Population genetics Halliburton Chapter 6-7

1. BI 3010 H07 Mutations Population genetics Halliburton Chapter 6-7 Mutations Mutations are the raw materials of genetic variation. Viable mutations are rare om most loci, but this varies strongly between loci. Although the allele frequency changing affect (i.e. evolution) may be modest on short time frames, it is the accumulated amount of allelic variants on evolutionary time frames that has enabled genetic differentiating between individuals, populations, species, families and higher taxa. The cause of mutations: Errors during DNA replication, uneven crossing-over, chromosome breaking, and meiotic non-separation (corresponding chromosomes do not go to separate daughter cells). Types of mutations: Mutations can take place in sex chromosomes as well as in somatic chromosomes. Those which affect single nucleotides are called point mutations. When a whole gene or several genes are duplicated we speak about gene mutations. Such events are evolutionary important because they give room for natural selection to act. For example, vertebrates usually have more than one locus (usually 2-3) coding for a specific protein, and often these loci are more or less tissue-specific so that e.g. in heart muscle one locus dominates the protein synthesis, while another dominates in liver tissue. Traditionally, mutations which affect single loci are called gene mutations, while those affecting the number of or structure of chromoso- mes are called chromosome mutations, but this nomenclature is not very satisfactory today.

2. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Mutations An alternative classification is: 1. Chromosome mutations (duplications, deletions, inversions, translocations) 2. Point mutations (Changes in one nucleotide) 3. "Indels": (Abbrev. for insertions/deletions. Small; one to a few hundred basepairs) 4. Gene-duplications (of one or several protein-coding genes) Aneuploidy: One extra or missing chromosome (e.g. in Down's syndrome with an extra copy of chromosome 21 in man). Polyploidy: The whole set of chromosomes is duplicated, so that individuals have three or more sets instead of two, as normally. This usually arises when cytokinesis (separation to daughter cells) don't take place during meiosis. More concepts: Inversions, which can involve several genes, tend to be inherited as units. Dobzkansky called such units "co-adapted gene complexes". There is evidence that such complexes are maintained by some form of natural selection, in that the so-called heterokaryotypes have higher relative fitness compared to homokaryotypes. Translocations arise when a segment from one chromosome attaches to a non-homologous chromosome. They can be resiprocal or not. Translocations are almost always lethal (giving abnormal gametes and disturbance of the gene regualtion). Many types of cancer in man are caused by such disturbances. Closely related specues often differs by only one or a few translocations. Fusions means that segments from two non-homologous chromosomes combine to a new chromosome (cf Fig. 6.1 in Halliburton; chrom. # 2). Fission is the opposite phenomenon.

3. BI 3010 H07 Mutations Population genetics Halliburton Chapter 6-7 Transposable elements: The insertion or deletion of long DNA sequences. Common in both pro- and eucariotes. When a transposable element moves into or out of a protein-coding locus we have a mutation. Such elements are connected with variation in quantitative traits (like bristle number in Drosophila), and hence interesting for breeding geneticists. Gene duplications: Individual genes, chromosome parts or whole chromosomes can be duplicated. The duplicate is a new copy of one or more genes in the genome. Because the very function of the gene is secured with only one copy, the evolutionary forces (mutation, selection) can act without the common restraints and create viable variants with new functions (cf "pseudogenes" which have lost their original function).Cf multiple loci for isozymes in vertebrates, often becoming tissue-specific.

4. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Mutations • Mutation models • Recurrent mutations: ”Wildtype” vs mutant, to and fro until an equilibrium (this is the model in PopG.exe). • q-bar =  / ( + )[ check formula with PopG.exe ] • where  is mutation rate and  = backmutation rate • Infinite alleles model: (Single basepair mutations). Each mutation creates a unique allele (Kimura & Crow 1964). A sentral model in population genetics. • Stepwise mutation model: Based on the situation observed by protein electrophoresis. Allows for backmutations and repeated mutations. Experience shows it is more relevant for micro- and minisatellites. • Infinite site model: Regards each nucleotide position ("site") as independent of others. It assumes that most positions don't mutate, and that those that mutate do it only once. This means that each "site" has only one or two alleles. Results from SNP studies appear to fit this model, which has two versions: linkage equilibrium (Kimura 1969) and linkage disequilibrium (Watterson 1975) between tightly linked positions.

5. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Mutations Mutation rates: Most mutation for coding DNA are harmful, and the frequency of mutants is a balance between mutation rates and natural selection. Therefore, observed mutant frequencies are low. The mutation frequencies can be calculated in many ways (per nucletide, locus, chromosome or genome). It must be made clear whether mutation rates are per cell division, generation or some unit of time. Here's an example from fruit fly (Drosophila sp.): Ca 36 cell divisions between zygote formation and gamete production in imago. If assuming 2x10-6 mutations per locus per cell division, it counts to 72x10-6 mutations per locus per generation (or per zygote). Mutation rates have been shown to vary enormously; by many orders of magnitude, among loci (see Table 6.1 in Halliburton). Mutations that cause genetic disorders typically show low frequencies (10-5 - 10-6 per locus per generation). Microsatellite loci can show much higher frequencies (10-3), which is the reason why they are better gene markers for short-time genetic differentiation processes; they will react faster to reproductive isolation/genetic drift than protein-coding loci. Mutation rates per nucleotide per generation are lower; ca 10-8 or less. The reason for this is that the proof-reading repair mechanism acting on DNA during replication. Mitochondrial DNA, which has fewer repair mechanisms, thus shows higher mutation rates per nucleotide. This means higher evolutionary rates in shorter time spans than for protein-coding loci.

6. BI 3010 H07 Mutations Population genetics Halliburton Chapter 6-7 Fitness effect of mutations: Harmful: Most frequent. Neutral: Frequencies largely unknown. Favourable: Rare Backmutations from harmful mutations are often less frequent than the mutation itself. Cleansing selection removes harmful mutations, or lower the frequency of them. Selection coefficients and population sizes play roles for the efficiency of this. In very small populations genetic drift can override selection, and more often lead to fixation of harmful mutant alleles. ”Silent”, or synonymous mutations in a codon (3rd codon position) do not change the resultant amino acid, and should thus be ideal gene markers for studies of differentiation by random genetic drift. From the genetic code it can be deduced that the ration between "replacement" and "silent" mutations should be 3:1. Studies in mammals have supported this; the portion that are neutral is 20-30%, and sometimes higher. The probability for a neutral mutant to become fixed in the population is 1/2Ne where Ne is the genetically effective population size [ check this using PopG.exe ]. . Favourable mutations are the raw material for adaptive evolusion. Natural selection can make these increase in frequency and eventually become fixed in the population. Since their initial frequency is very low (1/2Ne; heterozygote carrier), the probability that they are lost quickly by genetic drift is substantial (ca 37% in the first generation). It is assumed that the frequency of mutants with a substantial favourable effect is very low.

7. BI 3010 H07 Mutations Population genetics Halliburton Chapter 6-7 The span of mutational effects: Mutations with visible morphological effects are rare. Lethal recessive mutations are more rare then mutations with less dramatic effects. Mutational effects (fitness reduction) on heterozygotes: Lethal mutations: h = 0.03 Mild mutations: h = 0.3 -0.5 (h indicated how much the fitness (w) of the heterozygote is reduced) Simmons & Crow: ”The milder the effect of a mutant, the greater its dominance”. (Page 203) Mutation - selection equilibrium: When a harmful allele is rare, natural selection is less efficient in removing it (cf the eugenics problem treated previously). Simulation: Use PopG.exe, and set the fitness of a recessiv homozygote to 0 (i.e. S=1). Start with a low frequency of the mutant (recessive) allele, and a population size=10.000 (to reduce noise from genetic drift), and study the progress of the curves for frequency of the wildtype allele. Notice the asymptotic course, with less and less effect of selection over generations (cf the eugenics programs often advocated in the 1930ies).

