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Genetic Drift In small, reproductively isolated populations, special circumstances exist that can produce rapid changes in gene frequencies totally independent of mutation, recombination, and natural selection. These changes are due solely to chance factors. The smaller the population, the more susceptible it is to such random changes. This phenomenon is known as genetic drift. Neutral alleles Controversial when first proposed (Kimura 1968) Incontrovertible in 2001: DNA sequence polymorphisms are abundant In Eukarya, most of the genome is noncoding most sequence polymorphism lies in noncoding regions Most sequence polymorphisms appear selectively neutral • Not useful for studies of genetic adaptation • Ideal for detection of population substructure and phylogenetic relationships Genetic Drift For example, when women and their mates are both heterozygous (Aa) for a trait, we would expect that 1/4 of their children will be homozygous recessive (aa). By chance, however, a particular couple might not have any children with this genotype (as shown below in the Punnett square on the right). Unless other families have an unpredictably large number of homozygous (aa) children for this trait, the population's gene pool frequencies will change in the direction of having fewer recessive alleles. Genetic Drift The net effect of genetic drift on a small population's gene pool can be rapid evolution, as illustrated in the hypothetical inheritance patterns shown below. Note that the red trait dramatically increases from generation to generation. It is important to remember that this can occur independent of natural selection or any other evolutionary mechanism. Inbreeding in finite populations Assume a population size of N, therefore 2N alleles in population. Imagine eggs and sperm released randomly into environment (e.g. sea) What is the probability of 2 gametes drawn randomly having the same allele? 2N alleles gen 0 gen 1 probability = 1/(2N) Inbreeding in finite populations Therefore, after 1 generation the level of inbreeding is F1 = 1/2N After t generations the probability is 1 1 Ft 1 Ft1 2N 2N Why? gen t-1 gen t 1/(2N) 1 - 1/(2N) 1 1 Ft 1 Ft1 2N 2N Probability of picking 2nd allele Genetic drift and heterozygosity t 1 Ft 1 1 2N Genetic drift will to a gradual loss of genetic diversity Follow an individual locus and gene frequency will drift until one allele becomes fixed Genetic diversity: HT = (1 – 1/2N) * HT-1 Probability of identity: FT = 1/2N + (1 - 1/2N) * FT-1 Average time to fixation: 4N Several populations Genetic drift will make initially identical population different Eventually, each population will be fixed for a different allele If there are very many populations, the proportion of populations fixed for each allele will correspond to the initial frequency of the allele Small populations will get different more rapidly Importance of genetic drift Two causes for allele substitutions: Selection -> adaptive evolution Genetic drift ->non-adaptive evolution Most populations are geographically structured All populations are finite in size All genetic variation is subject to genetic drift but not necessarely to selection Genetic drift as a null hypothesis against which evidence for selection has to be tested Effective population size Effective population size < Census size (in most cases) The effective population size is the size of an ”ideal” population having the genetic properties of the studied population The effective population size is determined by Large variation in the number of offspring Overlapping generation Fluctuations in population size Unequal numbers of males and females contributing to 4NfNm reproduction Ne = 1 1 = n Ne Σ 1 Ni (Harmonic mean) (Nf + Nm) Effective population size What is an ideal population like? (Remember - each parent a has an equal and independent chance of being the parent of each descendent allele.) This is approximated by a Poisson distribution of reproductive success. (Reproductive success = # of offspring per parent, or per parental allele.) Effective population size Ft Ft 1 1 1 Ft 1 Ft 1 2Ne 2Ne Ne Effective population size Ft 1 1 1 Ft 1 Ft 1 2Ne 2Ne 1 Ne 2 Effective population size For diploids: where V is the variance in reproductive success among diploid individuals. (Note that the variance among individuals in reproductive success with a Poisson distribution is 2 in a steady-state population, so that Ne = N-1/2.)Note also that Ne can also be as great as 2N-1, if there is no variance in reproductive success. This fact is often used in animal and plant breeding to slow the loss of genetic material. 4N 2 Ne V 2 Effective population size 1 1 1 1 1 1 ....1 1 Ft 1 2 Nt 1 2 Nt 2 2 Nt 3 F0 Population size in natural populations does not remain constant Ne with population size fluctuations is approximately the harmonic mean of N over time: The harmonic mean is very sensitive to small values. (Ne << ) if N is variable 1 1 = n Ne Σ 1 Ni (Harmonic mean) 4NfNm Ne = (Nf + Nm) Backwards: the coalescent approach Simplification: 0, 1 or 2 offspring Coalesce: have the same parent Probability to coalesce: 1/N Probability Not to coalesce: 1 – 1/N t generations: (1-1/N)t Average time to coalesce for 2 genes: N For the whole population: 2N Founder effects Another important small population effect is the founder effect or founder principle. This occurs when a small amount of people have many descendants surviving after a number of generations. The result for a population is often high frequencies of specific genetic traits inherited from the few common ancestors who first had them. A new population emerges from a relatively small group of people. # of founders 4,000 500 # of generations 12 80-100 Current size 2,500,000 5,000,000 Hutterites Japan Iceland 80 1,000 25,000 14 80-100 40 36,000 120,000,000 300,000 Newfoundland 25,000 16 500,000 2,500 500 12-16 400 6,000,000 1,660,000 Population Costa Rica Finland Quebec Sardinia Founder effect example In the Lake Maracaibo region of northwest Venezuela, for instance, there is an extremely high frequency of a severe genetically inherited degenerative nerve disorder known as Huntington's disease. Approximately 