Interesting question. It is reminiscent of some of Zeno's paradoxes, such as that of Aquiles and the tortoise. There is always some space to be covered by Aquiles before he can reach the slowly moving tortoise as any distance, no matter how small, can always be broken down in half. Lynds later (much, much later) argued that Zeno's paradoxes can be resolved if we take into account that instants in time do not physically exist.

Perhaps we will have a hard time defining a species based on its Adam or Eve (I know that the use of biblical references is inappropriate when discussing evolution... but couldn't resist) because the chances of them instantaneously becoming a population of individuals that is sexually isolated is slim to say the least (if they are, due to an awkward mutation or any other process producing similar results, you have your answer right there: the offspring came first by instantaneously becoming a new species). It seems more plausible to imagine that the changes are much more gradual (like the shortening distances covered by Aquiles before overtaking the tortoise. Spoiler alert: he will overtake the tortoise). As such, I will leave you with another question: can a species be defined instantaneously? After all, to assess viable reproduction, we need time and, let us not forget, gametes produced today are different from those created yesterday...

I think that the solution is to view taxonomic classification as an artificial construct that can be useful tool, rather than a biological reality. As you say, the reality is a continuum and whatever definition of species you try to apply universally will come unstuck with specific cases. It becomes even more problematic when people try to define species through time, based on fossils etc. The question is: why do taxonomy at all? The answer is that, whilst flawed, it can be helpful.

The same problem also applies to populations and even individuals - especially for clonal organisms. If I get cancer, is that cancer still me, or a rogue organism that I have spawned? Are multicellular organisms really individuals at all, or just populations of cells exhibiting advanced kin selection?

Ultimately, it all comes down to the inheritance of genetic material. If this is primarily vertical, then organism taxonomy makes sense. For genes that are frequently inherited horizontally, you should forget about organisms and concentrate on molecular phylogenies. For bacteria in particular, that might be the only taxonomic reality we really have.

Hi Ariel, I am familiar with most of the literature on species concepts but none of them addresses the above paradox. It is simply ignored. Independent of the species concept, the problem remains that if you are to classify all individuals into species, then at the point of speciation, you would have to deliberately declare the offspring of a certain generation a species different from its parents. That paradox lies in the fact that we can visualize speciation with a phylogenetic tree a posteriori, but that speciation does not factually happen for the individuals involved in it at the particular moment. Consider a population of a species. They generate offspring at the same time and then die (like many insects do). That offspring is isolated into two populations that do not interbreed. These two populations evolve into separate species. Theoretically you would be able to identify the generation in which genetic isolation is complete. That generation would then for both population be classified as a new species (B, C). In both cases, the preceding generation would be classified as the ancestral species (A). This seems to make sense from the view of an integrated species concept, but if you consider just the two subsequent generations involved in this event and you look at them individual, they would represent the same species each. See visual example:

AAAAAAAABBBBBBB

AAAAAAAA | | | | | |

AAAAAAAACCCCCCC

Both phylogenetically and using an integrated species concept, the separation between the three species (lineages) becomes clear. However, if you just look at the event AB and the event AC, by all means B would have to be considered the same species as its parent generation A, and the same applies for C. By extension it follows that B = C (via A). We usually circumvent this problem, and cladists have done this in general, by ignoring that A ever existed (cladists do not recognize ancestors as taxa). In cases where we deal with an evolving species complex, we solve the problem by just recognizing a single species A. But these are abstract, practical solutions that ignore the reality in my opinion.

Sorry, my example got altered.... attaching here again

For Zeno's paradox I allways figured that if one takes the discrete nature of the Achilles and the turtle into accout (they are, after all, not geometric points and both have a physical extension) it is very easy to explain how Achilles outruns the turtle.

The problem with the phylogenetic way to solve the chicken-egg paradox is that the discrete unit needed to solve it is not the idividual (this is adressed by Robert Lücking's introduction to the question. Since the individual allways belongs to the same species as its direct genetic predecessor (parents for sexually reproducing organisms)). However the existence of units that can not be directly observed (eg. individuals) is in some way a construct (even if we aknowledge the existence of species in nature in contrast to species as a concept one can not observe a species, only individual specimen).

So I guess we need some axioms to to define the entity of chicken (not the chicken we observe but as in "what is a chicken?"; this is the discrete unit we need to solve the problem). And if we start defining chicken than we can define higher units as well (species, genus, family, order etc.). So with the right axioms ((i.e. the common ancestor of the entity we realise as a chicken and an entity we define as a (for a lack of better term) not-chicken)) we can answer the chicken-egg-problem.

