"A group of organisms capable of interbreeding and producing fertile offspring."The problem with this definition is that does not put Species, in terms of meaning, at the level of Organism. Being a group of organisms it turns out to be a mere classification, and that is the main problem with this definition, its lack of substance.
I defend that Prokaryotes represent a Two-Layer scheme while Eukaryotes a Three-Layer one (see The Truth about Species! - Part 3 - Inductive Nature).
What are those three layers? Simple, the existing two of Prokaryotes plus one, Species. In this Scheme we have, Environment, Species and Organism.
Prokaryotes vs. Eukaryotes, NS - Natural Selection, SS - Sexual Selection
Now, you may notice that Environment and Organism have a materialistic definition, an organism is any contiguous living system, and an Environment encompasses all living and non-living things occurring naturally on Earth or some region thereof. Note that this means that an Organism may be a single animal as it may be multiple, like in the case of ants, where an Organism as a living system is the Colony, maintaining this way the concept of interbreeding (colonies) and the notion of Species as the blueprint of colonies with all animals' characteristics and interactions, including the ones composing the same Organism that aren't able to reproduce (worker ants). So, bottom line, an Organism may also be something abstract, like a Colony of ants (Superorganism), as the sole unit capable of interbreeding and producing fertile offspring!
Question, why there isn't a materialistic definition for Species? Because most evolutionists refuse to see Species as something equally materialistic as an Organism.
Now we will try to construct our own materialistic definition:
"Species, a product of meiosis, is the proxy between Environment and Organism."And in which way Species is a proxy? In the way that evolution doesn't work on Organisms, instead, it works on this Proxy that we call Species.
Seeing Species as something real, something materialist, the definition is as natural as Environment or Organism.
The view of this Proxy makes it clear that, albeit some traits of Eukaryotic organisms increase the difficulty of reproduction, like the evolution of the intercrossing, they are the best prove that Evolution works on Species and not on Organisms. When it comes to Organisms, they only relate with this Proxy in a form of Sexual Selection. In conclusion, there isn't Natural Selection or Evolution for the Eukaryote Organism, the Species is there precisely for that.
If you still insist in exotic examples, like Asexual Species, note that Asexual Species are an impossibility, or if you prefer, simple unnatural to Eukaryotes.
"I have repeatedly stressed how difficul it is to state something general about asexuals that with reasonably accuracy will hold for all or at least most of them. One such generalization is, however, of great importance. It says that asexual lineages are, on average, shorter lived in evolution than sexual lineages. This conclusion is based on the fact that asexuality appears constantly among sexual eukaryotes, while no reverse evolution – from full asexuality to sexuality – is normally to reckon with. Nevertheless, the eukaryotic tree remains dominated by sexuality. This situation would not hold unless asexual lineages have a shorter lifespan on average than sexual lineages. The relative disadvantage of asexuality is directly seen in the eukaryote tree in all its immensity, where sexuality dominates all major branches. The same logic applies, however, also to every derived lineage, down to for example the water-flea Daphnia pulex that generate asexuals at a considerable rate and still retains sexuality as their basic reproductive mode (Paland et al. 2005; see Chapter 15)." - in Lost Sex, The Evolutionary Biology of Parthenogenesis
Tree of Life with Genome Size - Dismissing Asexual Species
