Why I believe the theory of evolution

Logic is, fundamentally, the evidence for evolution.

The modern theory of evolution is based on a few simple postulates:

1) Living things reproduce.

2) In the reproductive process living things pass on inheritable traits through some mechanism of inheritance (which turned out to be DNA).

3) The inhertance mechanism is not perfect and variations are introduced through some mechanism (this turned out to be mutation of DNA, insertion, replacement, deletion, etc..).

4) Conditions of the environment of the organism coupled with internal and inheritable traits of the organism will combine to determine an organisms reproductive fitness (the ability of the individual organism to survive to reproduce thus incorporating any traits that the individual may have evolved through mutation into the gene pool of the species). (This last one is called natural selection).


The rest of the theory of evolution follows logically from these postulates. We can do a few simple thought experiments to make this clear. But I'd like to introduce a few concepts which are based on these postulates:

1) Evolution is a markov process. In statistics markov chains are stochastic mathematical models in which the future evolution of the system is based only on the system's current state, not on any previous states. This means that because evolution is a markov process, your genome was entirely based on the DNA you got from your parents' gametes. The genes of your grandparents likewise completely determined the genes of each of your parents, and you and a partner will completely determine the genes of your children. In a markov model each step directly influences ONLY the following step in the model's evolution. The genomes of my grandparents can be completely ignored in analyzing my genome's evolution from the DNA of my parents. I'll just state the implication here for those who might miss is. The implication of this fact is that evolution is a branching process. If we were to map out a tree of descent based on the fact that the genes of my grandparents are irrelevant to mine and future generations that come from me, then lines of my parents are drawn directly to me, and from me and my wife directly to each of my children, and directly from each of my children and their future partners to their future children. At that following step I'm completely left out and you can see how, since I have 2 children, my children produce two branches from my one branch.

2) The concept of genetic drift. Mutations are random, and thus subject to laws that govern random processes. One of these is the law of large numbers. This expresses itself in a concept referred to as genetic drift. In a large population of reproductively fit individuals the genes that are the most well distributed will, due to the law of large numbers, be most likely to remain most well distributed unless there is a drastic environmental change or a new mutation which introduces a dramatic improvement in reproductive fitness. This is why some populations appear to remain static for many hundreds or thoughts of generations. In small populations, though, novel new mutations are more likely to become dominant in a population in a relatively short amount of time because the law of large numbers doesn't have a chance to assert itself. It's like rolling a die 6 times. In that small sampling of this random event you may roll a sequence like 1, 3, 2, 4, 3, 1; which means you rolled 1 2/3 of the time. 3 2/3 of the time 2 1/6 of the time, 4 1/6 of the time 5 0/6 of the time and 6 0/6 of the time. each number, though had an equal probability (1/6) of coming up. If you rolled the dice 6000 times you'll likely see a probability distribution for each number approaching 1/6, and the distribution will come closer to 1/6 as you increase the number of dice rolls. This is the law of large numbers and this is why in a large population new mutations are more likely to be lost than to assert themselves, and why the opposite is true in smaller populations.
 
3) Reproductive isolation.  Two populations of the same species can be considered reproductively isolated if for any reason members of one of the populations cannot reproduce with members of the other and vice versa.  This is usually due to geographic isolation, members of one population have been brought to an island somehow, or they migrated to a different and remote area, or they've decided to occupy a different ecological niche, or they just don't like members of their population that share a trait (like maybe a patch of yellow fur) whatever is the cause, the two populations should, genetically, be perfectly capable of interbreeding but for some reason never do.
 
4) Sexual selection.  Sexual selection is derived from natural selection, except instead of something from the environment helping to determine reproductive fitness it's the reproductive preferences of members of the species themselves.


Now that I have explained these concepts, let's get on with the thought experiment.

Let's suppose that a population of species A exists.  It's a simple population with only a thousand representatives, and only one variety.  Let's say that 8 males and 13 females of this population become carried away from the general population by a flood into a new area and never find their way back to the original population.  This new area is a little different from their old area with many new food sources but some familiar ones.  Also mostly familiar predators and a few new ones.  So we now have populations A1 and A2.  The two populations are reproductively isolated.  So new mutations in each population will not be available to members of the other population.  Now there are a few new selective pressures on population A2, there are a few familiar food sources in the new area but not enough of those to sustain a large population of their species.  Either A2 mutates adaptations that will allow them to take advantage of the new food sources, or they eventually over reproduce and die of starvation as the new area doesn't have the resources to support a large population of A.  Because mutations are random it's always possible that no mutations will happen which allow A2 to take advantage of the available and abundant new food sources, but because of genetic drift and the fact that A2 is a small population if they do mutate the necessary new features there is a relatively high probability, esspecially given the advantages, that the new mutation will take firm hold in that population's gene pool.  Now let's assume that A2 evolves the new traits necessary to make use of the new food sources.  This will be traits not present in the other population.  We're already starting to see divergence.  We also introduced some new predators.  The population A2 will also face a strong selective pressure to evolve some strategy for dealing with these new predators.  Maybe claws, camouflage, sharp teeth, intimidation tactics, the ability to run fast, burrow deep, climb trees, whatever.  Over time, esspecially given the fact that the environment is not static, food sources will evolve to defend themselves from this new predator A2 and predators will evolve strategies for more effectively hunting this new prey A2.  Natural disasters may happen, sexual selection may favor interesting new but mostly nonfunctional adaptations in A2 and different such mutations in A1.  Eventually over thousands of generations the two populations of A will have diverged so much from one another as to not be recognizeable anymore as members of the same species.

It should also be noted that a population's gene pool can only allow for mutations on genes and genomes that are already present within the population.  An introduction of a novel new fully formed, fully functional, and advantageous gene into the population in a single generation, while not impossible, is so improbable as to be practically impossible.  The theory of evolution does not say that such a thing could never happen, but it does say that we can't make a habbit of assuming it did in any significant number of instances and in fact should proceed as though it never could have unless there is overwhelming evidence that suggests it did.

Also keep in mind that in a population an advantageous gene only has to evolve once.  After that it's passed on to future generations through the process of inheritance.

Essentially if you want to disprove the theory of evolution your best chance is to attack postulates 3 and 4.  Show that mutations don't happen or that natural selection doesn't happen.  The scientific method has already established very convincingly that mutations do happen and natural selection is a real process, though, so good luck.