(Edit: removed a few (more) typos and inserted the term discrete unit in the second paragraph)

Like Richard, I think the paradox demonstrates the fundamental unreality of species but it does not deny the co-existence of divergent reproductive communities that we should recognise as such. It is just that we need gaps, in time or in extant genealogical linkage, in order to define these (and there will always be problems of drawing boundaries, such as when comparing allopatric populations).

The paradox echoes the problem of mate choice within populations. Individuals interact with each other as individuals not as species. Individuals linked by recombination share many traits and this affects their interactions. Mate preferences, some determined by genetically based traits that vary among species, may also vary among individuals of a given species in a non-reciprocal way (e.g. for a sexual species... F1 accepts M1 & M3 but not M2, F2 accepts M2 & M3 not M1, F3 accepts M1 & M2 but not M3). If individuals recognise each other as individuals, and not as conspecifics, this also undermines the reality of species.

Along with De Quieroz' papers on species as metapopulation lineages, a particularly insightful view on this topic is in :

- Frost & Kluge (1994) A Consideration of Epistemology in Systematic Biology with Special Reference to Species. Cladistics 10: 259-94

In which they argue that species are particulars, manefestations of processes, rather than discrete classes. Particulars, such as whirlpools, have inherently fuzzy boundaries. Species are always in the process of becoming or disappearing.

For me, the overall divergence of life on Earth and current Earth's overall biodiversity are substantial reasons that we can count on taxonomy not for just as an practical tool for handling the species (via identification keys) but also as a basic "measuring tool" in biology. Real phylogenetic (monophyletic) taxon should be determined by the spot of divergence (typically the apomorphy) that provoked occurrence of a new, altered sister-branch with a new character set. Even in a simplified two-dimensional view, this spot has both vertical value (time) and horizontal value (taxon). Of course, adding more dimensions would make the whole picture more realistic. So, I can look at this question simultaneously in both ways: whole living world share the continuum in overall evolution but still, all of its branches could be measured effectively with all of its known derived taxa, which could be understood and handled (especially today with the aid of modern phylogenetic methods and polyphasic taxonomic approach).

taxonomy is just a tool to classify things as other ranking systems used in our life... for example, grandparents, parents, uncle and unties, brothers and sisters... species is just as family that can be defined with different characters -- brothers and sisters from a family will have their own families, generation by generation, there are different families..

The solution lies in rejecting your first proposition: "If we define a species biologically as a population of (potentially) interbreeding individuals".  Why would you do that?  Interbreeding may be one way we might recognise a species but it is not the definition of that species (more a consequence) and it doesn't always give satisfying results (look at hybrids).  Species, and phylogenies, are better seen as emergent properties from the interactions among many individuals and they need to be viewed at the right scale.  Look at Hennig's "Phylogenetic Systematics" and you will see a diagram showing a hypothetical example of a network of individual parent-offspring relationships over time.  Zoom out and the broad tangled rope looks like the thin line of a cladogram and the branching point (speciation) is clear and sharp.  You can see similar representations in recent literature where gene trees are superimposed on species trees (the coalescence of a mitochondrial lineage might post-date or pre-date a speciation event).  An analogy would be a physicist looking at  a container of gas asking "what is the pressure and temperature of one particular molecule?"  Stand back and look at the big picture.

the first question was "who is the first- chicken or egg" I think as a zoologist we didnot give any name to an egg it is a common noun  while chicken as a taxon with respective scientific name. it can come around as an egg is an evolutionary means of reproduction through which a new offspring comes and chicken (hen) lays eggs to continued its race after fertilization of male and female cells, without fertilization that egg will not come out as a chicken. it is an never ending question and many had proved and many will proved it, as a biologist with firm faith on evolutionary processes with continuous variation chicken will be first and eggs  come far latter in evolutionary process.  

@Chingangbam, I don't understand your answer. In evolutionary terms, eggs pre-date chickens by a lot!

As far as my understanding goes egg is an evolutionary mode of reproduction and chicken is a taxon of particular identity. Egg developed into chicken exclusively after fertilization and without fertilization the particular does not developed into a chicken. So in order to produced the chicken, both male and female parents are required. So egg might developed latter the chicken. In short chicken is far ahead of chicken.

My answer for the question is, that the paradox is only apparent: species are real, but their borders [especially - but not only! - "vertical" (in time)] are blurred, like almost all natural boundaries in the world ["such is the “nature of the Nature” that natural boundaries are rarely “crisp”!" - see the attached publication (p. 530)].

Article HOŁYŃSKI R.B. 2011. Philosophy, evolution, and taxonomy, or:...