File:Sewall Wright.jpg Soubor:Two cheetahs together.jpg DRIFT Kimura HW: infinite population but in real world population sizes finite Þ random processes, nonadaptive evolution Why randomness? when number of repetitions finite probability of an event ¹ its frequency (cf. H-W principle) 10 coins ® in more than 75 % cases the ratio differs from 1 : 1 Pascal´s triangle: 11 possible results: 0×, 1×, 2×, ..., 10× „head“ Výsledok vyhľadávania obrázkov pre dopyt pascal triangle 20 hodů, 100 mincí 20 hodů, 10 mincí S větším počtem mincí menší rozptyl kolem očekávané hodnoty Sampling Náhodný výběr gamet z genofondu (sampling error): Výsledkem náhodného výběru je kolísání frekvencí mezi generacemi = „random walk“ Wrightův-Fisherův model » Hardyho-Weinbergův model pro malé populace Sampling Random sampling from gene pool (sampling error): Random sampling results in fluctuations of allele frequencies across generations = „random walk“ Wright-Fisher model » Hardy-Weinberg model for finite populations nový-1 Hiccup! „random walk“ sea footbridge ? ? Drunk sailor Plop! footbridge width N N Plop! narrower footbridge we don´t know where he will fall we can surmise he will fall on the left! 1 populace 2N = 20 1 populace 2N = 2000 allele fixation/ extinction earlier higher fluctuation of frequency across generations Modelling drift: Fluctuation of frequencies across generations stronger in small populations (~ drunker sailor). 5 populací 2N = 2000 5 populací 2N = 20 some alleles are fixed... ... others disappear Conclusion 1: Drift results either in allele fixation or allele extinction. Conclusion 3: Probability of allele fixation equals its frequency. Conclusion 4: Mean time to fixation of a new allele » 4N. Probability of fixation of a new allele in diploids = 1/(2N) Conclusion 2: Drift results in loss of variation in demes. Modelling drift: in each generation new sampling from the gene pool with changed frequency... ... these samplings are independent in individual demes Conclusion 5: Drift results in divergence among demes. Peter Buri (1956): 107 populations of D. melanogaster zeroth generation: 16 heterozygous bw75/bw individuals in each population in each generation random sampling of 8 males and 8 females 19 generations http://i305.photobucket.com/albums/nn214/matchingmole/Ancient%20World/browndrosophila.jpg Buri (1956): in the first generation most populations around p = 0,5 ultimately most populations either p = 0 or p = 1 population divergence Drift7 DRIFT mathematical simulation (difussion aproximation) simulation with initial frequency p = 0,1 http://www.stoplusjednicka.cz/sites/default/files/foto-dne/2014/02/laj_hh1c9863.jpg http://calphotos.berkeley.edu/imgs/256x384/6666_6666/1007/0282.jpeg http://calphotos.berkeley.edu/imgs/256x384/6666_6666/1007/0283.jpeg http://s3.quazoo.com/Pictures/Collections/14/719797/CoverImage_719797.jpg Eg.: Galapágos lava lizard (Microlophus albemarlensis) http://upload.wikimedia.org/wikipedia/commons/7/77/Galapagos-satellite-esislandnames.jpg sea level 17 and 12 thousand years ago and nowadays lizards on larger islands have higher variation M. Jordan, H. Snell (2002): 17 populations 11 microsatellite loci skenovat0001 Evolution of selectively neutral traits is random Darwinian evolution: „survival of fittest“ neutral evolution: „survival of luckiest“ Effective population size = the number of individuals of ideal Wright-Fisher population displaying the same rate of drift as the studied non-ideal population Efective population size Real populations differ from the WF model (fluctuations of N, different reproductive success and mortality, unequal sex ratio, ....) ® effective population size Ne allows us to measure drift in non-ideal populations Like in the inbreeding coefficient there is no single effective population size!! Some factors decrease Ne relative to N: overlapping generations fluctuating population size across generations different number of breeding males and females high variation of the number of offspring within populations Caution! Under some circumstances the effective population size can be higher than N!! harmonic mean Effect of fluctuating population size: effective size can be approximated as harmonic mean Þ strong influence of small N!! http://pad1.whstatic.com/images/thumb/9/9c/Calculate-the-Harmonic-Mean-Step-4.jpg/670px-Calculate-t he-Harmonic-Mean-Step-4.jpg https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRff13RjQPSJ9DvQ4AO51wRDuAypXofBW19pFs83y2kSjH