10. Genetic variation and fitness

1. 10. Genetic variation and fitness Hardy Weinberg law According to the Hardy Weinberg law gene frequencies are constant. How can evolution occur? Assume a gene with two alleles A and B that occur with frequency p and q = 1-p. Assumptions of the Hardy Weinberg law 1. No mutations to generate new alleles (no genetic variability) 2. Mating is random 3. The population is closed 4. The population is infinitively large 5. Individuals are equivalent The frequency of heterozygotes is highest at p = q = 1/2 None of these assumptions is fully met in nature. Thus, gene frequencies permanently change Therefore, evolution must occur! What is the frequency after crossing?

2. Mutation rates Assume the number of mutation events M in a genome is proportional to the total amount of the mutation inducing agent D, the dose Equilibrium conditions The change in p is the sum of forward and backward mutations Mutation rate m The change in gene frequency is assumed to be proportional to actual gene frequency multiplied with the mutation rate. At equilibrium dp/dt = 0 Under constant forward and backward mutation rates p and q will achieve equilibrium frequencies. Otherwise they will permanently change. The change of gene frequency follows an exponential function

3. Immigration of alleles Nonrandom mating If mating is totally random a population is said to be panmictic. Assume a population has an allele A with frequency p. Due to migration the next generation gets individuals from outside by immigration and looses individuals by emigration. Let i denote the immigration and e the emigrate rate. Both processes are assumed to be proportional to actual density. The total number of individuals before migration was N0. Ni individuals immigrated, Ne emigrated A special type of nonrandom mating is inbreeding. Inbreeding results in the accumulations of homozygotes. Inbreeding depression due to homozygosity in Italian marriages 1903-1907. Constant immigration of individuals causes a linear change in allele frequency

4. Individuals are not equivalent If individuals are not equivalent they have different numbers of progenies. Selection sets in What is the unit of selection? Selection changes frequencies of genes. The gene is therefore a natural unit of selection. However, selection operates on different stages of individual development. Five levels of natural selection Zygotes Intragenomic conflict occurs when genes are selected for at earlier stages of development that later may be disadvantageous. This can occur if they are transmitted by different rules Compatability selection Ontogenetic selection Gametes Children Gametic selection Viability selection • Examples of such genes • Transposons • Cytoplasmatic genes Mating success Parents Adults

5. Individuals are not equivalent The ultimate outcome of selection are changes in gene frequencies due to differential mating success. Selection changes the frequency distribution of character states Diversifying selection Directional selection Stabilizing selection Parent Offspring Phenotypic frequency Phenotypic frequency Phenotypic frequency Phenotypic character value Phenotypic character value Phenotypic character value

6. Selection changes the frequencies of alleles The absolute fitnessW of a genotype is defined as the per capita growth rate of a genotype. Using the Pearl Verhulst model of population growth absolute fitness is given by the growth parameter r of the logistic growth function for each genotype i. The relative fitness w of a genotype is defined as the value of r with respect to the highest value of r of any genotype. w = W / Wmax. The highest value of w is arbitrarily set to 1. Hence 0 ≤ w ≤ 1 The value s = 1 - w is defined the selection coefficient that measures selective advantage.s = 1 means highest selection pressure. s = 0 means lowest selection pressure. A general scheme for two alleles

7. How do allele frequencies change after selection? The mean fitness is defined as the average fitness of all individuals of a population relative to the fittest genotype. The change of frequency of p is then The general framework for studying allele frequencies after selection.

8. 1. The dominant allele has the highest fitness w11 = w12 > w22 2. Heterozygotes have the highest fitness (heterosis effect) w11 < w12 > w22 w11 = w12 = 1 w22 = 1 - s w12 = 1 w11 = 1 - s , w22 = 1 - t Rat poisoning with Warfarin in Wales shows how fast advantageous alleles become dominant The heterosis effect stabilizes even highly disadvantageous alleles in a population

9. 4. The recessive allele has the highest fitness w11 = w12 < w22 3. Heterozygotes have the lowest fitness w11 > w12 < w22 w11 = w22 = 1 w12 = 1 - s w22 = 1 w12 = 1 - s , w11 = 1 - s Heterozygote disadvantage leads to fast elimination of the allele with initially lower frequency. Recessive allele frequency increases slowly. It may take a long time for a rare recessive advantageous allele to become established

