Download Week 5: The Hardy-Weinberg equilibrium, population differences

Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University Week 5: The Hardy-Weinberg equilibrium, population differences
and inbreeding
5.1: Allele and genotype frequencies
Two questions we’ll answer by looking at variation, one gene at a time: ● Can we predict genotype frequencies from allele frequencies? If “sometimes,” when? ● Do genotype frequencies intrinsically change over time, or do they remain constant? A hypothetical scenario: ● Two alleles ­ A and a ­ and three possible genotypes ­ AA, Aa and aa ● Each has a ​
frequency​
, totaling 100% ○ Example: If 78% of alleles are A, 22% are a ○ 25% of individuals are AA and 50% are Aa, so 25% are aa. ● Calculating genotype frequencies: ○ Assuming every individual is diploid (2N), we can get them by counting (population info from a box shown in slide) ■ Total number of individuals = 10 ■ Frequency AA = 1/10 = 0.1 ■ Frequency Aa = 6/10 = 0.6 ■ Frequency aa = 3/10 = 0.3 ■ The total ALWAYS adds up to 1. ● Calculating allele frequencies ○ Assuming every individual is diploid (also, this is same population as above) ○ We ​
could ​
count the A’s and a’s: ■ 20 total alleles (10 genotypes) ■ freq(A) = 8/20 = 0.4 ■ freq(a) = 12/20 = 0.6 ○ But here’s a better way: ■ freq(A) = freq_AA + ½ freq_Aa = 0.1 + ½(0.6)= 0.4 ■ freq(a) = freq_aa + ½ freq_Aa = 0.3 + ½(0.6) = 0.6 ● One could think of the world as a pool of gametes (or not, because that’s kind of icky) ○ All individuals of sexual species ​
start​
as 2 gametes ■ Gametes are 1N ■ Many marine invertebrates “spew” gametes into the water that make individuals ○ We can use ​
joint probability​
multiplication to determine genotype frequencies in offspring ■ 60% of sperm are A and 60% of eggs are A 40% of sperm are a and 40% of eggs are a ■ What’s the probability of an AA individual? Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● The joint probability that fertilization involves an A sperm and an A egg. ● So, 0.6 x 0.6 = 36% ■ The probability of aa is calculated the same way: 0.4 x 0.4 = 0.16 ■ But there are TWO ways to make an Aa zygote. ● A sperm + a egg → 0.6 x 0.4 = 0.24 ● a sperm + A egg → 0.4 x 0.6 = 0.24 ● add those together and you get 0.48 ○ Another way of looking at the same thing: a modified Punnett square showing the relative amounts of A and a gametes ■ Can we calculate the allele frequencies? YES ­ you can always​
do this when you have the genotype frequencies. ● AA: 0.36 → all A ● Aa: 0.48 → half A ● Frequency of A = 0.36 + ½(0.48) = 0.6 ● Frequency of a = 0.16 + ½(0.48) = 0.4 ○ This is a self­perpetuating process ­ the offspring’s allele frequencies will remain the same, as will their offspring’s, etc. ■ Allele A frequency was 0.6 in gametes ■ Gametes created 0.36/0.48/0.16 genotype frequencies ■ These genotypes produce 0.6 A gametes ○ Thus, this is a process that is basically stable (built on the assumption that gametes come together at random based on their proportions). This stability is known as the Hardy­Weinberg equilibrium. 5.2: The Hardy-Weinberg equilibrium
● The ​
Hardy­Weinberg equilibrium​
is a pattern first described by Godfrey Hardy & Wilhelm Weinberg in 1908. William Castle described a similar effect in 1903. ○ Until 1902, people thought dominant alleles would intrinsically increase in a population ○ Some assumed rare alleles would always be lost eventually. ○ In 1908, Hardy & Weinberg independently showed both assumptions are ​
not true ■ Allele and genotype frequencies stay stable ​
when some assumptions are made​
..28 ● Let’s formalize the math: ○ Alleles (assumes population has only two): Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ Frequency of A = p ■ Frequency of a = q
■ p + q = 1 ○ Genotypes: 2
■ Frequency of AA = p​
■ Frequency of Aa = 2pq 2
■ Frequency of aa = q​
2​
2​
■ p​
+ 2pq + q​
= 1 2​
2
■ AND: p + q = p​
+ 2pq + q​
● Here is what the Hardy­Weinberg equilibrium looks like plotted on a graph. ○ X axis ­ frequencies of A and a ○ Y axis ­ frequencies of the different genotypes ■ Heterozygote (Aa) peaks around 50% ■ Extremes seen at either end: if aa = 1, both AA and Aa = 0, etc. ○ This allows you to infer genotype frequencies from allele frequencies, but certain conditions must be met. ● Three important points: ○ You can ​
always​
know genotype frequencies from genotype counts. ■ Add up the total, then divide each by that total ■ AA: 8 → 8/200 = 0.04 ■ Aa: 64 → 64/200 = 0.32 ■ aa: 128 → 128/100 = 0.64 ■ Frequencies MUST total 1 ○ You can ​
always​
know allele frequencies from genotype frequencies. ■ All of homozygote + ½ of heterozygote ■ Using frequencies above. ■ p(A) = 0.4 + ½(0.32) = 0.2 ■ q(a) = 0.64 + ½(0.32) = 0.8 ■ Frequencies MUST total 1 ■ This works because alleles are ​
ingredients ​
of genotypes ○ But you ​
CANNOT​
always know genotype frequencies from allele frequencies. ■ Let’s say p(A) = 0.5 and q(a) = 0.5 ■ Could have what’s expected under Hardy­Weinberg: ● AA: 0.25, Aa: 0.5, aa: 0.25 ■ BUT there are other possibilities, like: ● AA: 0.45, Aa: 0.10, aa: 0.45 ● AA: 0.5, Aa: 0, aa: 0.5 ■ Why? ● Genotypes are ​
specific combinations​
of alleles. ● Many combinations are possible. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● So, back to Hardy­Weinberg: ○ It allows the prediction of genotype frequencies from allele frequencies ​
under certain conditions​
: ■ Random mating (multiplying probabilities rule) ■ No selection, migration or mutation at that locus ■ Infinite population size ­ no “genetic drift” ■ In short, it predicts a completely boring population that probably could never exist. ○ So why bother? It provides a ​
null hypothesis​
. ■ By seeing ​
how​
natural populations deviate from the HW expected genotype frequencies, we infer what interesting evolutionary forces are operating. ● Testing for Hardy­Weinberg ○ Is this at HW? → AA: 245, Aa: 210, aa: 45 ■ Figure out true genotype frequencies ● total = 500 ● AA: 245/500 = 0.49 ● Aa: 210/500 = 0.42 ● aa: 45/500 = 0.09 ■ Figure out true allele frequencies ● p(A) = 0.49 + 0.21 = 0.7 ● q(a) = 0.09 + 0.21 = 0.3 ■ Figure out HW “expected” genotype frequencies 2​
2
● p + q = p​
+ 2pq + q​
2​
2​
● p​
= 0.7​
