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Genetic Load and Introduction Neutral Theory 1. Mutation 2. Polymorphism 3. Substitution

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Genetic Load and Introduction Neutral Theory 1. Mutation 2. Polymorphism 3. Substitution Neutral theory 1: Genetic load and introduction Neutral theory 1. Mutation 2. Polymorphism Neutral theory: connected these is a new (radical) way 3. Substitution 1 Neo-Darwinism 1. genetic variation arises at random via mutation and recombination 2. populations evolve by changes in allele frequencies 3. allele frequencies change by mutation, migration, drift and natural selection 4. most mutations are deleterious 5. most adaptive phenotypic effects are small so changes in phenotype are slow and gradual • some such changes can have large discrete effects 6. diversification occurs by speciation • usually a gradual process • usually by geographic isolation 7. microevolution ⇒ macroevolution Neo-Darwinism Balance school Classical school • Most new mutations are deleterious • Most new mutations are deleterious • Natural selection is of central importance • Natural selection is of central importance •Polymorphism is a function of selection •Polymorphism is a function of selection • Polymorphism is common • Polymorphism is very rare •Balancing selection is comparable to • Positive Darwinian selection and purifying selection in micro-evolution balancing selection are rare with respect to purifying selection in micro-evolution • Genetic variation connected to morphological variation. • Too much “genetic load” for genetic variation to connect with morph. variation • Prediction: most populations will be heterozygous at most loci •Prediction: most populations will be homozygous at most loci 2 “It is altogether unlikely that two genes would have identical selective values under all the conditions under which they may coexist in a population. … cases of neutral polymorphism do not exist … it appears probable that random fixation is of negligible evolutionary importance” ⎯Ernst Mayr Neo-Darwinism 1930’s: ⎯ no way to test the predictions of different schools ⎯ arguments centered on mathematical models 1950’s and 1960’s: ⎯ protein sequencing (slow and painful) ⎯ protein gel electrophoresis (fast and cheap) 3 Protein electrophoresis: big changes in the 1960’s (A) Diagram of a protein gel electrophoresis apparatus, and (B) a photograph of a “stained” protein gel, the blue “blotches” are the proteins, their position indicates how far they migrated in the electric field. A B Protein electrophoresis: the results are in … Lewontin and Hubby (1966): Harris (1966): • 5 natural populations of Drosophila • Humans • 18 loci • 71 loci • 30% of loci (27 over the 5 popn.s) • 28% (20) were polymorphic were polymorphic • Human heterozygosity: 7% (2-53%) • Fruitfly heterozygosity: 11% Balance school: predictions correct ! Classical school: predictions wrong (But, what about load!) Lewontin and Hubby (1966) suggested that some of the polymorphism must be neutral 4 Genetic load Genetic load: the extent to which the fitness of an individual is below the optimum for the population as a whole due to the deleterious alleles that the individual carries in its genome. Genetic load: the difference between the average fitness of the population and the fitness of the best genotype. It measures the probability of selective death of an individual in a population. W = average fitness Genetic load (L) = 1 - W Genetic load: an example Two alleles (A and a) with frequencies p = q = 0.5: Survival to reproduce: AA = 40% Aa = 50% aa = 30% The relative fitness values are: AA = 0.8 Aa = 1 aa = 0.6 The mean fitness of the population = 0.25(0.8) + 0.5(1) + 0.25(0.6) = 0.85 The load of this population (L) = 1 – 0.85 = 0.15 [Note that if every member of the population had the same genotype the average fitnes would equal 1 and the load on the population would be zero.] Selective death (or genetic death): the chance that an individual will die without reproducing as a consequence of natural selection. [e.g.,15% of offspring in above] 5 Genetic load: the cost of selection [ or “Haldane’s dilemma”] Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity. no selective death: large excess no selective death: small excess 120 120 100 100 80 Background 80 mortality when all 60 individuals have the 60 same fitness 40 40 Background mortality when all 20 20 individuals have the same fitness 0 0 12 12 Population declines: Genetic death > reproductive excess Genetic load: the cost of selection [ or “Haldane’s dilemma”] Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity. Consider a new muation to an beneficial domiant allele: it takes time for selection to remove the “old” [deleterious recessive] allele from the population. Change in recessive allele