Chapter 3: The Modern Synthesis

Population Genetics

Evolution can be described in many ways; one way is look at evolutionary change as a change in genotype frequencies over time. If organisms are considered evolutionarily successful if they have more offspring, and offspring are created from genes, then changes in gene frequencies (or more specifically, genotype frequencies) will reflect successful evolutionary phenotypes. Researchers in the field of population genetics examine populations in terms of differing proportions of particular genotypes in order to determine what, if any, evolutionary forces are active in that population.

Hardy-Weinberg Equilibrium

One of the theoretical tools utilized by population geneticists today was independently developed in 1908 by a British mathematician named G. H. Hardy, and a German physician named W. Weinberg. The Hardy-Weinberg equation expresses an ideal distribution of genotypes within a population, assuming that the gene frequencies are known. The validity of the results from Hardy-Weinberg analysis is contingent upon five factors, all of which must be in effect :

1. no mutation
2. infinitely large population
3. random mating
4. no migration
5. no genetic drift

If all parameters are met, the genotype frequencies should emerge in constant proportions based on the individual gene frequencies. This is because the above parameters work to keep the probability of a particular gene being passed on to the next generation at a very statistically predictable level. Therefore, by calculating the probability of each possible genotype based on the contribution of each parent, the frequency of each genotype can be predicted. Supposing two alleles - A and a - are present in a population where frequency(A) = p and frequency(a) = q, the possible genotypes should occur in the following proportions:

• The proportions of the three possible genotypes - AA, Aa, and aa - are 1 : 2 : 1
• The Hardy-Weinberg Equilibrium can therefore be expressed as the equation, p² + 2pq + q² = 1, where p = f(A) and q = f(a)

A glance at the above parameters suggests that it is very unlikely they will all be fulfilled within any given natural population. However, as with other theoretical notions based on ideal principles, the main product of these calculations is to provide a comparison by which a population geneticist can assess why the sampled population is not conforming to ideal behavior.

Example 1

In a population of lab-bred flies, a gene controlling eye color is discovered. The R allele produces regular colored eye pigment, while the r allele produces red pigment. Individuals that are heterozygous (Rr) have pink eyes. In a population of 150 flies, 15 flies have red eyes, 90 have normal eye color, and 45 have pink eyes. Check if this population is in Hardy-Weinberg equilibrium.

Step 1: Determine gene frequencies

Given this information, calculating the allele frequencies is simply a matter of counting up all of the alleles.

• Remember, each parent carries two alleles, so the total # of alleles twice the population.
• Also remember that heterozygous individuals carry one of each allele.

Taking these two factors into account,

• f(R) = [(90*2)+(45] / 300 = 225/300 = 0.75
• f(r) = [(15*2)+(45)] / 300 = 75/300 = 0.25

Step 2: Determine expected genotype frequencies

Plugging the frequencies of each allele into the Hardy-Weinberg equation, we find the expected numbers of each genotype in the population:

• f(RR) = p² = f(R)*f(R) = 0.5625
• f(rr) = q² = f(r)*f(r) = 0.0625
• f(Rr) = 2pq = 2*[f(R)*f(r)] = 0.375

• 84 normal-eyes flies (AA)
• 9 red-eyed flies (aa)
• 56 pink-eyed flies (Aa)

Step 3: Compare with original population numbers

Comparing the expected numbers with the actual numbers of each phenotype, population geneticists can determine if populations are either in equilibrium (or very close to it) or are experiencing disequilibrium of some sort. In this example:

In this example, the population is not in equilibrium since the expected and observed values do not match. Disequilibrium can be attributed to different possible mechanisms, depending on (1) the context of the population, and (2) the manner in which the population is skewed.

Disequilibrium

Disequilibrium refers to a difference between observed and expected ratios of genotypes within a given population as we saw above. This situation may come about as a result of small population size (which accentuates the effects of genetic drift), migration, and selective forces which favor or hinder particular phenotypes. Additionally, disequilibrium can arise in situations of non-random mating. What needs to interpreted are the relative proportions of each genotype (and their corresponding phenotypes), how these compare with expected values, and the elements of the environment which could promulgate evolutionary changes.

For instance, in the above example of fruit flies, the lower incidence of pink-eyed flies suggests that there may be selective forces acting against their survival, or perhaps encouraging both homozygous conditions over the heterozygous one. Or perhaps the flies are more likely to select mates with the same eye color, leading to a slight reduction of heterozygous individuals each generation.

Hidden Variation