= 0.49 ● 2pq = 2(0.7)(0.3) = 0.42 2​
2​
● q​
= 0.3​
= 0.09 ■ Do true frequencies = expected frequencies? ● YES! ○ One for you to try on your own: AA: 400, Aa: 200, aa: 400 ■ Figure out true genotype frequencies ● total = 1000 ● AA: 400/1000 = 0.4 ● Aa: 200/1000 = 0.2 ● aa: 400/1000 = 0.4 ■ Figure out true allele frequencies ● p(A) = 0.4 + 0.1 = 0.5 ● q(a) = 0.4 + 0.2 = 0.5 ■ Figure out HW “expected” genotype frequencies 2​
2
● p + q = p​
+ 2pq + q​
2​
● p​
= 0.25 ● 2pq = 0.5 2​
● q​
= 0.25 Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ Do true frequencies = expected frequencies? Not this time. 5.3: Deviation from Hardy-Weinberg equilibrium - the Wahlund effect
● Real data: ○ Navajo populations ■ MN blood type: ● MM: 305 → 0.845 p(M) = 0.917 ● MN: 52 → 0.144
q(N) = 0.083 ● NN: 4 → 0.011 ● Total: 361 ■ HW predicted (very close): ● MM: 0.841 ● MN: 0.152 ● NN: 0.007 ○ Aborigine populations ■ MN blood type: ● MM: 22 → 0.030
p(M) = 0.178 ● MN: 216 → 0.296
q(N) = 0.822 ● NN: 492 → 0.674 ● Total: 730 ■ HW predicted (again, very close): ● MM: 0.031 ● MN: 0.293 ● NN: 0.676 ○ Mixed population of both of the above ■ MN blood type: ● MM: 327 → 0.300
p(M) = 0.423 ● MN: 268 → 0.246
q(N) = 0.577 ● NN: 496 → 0.454 ● Total: 1091 ■ HW predicted (NOT close this time) ● MM: 0.179 ● MN: 0.488 ● NN: 0.333 ● Dramatically different from the two individual groups ○ predicts nearly half MN, when we actually get ¼ ● Why might we see this deviation ­ the combination of two HW groups being non­HW? ○ We cannot assume ​
random mating​
­ that any two individuals as likely to breed as any other two individuals ■ A Navajo lady isn’t as likely to breed with an Aborigine as she is with another Navajo. ○ The result is too few heterozygotes ­ 0.246 observed, rather than expected 0.488 Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ This is called the ​
Wahlund effect​
: sampling across populations gives an underrepresentation of heterozygotes relative to HW. ● Why does it matter if something is HW or not? ○ The first step in genome­wide association studies of genetic diseases is usually to test for HW. ○ Why? Because GWAS ​
assumes​
HW (or nearly so) ■ Assumes linkage disequilibrium detected between marker alleles and disease alleles is caused by close proximity/lack of recombination. ● 20% of those with AA genotype have disease ● 5% of those with aa genotype have disease ● Thus, association between A marker genotype and disease ■ Being in ​
different populations​
(ie, non­random mating) also creates LD. ■ An extreme example: ● Population 1 is all AA and Population 2 is all aa ● If disease is more abundant in P1 than P2 … ○ Would you say AA is more likely to have the disease than aa? Yes. ○ This is actually a fake LD between disease and gene A. ○ The disease gene may be on a different chromosome, or the disease may not even be influenced by genetics at all. ○ If there are allele frequency differences between populations at a SNP, and there are disease incidence differences between those populations, it’ll erroneously look like a gene near the SNP causes or contributes to the disease. ○ Testing for HW helps you avoid this error ­ it identifies if you’re looking at one interbreeding population or more. ○ Although it’s very important to test for HW, it’s often not done … ■ 2006 study: Exclusion of studies in which HW was violated changed conclusions and statistical significance of gene­disease associations ■ 2005 study: testing/reporting for HW is often neglected; published reports rarely admit the deviations. ○ A real example where an HW test WAS done but misinterpreted: ■ 2000 study of BRCA2 variants (newborn males from UK hospital) ● AA: 644 → 0.539
p(A) = 0.721 ● Aa: 435 → 0.364
q(a) = 0.279 ● aa: 116 → 0.097 ● Total: 1195 2​
■ p​
= 0.520 ■ 2pq = 0.402 2​
■ q​
= 0.078 ■ A statistically significant deviation from HW ­ too few Aa (heterozygotes) observed. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ The authors inferred that Aa are less healthy than AA or aa. ■ A much more likely conclusion: A place like London has lots of subsets of the population. People of Indian descent, for example, are more likely to have kids with others from their group. ● An ironic tidbit to end on: At age 62, lamenting the waning of his math ability, Hardy wrote that he’d “never done anything ‘useful’” ­ never made a discovery that made “the least difference in the amenity of the world.” ​
He was very wrong on this. 5.4: Differences between populations - origins and quantifying
● Recap: Navajo and Aborigine populations each showed HW equilibrium in blood type genotype frequencies, but the combination of the two populations did not ­ there was a deficiency of heterozygotes from what would be expected under HW. This is what’s called the Wahlund effect. ● Populations differ: ○ May have different allele and genotype frequencies ○ But they may also have alleles at some genes not found in other populations if ■ it’s a very recent new mutation, or ■ populations are in complete isolation ● Differences arose via mutation, then spread ○ Ancestors aa bb ○ Population splits into 2 groups ■ #1 ­ new mutation to A ■ #2 ­ new mutation to B ○ New mutations spread ● Groups within a species are different yet related ○ May have alleles not found in other groups ○ May have very different genotype/allele frequencies (this is more likely) ● How do we quantify these differences? ○ “Fixed” difference ­ all individuals differ; this is the simplest thing to quantify ■ pop. 1: all AA
pop. 2: all aa ■ if you go back to the ancestor, presumably they had same alleles but something arose and spread to create the difference ■ This happens, but it’s not very common within a species, and generally not true among modern human ethnic groups. ○ More common: frequency differences of all alleles and genotypes ■ pop. 1: p(A) = 0.7
pop. 2 p(A) = 0.5 ■ We’re measuring differences between populations, not individuals. ● We can’t apply these to an individual ­ for example, by saying that someone with a big A MUST be of Middle Eastern descent. ● Deviation from HW allows you to quantify allele frequency differences ○ Assuming two populations at HW ■ If each is sampled by itself, you’ll see HW Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ If both are sampled together, you’ll see deviation from HW (Wahlund effect) ○ How large the deviation is from HW​