frequency over time under different intensities of negative selection 1 s = 0 0.9 s = 0.01 0.8 0.7 allele a 0.6 s = 0.1 0.5 s = 0.5 s = 0.9 0.4 0.3 Frequency of 0.2 0.1 0 1 26 51 76 101 126 151 176 201 226 251 Generations There is a cost to selection, in genetic death, during this time period 6 Genetic load: the cost of selection [ or “Haldane’s dilemma”] Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity. Population declines: Genetic death > reproductive excess Haldane’s “Cost of selection” (1957) Assume directional selection of a new mutation: propotion that die due to selection L C × N gives the total C = ∑ = ∑ × N e proportion that survive W e selective death; this 1424444444 434444444 over all generations it takes to fix the allele must be sum over generations it take to fix the allele Genetic load: the cost of selection [ or “Haldane’s dilemma”] Genetic load has implications for the long term fate of a population. Haldane: the total load tolerated by a population is bounded by its excess reproductive capacity. Suppose L = 0.1 Load = 10% population reduction Total size = 500 individuals Reproductive size: 450 Cost of selection (C) = L/ W = 0.1/0.9 = 0.111 st C1 x Ne = 50 extra individuals per 1 generation Total generation to fix allele = 100 Population 1: Population 2: Population 2: Reproductive excess = 0 Reproductive excess = 0.1 Cost = C - R Cost = 0.111 – 0.1 = 0.011 Generation = 53 Generation = 100 … “soft selection” - Extinction: C53 = 499.1 - fixed beneficial allele -C100 = 334.6 - survival: N =165.4 7 Genetic load: sources 1. Mutational load 2. Substitutional load [Haldane’s load] 3. Segregational load Genetic load: mutational Let’s assume: (i) new mutations are deleterious alleles, and (ii) recessive. Remember the approximation of the equilibrium frequency of deleterious alleles [See population genetics, Topic 5 for a review]: q = (µ/s)1/2 Remember that population load is: L = 1 - W And remember that the average fitness under these assumptions was: W = 1 – sq2 We can make substitutions: L = 1 - W L = 1 – (1 – sq2) L = 1 – (1 – s(µ/s)) L = 1 – (1 – µ) L = µ It is interesting that we estimate that the load is equal to the mutation rate. Because it suggests that the load is approximately independent of the reduction in fitness caused by the mutant (s). 8 Genetic load: mutational Mutational load is minor: 1. Equilibrium yields a polymorphism involving an allele that is very rare in the population 2. The load is trivial for the population, as the required excess reproductive capacity is not large. Defining directional selection Directional selection: selection that favours the phenotype at an extreme of the range of phenotypes. 1 0.8 wAA > wAa > waa 0.6 0.4 Fitness 0.2 0 AA Aa aa Genotypes Directional selection: can be subdivided into two broad categories. These subtypes have been given different names, leading to a possible point of confusion. The next page is an attempt to clarify this issue. 9 Defining two types directional selection Type 1: Positive Darwinian selection: directional selection for fixation of a new and beneficial mutation in a population . Positive selection: Same as above. [Note that the above term is also shortened to “Darwinian selection”; this is a bad habit of which I am very guilty.] Type 2: Negative Darwinian selection: directional selection for removal of a new and deleterious mutation from a population. Negative selection: same as “negative Darwinian selection”. Purifying election: same as negative selection Genetic load: substitutional = substitution by “type 1” directional selection Deleterious recessive Genotype AA Aa aa 2 2 Frequency p0 2p0q0 q0 1 1 1 - s wmodel w 1 1 0.66 Haldane’s “cost of selection” is associated with fixation of an allele under a model such as the one above. Haldane assumed this type of load to estimate that the maximum rate of fixation of mutations in humans could not exceed 1 in 300 generations 10 Genetic load: segregational The model Genotype AA Aa aa 2 2 Frequency p0 2p0q0 q0 w 1 – s1 1 1 – s2 Segregational load is a big problem for the balance school: Well known examples exist; Haemoglobin, MHC locus, etc. Balance school would extend this to most polymorphic loci in the genome. Let’s see if this will work. Humans: 30% of loci are polymorphic (from Harris 1966) 30,000 genes (from recent genome projects), so 9000 are polymorphic Let’s assume a very small load on average: L = 0.001 Let’s assume that only half are under balancing selection (4500) [remember the balance school predicted a majority would be under balancing selection] Fitness of an individual locus = 0.999 Fitness over whole genome = 0.9994500 = 0.011 Load = 1- 0.011 = 0.989 [That is huge!!!] Cost = 0.989/0.011 = 89 [Do you know of any humans with families that big?] Genetic load: other 1.
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