First off, bear in mind that if a gene (or pseudogene) is characteristic of a species, what’s happened is that it’s become “fixed” by virtue of being present in all members of the population. Take human hemoglobin, for example. Since all humans have human hemoglobin genes, then matings between humans will always produce children with human hemoglobin genes.
I realize that this sounds like stating the obvious, but once you phrase it that way you realize that one good question to ask about evolutionary biology is, “How do new genes end up being present in all members of the population, so that they become part of the genome of the species?” In order to ask this question, you have to start from highschool Mendelian genetics. If there is a gene for brown hair (B) and a gene for blond hair (b), then in high school you learned how to determine what percentage of offspring would be BB, Bb, or bb given parents that were BB, Bb, etc.
Since we’re talking about populations, you can mathematically extend the concepts of Mendelian genetics to deal with a large population, rather than just two parents. Thus if you know that 10% of the parents are BB, 32% are Bb, and the remainder are bb, and they mate more or less at random, you can calculate the percentages of offspring that will have each combination of genes. These equations are called the Hardy-Weinberg equations, and over several generations the population will reach the Hardy-Weinberg equilibrium, where the percentages of parents with each combination of genes equals the percentages of offspring with each combination.
Now, the Hardy-Weinberg equations, in and of themselves, are a little simplistic. For one thing, you have issues of genetic crossover, which I mentioned in the FAQ. If you want to calculate the percentage of offspring in each generation with two brown hair genes and two blue eye genes, you have to take into account the fact that those two genes might be on the same chromosome, and thus they will tend to be passed on together. (Conversely, genetic crossover will disrupt this linkage, so you can add another correction factor. Bear in mind that these corrections aren’t some post hoc fudge factor to make the facts fit evolution. We know that genetic crossover really happens and we can experimentally measure the value of the correction. We also know that the principles of Mendelian genetics upon which the HW equations are based are well established by experiment. In the end, we need to include extra correctional factors in the HW equations to make them describe reality in detail. You could draw an analogy to the equations for motion: the base HW equations are like Newton’s laws, and the factors like crossover are like Einstein’s more accurate corrections which come from Relativity.)
One mathematical correction which must be added involves statistical fluctuations. In practice, some couples will have more children than others, or freak accidents will, purely at random, wipe out slightly more BB children than Bb children, etc. These statistical fluctuations are more extreme for small populations, and the math for treating them was well-known from statistics before it was applied to population dynamics.
Well, I’m afraid I have to leave the computer right now. I’ll finish the argument later.
-Ben