when both are sampled together quantifies the difference in allele frequencies. ● The measure we’ll use is F​
ST ○ Ranges from 0 to 1 ■ 0: no allele frequency differences ■ 0 < F​
< 1: allele frequencies differ somewhat ST​
■ 1: “fixed” difference between populations ○ F​
= ​
HW predicted 2pq ­ % observed heterozygotes ST​
HW predicted 2pq ○ Example: ■ Pop. 1:
Pop. 2 AA: 100
AA: 0 Aa: 0
Aa: 0 aa: 0
aa: 100 ■ Total: AA: 100, Aa: 0, aa: 100 (total genotype count = 200) ■ AA = .37+.24 = 0.5
p(A) and q(a) = 0.5 Aa = 0
HW 2pq = 0.5 (observed = 0) aa = 0.5 ■ F​
= (0.5­0)/0.5 = 1 ­ fixed difference ST​
○ Another, less extreme, example: ■ Pop. 1:
Pop. 2 AA: 250
AA: 490 Aa: 500
Aa: 420 aa: 250
aa: 90 ■ Total: AA: 740, Aa: 920, aa: 340 (total genotype count = 2000) ■ AA = 740/2000 = 0.37
p(A) = 0.6 Aa = 920/2000 = 0.46
q(a) = 0.4 aa = 340/2000 = 0.17
HW 2pq = 0.48 (observed = 0.46) ■ F​
= (0.48 ­ 0.46)/0.48 = 0.042 ST​
○ Now try using the real data from the Navajo­Aborigine mix: ■ MN blood type totals: MM: 327 MN: 268 NN: 496 Total: 1091 ■ Observed: MM: 0.30
p(M) = 0.423 MN = 0.246
q(N) = 0.577 NN = 0.454
HW 2MN = 0.488 ■ F​
= (0.488­0.246)/0.488 = 0.496 ­ a fairly large F​
consistent with the ST​
ST​
idea of no gene flow between the two populations. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● Recap: ○ F​
is larger when comparing populations that are more different in allele ST​
frequencies. ○ If allele frequencies are identical, F​
= 0. ST​
○ If a fixed difference, F​
= 1 ST​
● F​
measures among human populations (data from 1,110,338 SNPs in a 2010 study) ST​
○ African­Americans/Europeans: F​
= 0.11 ST​
○ African­Americans/Chinese: F​
= 0.15 ST​
○ Europeans/Chinese: F​
= 0.11 ST​
○ F​
s among European populations <0.01 ST​
● What is F​
, in words? ST​
○ The % heterozygous of randomly chosen alleles within populations (observed) relative to that expected in the entire species (2pq) ○ Measures ​
difference in allele frequencies ○ But why don’t we see higher F​
among human populations? ST​
■ Some F​
assumptions are violated in humans ST​
● Supposed to be applied to genes experiencing little/no natural selection ● Susceptible to differences (and historic changes) in population size among groups ■ The biggest reason: we actually do have a fair amount, or closer to random mating, across populations. We’ll discuss this in the next video. 5.5: Differences between populations - effects of gene flow
● Gene flow​
(migration/movement among populations where you go and reproduce) is referred to as “the great homogenizing force in evolution” ○ Makes populations’ allele frequencies converge ■ Prevents (and undoes) divergence ● How does gene flow happen? ○ Organisms (or gametes) move to a new location ​
and reproduce there​
. ○ Math for it assumes it’s random with respect to genotype ■ Particular genotypes are not more likely or less likely to migrate. ● Some general models of gene flow ○ Continent­island model​
(top in b/w diagram) ■ Continent’s effect on island huge; island’s effect on continent negligible. ■ Example: ● Red line depicts allele frequency on the continent (starts at 0.5) Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● Blue line depicts allele frequency (starts at 0.5) ● Migration rate = 1% ● 500 generations ● Island allele frequency converges onto the continent value. ○ Island model ■ Multiple populations affecting each other’s allele frequencies (middle in b/w diagram) ■ Example: ● 4 islands exchange genes with each other: ○ p = 0.9 ○ p = 0.65 ○ p = 0.35 ○ p = 0.1 ● Again, migration rate = 1% and this is modeled over 500 generations. ● All four converge on the mean value of the islands. ■ There is also the stepping­stone model (bottom in b/w diagram ­ we won’t really discuss this one much) ● Relevant variables: What affects the ​
speed of convergence​
­ how fast the allele frequencies become similar? ○ Migration rate​
­ how many migrants move ■ More migration leads to bigger changes ○ How different​
the allele frequencies are ■ More different allele frequencies causes bigger change. ○ Number of generations​
is obviously important too ­ even low levels of migration over long period could erase all divergence. ○ There are assumptions here, including ■ Migration rates are symmetric ■ Migration rates are independent of genotype ■ Migration rates involve no difference in fitness ● An example of application: ○ Glass & Li estimated European gene flow into African­Americans ■ Study done in 1950s, estimated 10 generations ■ Got PTC allele frequencies of: ● Europeans
p(T) = 0.455 ● West Africans
p(T) = 0.835 ● African Americans p(T) = 0.697 ■ Did some very simple math (which we won’t get into here) and were able to give a per­generation estimate of 0.0358 (3.58%) ● Total contribution: ~31% Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ PTC = something particular individuals can taste very strongly, while other individuals cannot. Has a very simple genetic basis; given to subjects using test papers. 5.6: Inbreeding
● Differences in allele frequencies are often driven by patterns of gene flow and interbreeding ○ True when looking at different populations ­ BUT it doesn’t have to be “between populations” ○ Related concept: inbreeding ■ Breeding between closely related individuals ■ Capacity for dispersal often limited ­ individuals can’t go somewhere else to breed, so, to quote the song, they “love the one they’re with.” ■ Changes distribution of genotypes​
. ● An extreme form of inbreeding: self­fertilization (found in some plants) ○ Imagine this population started at 25% AA, 50% Aa, 25% aa ○ What happens if this plant self­fertilizes? (Gen 0) ■ AAs produce more AAs ■ Aas produce ¼ AA, ½ Aa, ¼ aa ■ aas produce more aas ○ Gen 1: After 1 generation, genotype frequencies become 37.5% AA, 25% Aa, 37.5% aa ■ Again, a reduction in heterozygotes relative to what we saw previously ○ Gen 2: 43.75% AA, 12.5% Aa, 43.75% aa ○ And so on … ○ Eventually you’ll reach 50% AA / 50% aa / no heterozygotes ○ Every generation, the heterozygote fraction goes down and feeds alleles into homozygotes ­ creates “pure breeding” lines ● How do we quantify inbreeding? ○ Inbreeding (even if not self­fertilizing) reduces the percentage of heterozygotes ■ Feeds alleles into homozygotes ○ Reduction in % heterozygotes from HW expected quantifies inbreeding ○ We’ll use something called ​
