and the PSC can be summed up insofar as that the BSC defines a species as a consequence of manifest evolutionary history, while the PSC defines a species as a consequence of manifest evolutionary potential. Thus, a PSC species is "made" as soon as an evolutionary lineage has started to separate, while a BSC species starts to exist only when the lineage separation is complete.

Another article from Wikipedia covers the species problem. A historical review of the idea of the "species" is interesting. The idea of reproductive isolation is paramount.

Quotations on the species problem

"... I was much struck how entirely vague and arbitrary is the distinction between species and varieties" Darwin 1859 (p. 48)^[7]

"No term is more difficult to define than "species," and on no point are zoologists more divided than as to what should be understood by this word". Nicholson (1872) p. 20^[44]

"Of late, the futility of attempts to find a universally valid criterion for distinguishing species has come to be fairly generally, if reluctantly, recognized" Dobzhansky (1937) p.310 ^[11]

"The concept of a species is a concession to our linguistic habits and neurological mechanisms" Haldane (1956) ^[35]

"The species problem is the long-standing failure of biologists to agree on how we should identify species and how we should define the word 'species'." Hey (2001) ^[39]

"First, the species problem is not primarily an empirical one, but it is rather fraught with philosophical questions that require-but cannot be settled by-empirical evidence." Pigliucci (2003) ^[38]

Reproductive Isolation (Wikipedia):

Reproductive isolation

Adapted from Wikipedia, the free encyclopedia

(wikipedia also has an article on Speciation.

An important concept in evolutionary biology, reproductive isolation is a category of mechanisms that prevent two or more populations from exchanging genes. The separation of the gene pools of populations, under some conditions, can lead to the genesis of distinct species. Reproductive isolation can occur either by preventing fertilization, or by the creation of a degenerate or sterile hybrid, such as the case with the common mule and the hinny.

Three sections:

1 Fertilization barriers (pre-zygotic)

... Everything from a physical barrier (such as an ocean) formed between two populations, to ethological (behavioral) differences, to errors in cell division that cause incompatibility between populations.

Speciation by reproductive isolation is frequently seen in plants, with errors in division during mitosis doubling the number of chromosomes and thereby preventing even pairing of chromosomes with normal gametes during fertilization.
For various species that bloom seasonally, the time of gamete release can prevent hybridization, a temporal isolation.
For animal species, mating might be stymied.
Incompatible genitalia forms a mechanical reproductive isolation,
members of opposite sexes often fail to recognize one another, due to some morphological difference used to identify a potential mate.
The gametes of different species are frequently incompatible, and do not form a viable zygote.
Sperm may not possess the proper enzymes for penetrating the coat of the ovum, or
have the proper chemical markers to signal the egg cell to accept it.

2 Hybrid barriers (post-zygotic)

The first is gametic: the gametes successfully combine, but then immediately die .
The second is zygotic: the zygote forms but quickly dies.
The third is embryonic or larval: which is spontaneous abortion of the hybrid fetus.
The fourth is hybrid inviability: the offspring is born but is unfit, quickly succumbs to environmental pressures, and dies.
The fifth is hybrid sterility: the offspring can produce no offspring of its own, isolating its genes from both parental groups. Finally, hybrids that do produce offspring can, potentially, produce sterile progeny.