Lecture 1-42: Population Genetics

What is the new mutation rate?

10^-7 to 10^-8 per locus per generation for SNPs For rare autosomal dominants: mu = n/2N n = number of affected patients born to unaffected parents N = total number of births -difficulties in determining prevalence figures if variation in expression, penetrance, age-of-onset (die before manifesting e.g. HD), locus heterogeneity. Assumes 100% penetrance and ascertainment

Can assume dominants are heterozygous

2pq > q2 For a dominant disorder to be homozygous require both parents to be affected or a new mutation (unlikely). WAIT WTF THINK ABOUT THIS AGAIN DIDN'T GET IT In reality homozygotes are usually more severe, even lethal or undocumented

Can assume parents of an autosomal recessive are both carriers (heterozygous)

2pq > q2 For one of the parents to not be a carrier requires a new mutation (very unlikely). Even if the mutation rate of CF was as high as 10-4 then >99% of CF children would be born to carrier parents. If one parent had two mutations they themselves would be affected.

Disease Frequency and Consanguinity.

As disease gets rarer, the more likely the parents are to be related (% consanguinity goes up)

Exceptions to Random Mating (Non-Random Mating: Usually increase frequency of homozygotes)

Assortative mating -Usually positive, generally increase the proportion of homozygotes compared to HWE -Stratification into subgroups e.g. Race, ethnic groups e.g. congenitally deaf , religious etc. (except redheads lol) Negative Assortative mating ( increases the proportion of heterozygotes) Consanguinity -allows uncommon alleles to become homozygous Little long term consequence to the population

Fitness

Assume no selection, all genotypes equally viable i.e. no effects on fertility and viability leading to unequal contribution to the next generation. Natural Selection is the operation of forces that determine the relative fitness of a genotype in the population, thus affecting the frequency of the gene concerned. s = coefficient of selection. f = genetic fitness(1 - s) fitness (f) is the probability of transmitting genes to the next generation and of the survival in that generation to be passed on to the next, in relation to the average probability for the population.

In X-linked recessive traits, derive FEMALE heterozygous frequency from the MALE birth rate

Assuming Hardy-Weinberg for an X-linked recessive trait, derive q directly from frequency in male births (q) NOTE: It's NOT q^2. 1-q is p, carrier females will be 2pq. e.g. 1/5,000 male births so q = 1/5,000 so 2pq = 1/2,500 (carrier females) q2 = 1/25,000,000 (affected females very rare) Ratio of carrier females to affected males 2:1 Ratio of affected males to affected females: 5,000 : 1

In autosomal recessive traits, derive heterozygous frequency from the homozygous RECESSIVE frequency

Assuming Hardy-Weinberg for an autosomal recessive trait, derive q from Q (q2 ) and p from q (i.e. 1 - p) and determine H from 2pq : (A/A + A/a) + a/a (P +H) Q (p2 + 2pq) + q2(USE THIS)

Balance between mutation rate and Selection

At equilibrium new mutations replace lost disadvantageous alleles (removed by selection) . For most autosomal recessive genes q = 0.02 to 0.003 2pq = 1/25 to 1/167 ~10% of individuals carry a new detrimental mutation q = mutant allele frequency mu= mutation rate s = selection

Selection

Dominant alleles are expressed in heterozygotes i.e. are openly exposed the consequences of selection are more obvious so they tend to be milder than recessives on average e.g. dominant lethals are removed straight away Selection against X-linked recessive versus autosomal recessive alleles is more efficient due to "exposure" in hemizygous males. Selection against polygenic characters is less effective - new equilibrium will be established only gradually

Genetic Drift and Migration

Efficiency of selection greater in ISOLATES. Drift was possibly more important in prehistoric times when our species was broken up into hunting camps, tribes and clans. 10,000-100,000 years ago drift was more important than now because population size was much smaller Migration can reverse the effects of Drift on the ratio of Homozygotes/Heterozygotes -Increase ratio of het. to hom. (increase freq. of het. b/c Hardy-Weinberg)

Most frequent use of H-W is to determine heterozygote frequency from the recessive birth rate.

For example the frequency of Cystic Fibrosis (CF) in Caucasians is one in 2,500 births (CF is an autosomal recessive). Assuming Hardy-Weinberg: f(a/a) = q2 = 1/2,500 q = square. root. of 1/2,500 = 1/50 p = 1 - q = 49/50 H = 2 pq = (2 x1/50 x 49/50) = ~1/25 (since 49/50= ~1) i.e. One in 25 people is a CF carrier

Gene Frequencies

Genetic constitution of a population, referring to the genes it carries frequencies of all alleles at any one locus must add up to UNITY