Wright’s inbreeding coefficient​
(F) ■ Very similar to F​
ST ■ F ranges from 0 to 1 ● 0 = at HW expectation for % heterozygotes ● 0 < F < 1 = somewhat fewer heterozygotes than predicted ● 1 = no heterozygotes ■ F = ​
HW predicted 2pq ­ % observed heterozygotes HW predicted 2pq ■ Example: You’re studying a population with the genotypes: AA (553), Aa (294), aa (153) → total 1000 ● AA = 0.553
p(A) = 0.7 Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University Aa = 0.294
q(a) = 0.3 aa = 0.153 ● HW expectation: AA (0.49), Aa (0.42), aa (0.09) ● F = (0.42 ­ 0.294)/0.42 = 0.30 → pretty severe inbreeding ■ Another example to try, involving real genotypes on Croatian islands (and skipping the genotype­count step): ● AA: 0.8136
p(A) = 0.9 Aa: 0.1728
q(a) = 0.1 aa: 0.0136 2​
2
● HW: p​
+ 2pq + q​
0.81 + 0.18 + 0.01 ● F = (0.18­0.1728)/0.18 = 0.04 estimated inbreeding coefficient ■ So what is the difference between inbreeding F and F​
? ST​
● Both based on same principle ○ Seeing fewer heterozygotes than HW prediction ○ Indicates ​
non­random mating ○ Symptom of Wahlund effect ● Apply inbreeding F when looking at individuals ​
within one population ● Apply F​
when quantifying the difference ​
between populations ST​
■ How is this calculation used? ● Association between inbreeding and health/disease ○ example: effects on fetal growth in Beirut ● Patterns of gene flow between social classes ○ example: consanguineous marriage between social/occupational class boundaries in Pakistan ● Other cultural effects on patterns of breeding ○ example: consanguinity in Spain and its socioeconomic, demographic and geographic influences ● But isn’t inbreeding ​
bad​
? ○ By itself​
, inbreeding only changes the distribution of alleles among genotypes ­ it does not make any alleles “go away.” ○ Nonetheless, many know of ​
inbreeding depression​
­ this requires natural selection as well as inbreeding. ○ Populations often harbor many ​
individually​
rare recessive mutations ■ A few new detrimental mutations each generation ■ Because they’re both rare and recessive, their effects are often not seen. ■ But if two relatives mate: ● They’re likely to have the same recessive mutation. ● They’re more likely to produce homozygous offspring. ○ Effects of this are often seen in dog breeds: Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ Breeding of relatives has created many dog breeds that have maintained “desirable” qualities such as behavior, appearance, etc. ■ The inbreeding F in some dogs > 0.5 (which is unusual) ● F = 0.7 in some poodle varieties ● A UPenn study showed 75% of puppies with inbreeding F > 0.67 die within 10 days ● King Charles spaniels get syringomyelia (skull too small for brain) ● Other dogs connected to problems: ○ Boxers ­ high epilepsy ○ Pugs ­ breathing problems ○ Bulldogs ­ often cannot mate or give birth unassisted ○ Mastiffs, St. Bernards, Great Danes ­ hip dysplasia ○ Again, what’s happening is you’re eliminating heterozygotes ­ and by making dogs homozygous, the recessive bad effect becomes visible. Week 6: Natural selection and genetic drift
6.1: Natural selection fundamentals
● What is natural selection? ○ “preservation of favourable variations and the rejection of injurious variations” ­ Darwin (1859) ○ He presented his idea simultaneously with A.R. Wallace. Their emphases differed, but both are correct: ■ Darwin: emphasized competition within species ■ Wallace: emphasized environmental pressures ● Requirements for evolution by natural selection ○ Variation in traits ○ Heritability of traits ○ Trait variants affect survival or reproduction ● Quantitative traits vs. single locus ○ We already discussed selection in the context of heritability: H = R/S ■ How much genetic component of variation there is dictates amount of selection’s response ■ Response often from change in allele frequencies at multiple loci ○ Can also be studied at a single locus or gene ● What does selection do to alleles at individual loci ○ Affects abundance of particular genotypes ■ Example: AA: good, Aa: good, aa: “less good” (dead?) ○ Affects frequency of alleles in population ■ The result of the scenario above is fewer a alleles remaining in the population Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ Dominance of alleles matters for selection. ■ If a were dominant, Aa would ALSO be dead. ● So, how often does natural selection happen in humans? ○ Strong selection in humans ­ single loci ■ Spontaneous bad mutations are common ■ Half of pregnancies are never detected because they spontaneously abort very early. ● Half of spontaneous abortions result from genetic problems ­ thus, ¼ of all human fertilizations are immediately eliminated by natural selection. ○ Weaker selection in humans ­ single loci ■ Historically, all humans were lactose­intolerant as adults. ■ Estimates suggest the lactose­intolerant have about 5% fewer kids than lactose­tolerant. ■ After a new mutation arose, most people are now “lactase persistent” (lactose­tolerant) as adults ● What is the effect of 5% more kids? Effect can be simulated with AlleleA1​
software ○ fitness of AA (intolerant) = 0.95 ○ fitness of Aa and aa (tolerant) = 1.00 ○ Time: 5000 years ○ All were AA and then new mutation a arose in Africa 5,000 years ago. ○ The simulator finds only 20% of adults are lactose­intolerant today ­ not far from what we actually see in human populations. ■ Weak selection over long periods of time can lead to very big changes in allele frequencies. ● Darwin actually suggested this. ● Selection uses “​
relative​