8. Population genetics Halliburton Chapter 6-7 BI 3010 H07 Mutations When the allele frequency of a harmful mutant is affected by (recurrent) mutation rate and natural selection, it will eventually reach an equilibrium given ny: q = SQR(/s) [ where genotypic fitnesses are: A1A1: 1, A1A2: 1-hs, og A2A2: 1-s] Under certain assumptions this formula can be used to calculate mutation rates at a locus. It has been used, together with observations, to argue that lethal mutations have certain harmful affect even in heterozygotes. [ simulate using PopG.exe ] Mutational load (genetic load) Single locus: All selection works through differential mortality, and therefore increases the total mortality in the population so that mean fitness is reduced. Mutation-selection equilibrium therefore creates what is called "genetic load" or "segregational load"; a general reduction of the health of the population. For a completely recessive mutation in equilibrium with selection the genetic load (L) is: L = , and for a not completely recessive mutation: L = 2 In other words; in the equilibrium situation the mutational load is only depending on the mutation rate, not on the harming effect and the severity of the mutation. The reason for this is that very harmful mutations progress towards a lower equilibrium frequency, which is balanced by the strong selection against them. Summed over the entire genome (n loci): L = 2n(-bar), where -bar is the mean mutation frequency over n loci. An estimate from fruit fly: 0.4% reduction in viability (fitness) per generation, 1.2% per zygote. Important concepts: Muller’s ratchet, mutational meltdown (Halliburton p. 210).

9. BI 3010 H07 Mutations Population genetics Halliburton Chapter 6-7 The faith of a new mutation: Most mutations are lost after few generations due to selection or genetic drift. What is the probability that a neutral mutation is lost already after one generation? Or after two, or any generation in future? If the neutral mutant is a heterozygote the probabilities for survival or loss in the first generation are: Pr(survival) = 1 – 1/e = 0.632, i.e. ~ 63% and Pr(loss) = e-1 = 0.368, i.e. ~ 37% The probability for loss during 10 generations is more than 80%. The probability that a mutant allele survives and eventually is fixed in the population depends on the effective population size and is: Pr(Fixation) = 1/2Ne, i.e. it's initial frequency! [ check formula with PopG.exe ]

10. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Genetic drift • Genetic Drift: • If we define evolution as any change in allele frequency in the populations, it is easy to see that genetic • drift for neutral alleles can propel evolutionary change. The change is, however, unpredictable because • it is stochastic. Genetic drift can be seen as a sampling error from one generation to the next. • The theory on this was developed by Sewall Wright in the 1930ies and 1940ies. Genetic drift is the • random variation in allele frequencies from one generation to the next. It has two causes: • Mendelian segregation – a diploid individual holds two copies of each gene, but produces gametes • with only one copy each. • Population size is not infinitely large - any population (or generation) is a random subset of the • gametes that were produced by the parental population (or generation). • Four main aspects of genetic drift: • The direction of the change in allele frequencies is unpredictable. An increase or decrease is equally • probable in any generation (except at allele frequencies very close to 0 or 1). • The magnitude of genetic drift depends on the effective population sizes. The smaller the population, • the larger the average gene frequency change from one population to the next. • The long term effect of genetic drift is to reduce genetic variability within a population (fixations). • Genetic drift causes populations to diverge genetically from each other by time. • Genetic drift reduces genetic variation within populations, but increases it between divergence them. • NB! Simulate various scenarios with the software PopG.exe.

11. BI 3010 H07 Genetic drift Population genetics Halliburton Chapter 6-7 The binomial distribution: Describes the distribution of outcomes in a set of n independents trials where each has two possible outcome. Let the probability for one outcome (success) be p, and for the other (failure) be (1-p). Let X be a random variable which describes the number of successes in n trials. X can take the values 0,1,2,....n. The binomial distribution describes the probability (Pr) for each of the possible outcomes (i.e. number of successes in n trials). Let x denote a specific outcome for X. Then Pr(X=x) = [ n! / (x!(n-x)! ] [ px(1-p)n-x] Example: The probability for getting a 1 when throwing a dice once is 1/6. The probability of getting exactly two "1"s (x=2) in five throws (n=5) is Pr(X=2) = [5! / 2!3!] [ (1/6)2 (5/6)3] = 0.16

