**Lecture notes**
**Null hypotheses regarding the distribution of genetic variation**
**I. What is a null hypothesis and how is it useful?**
A. **Null hypothesis**: a testable hypothesis that is often formulated on the basis of the simplest set of assumptions 1. In the null hypotheses considered here, the assumptions involve the absence of forces such as selection and drift, and predictions follow only from the assumptions of Mendelian genetics 2. These null hypotheses do not model reality, which is complex, but allow us to see how well real data conform or deviate from the model 3. Deviations from the null hypotheses provide information about processes that must therefore be operating in natural populations 4. Null hypotheses thus allow the formulation of more realistic, well-informed hypotheses based on tested *a priori* assumptions 5. Hypotheses allow the analysis and reconstruction of models: because nature is complex, it must be broken up into parts (deconstruction) to see how each part or force works on an individual basis, and then we have to figure out how the parts work together in the whole (reconstruction) B. Themes of null hypotheses underlying the genetic theory of evolution 1. Genetic variation within a population is described by the frequency of alleles at each locus and the degree to which these alleles are organized into nonrandom combinations 2. The main set of assumptions underlying the major null hypotheses of evolutionary genetics can be summarized as a "**Mendelian population**" in which: a. Mating is random such that each individual has mating access to any other (panmictic) b. Population size is infinitely large (or at least hugely vast) c. There is no mutation and there is no "gene flow" (e.g., no new alleles, no migration) d. There is no selection (all alleles have identical fitness and are thus "neutral") e. Genes behave as Mendelian factors: i. They segregate independently and randomly into gametes ii. The assort independently and randomly into zygotes 3. No real population is perfectly Mendelian, but the usefulness of the model is in the specific results produced by deviations from each of these *a priori* assumptions **II. Null hypothesis for the distribution of variation at one locus**
A. Assumptions of the Hardy-Weinberg (HW) theorem: a Mendelian population, two alleles at frequencies p, q (can be extended to more alleles) B. Predictions: 1. A binomial distribution of genotype frequencies will be established in a single generation 2. Neither the allele frequencies nor the genotype frequencies change in subsequent generations (i.e., the genotypes have reached a HW equilibrium) (Lecture notes and exercises concerned with the derivation and implications of this null hypothesis can be reached by clicking here or on the "Variation: One Locus" button below.) (Return to top of page.) **III. Null hypothesis for the distribution of variation at two loci**
A. Assumptions underlying linkage equilibrium: a Mendelian population, loci are unlinked (not on the same chromosome) B. Prediction of linkage equilibrium: combined frequencies of "coupling gametes" will equal the combined frequencies of "repulsion gametes" C. Correlaries: 1. If 2 loci are not linked (if the recombination frequency is greater than 0.5), then alleles at these loci may be nonrandomly associated under particular conditions (e.g., when 2 isogenic populations have mixed recently) 2. Linkage equilibrium is not established in one generation, but **linkage disequilibrium** decreases each generation by the recombination "distance" (frequency) between the loci 3. The rate at which linkage disequilibrium decays: a. Is by half each generation if the loci are not linked b. Is extended by the degree to which loci are linked (closer linkage maintains disequilibrium longer) (Lecture notes and exercises concerned with the derivation and implications of this null hypothesis can be reached by clicking here or on the "Variation: Many Loci" button below.) (Return to top of page.) **IV. Additive model for continuous variation**
A. Assumptions: 1. Mendelian population 2. Alleles act additively (there is no dominance): phenotypes result from the simple sum of the additive effects of these alleles B. Predictions: 1. Even though genes are discrete entities, if each locus has a slight additive effect, these discrete genes can determine "continuous" variation 2. The magnitude of the phenotypic variance is directly proportional to the (predicted) frequency of heterozygotes in the population (and highest when allele frequencies are equal) 3. The degree to which progeny look like their parents is determined mainly by the fraction of the phenotypic variance due to additive inheritance 4. If the phenotype is determined by additive inheritance and allele frequencies do not change, the mean phenotype remains the same (Lecture notes and exercises concerned with the derivation and implications of this null hypothesis can be reached by clicking here or on the "Variation: Many Loci" button below. Note that this course will not cover this topic in depth at all.) (Return to top of page.) |