fitness” of genotypes ○ In lactase example: ■ AA: 0.95, AA: 1.00, aa: 1.00 ■ AA has 5% fewer kids successfully on average than aa or Aa ○ Being “selected against” doesn’t mean something is bad by itself ­ just not as good as the alternative. ■ Humans survived for a long time as AA (lactose intolerant) ○ A silly music analogy: A new mutation is like a newly released cover of a previously released song. ■ The original cover was popular/successful ● “I Love Rock & Roll” originally by the Arrows, 1975 ■ The cover may be more successful ­ spreads (via sales) and causes everyone to forget the original. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● People are more likely to know “I Love Rock & Roll” from Joan Jett and the Blackhearts’ 1982 cover. ■ Or the cover may be less successful ­ around briefly, then it dies off. ● Let us never speak of Britney Spears’ 2002 cover again. ○ An example: Let’s say BB produces average 3.2 surviving offspring; Bb produces 3.0; and bb produces 2.4. ■ The most fit genotype is BB ­ it does the best job of replacing itself ● Call it 100% of maximum fitness = w(BB) = 1.00 ● Others are a percentage of this maximum: ○ w(Bb) = 3/3.2 = 0.94 (6% less fit than BB) ○ w(bb) = 2.4/3.2 = 0.75 (25% less fit than BB) ● What are the effects on Hardy­Weinberg? ○ Assume all aa individuals die at age 10. ○ At age 8: AA: 490, Aa: 420, aa: 90. Is this population at HW? Yes. ■ p(A) = 0.70 ○ At age 25: AA: 490, Aa: 420, aa: ­­dead­­. ■ Selection altered genotype frequencies, resulting in deviation from HW. ■ It also altered allele frequencies: p(A) = 0.769 ○ Is aa gone for good? NO. ■ Assuming random mating, we use the new allele frequencies to predict 0.054 aa offspring 6.2: Types at single loci
● Selection and dominance ○ In previous example, all adult aa die. ○ We’re changing the allele names from A and a to M and N (to avoid lowercase letters implying recessiveness) ○ Example 1: Which allele is dominant/recessive here? ■ w(MM) = 1.00; w(MN) = 1.0; w(NN) = 0 ■ MM and MN have same relative fitness, so it must be N that’s recessive ■ The recessive form is detrimental (“bad”) in this case ­ but it isn’t always. ○ Example 2: w(MM) = 1.00; w(MN) = 0; w(NN) = 0 ■ What allele is dominant? N. ■ What will this selection do differently? ● Selection likely to be much quicker, since you’re eliminating ALL N from the population at once ­ not just a subset of N. ● With a dominant detrimental, the heterozygotes also respond to select. ○ Example 3: ww(MM) = 1.00; w(MN) = 0.5; w(NN) = 0 ■ Which one is dominant? ​
Neither​
­ no homozygous has the same relative fitness as this heterozygous. ​
This is a case of “no dominance.” Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ In all three cases, we assume NN is the worse one ­ this is called ​
directional selection​
. ■ In this case, selection pushes toward elimination of the N allele over time, while MM remains perfectly healthy. ■ Example 1 is slow to eliminate Ns; example 2 is fast to eliminate them, and example 3 it would be intermediate. ● Effect of dominance with directional selection (simulated in AlleleA1): ○ Dominant detrimental ■ w(MM) = 1.0, w(MN) = 0.5; w(NN) = 0.5 ■ Since no Ns can hide, they go away pretty quickly ­ this results in a sharp curve. ○ Recessive detrimental ■ w(MM) = 1.0, w(MN) = 1.0, w(NN) = 0.5 ■ NNs are removed pretty readily, but MNs survive ­ this results in a more gradual curve, especially near the end. ■ Some Ns remain in the population for a fairly long period of time. ■ This is the case for most “bad” mutations, and many known genetic diseases, such as Tay­Sachs and cystic fibrosis ­ they’re maintained by carriers, and selection is inefficient for getting rid of them. ■ This is also the case in the lactose­intolerance example we discussed earlier. Types of direction on a single locus: ● Directional selection ­ one allele ​
eventually​
replaces the other, eliminating variation. ○ w(AA) ≤ w(Aa) ≤ w(aa) OR w(AA) ≥ w(Aa) ≥ w(aa) ○ Recessive detrimental: w(AA) = 1.00; w(Aa) = 1.00; w(aa) = 0 → all AA ○ No dominance (intermediate dominance): w(AA) = 1.00; w(Aa) = 0.5; w(aa) = 0 → all AA ○ w(AA) = 0.1; w(Aa) = 0.2; w(aa) = 1.00 → all aa ○ Lactase persistence: w(AA) = 0.95; w(Aa) = 1.00; w(aa) = 1.00 → aa (lactose­tolerant) ■ May not happen in real life because lactase is available over­the­counter. ● Heterozygote advantage (or ​
overdominance​
) ○ The most fit genotype is the heterozygote (Aa) ■ w(AA) = 10.85; w(Aa) = 1.00; w(aa) = 0.05 ○ One allele does NOT replace the other ­ variation is maintained ○ Leads to a stable equilibrium ■ Both alleles are retained in the population ■ Alleles go to equilibrium frequencies. ■ If they’re not at that equilibrium frequency, they go back to it (oscillate around that point). ○ Example: Sickle­cell anemia and malaria resistance. ■ Malaria a big threat for much of the developing world Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● ~4% chance of dying from malaria in sub­Saharan Africa. ● Mosquito bites transmit ​
Plasmodium ​
protozoa, which causes malaria ■ Sickle­cell anemia is a recessive genetic disease (aa) ● Sickle cells die faster than normal red blood cells ● They deliver less oxygen to cells ● Symptoms include chronic pain and fatigue. ■ If heterozygote (Aa), it’s called sickle­cell trait ● These people are usually healthy but cells may sickle during intense physical exertion. ● They’re also ​
more​
resistant to malaria! ○ Previously thought that the invasion, growth, development of ​
Plasmodium ​
may be reduced in Aa blood cells ○ 1 recent study suggests Aas are more tolerant to sickle­cell symptoms but retain the same infection load. ○ Another recent study suggests infected Aa cells are more likely to be eliminated by the spleen, since being Aa eliminates one defense of ​
Plasmodium​
. ■ Thus, sickle cell exhibits a heterozygote advantage ​
in some populations. Sub­Saharan Africa Sample fitness AA ­ susceptible to malaria w(AA) = 0.85 Aa ­ generally fine w(Aa) = 1.00 aa ­ sickle­cell anemia disease w(aa) = 0.05 ● What would be the fate of the a allele if it arose as a mutation in the AA population? ○ AlleleA1 simulation shows it would rise slightly and come to an equilibrium, stabilizing around a frequency of 0.136. ○ Let’s try the math ourselves: q(a) = ​
1­w(AA) (1­w(aa)) + (1­(w(AA)) q(a) = 0.15/(0.95 + 0.15) = 0.15/1.1 = 0.136 ● Heterozygote disadvantage (or ​
underdominance​
) ­ there aren’t many good examples of this. It’s unstable ­ could be argued to maintain variation, but only under unrealistic circumstances. ○ The least fit genotype is the heterozygote ■ w(AA) = 1.00; w(Aa) = 0.2; w(aa) = 0.5 ○ This leads to an ​