150 people in the area during the 1990's had this fatal condition and more than 1,000 others were at high risk for developing it. All of the Lake Maracaibo region Huntington's victims trace their ancestry to one woman who moved into the area a little over a century ago. She had an unusually large number of descendents and was therefore the "founder" of this population with its unpleasant genetically inherited trait. Founder effect example It is also possible to find the results of the founder effect even though the original ancestors are unknown. For example, South and Central American Indians were nearly 100% type O for the ABO blood system. Since nothing in nature seems to strongly select for or against this trait, it is likely that most of these people are descended of a small band of closely related "founders" who also shared this blood type. They migrated into the region from the north, mostly by the end of the last Ice Age. Bottleneck In some species, there have been periods of dramatic ecological crisis caused by changes in natural selection, during which most individuals died without passing on their genes. The few survivors of these evolutionary "bottlenecks" then were reproductively very successful, resulting in large populations in subsequent generations. The consequence of this bottleneck effect is the dramatic reduction in genetic diversity of a species since most variability is lost at the time of the bottleneck. Migration A cline is a gradual change in allele frequency along a geographic gradient Ecotypes are genetically distinct forms that are consistently found in certain habitats. Changes in allele frequency can be mapped across geographical or linguistic regions. Allele frequency differences between current populations can be correlated to certain historical events. Contrary to selection and genetic drift gene flow homogenizes allele frequencies Genetic diversity is restored if immigrants carry new alleles or alleles which are rare in the population Patterns of geographic variation Sympatric, parapatric and allopatric variants Subspecies are recognizable geographic variants within a species (usually subject to discussions) A hybrid zone is a region where genetically different parapatric species or population interbreed. Character displacement: sympatric populations of two species differ more than allopatric populations Allele distributions can reflect historical events Creutzfeldt-Jakob disease (CJD) is caused by a mutation in the prion protein 70% of families with CJD share the same allele Families from Libya, Tunisia, Italy,Chile and Spain share a common haplotype. These populations were expelled from Spain in the Middle Ages. Genetic drift and mutation no mutation 1 1 Ft 1 Ft1 2N 2N gen t-1 gen t 1/2N 1 - 1/2N 1 1 2 2 Ft 1 m 1 1 m Ft1 2N 2N Probability of neither of 2 alleles being mutated is (1-m)2 Equilibrium Between Mutation and Drift Run the recurrence equation over and over and eventually it will settle down to an equilibrium Probability of gen t-1 gen t 1/2N picking 2nd allele and it not being mutated 1 - 1/2N 1 1 2 2 Ft 1 m 1 1 m Ft1 2N 2N 1 ˆ F Ft Ft1 1 4Nm Gene flow 2N m ? Probability of identity: FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m)2 (assumes that the immigrants are different from each other) N = 100 m=0 0.9 0.9 0.8 0.8 0.7 0.7 N = 100 0.6 0.5 0.4 m = 0.01 0.3 0.2 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0 0 0 50 100 150 200 0 50 100 150 200 (Mutation has the same effect) 2N μ ? Probability of identity: FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – μ)2 Assumes that each mutation creates a new allele: Infinite allele model Mutation also retards the loss of genetic variability due to genetic drift Equilibrium After a long time (the longer the larger the population) there will be an equilibrium between genetic drift, gene flow and mutation FT = [1/2N + (1 - 1/2N) * FT-1] * (1 – m- μ)2 F and H will not change any more (if everything remains constant !!) F 1 4N μ + 1 Mutation – drift equilibrium F 1 4N m + 1 Migration – drift equilibrium Migration Models – Island Model One Way Migration m is the probability that a randomly chosen allele is a migrant Main Land P* Change of allele frequency with one way migration •A is fixed on the island •a arrives from the mainland at rate m =0.01 p P A in generation 1 on the island p P A in generation 2 on the island p 1 m p mp * Island p p p* 1 m p p * pt p * 1 m p0 p * t Mutation and Migration m = 10-4 pt p0 1 m m = 10-2 t pt p * 1 m p0 p * t 0.484 0.507 1 m 0.474 0.507 10 Estimation of m 10 generations Present allele frequency in “island” = pt = 0.484 Allele frequency in mainland p* = 0.507 Initial allele frequency in island = p0 = 0.474 m = proportion of migrant alleles each generation 0.484 0.507 1 m 0.474 0.507 10 0.484 0.507 10 1 m 0.474 0.507 0.484 0.507 0.964 0.474 0.507 m 0.035 1 m 10 Estimation of M 10 generations Present allele frequency in “island” = pt = 0.484 Allele frequency in mainland p* = 0.507 Initial allele frequency in island = p0 = 0.474 m = proportion of migrant alleles each generation 0.484 0.507 1 m 0.474 0.507 10 0.484 0.507 1 m 0.474 0.507 10 0.484 0.507 10 1 m 0.474 0.507 0.484 0.507 0.964 0.474 0.507 m 0.035 1 m 10 Island Model of Migration Many large subpopulations Average allele frequency = frequency in migrants The change frequency in the subpopulations: pt p 1 m p0 p t p10 0.5 1 0.1 0.2 0.5 0.395 10 p p p = 0.2 p10 0.5 1 0.1 0.8 0.5 0.605 p = 0.8 10 p 0.2 0.8 2 m = 0.10 Change in allele frequency over time Five subpopulations 1, 0.75, 0.5, 0.25, 0 Summary Genetic drift: In a finite population allele frequencies fluctuate at random and eventually one allele will be fixed After 4N generations all individuals descend from one ancestor Genetic diversity is lost more rapidly in small populations Inbreeding reduces the number of heterozygotes Inbred individuals can have lower fitness: inbreeding depression The genetic composition of isolated populations diverges under the effect of genetic drift Gene flow homogenizes allele frequencies among populations After a long time, the genetic variability in a population reaches an equilibrium level: mutation – immigration – drift equilibrium