Hardy-Weinberg Proportions

If a population is in Hardy-Weinberg equilibrium then genotype frequencies can be derived from gene frequencies Use genotypes to derive allele frequencies to derive the H-W expected frequencies KNOW KNOW KNOW usually: 2pq >> q2 For disease-causing alleles (q), expect many more heterozygotes than homozygotes On test, he said if you see a number easily square-rootable, then probably need H-W

Population Size

Large Population Size (100s rather than 10s) Effective population size was ~10,000 for most of our history (even though world pop. recently topped 7 bill) no random fluctuations leading to sampling variation Inbreeding is inversely proportional to population size Small population size -Founder Effect - bottlenecks, island populations. -Random Genetic Drift e.g. Choroideremia is commoner and PKU rarer in Finland

Mutation

Mutation rate will alter allele frequencies very slowly -To change the frequency of an allele from 1.0 to 0.5 with mu = 10^-5 would require 70,000 generations (1.4 million years) Mutation rate - the rate of mutation per locus per generation or the rate per locus per gamete Mutation is the only source of genetic variability but acting alone it has minimal effect on allele frequencies ~1 in 100 million base pairs per generation Mutation rate higher on Y chromosome and on mitochondria

Migration

No migration; a population's gene frequencies will be altered if there is immigration from another population with different gene frequencies; will increase frequency of Heterozygotes Also called GENE FLOW

Genetic drift - Bottleneck Effect

Notice the change in blue and yellow after the bottleneck

Ratio of carriers to autosomal recessive affected individuals

RATIO increases as the frequency of the disease decreases the rarer the disease ( the smaller q) the greater the ratio of carriers( 2pq) to affected individuals (q2 ) - so becomes harder to remove disease alleles q = 0.02 ratio is 98 : 1 q = 0.003 ratio is 600 : 1

Races

Race is a geographically or culturally more-or-less isolated division whose gene pool differs from that of similar isolates. At the simplest level, each of us carries a set of genes that affects the color of his or her skin (often a surrogate for race). The exact number of these genes isn't known, but they represent only a small fraction of the estimated 20,000+ total genes in our genomes It can be useful to know a families' racial/ethnic background, particularly in the multicultural US so as to give more accurate estimates of: -disease incidence -carrier frequencies -mutation frequencies

Random Mating

Random Mating (panmixia) is when any individual has an equal chance of mating with any other individual in the population

H-W Assumptions

The population is large, and matings are random with respect to the locus in question Allele frequencies remain constant over time because: -There is no appreciable rate of mutation. -Individuals with all genotypes are equally capable of mating and passing on their genes i.e. there is no selection against any particular genotype. -There has been no significant immigration of individuals from a population with allele frequencies very different from the endogenous population.

Genetic Background

Variation within race (85%) is greater than between races (6-10%) Two randomly chosen individuals are expected to differ at ~15,000,000 bases (of the 3,000,000,000) CNV means that we differ from each other, on average, in copy number at 73-87 genes We are 99.5% the same!! degree of diversity in humans is less than what typically exists among other species, due to a recent bottleneck

Heterozygous advantage

balanced polymorphism Sickle cell anemia/ plasmodium Tay-Sachs heterozygotes maybe more resistant to TB Certain toxins produced in bacterial diarrhea cause over-secretion of chloride; give CF heterozygotes an advantage in resistance to cholera NOTE If heterozygous advantage of a particular genotype is present but unrecognized, the mutation rate of the gene may be grossly overestimated. A relatively small selective advantage in the heterozygote can outweigh a large disadvantage in the homozygote

Genotypes

genotypes must also add up to unity P + H + Q = 1 P = homozygotes for one allele Q = homozygotes for the other allele H = heterozygotes observe the phenotype, but sometimes we can derive the genotypes assuming H-W is true and thus the allele frequencies

Unity

p + q = 1 (two allele gene) p = frequency of one allele q = frequency of other allele

Recessives appear sporadic

rare recessive condition most children come from marriages of two carriers i.e. most affected children will have unaffected parents (and most of their relatives will also be unaffected) and will appear SPORADIC. consider all types of marriages that can produce affected offspring, the vast majority are between two carriers (others involve affected parents or new mutations). Virtually all parents of affected individuals with a recessive disease will be carriers. (as mentioned above)

Consanguinity (inbreeding)

relationship by descent from a common ancestor. found proportionally more often in rare recessive disease the absolute risk of abnormal offspring in first cousin marriages is less than double the population risk; consanguinity at the level of third cousin or less is not considered significant. we each carry on average more than 10 detrimental recessive genes results in increased frequency of autosomal recessive disorders compared to H-W expected incidence.

Hardy-Weinberg Law

single autosomal locus with two alleles A and a with frequencies p and q ( p + q = 1) random mating, i.e. random mixing of sperm and eggs then the expected genotype frequencies in the progeny are: A/A A/a a/a P + H + Q = 1 p2 + 2pq + q2 = 1 (freq. if in H-W equilibrium) KNOW THIS