unstable​
equilibrium (0.27272727) ■ If starting below equilibrium, you go to a loss. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ If starting above equilibrium, you go to a fixation and lose the ​
other allele entirely ■ If starting (and staying) at equilibrium, alleles persist ­ but this is very unlikely in a real population. ● Frequency­dependent selection (specifically, the negative variety) ­ maintains variation. ○ Previous examples assumed fitness was independent of the rest of the population. ○ Sometimes it’s better to be “rare” ­ fitness may depend on your relative abundance. ○ But being “better” makes you become more common. ○ This eventually leads to equilibrium. ○ Example: sex ratio ■ Sex (male vs. female) is determined genetically in many species. ● In mammals, XX­XY means they’re mostly locked in to 50­50 ratio by transmission. ● In other species, alleles at a gene cause an individual to become male vs. female. ■ If females are rare, is it better to produce male or female offspring? ● The rare type, because you’re more likely to mate. ● Would selection favor male or female allele? ○ Outcome of negative frequency­dependent selection ■ When rare, allele has advantage ■ When common, allele has disadvantage ■ Genetic variation is maintained in the population ■ If you have 2 alleles, what do you predict the equilibrium allele frequency to be? Assuming it’s symmetric, 50% (1/number of alleles) ■ What if a third allele is introduced into the population? ● ⅓ ● All of these single­locus selection types affect genotype and allele frequencies, but act on ​
phenotype​
. 6.3: Types acting on traits
● Natural selection can be studied in the context of either quantitative traits or a single loci ○ Darwin thought of natural selection in the context of variation of traits (as many breeders do). ○ It can also be studied in the context of phenotypes, as in our discussions of heritability ■ Don’t necessarily need to know the underlying genes to infer the type of selection operating. ● We’ll look at three types of selection, inferred from phenotypes: Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ directional selection​
­ favors individuals at one end of the distribution ■ This causes a change in the mean of the population over time. ■ Example: pink salmon weight ­ over time, smaller and smaller salmon (more likely to be thrown back by fishermen) were caught. ■ not the same as the previous “directional selection” we discussed. ○ stabilizing selection​
­ favors individuals with intermediate values ■ No change in mean, but you lose some of the extremes ■ Not the same as overdominance ­ that involves looking at a single gene; here, we’re looking for a pattern in phenotypes ■ In 1898, a New Englander named Bumpus was interested in sparrows. When a huge ice storm killed a bunch of birds, he brought in 136 that weren’t doing too well ­ 64 died, 72 lived. ● He found the mean weight of the survivors was the same as the mean of the dead. ● But all birds weighing more than 28g or less than 23g died. ■ An example in humans: birth weight ○ disruptive selection​
­ favors individuals with extreme values (at both ends of the distribution) ■ No change in the mean, but loss of intermediate phenotypes ­ greater variance over times ■ The exact opposite of stabilizing selection ■ Example: female African finches ­ peaks in beak­size chart corresponds with specialization to eat two types of sedge seeds. Intermediate birds aren’t as good at either, and aren’t as fit. ● Final thoughts: Is selection “good” or “bad” for a population? ○ Natural selection preferentially reduces/eliminates “bad” genotypes. ○ The average fitness of all individuals ​
remaining in the population after selection goes up. ■ Since bad alleles are removed, simple directional selection gives long­term improvement to the population. ○ Fisher’s fundamental theorem of natural selection ­ the rate of increase in fitness is equal to the genetic variance in fitness. ■ If there’s a lot of variance in fitness, you’ll see large step changes. 6.4: Case studies and examples
● Case studies of mimicry ○ Mimicry​
: organisms evolving to resemble another. ○ It’s presumed to be adaptive when the “model” species has a warning coloration that causes predators to fear or avoid it ­ this makes the other organism less likely to be harassed or eaten. ○ Two general types: ■ Batesian mimicry​
­ the mimic isn’t dangerous, but the model is ­ derives advantage only for the mimic Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● example: nonvenomous king snake resembles venomous coral snake ■ Müllerian mimicry​
­ a lot of dangerous species evolving to look like one another, thus deriving a mutual advantage. ● example: tropical butterflies evolving to look like another type in their specific local population. ● Variation across space and time ○ Ecogeographic rules ­ patterns of variation within or among species that correlate with geography. ■ Bergmann’s rule ­ animals tend to be bigger in cold environments or high latitudes. ● Why might this be? Perhaps it increases volume but not surface area, which might help hold in heat. ■ Allen’s rule ­ animals tend to have shorter appendages in cold environments. ● Again, could be attributed to heat loss ● Example: polar bears’ shorter ears; house sparrow bill size ■ Gloger’s rule ­ animals tend to be more heavily pigmented in high humidity ● typically true near the Equator ● may be related to bacterial activity ● may also be true in humans, but the evidence to suggest is far from perfect. ○ Here we’ve been looking at genotypes, but the same types of geographic patterns can be seen in alleles, too ■ Drosophila pseudoobscura​
alleles on third chromosome ­ we’ll focus on one called Arrowhead (AR) ● Dobzhansky found a correlation between AR frequency and altitude (increased as the altitude of populations’ homes increased). ● Also patterns based on humidity and latitude ○ There are also temporal patterns with alleles: ■ D. pseudoobscura​
