Have a coin handy? Flip it.
If your coin is fair, I can guess that it's come up heads and have a fifty percent chance, or probability equal to 0.5, that I've guessed correctly. Now, flip the coin ten times in a row. How many times did heads come up? Again, the best guess is that it came up five times—but it's not all that unlikely that it came up six times, or four, or even as many as eight.
Evolution at random
The basic principle behind genetic drift is that each generation is a process of sampling from the parental population to create a population of offspring. As most folks know from discussions of opinion polls, smaller samples tend to be less representative of the pool from which they are drawn. Say a population of annual plants begins with equal numbers of plants bearing blue flowers or white flowers. If only ten seeds survive from that population to form the next generation, you would expect them to be five blue-flowered and five white-flowered seeds. However, it's just like flipping a coin ten times: the probability of drawing six blue seeds is actually a little less than 21%, or one in five. The probability of drawing nine blue seeds is almost one in one hundred—small, but hardly impossible.
Consider, too, that once you draw six blue seeds, it becomes slightly more likely that you'll draw seven in the next generation, which makes it slightly more likely you'll draw eight in the next. Repeated selection of small samples means that traits can drift to fixation (or loss, depending on your perspective), so that everyone in the population has the same trait. Rare traits are more likely to be lost to drift, and large populations are less prone to its effects. This is nicely illustrated in this online simulation from the University of Connecticut—over time, a focal gene fixes or disappears from the population as a function of the population size and the initial frequency of the gene.
In general, drift interferes with the efficient operation of natural selection. Even in relatively large populations, the probability that a new beneficial mutation will become fixed is approximately twice the selective benefit of that mutation—typically very small. (This is from a 1927 paper by J.B.S. Haldane that doesn't seem to be online in any form, but which is discussed by Otto and Whitlock in a 1997 paper extending the classic result.) In a small enough population, a trait can become fixed even if it reduces its carriers' fitness [PDF].
Evolving differences without selection
As I've discussed above, the effect of drift in a single population is to reduce variation as rare traits are lost to chance. This means that, when more than one independently-evolving population is considered, drift actually increases variation among them [$a], as different traits fix or are lost in each. That is, drift can make isolated populations evolve into different species even if they experience identical regimes of natural selection.
Woodland salamanders (genus Plethodon: left, P. vehiculum; right, P. yonahlossee) have diversified not by adapting to different environments, but by being homebodies. Photos by squamatologist.A flagship example of this sort of non-adaptive diversification are the woodland salamanders of eastern North America, genus Plethodon. Woodland salamanders are quite diverse, having accumulated more than 40 species in the last 27 million years, but all of these species live in more or less the same habitat, under the leaf litter in moist Appalachian forests, and many are "cryptic" species distinguishable only by DNA analysis. How, then, did Plethodon become so diverse?
The answer is simply that woodland salamanders don't travel very well. Salamanders need moist environments–they breathe through their skin, which doesn't work well if it dries out—and so have difficulty moving from one stream drainage to another. This means that it doesn't take much distance to isolate one Plethodon population from another, allowing drift to take them in different directions. Salamanders form new species, in other words, by staying at home.
This effect of drift means that biologists must adjust their "null" expectation when they observe differences in natural populations—the mere fact that some Joshua trees look different from other Joshua trees does not necessarily mean that natural selection has created those differences. Furthermore, the degree to which drift or selection can generate differences among populations depends strongly on the fourth force in the Big Four, which I'll discuss next week: migration.
Godsoe, W., Yoder, J., Smith, C., & Pellmyr, O. (2008). Coevolution and divergence in the Joshua tree/yucca moth mutualism. The American Naturalist, 171 (6), 816-23 DOI: 10.1086/587757
Kozak, K., Weisrock, D., & Larson, A. (2006). Rapid lineage accumulation in a non-adaptive radiation: phylogenetic analysis of diversification rates in eastern North American woodland salamanders (Plethodontidae: Plethodon) Proc. Royal Soc. B, 273 (1586), 539-46 DOI: 10.1098/rspb.2005.3326
Lande, R. (1992). Neutral theory of quantitative genetic variance in an island model with local extinction and colonization. Evolution, 46 (2), 381-9 DOI: 10.2307/2409859
Otto S.P., & Whitlock M.C. (1997). The probability of fixation in populations of changing size. Genetics, 146 (2), 723-33 PMID: 9178020
Wright S (1931). Evolution in Mendelian populations. Genetics, 16 (2), 97-159 PMID: 17246615