12. BI 3010 H07 Genetic drift Population genetics Halliburton Chapter 6-7 "Genetic drift reduces genetic variability within populations" Concepts: Identity by descent (ibd) and Identity by state (ibs) Identity by state (IBS): Alleles which are functionally equivalente. Identity by descent (ibd): Alleles which are inherited from a common ancestor in the last or previous generations. The probability of two alleles being ibd is 1/2N and is called the inbreeding coefficient, f. This probability increases each generation, because each generation of sampling creates a new possibility for ibd to be added to the existing value of f. The recursion equiation is: ft+1 = 1/(2N) + [(1 – 1/(2n) ]ft Reduction in heterozygosity caused by genetic drift: H, or the proportion of heterozygotes in the population, is by the Hardy-Weinberg law given by the allele frequencies as H=2p(1-p), which has its maximum p=0.5 at a 2-allel locus. When the allele frequencies approaches 1 or 0, the heterozygosity approaches zero. Genetic drift makes allele frequencies approach the extremes fixation/loss sooner or later, and the heterozygosity to be reduced by an amount 1/2N each generation.

13. BI 3010 H07 Genetic drift Population genetics Halliburton Chapter 6-7 "Genetic drift leads to differentiation between populations": The variance of an allele frequency p after one generation of binomial sampling is: Var(pt+1) = pt(1-pt)/2N, and this variance increases over generations. In generation t it s: Vart(p) = p0(1-p0) [ 1- (1 – 1/2N)t ] (Study Fig. 7.6 – 7.9 pp 232-233 in Halliburton) Effecive population size ( (Ne): Definition: The size of an "ideal" population which has a genetic drift equal to the one under study. By "ideal" is meant constant size, equal sex proportion, and equal number of offspring in all matings. Effect of unequal sex ratio: Ne = 4Nm*Nf / (Nm + Nf) which means that with e.g. 1 male, even 100 females will not constitute an effective population size larger than approximately 4. Such a population will loose genetic variation (measured as heterozygosity) at a high rate due to strong genetic drift.

14. Population genetics Halliburton Chapter 6-7 BI 3010 H07 Genetic drift Variation in effective population size over generations: Variation in family sizes within populations: Ne = 4N / (VK +2), where K=family size, and VK the variance in family size. X-linked loci: Y-linked loci: mtDNA loci: This harmonic mean is always less than the arithmetic mean when Ne varies. Episodes with small populations sizes always have strong reducing effect on Ne. NB! Family size means the number of offspring surviving to reproduction. In stable populations both the mean and the variance of k is 2. Founder effects (and population bottlenecks) give genetic drift dependent on founder Ne, and changes the allele frequencies accordingly. The heterozygosity is reduced each generation by a quantity:  H = - [1 / (2Ne)]

15. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Genetic drift The heterozygosity at an equilibrium between genetic drift and mutation is: H = 4Ne / (4Ne + 1) Genetic drift, population dynamics, and extinction (rules of thumb): Minimum viable population size on short term: Ne = 50 Minimum viable population size on long term: Ne = 500-1000 (adjusted by Lande (1995) to 5000-10000 individuals). How important is genetic drift in nature? A population is "small" and genetic drift is a significant evolutionary force when, related to the other evolutionary forces (mutation, selection, and immigration): 4N < 1 4Ns < 1 4Nm < 1 The long term effects of genetic drift and mutations are clear; all populations will loose genetic variation and accumulate harmful mutations. Many favourable mutations will be lost, which hampers the ability for long term adaptability. The severeness of these effects depends strongly on the effective population size.

16. BI 3010 H07 Population genetics Halliburton Chapter 6-7 Genetic drift Genetic drift and natural selection: Natural selection changes allele frequencies in a predictable manner (cf the relative fitness and selection coefficients of genotypes). Genetic drift also changes allele frequencies, but in an unpredictable way. Which of these two forces will dominate depends on the size of the fitness advantage, and the population size. In very small populations, genetic drift will be so strong that it hampers or even overrides the effect of selection (cf fig. 7.16 and 7.17 in Halliburton), and even favourable mutations will appear, evolutionary seen, as if they were neutral. This means they can more easily be lost from a small population. NB! Simulate various scenarios with software PopG.exe. The probability of fixation for a recessive favourable mutation (Kimura 1962) is: Pr(fix)  1.13 s/(2N) where s is the fitness advantage for a homozygote (i.e. double dose) for the mutation. [ Pr(fix) for a neutral mutation = 1/(2N). Compare!]

17. BI 3010 H07 Genetic drift Population genetics Halliburton Chapter 6-7