’s AR becomes less abundant as it gets hotter over the year. ● Sacrifice for family members Why do some animals sacrifice their ability to reproduce to help others, often relatives? ● Darwin: “Selection may be applied to the family, as well as the individual, and may thus gain the desired end.” ● An example: ○ If you’re selfish and just have your two kids, you pass on half of your genetic information to each offspring ­ and your alleles live on. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ If you have no kids, nothing gets passed on and your alleles die with you. ○ If you have four sisters ­ each of whom shares half your genetic information ­ and they have two kids each, your nieces each share a quarter of your genetic information. ■ Counterintuitively, it’s actually more beneficial for you to die in the process of helping your sisters have offspring that survive than it is for you to just have your two kids. Your alleles live on twice as well. ● Kin selection​
­ evolutionary strategy that favors the reproductive success of an organism’s relatives, even when at a cost to the organism’s own reproduction. ○ Evolutionary biologist J.B.S. Haldane ­ asked if he’d give his life to save a drowning brother, said “No, but I would to save two brothers or eight cousins.” ○ A possible example: the Belding’s ground squirrel and the alarm calls it uses in the event of imminent threat.
■ Dangerous for the caller, which stands up and thus becomes more conspicuous ■ Possibly evolved/spread to help relatives ● Females do alarm call more frequently when relatives are around. 6.5: Genetic drift and sampling error
One of Hardy­Weinberg’s assumptions is an infinite or near infinite population size. Since that’s generally not going to happen, there’s bound to be some sampling error ­ this is called genetic drift​
. ● Contrasting natural selection and genetic drift: ○ Natural selection is predictable ■ Some genotypes have a higher fitness ● Higher fitness leads to more offspring ● Genotypes become overrepresented ■ If the fitness is known, then change by natural selection is predictable. But not all evolutionary change is … ● Because species have a finite number of individuals, random chance matters. ○ Say you’ve got a bag of marbles, half brown and half blue. ■ If you picked out exactly four marbles to start a new bag, how many of each color would you get? ● Only about a 12% chance of getting the same color on all four ■ What if you picked out two? ● There’s now a 50% chance of getting all the same color. ○ That last example illustrates ​
sampling error​
: ■ Picking 4 marbles is likely to get you roughly “right” proportions (the proportions of the original pool). Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ■ Picking 2 is NOT likely to get you roughly right proportions. ■ By picking more, you get a more ​
representative sample​
of the original pool ○ The same principle applies in nature: ■ Populations are not infinite ■ Frequently, a small (not perfectly representative) sample of gametes form the next generation. ● Allele and genotype frequencies change ■ The effect compounds over time. ○ Sampling error is random in direction ​
over one generation ■ Assuming there is more than one allele, any allele is ​
about equally likely to increase or decrease in frequency​
in one generation by sampling error. ■ If p=0.6, it’s about equally likely to be less than or greater than 0.6 (but very unlikely to be exactly p=0.6 again) ■ Allele frequency “drifts” due to sampling error ­ thus, genetic drift. ○ Small changes are likely; big changes are possible but unlikely ■ If you tossed a coin 10 times (similar to p=0.5) you might get heads on 5 tosses. ● Getting more or less than 5 is equally likely ● It’s very unlikely you’ll get 0­1 heads, or 9­10 ○ (Chance of hitting heads all 10 times is 1/1000) ■ Same concept applies to populations. ● Original population has p(A)= 0.6 ● At right is the probability of p(A) after 1 generation (assuming 10 diploid offspring) ● The magnitude of the change compounds and relates to the population size. ○ Greater changes occur in the allele frequency if the sample (population) is smaller. ○ Here, we have a population size of about 400, A1 starts at 0.5, and we’re seeing random changes over ​
eight populations. ○ The little green tuning fork thing on the left side is the approximate average size of a change in one generation. ○ When we reduce population size to 40, the step size of changes is much bigger. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ And at a population size of 4? All variation is lost and the step size is very large. ● How big are the individual steps (on average)? ○ Variance in allele frequency due to one generation of drift = (pq)/(2N) ■ p and q are allele frequencies; N is population size. ■ 2N used because these are diploid organisms ○ Standard deviation is (slight over­)estimate of average allele frequency change in one generation: √ (pq)/(2N) ■ in other words, the square root of the variance. ○ For N = 4, p = 0.5, q = 0.5, average change estimate ~0.18 ■ Likely to go to p=0.68 or p=0.32 ­ ​
average; could be more or less ○ For N=40, p=0.5, q=0.5, average change estimate ~0.06 ○ For N=400, p=0.5, q=0.5, average change estimate ~0.02 ● Takeaways from this lecture: ○ Drift is strongest in small populations ○ Drift is neither predictable in direction in one generation nor exactly replicable in degree ■ You can get different results under the exact same conditions ○ Drift can cause big changes in allele frequency over time. 6.6: Sampling error over many generations
● Long­term effects of drift ○ Start with variable population, 2 alleles (example: p(A) and q(a) are both 0.5) ■ After many, many generations, p(A) = 0 or 1 ■ Why? Once you get to 0 or 1, there’s no variation because one allele is completely gone ­ so you can’t “drift” back ○ What if you start with a variable population, 2 alleles (p(A) = 0.6, q(a) = 0.4)? ■ Is population likely to be fixed for A or a over time? ■ Analogy: If a blindfolded man starts walking aimlessly from dead center between 0 and 1, he’s about equally likely to hit one as the other. ● But if he starts closer to 1 than 0, he’s more likely to reach 1. ● Probability of a long­term outcome is predictable ○ In one generation, it’s roughly equally likely for an allele’s frequency (p(A)) to go up and down ○ But long­term “loss” or “fixation” of an allele is more predictable ■ If p(A) = 0.5, equally likely ■ if p(A) < 0.5, more likely that allele will be lost ■ if p(A) > 0.5, more likely that allele will be fixed ○ Probability of ​