aZ7pgSw http://pad1.whstatic.com/images/thumb/f/f6/Calculate-the-Harmonic-Mean-Step-2.jpg/670px-Calculate-t he-Harmonic-Mean-Step-2.jpg mean much closer to the lower value Effect of biased sex ratio: Till now we assumed the same number of breeding males and females Nm = number of breeding males, Nf = number of breeding females Sexratio the higher deviation from equal sex ratio, the lower Ne effect of sex ratio on Ne different for various genetic traits! it follows from this formula that if there is only a single breeding male in the population Ne » 4 regardless of the total number of individuals Nm = 1: Effect of biased sex ratio: seal5 southern elephant seal: sex ratio within a harem 1:40*) *) effective ratio 1:4-5 due to cuckoldry and short period of male´s dominance (1-2 years) http://files.usa2009.webnode.cz/200000251-ca06ecb011/DSCF2965.JPG http://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Mating_scene_with_elevated_Alpha_Male._Ele phant_Seals_of_Piedras_Blancas.jpg/285px-Mating_scene_with_elevated_Alpha_Male._Elephant_Seals_of_P iedras_Blancas.jpg Effect of unequal reproductive success: If a gene is affected by selection variance of the number of offspring among members of a population is high (individuals with a positive allele have more offspring) Þ Ne for this gene is lower than for a neutral gene Reproductive success on the gene level: Each genetic trait requires its own Ne: For genes on autosomes, sex chromosomes, and mtDNA there are different effective population sizes: autosomes: Ne 4 Ne X, Z: ¾ Ne 3 Ne Y, W, mtDNA: ¼ Ne 1 Ne COALESCENT under drift some alleles disappear from a population Þ when there are no mutations ultimately all gene copies have a common ancestor „forward“ approach we can proceed also back in time – „backward“ approach ® moving back in time till two or more gene copies „fuse“ = coalescent event the most recent common ancestor (MRCA) Koalescence1 Wright-Fisher model: Koalescence2 Koalescence3 coalescent sample MRCA Coalescence and effective population size from the coalescent theory several interesting consequences follow: in small populations coalescent rate higher than in large populations Þ we can estimate Ne but we can estimate also changes of Ne in time declining population expanding population The same effect of selection on the coalescent tree shape: Bottleneck bottle.jpg BOTTLENECK and FOUNDER EFFECT population decline decrease of variation depends on population growth rate variation more reduced under stronger bottleneck bottleneck reduces variation magnitude of this reduction depends on reduction of Ne and duration of bottleneck rate of decrease of variation different for various genetic traits (autosomes, mtDNA, Y...) – different Ne! III.jpg Bottleneck: bottleneck N = 1000 N =4 N = 1000 FE.jpg FE.jpg FE.jpg Founder effect: colonization of a novel territory (eg. island) because of a small numer of founders (even a single pregnant female) ® random change of allele frequencies ® reduction of variation different environmental conditions ® speciation Examples of founder effect and bottleneck cheetah 30 individuals of Acinonyx jubatus reineyi from E Africa, 49 protein loci: only 2 loci polymorphic (P = 0,04), mean heterozygosity Ho = 0,01 98 individuals of A. j. jubatus from S Africa: P = 0,02, Ho = 0,0004! south-African individuals accept skin grafts of the east-African subspecies without problems Þ monomorphism of MHC genes assumed strong bottleneck in the past Cheetah golden hamster File:Golden hamster front 1.jpg 1930: Israel Aharoni (Hebrew Univ., Jerusalem) – female with offspring escape of several individuals from captivity 1931: transport of several individuals to Britain 1937: private breeders Recent genetic analyses including mtDNA ® all golden hamsters currently kept in breeding colonies are descendants of a single female, probably that of 1930 mostly presented as an example of bottleneck but it is rather an example of founder effect northern elephant seal On, ona a ono (Mirounga angustirostris) Mirounga angustirostris: in 19th century almost eradicated ® 1892 last 8 individuals on the island of Guadelupe killed for museum collections fortunately 10-20 individuals passed unnoticed ® today > 100 000 inds. M. Bonnell a R.K. Selander (1974): blood samples of 159 individuals electrophoresis at 21 loci ® no variation likewise Hoelzel et al. (1993), 62 loci http://www.rodplanck.com/images/gallery-large/mammals/Rod_Planck__NXS67982007_11_04_124041-1.jpg