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Leauki,

I've been half-following some of your recent discussions on this topic and I read the first part of this post carefully. What I've seen from your recent comments is that you either intentionally or mistakenly conflate the epistemology and the ontology of species. Yes, species concepts are difficult for many, including many professional biologists, in part because it's hard to grasp what it is that makes a species. Let me elaborate:

Many people who have had only basic biology or who are only exposed to people like Ernst Mayr come away with the impression that the Biological Species Concept is the only game in town. Mayr's definition has varied over the years somewhat, but it's usually formulated something like this: a species is a group of actually or potentially interbreeding organisms.

This is a working definition that has been around in the literature since the 1940's. It has a number of problems. The most significant of these from an evolutionary perspective is that it is utterly ahistorical. A group of organisms that is capable of breeding in a moment in time tells us nothing, ultimately, about the relationships among those organisms, let alone relationships of that group of organisms with any other group. E.O. Wiley originally developed the Evolutionary Species Concept to help with this; it characterizes a species as a group of organisms that is on its own evolutionary trajectory. The problem with Wiley's concept is that its application is problematic because, outside of a laboratory, it is difficult to quantify when a group may be on a particular evolutionary trajectory. The ornithologist Joel Cracraft formulated the Phylogenetic Species Concept as a "practical" corollary to the ESC. It defines a species as a group of organisms on its own evolutionary trajectory as demonstrated by the presence of one or more fixed traits. (There are undoubtedly some better formulations of all of these on the web, but you'll have to pardon me as I'm doing this from memory and I haven't been what you'd call a practicing biologist for about 9 years now.) You'll note that the distinction between the ESC and the PSC is precisely a question of demarcation; in other words, a phylogenetic species is something that is clearly within the limits of our epistemological capability to distinguish whereas there may be many evolutionary species that are real but that we are not capable of discerning for lack of a fixed trait (thus, they are real in an ontological sense but we lack the wherewithal to delimit them).

My point is that species are not constructs of the scientific community and it actually does matter how we define them (or in the sense that I'm describing, it's more accurate to say that it's important to be clear on how we can discover them). Now, what does this discussion have to do with the "origin of species"? There are, broadly speaking, two different kinds of evolutionary change, anagenesis and cladogenesis. Anagenesis refers to change along a "branch" of an evolutionary tree, while cladogenesis refers to a "splitting" event, where an ancestral species splits into two distinct groups, an original which continues on its own evolutionary trajectory and a distinct set of organisms which begin to move on a separate trajectory.

There's a substantial literature (of course) on these topics and I have no idea how familiar you are with it. I'm sure you've read Darwin. I would also recommend Willi Hennig's 1966 Phylogenetic Systematics. In addition, in the primary literature, there are great papers on these topics, notably in the journals Cladistics and Systematic Biology (I especially recommend the works of Arnold Kluge of the University of Michigan); if there's a decent university library where you live, these shouldn't be hard to come by.

By the way, I have to ask: why is this article tagged with "smurfs"?

I know of the different definitions of species, but it is really quite immaterial how you define "species". My point is not about the definition of species but about how one species can evolve into two without crossing a "species border".

Any definition of "species" will work.

There is no working definition of "language" either, but few will argue that English and German are not two distinct languages.

I personally define two dialects as distinct languages if they are two or more consonant shifts away from each other.

I suggest you read the article again based on the assumption that it is about not crossing a species border rather than defining what that border is.

Proto-Germanic evolved into both English and German without ever crossing a "language border". Defining such a border would thus be unecessary. If we can prove that a border doesn't exist on our path, we don't need a mechanism to find it.

Hysterical reasons. I used smurfs for many gedanken experiments about evolution and science. Since then I tag all documents about evolution with "smurfs".

I don't know, Leauki: how can you characterize a transition without understanding what is making that transition? People seem to think this is much less important than it actually is. If you accept uncritically, for example, the BSC (and you can tell that I don't), the "border" is the point at which one group of organisms evolves a novel genetic or phenotypic feature that makes it reproductively incompatible with another.

Very simple. I am not characterising a transition. I am arguing that no transition ever takes place.

A "transition" is a move over a certain step size. But that never happens. Neither languages nor species ever become very different in one generation and no transition ever takes place.

Such a point doesn't exist. You are confusing the parent generation of a generation of animals with another population of animals.

While two distinct populations will indeed become incompatible with another population at some point, defining that point is really not necessary to understand how the animals evolve.

If you have generations of an animal population, no generation i+1 will ever be incompatible with any generation i in the same population. But different generations i will (eventually and possibly) be incompatible with other generations i of other populations. However, no "border" is ever crossed and any generation i and i+1 always remain compatible.

It doesn't matter how you define the border, because the border is never crossed, regardless of how you define it.

English and German are distinct languages, but neither language has seen speakers that would be on the "other side" of a "language border" from their parent generation of whom they learned their particular dialect.

Well, we agree on your second paragraph here.