eventual ​
fixation of A = p(A). Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ●
●
●
●
■ If we do 4 sample runs in AlleleA1 with p(A) = 0.75 and a population size of 100, it hits 1 three out of the four times. ■ Still some chance for an allele to get lost despite starting out abundant (that’s what happened in the other sample run). So far, we’ve just looked at what happened in one population. What happens if we look at whole ​
species​
, including some isolated populations? ○ If all 4 populations of Galapagos land snail started with p(A) = 0.75: ■ What would the allele frequencies be in the populations many years later? ● We’d expect, on average, three of the populations to be fixed and one to be lost. ■ What would the ​
average​
p(A) across all populations be many years later? ● It’s still 0.75 across the species ­ the allele still exists in some populations despite dying out in others. Points to remember ○ Drift eventually leads to allele fixation or loss in every population ○ Starting allele frequency ­ p(A) ­ is a long­term probability of the allele’s fixation ■ (1­p(A)) is a long­term probability of allele’s loss ○ In a species with many isolated populations, the overall species retains variation with the same p(A), despite individual populations’ fixation/loss. Interaction of genetic drift and natural selection: Can genetic drift make “bad” alleles spread (or even be fixed)? ○ If the population size is small (i.e. drift is strong), genetic drift can sometimes counteract weak selection to spread or fix a “bad” allele. ■ Won’t ​
always​
counteract selection, because drift is random in direction in each generation. ● May push in the same direction, too. ■ 6 simulations of strong drift and weak selection p(A) = 0.5, w(AA) = 0.98, w(Aa & aa) = 0.0, N = 100 ● AA is a recessive detrimental ­ only 0.02 from other genotypes ● 1 of the 6 actually loses little a ­ the better allele! This is a case when genetic drift overpowers selection. ○ What happens if the population size is larger (1,000), resulting in weaker drift? ■ 6 simulations (all numbers but population size are same as above) ● Consistent trajectory of decrease that, if we followed it out enough, would eventually end in loss of A. ● More noise than the previous example. An extreme case of genetic drift: founder effects ­ strong genetic drift when a new population is established by a very small number of individuals from a larger population. ○ Often associated with colonizing islands Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ○ Sometimes causes spread (or fixation) of even detrimental alleles, since drift is strong. ○ Cause diseases or traits to be common in certain human populations. ■ Polydactyly in the Amish ■ Tay­Sachs disease in Ashkenazi Jewish ● Half the Ashkenazis trace their ancestry to four women. ■ Huntington’s disease in Mauritius ■ Red hair among the Irish 6.7: Rate of neutral molecular evolution
Are long­term effects of mutations and genetic drift predictable? ● New mutations arise at some rate ● Mutations in some parts of genome are “neutral” ­ have no effect on fitness ○ Might spread or be lost by drift ○ Can we predict the ​
rate​
at which they arise and spread to fixation? ■ Ancient population sizes unknown ● Let’s try breaking the problem up into pieces: ○ Mutations arise (we’ll call the rate μ) ■ Could be mutations per year or per generation ­ we’ll use “per year” here. ­9​
■ Example: μ = 1 x 10​
mutations per year per base pair studied ○ In bigger populations, you’re more likely to get a mutation (just because there are more alleles present) ■ Rate of getting new mutations = 2Nμ ● 2N is because these are ​
pairs​
(diploid) ○ The mutation must then also fix by drift ■ What’s the probability of fixation of a new mutation in diploids? ● Probability of new mutation arising x probability of new mutation fixing = 2Nμ + 1/(2N) → μ ● Large populations have more chance of a mutation arising, but a smaller chance it will fix ● The rate of neutral molecular evolution does not depend on population size. ○ How do we apply this calculation? ­9​
■ Mutation rate for human pseudogenes is roughly 1 x 10​
mutations per year per base pair ● pseudogene = a gene that is no longer functional, so any mutations within it are going to be neutral. ■ Let’s say we want to know the divergence time between humans and mouse lemurs ● Sequence a pseudogene and see 150 base differences in 1,000 base pairs between the two. Not unusual. Lauren Phillips Introduction to Genetics and Evolution, Winter 2014 Mohamed A.F. Noor, Duke University ● We can use this to determine how far back the two shared a common ancestor ­9​
● 1 x 10​
mutations per year per base pair ­6​
1 x 10​ mutations in 1,000 bp/year (1,000 times greater) 6​
invert numbers: so 10​
years/1 mutation in 1,000 bp 6​
● see 150 mutations: 150 mutations x 10​
years/mutation = 1.5 x 8​
10​
years ​
total​
divergence 7​
● BUT, ​
two​
branches, so we divide by two: 7.5 x 10​
years to ancestor (75 million years) ■ Here’s another one to try: time to ancestor for humans and tamarin ­9​
● 1 x 10​
mutations per year per base pair ● Screened 10,000 bp of sequence ● Found 860 mutations ­9​
­5​
● (1 x 10​
) x 10,000 = (1 x 10​
) mutations in 10,000 bp/year 5​
invert numbers: 10​
years/1 mutation in 10,000 bp 5​
7​
860 mutations x 10​
years/1 mutation = 8.6 x 10​
years total divergence 7​
● two branches → 4.3 x 10​
to ancestor (43 million years) ■ If you’re interested, ​
http://timetree.org​
allows you to look up more molecular estimates of divergence times between species. ● NEXT WEEK … Nucleotide variation within and between species. ○ Some mutations are advantageous; many mutations are bad ○ How much of the genome ​
actually​
evolves solely via mutation and genetic drift (“neutrally”)? ○ Two schools of thought since the 1960s: ■ Neutralists ­ most nucleotide variation within and between species is neutral ■ Selectionists ­ very little nucleotide variation is neutral