Hoelzel et al. (1999): DNA markers On, ona a ono (Mirounga angustirostris) northern elephant seal (Mirounga angustirostris) southern elephant seal (Mirounga leonina) Hybrid zone_Fig.1.jpg mouse-frog ~ 500 tis. FE in house mouse Neolit musculus domesticus M. m. domesticus Mus musculus musculus nuclear DNA mtDNA mouse colonization of Europe humans a) Las Salinas (Dominican Republic): Altagracia Carrasco: several children with at least 4 men Carrasco heterozygous for substitution T ® C in 5th exon of the 5-a-reductase 2 gene Þ TGG (Trp) ® CGG (Arg) at the 246th position of the protein the enzyme catalyzes transformation of testosterone to DHT (dihydrotestosterone) low activity of the mutant enzyme in homozygotes Þ boys have testes but other traits are female in puberty testosterone production increases Þ transformation to men in Salinas high frequency of the mutation Þ the word guevedoces (= „penis in 12“) [USEMAP] DHT http://jetzt.sueddeutsche.de/upl/images/user/be/bergerac/text/regular/704124.jpg http://jetzt.sueddeutsche.de/upl/images/user/be/bergerac/text/regular/704124.jpg http://www.mojaprostata.sk/source/image/historia/historia_img7.jpg Tristan da Cunha: 1816 military garrison 1817 garrison withdrawn; Skottish corporal William Glass and his family founds a small colony (20 individuals in total) ® founder effect during 80 years 2 strong bottlenecks File:Tristan Map.png III.9.tif tristan.jpg 1851: a missionary arrival 1853: death of W. Glass 1856: departure of 25 Glass´s descendants to America, departure of other 45 people with the missionary Þ 103 inds. (1855) ® 33 (1857) ... 1st bottleneck 1th bottleneck III.jpg strong change tristan.jpg population growth 1857–1884: population growth Þ conservation of changes caused by previous bottleneck ® less changes during 27 years than during 2 years 1855– 1857 III.jpg minimal change 1884–1891: drowning of 15 men, only 4 adult remains, of whic 2 very old („Island of Widows“) ® departure of many widows with their children Þ 106 inds. (1884) ® 59 (1891) ... 2nd bottleneck tristan.jpg 2nd bottleneck population growth again, the following growth has „frozen“ the changes 2nd bottleneck 1st bottleneck 2nd bottleneck 1st bottleneck Genetic changes during population growth lower than during bottlenecks Inbreeding on Tristan da Cunha: growth of F Despite the outbreeding strategy (choice of the least related partner), ie. FIS < 0, the level of autozygosity increased ? no unrelated woman available! Inbreeding on Tristan da Cunha: growth of F Despite the outbreeding strategy (choice of the least related partner), ie. FIS < 0, the level of autozygosity increased RELATION BETWEEN DRIFT AND GENE FLOW Obrázek1 higher gene flow lower gene flow Gene flow and drift have opposite effects: drift increases divergence among demes ´ migration „homogenizes“ demes RELATION BETWEEN DRIFT AND SELECTION relation between fitness and allele frequency: adaptive landscape Sewall Wright The notion of adaptive landscape has 2 mutually incompatible meanings: 1.Allele combinations: fitness values assigned to genotypes N genotypes ® N + 1 dimensions discontinuous surface, population = cluster of points 2.Average allele frequencies number of dimensions = number of sets of allele frequencies continuous surface Adaptive landscape: wright.jpg Lanscape selection „pulls“ the population up 3 phases of SBT: 1. contemporary fitness reduction of a local population due to drift ® chance to approach the area of attraction of a higher peak Shifting balance theory (SBT) Assumptions: environment changes Þ populations in constant change mutations Þ new dimensions, new ways upwards small populations (drift) Þ possibility to move down to adaptive valleys 3 phases of SBT: 2. intrademic selection ® „pulling“ of the population towards a new peak 3. interdemic selection ® spread of the deme´s members at the higher peak to surrounding demes The whole proces seen as shifting of the balance between drift, intrademic, and interdemic selection 2 views on evolution in populations: S. Wright R.A. Fisher small local populations large panmictic populations combination of selection, drift and mutation and selection migration epistasis, pleiotropy, additive effects of genes, dependence of allele effects on context allele effects independent of context speciation as a byproduct of local disruptive or locally divergent selection adaptations in epistatic systems File:Sewall Wright.jpg File:R. A. Fischer.jpg