Warmup, Part 0 - Preamble: Hardy-Weinberg equilibrium and population genetics calculations In order to get started, we have to make sure you have the basic “Newton’s First Law” of population genetics well in hand – the Hardy-Weinberg equilibrium theory. Calculation of allele and genotype frequencies is central to what follows. We review this below, along with an explicit example of H-W calculations, followed by questions that everyone should answer and turn in as part of their lab report. If you already feel comfortable with the H-W calculations, you can skip the exposition section below and proceed directly to the questions. (I know the material below is presented in a very, very elementary and expository way – please, if it seems overlong and boring to you, try the ‘challenge’ problems at the end to make certain you are secure in your knowledge. I have tried to review basic terminology like ‘allele’, ‘homozygous,’ etc., just to make sure we’re all on the same page.) Population geneticists study frequencies of genotypes and alleles within populations rather than the ratios of phenotypes (external forms) that Mendelian geneticists use. By comparing these frequencies with those predicted by null models that assume no evolutionary mechanisms are acting within populations, they draw conclusions regarding the evolutionary forces in operation. In a constant environment, genes will continue to sort similarly for generations upon generations. The observation of this constancy led two researchers, G. Hardy and W. Weinberg, to express an important relationship in evolution. The law that describes this relationship bears their names. The Hardy-Weinberg Equilibrium Theory serves as the basic null model for population genetics. Every individual has alleles (=variants of the same gene) that were passed on from their parents. If we take all of the alleles of a group of individuals of the same species (that is, a population) we have what is called the gene pool. The frequency, or proportion, of individuals in that population that possess a certain allele is called the allele frequency. Populations can have allele frequencies, but individuals cannot. This makes populations a reasonable hierarchical unit, or level, to study evolution, on the assumption that evolution is basically the study of the change in allele frequencies over time. (You should be prepared to defend or attack this statement! How is it true? How is it not true?) Allele Frequencies Consider an individual locus (= roughly, ‘gene’) and a population of diploid individuals where two different alleles, A and a, can be found at that locus. If your population consists of 100 individuals, then that group possesses 200 alleles for this locus (100 individuals x 2 alleles at that locus per individual). The number of A alleles present in that population expressed as a fraction of all the alleles (A or a) at that locus represents the frequency of the A allele in the population. 1. To calculate allele frequencies for populations of diploid organisms, first multiply the number of individuals in the population by 2 to obtain the total number of alleles at that locus. 2. Select one of the alleles for your first set of calculations. Let’s first choose the A allele from the example provided above.a. Individuals homozygous for the A allele (“homozygous”= all one type, e.g., all A’s) will each possess 2 A alleles. Multiply the number of AA homozygotes by 2 to calculate the number of A alleles. b. Heterozygotes will each possess only one A allele. c. The total number of A alleles in the population = [(the number of Aa heterozygotes) + (2 x the number of AA homozygotes)] 3. The frequency of the A allele = [(total number of A alleles in the population) / (total number of alleles in population for that locus)] 4. The frequency of the a allele = (1 - frequency of the A allele) Genotype Frequencies Consider the same population, locus, and alleles described above. Genotype frequencies represent the abundance of each genotype within a population as a fraction of the population size. In other words, the frequency of the AA genotype represents the fraction of the population homozygous for the A allele. 1. To calculate genotype frequencies for populations of diploid organisms, first determine the number of individuals with each genotype present in the population. In the example used above, you would count the number of individuals with the following genotypes: AA, Aa, and aa. 2. To determine the frequency of each genotype, divide the number of individuals with that genotype by the total number of individuals in the population. a. Frequency of AA genotype = # AA individuals / population size b. Frequency of Aa genotype = # Aa individuals / population size c. Frequency of aa genotype = # aa individuals / population size IMPORTANT NOTE: Unless you know that a population meets Hardy-Weinberg equilibrium assumptions, you must use the above procedure to calculate genotype frequencies. If you know that a population meets Hardy-Weinberg expectations, then you can calculate genotype frequencies using allele frequencies and the Hardy-Weinberg equations (see below). Assertions of the Hardy-Weinberg Equilibrium Theory The Hardy-Weinberg Equilibrium Theory refers to loci within populations that experience no evolutionary forces. For such populations the theory asserts that: 1. Allele and genotype frequencies should remain constant from one generation to the next. That is, no evolution should occur at these loci. If, at a certain gene locus, there are only two alleles, each will have a frequency such that the frequency of one allele plus the other equals 1. Remember, we are discussing the frequency in a population, not in an individual. Formally, we can state the allelic frequency in a population as follows: p = Frequency of allele A = freq(A) q = Frequency of allele a = freq(a) and p + q = 12. Given a certain set of allele frequencies, genotype frequencies should conform to those calculated using basic probability. In a one locus/two allele system such as the one described above, the genotype frequencies should be as