2) one locus with three alleles. Estimated allele frequencies are based on a sample of 502 individuals.
| Blood | Observed | Expected number of genotypes | Observed – Expected | (Observed – Expected)2/Expected | |
|---|---|---|---|---|---|
| Hypothesis 1: fA = 0.293, fa = 0.707, fB = 0.153, fb = 0.847 | |||||
| O | 148 | 502(0.707)2(0.847)2 = 180.02 | −32.02 | 5.69 | |
| A | 212 | 502(0.500)(0.847)2 = 180.07 | 31.93 | 5.66 | |
| B | 103 | 502(0.707)2(0.282) = 70.76 | 32.24 | 14.69 | |
| AB | 39 | 502(0.500)(0.282) = 70.78 | −31.78 | 14.27 | |
| Hypothesis 2: fA = 0.293, fB = 0.153, fO = 0.554 | |||||
| O | 148 | 502(0.554)2 = 154.07 | −6.07 | 0.24 | |
| A | 212 | 502[(0.293)2 + 2(0.293)(0.554)] = 206.07 | 5.93 | 0.17 | |
| B | 103 | 502[(0.153)2 + 2(0.153)(0.554)] = 96.85 | 6.15 | 0.39 | |
| AB | 39 | 502[2(0.293)(0.153)] = 45.01 | −6.01 | 0.80 | |
The number of genotypes under each hypothesis can then be found using the expected genotype frequencies in Table 2.6 and the estimated allele frequencies. Table 2.7 gives the calculation for the expected numbers of each genotype under both hypotheses. We can also calculate a chi‐squared value associated with each hypothesis based on the difference between the observed and expected genotype frequencies. For hypothesis 1, χ2 = 40.32, whereas, for hypothesis 2, χ2 = 1.60. Both of these tests have one degree of freedom (4 genotypes −2 for estimated allele frequencies −1 for the test), giving a critical value of χ20.05,1 = 3.84. Clearly, the hypothesis of three alleles at one locus is the better fit to the observed data. Thus, we have just used genotype frequency data sampled from a population with the assumptions of Hardy–Weinberg equilibrium as a means to distinguish between two hypotheses for the genetic basis of blood groups.
Problem box 2.3 Inheritance for corn kernel phenotypes
Corn kernels are individual seeds that display a wide diversity of phenotypes (see Figure 2.10 and Plate 2.10). In a total of 3816 corn seeds, the following phenotypes were observed:
Purple, smooth 2058
Purple, wrinkled 728
Yellow, smooth 769
Yellow, wrinkled 261
Are these genotype frequencies consistent with inheritance due to one locus with three alleles or two loci each with two alleles?
Figure 2.10 Corn cobs demonstrating yellow and purple seeds that are either wrinkled or smooth.
2.5 The fixation index and heterozygosity
The fixation index (F) measures deviation from Hardy–Weinberg expected heterozygote frequencies.
Examples of mating systems and F in wild populations.
Observed and expected heterozygosity.
The mating patterns of actual organisms frequently do not exhibit the random mating assumed by Hardy–Weinberg. In fact, many species exhibit mating systems that create predictable deviations from Hardy–Weinberg expected genotype frequencies. The term assortative mating is used to describe patterns of non‐random mating. Positive assortative mating describes the case when individuals with like genotypes or phenotypes tend to mate. Negative assortative mating (also called disassortative mating) occurs when individuals with unlike genotypes or phenotypes tend to mate. Both of these general types of non‐random mating will impact expected genotype frequencies in a population. This section describes the impacts of non‐random mating on genotype frequencies and introduces a commonly used measure of non‐random mating that can be utilized to estimate mating patterns in natural populations.
Mating among related individuals, termed consanguineous mating or biparental inbreeding, increases the probability that the resulting progeny are homozygous compared to random mating. This occurs since relatives, by definition, are more likely than two random individuals to share one or two alleles that were inherited from ancestors they share in common (this makes mating among relatives a form of assortative mating). Therefore, when related individuals mate, their progeny have a higher chance of receiving the same allele from both parents, giving them a greater chance of having a homozygous genotype. Sexual autogamy or self‐fertilization is an extreme example of consanguineous mating where an individual can mate with itself by virtue of possessing reproductive organs of both sexes. Many plants and some animals, such as the nematode Caenorhabditis elegans, are hermaphrodites that can mate with themselves.
There are also cases of disassortative mating, where individuals with unlike genotypes have a higher probability of mating. A classic example in mammals is mating based on genotypes at major histocompatibility complex (MHC) loci, which produce proteins involved in self/non‐self recognition in immune response. Mice are able to recognize individuals with similar MHC genotypes via odor, and based on these odors, avoid mating with individuals possessing a similar MHC genotype. Experiments where young mice were raised in nests of either their true parents or foster parents (called cross‐fostering) showed that mice learn to avoid mating with individuals possessing odor cues similar to their nest‐mates' rather than avoiding MHC‐similar individuals per se (Penn and Potts 1998). This suggests that mice learn the odor of family members in the nest and avoid mating with individuals with similar odors, indirectly leading to disassortative mating at MHC loci as well as
