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 è macroevolution Neo-Darwinism 1. genetic variation arises at random via mutation and recombination 2. populations evolve by changes in allele frequencies 3. Neo-Darwinism : Everything is subject to allele frequencies change by mutation, migration, drift and natural selection 4. most mutations are deleterious Natural selection ; therefore drift on 5. most adaptive phenotypic effects are small so changes in phenotype are slow and gradual neutral alleles can be ignored (it just • some such changes can have large discrete effects doesn't happen). 6. diversification occurs by speciation • usually a gradual process • usually by geographic isolation 7. Microevolution è macroevolution 2
Neo-Darwinism Classical school Balance 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 very rare • Polymorphism is common • Positive Darwinian selection and • Balancing selection is comparable to balancing selection are rare with respect to purifying selection in micro-evolution purifying selection in micro-evolution • Genetic variation connected to • Too much “ genetic load ” for genetic morphological variation. variation to connect with morph. variation • Prediction : most populations will be • Prediction : most populations will be heterozygous at most loci homozygous at most loci “ 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 3
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 ) 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 4
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 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 5
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 load on the population would be zero.] [ Note that if every member of the population had the same genotype the average fitnes would equal 1 and the 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 ] 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 (birth rate exceeds death rate). no selective death: large excess no selective death: small excess 120 120 100 100 80 Background 80 60 mortality when all 60 individuals have the 40 same fitness Background 40 20 mortality when all 20 individuals have the 0 same fitness 0 1 2 1 2 Population declines: Genetic death > reproductive excess 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. Consider a new mutation to an beneficial dominant 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 Frequency of a allele 0.7 0.6 s = 0.1 0.5 s = 0.5 s = 0.9 0.4 0.3 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 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 × N e C C × N e gives the total proportion that survive W selective death; this � � � � � � � � � � � � � � � � � � � must be sum over over all generation s it takes to fix the allele generations it take to fix the allele 7
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/ = 0.1/0.9 = 0.111 W C 1 x N e = 50 extra individuals per 1 st generation Total generation to fix allele = 100 Population 1: Population 2: Population 2: Cost = C - R Reproductive excess = 0.1 Reproductive excess = 0 Cost = 0.111 – 0.1 = 0.011 Generation = 100 Generation = 53 … “ soft selection ” - Extinction: C 53 = 499.1 - fixed beneficial allele - C 100 = 334.6 - survival: N =165.4 Population 1: Population 2: Reproductive excess = 0 Reproductive excess = 0.1 C = 0.111 C = 0.111 – 0.1 = 0.011 Extinction: At gen. 53 N =0 Fixation: At gen. 100 N = 165 450 49.95 400.05 450 4.95 445.05 1 s = 0 0.9 s = 0.01 0.8 0.7 0.6 s = 0.1 0.5 s = 0.5 s = 0.9 400.05 44.40555 355.6445 445.05 4.89555 440.1545 0.4 0.3 0.2 0.1 0 1 26 51 76 101 126 151 176 201 226 251 355.6445 39.47653 316.1679 440.1545 4.841699 435.3128 316.1679 35.09464 281.0733 435.3128 4.78844 430.5243 281.0733 31.19913 249.8741 430.5243 4.735767 425.7885 249.8741 27.73603 222.1381 425.7885 4.683674 421.1049 222.1381 24.65733 197.4808 421.1049 4.632154 416.4727 197.4808 21.92037 175.5604 416.4727 4.5812 411.8915 175.5604 19.48721 156.0732 411.8915 4.530807 407.3607 156.0732 17.32413 138.7491 407.3607 4.480968 402.8797 8
Genetic load: sources 1. Mutational load 2. Substitutional load [Haldane ’ s load] 3. Segregational load 1. Genetic load: mutational (effect of a single locus) 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 8 for a review]: See PopGen Topic 8 q = ( µ /s) 1/2 Remember that population load is: W L = 1 - And remember that the average fitness under these assumptions was: See PopGen Topic 5 W = 1 – sq 2 We can make substitutions: L = 1 - W L = 1 – (1 – sq 2 ) L = 1 – (1 – s( µ /s)) L = 1 – (1 – µ ) L = µ load is approximately independent of the reduction in fitness caused by the mutant ( s ). It is interesting that we estimate that the load is equal to the mutation rate. Because it suggests that the Why ? 9
Frequency of a allele µ = 0.0001 The reason why mutational load is approximately independent of the reduction in fitness caused by the mutant ( s ) s = 0.1 ( W aa = 0.9) µ = mut rate A → a higher equilibrium freq (a) lower selective death (lower s) a µ = 0.01 µ = 0.001 lower equilibrium freq (a) higher selective death (higher s) (most likely here in natural popn) 10
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