10. Reported values of selection coefficients Survival difference Endler (1986) compiled selection coefficient (s = 1 – w) for discrete polymorphic traits • Survival differences are: • mostly small. • Reproductive difference are larger. • The proportion of significant differences in reproductive success is higher than for the survival difference. • In many species only a small proportion of the population reproduces successfully. Reproductive difference All values Only statistically significant values

11. Classical population genetics predicts a fast elimination of disadvantageous alleles. Polymorphism should be low. Natural populations have a high degree of polymorphism Balancing selection Heterozygote advantage Balancing selection within a population is able to maintain stable frequencies of two or more phenotypic forms (balanced polymorphism). This is achieved by frequency dependent selection where the fitness of one allele depends on the frequency of other alleles. In heterozygote advantage, an individual who is heterozygous at a particular gene locus has a greater fitness than a homozygous individual. Cepaea nemoralis Shell colour and habitat preference of European Helicidae Sickle cell anaemia

12. The fundamental theorem of natural selection k groups with n members Parents k groups with n’ members Children The arithmetic mean and covariance of n elements grouped into k classes is defined as Now consider the average value of a morphological or genetic character z that changes from parent to child generation as Dz = z’-z. The Price equation is the basic mathematical description of evolution and selection

13. The fundamental theorem of natural selection If we take the change of w we get from z=w If w’ differs only slightly from w we get Fisher’s fundamental theorem of natural selection Sir Ronald Aylmer Fisher1890-1962 Sir Ronald Aylmer Fisher1890-1962 The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time. Selection effect Innovation effect Selection effect Change in fitness The Fisher Price equations are tautologies. They are simple restatements of the definitions of mean and variance. Nevertheless, they are the basic descriptions of evolutionary change Because mean fitness and its variance cannot be negative, the fundamental theorem states that fitness always increases through time Evolution has a direction

14. Adaptive landscapes Sewall Green Wright (1889-1988) Species A Species B Global peak Local peak Mean fitness Adaptive peak Species occupy peaks in adaptive landscapes To evolve they have to cross adaptive valleys High adaptive peaks are hard to climb but when reached they might allow for fast further evolution but also for long-term survival and stasis. Adaptive landscapes

15. Evolution without change in fitness Genetic drift A1 A2 Motoo Kimura (1924-1994) Assume a parasitic wasp that infects a leaf miner. Take 100 wasps of which 80 have a yellow abdomen and 20 have a red abdomen. A leaf eating elephant kills 5 mines containing red and 3 mines containing yellow wasps. By chance the frequencies of red and yellow changed to 15 red and 77 yellow ones. The new frequencies are red: 15/(15+77) = 0.16yellow: 1-0.16 = 0.84 A3 A4 A5 During many generations changes in gene frequencies can be viewed as a random walk Time

16. A random walk of allele occurrences At low allele frequencies survival times are approximately logarithmic functions of frequency Survival times of alleles The Foley equation of species extinction probabilities applied to allele frequencies

17. Effective population size If we have N idividuals in a population not all contribute genes to the next generation (reproduce). The effective population size is the mean number of individuals of a population that reproduce. The frequency of heterozygotes in a neutral population is For a mutation rate of u0 = 10-6 we get Consider a population of effective population size Ne. Let ue be the neutral mutation rate at a given locus. Neutral mutations are those that don’t effect fitness. The number of new mutations is 2Neue. The number of neutral mutations that will be established in a population is therefore (1/2Ne)*2Neue =ue At fairly high population sizes neutral theory predicts high levels of polymorphism. Neutral genetic drift explains the high degree of polymorphism in natural populations.

18. Lynch and Connery 2003 Genome complexity and genetic drift Assume a newly arisen neutral allele within a diploid population of effective size Ne. The rate of genetic drift is therefore 1/2Ne. Given a mutation rate of u of this allele u2Ne mutations will occur within the population. The average number of neutral mutations is M = 4Neumeasuring M allows for an estimate of the effective population size Ne if u is constant. Mutations are removed Mutations can be fixed by genetic drift The low effective population sizes of higher organisms increase the speed of evolution to a power because a much higher proportion of mutations can be fixed through genetic drift. In accordance with the Eigen equation only small effective population sizes allow for larger genome sizes.

19. Today’s reading All about selection: http://en.wikipedia.org/wiki/Natural_selection Polymorphism: http://en.wikipedia.org/wiki/Polymorphism_(biology) Fundamental theorem of natural selection: http://stevefrank.org/reprints-pdf/92TREE-FTNS.pdf and http://users.ox.ac.uk/~grafen/cv/fisher.pdf