(idea) by jmc Mon Oct 08 2001 at 20:41:23
I'd like to offer what I hope is a compelling "proof" (and I use the word with reluctance, since it will be shoddy at best; I'm neither a biologist nor a logician) that microevolution cannot actually create new species.  I don't have much to say about the science involved because I lack authoritative scientific knowledge, but I can offer a (quasi) logical proof based on the mechanics of the question.  Ok, ok, it's not really a proof.  But it has symbols, so it must be right.  Right?

Definitions:

  1. Microevolution: evolutionary change within a species.
  2. Macroevolution: evolutionary change that results in speciation; the change of one species into another.
  3. Species: two organisms are of the same species if, by mating, they can produce fertile offspring.
let:
  1. A be the original species.
  2. A^n be a permutation of A obtained by microevolution.
  3. B be a second species that evolved from A.
  4. m() be the process of change within a species (microevolution).
  5. M() be the process of speciation (macroevolution).

    m() and M() accept as arguments any species name (that is: A, A^n, B, etc).

The process of microevolution can only result in changes within a species.  Therefore, for all m(A), the result can only be a permutation of A, A^n.  m(A) can never result in a species B, because m() cannot cause a change in species.

So, looking at the spectrum of organisms as species A evolves to species B, we could see many permutations of A caused by m(), but if m() is the only mechanism changing the original species, we will never see a B.  In order for B to be produced, there must be exist some mechanism M() capable of causing speciation.

This of course assumes that change happens along a continuum like

    A --> A^x --> A^(x+1) --> A^(x+2) --> ... -> A^(x+n) --> B
and it's that last step in the chain from A^(x+n) --> B that microevolution by definition cannot accomplish.  There must be some process M() if B is to evolve from A or some permutation of A.
If any of the numerous noders with more expertise/ability/experience in logic and biology find problems in the above writeup, please /msg me.  I like eating my words.  They're tasty.

Pursuant to that: several nice people have informed me that the reason this "proof" (and I agree with their scare quotes) is shoddy is that the aim of the proof is already contained within the definitions.  They're right, of course, but I'd like to stress that the definition of microevolution above is not mine. The Other Dan offers the accepted scientific definition of microevolution: "a small change within a species" but goes on to say that "[m]icroevolutionary change does lead to the creation of new species."  All my "proof" is attempting to do is show that these points are irreconcilable.

I like it!