What I'm actually arguing is that the classic allopatric speciation model has a distinct temporal border, and it is the one I described above. In allopatric speciation, a single population (of animals, if you like, but it really can be any multicellular life form [prokaryotes and species distinctions are a bit of a headache]) is divided by the appearance of a geographic barrier--say, an orogenic event; then, these populations continue to evolve; one eventually develops a fixed trait or (if you prefer) is rendered non-interfertile with the other population and is a distinct species. The other population may also develop into something distinct from the ancestral group or it may not.

I don't entirely understand your third paragraph, but I'm pretty sure I disagree with it. If I take the last sentence "generation i and i+1 always remain compatible," this seems to display a misunderstanding of population genetics. Traits that are favored by selection will tend to spread rapidly through succeeding generations resulting in fixity and in that case, no the generations may not be compatible with one another (in a reproductive sense).

Let's test this.

You are saying that generation i and i+1 can be incompatible, i.e. different species. (You disagree with the statement "any generation i and i+1 always remain compatible".)

Let's say generation 1 gets divided into two populations A and B. (For the sake of simplicity let's assume that a generation is always exactly the same amount of time.)

You would be saying that somewhere between generations, a population crosses a species border.

I am saying that this will never happen.

So while generation A42 is the same species as (and compatible with) A41, A42 and B42 might be different species (and incompatible).

Unless we mix populations A and B again, it doesn't matter whether the current generations of A and B are still compatible.

(Whether or not either population evolves into something distinct from the original AB1 generation doesn't matter as time doesn't preserve generations and AB1 will never meet later generations of A or B.)

If, on the other hand, we ever find evidence for a generation i+1 being a different species from a generation i, i.e. evidence for one species turning into another within one generation, we would have shown the theory of evolution to be wrong.

I don't understand your argument.

You say that there is a temporal border and then proceed to describe not a temporal but a location-based border.

Leauki,

Note that I said "through succeeding generations"; unless we're discussing a very small population of extremely simple organisms, it's not really going to be possible to fix or extirpate an allele within the span of a single generation. I don't think we're disagreeing on that point.

What I am saying is that it is possible over several generations for a population to evolve such that the population at time t+n is not reproductively compatible with the population (which would be composed of different individuals) at time t.

I also think your last statement (

It's a temporal border in the sense that there is a point in time when speciation is said to occur and that is when we delineate these groups as distinct species. The physical border you're referring to is a component of the allopatric (meaning, as I'm sure you know "different place") model. This is as opposed to parapatric or sympatric models of speciation, where such changes take place either on the periphery of the range of a population or in the same physical location.

That is irrelevant as generations i and i+1 are only one generation apart.

I do not doubt that "succeeding generations" will eventually become incompatible. (In fact that was my point.) But when you disagree with my statement about two generations that are one generation apart, any argument that requires more than one generation distance doesn't even address my statement.

That is true, but what does it have to do with my statement about the current parent and child generations?

Perhaps. Unless I give numbers I tend to speak in broad terms.

Ok. I don't think there is such a point in time; not generally or often anyhow. Maybe in freak cases when due to some weird genetic mutation a child generation of one parent is very different. But as a general rule a child generation is always compatible with its parent generation and hence there is no cut-off point as you describe.

I also don't remember a single case where biologists delineated as distinct species different generations of the same population.

(Note that those generations would have to be parent and child generation IF there were a distinct point that delimits the two species like that.)

A(2) is the same species as AB(1).

A(3) is the same species as A(2).

B(2) is the same species as AB(1).

B(3) is the same species as B(2).

A(n) is the same species as A(n-1).

B(n) is the same species as B(n-1).

But A(n) is not necessarily the same species as B(n).

An ancestor of a species is not a different species.

For a tree with a branch R which itself branches into two smaller branches S and T, the following is true:

1. S and T are not the same branch.

2. R and S are not different branches.

3. R and T are not different branches.

For what it's worth, I don't think we're using the tree metaphor in the same way. You seem to be using a diagram to make a point about entities, whereas I'm speaking of a phylogenetic tree, which posits relationships among terminal and ancestral taxa.

This makes no sense to me. Please clarify.

For a trivial case, I could point to polyploidy resulting from hybridization in plants. The offspring are definitely considered distinct species by botanists. This would probably fall into the "weird genetic mutation" category you describe, although it's hardly uncommon.

I think we're in agreement on this, except for extraordinary cases.

However, that wasn't my point. My point was that this exists:

If you dispute that this occurs, then I don't understand how you propose that species evolve (this is why species concepts are important).

In that case I really don't understand how you disagreed with my statement about parent generations and their child generations.

I think we use different definitions of "point".

It may be that I wasn't clear in my statement or perhaps further discussion of the topic clarified my thinking in my own mind; in any case, yes, I would say that it is unusual, except in the case of things like dramatic genetic change (like polyploid hybrids), for i and i+1 to be incompatible.