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Population Genetics
10/30/2008 9:23:00 AM
Probability Basics
 Probability is the chance that something will happen. It is the
number of times a certain outcome happens in a certain event.
o P(a)=number of outcomes A/total number of outcomes
 Mutually exclusive events (OR statements) are additive. Add the
probabilities together. Each probability is calculated independently
of each other.
 Successive independent events (AND statements) are
multiplicative. Multiply the probabilities. Each probability is
calculated independently of each other.
Population Genetics
 Allele frequencies are the proportions of a specific allele in relation
to the total number of alleles in a population. p and q
 Genotype frequencies are the proportions of a specific genotypes in
relation to the total number of genotype in a population
p2+2pq+q2=1
 Phenotype frequencies are the proportion of a specific phenotype in
relation to the total number of phenotypes in a population
Hardy Weinberg Equilibrium—equation derived from an F1 cross
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Autosomal recessive
o p=frequency of the dominant allele
o q=frequency of the recessive allele
o p2=frequency of homozygous dominant genotype
o 2pq=frequency of the heterozygous genotype
o q2=frequency of homozygous recessive allele
Two alleles
o p+q=1
o p2+2pq+q2=1
Three alleles
o p+q+r=1
o p2+2pq+2pr+2qr+q2+r2=1
 In X linked recessive, male and female HW equations must be used
because genotypic frequencies are different. The p and q will be
the same, but there are no carriers in the male population. They
are all affected.
Disturbances of the Hardy Weinberg Equilibrium Equation
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Non Random Mating—increase in homozygosity
o Assortative Mating
 Partners select a mate based on a shared trait or
characteristic
o Consanguineous Mating
 Mating with persons of close relation
Small Population
o Genetic Drift
 Random movement of frequencies to on side or
another.
o Gene Fixation
 Once a gene frequency achieves 100%, the gene is
considered fixed
o Founder Effects
 If there is a higher proportion of an allele in a founding
population than the general population, that allele will
maintain that higher frequency, barring reproduction
outside that segregated population
o Bottleneck
If from a large population, a small number are moved
to a isolated location, the proportions will mimic the
small number moved, not the general population.
Mutation—new mutations introduce new alleles into the equation
Selection
o If a specific phenotype is not reproductively fit, it will not
reproduce and its genes will not be passed on
o Heterozygote Advantage—Some conditions confer resistance
to other diseases (Tay SachsTuberculosis, Cystic
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Fibrosisanti Diarrheal, Sickle CellMalaria)
 Gene Flow—migration of alleles across a population
Mutation Selection Equation
 Fitness (f) is a measurement of the number of offspring a person
has that grow to reproductive age.
o F=0 when offspring never survive to reproduce, all observed
cases of a diseased person arise from a new mutation
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o F=1 when offspring have normal reproductive fitness. Most,
if not all, cases arise from inheritance of a mutant allele from
a parent (or both)
The coefficient of selection (s) is the loss of fitness (1-f=s)
Mutation rates must be able to balance the number of mutant
alleles lost in a generation due to selection to remain in HW
equilibrium.
o Autosomal dominant
 µ=(1-f)q
o Autosomal recessive
Selection doesn’t really factor into the HW equation due
to the low frequency of expression of the diseased trait
o X-Linked recessive
 µ=sq/3
 For x linked lethals, the mutations cause 1/3 of the
copies to be lost every generation (all males die, only
females can have the diseased allele as carriers)
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Inbreeding
10/30/2008 9:23:00 AM
Consanguineous mating is mating between close relatives. Offspring of
consanguineous matings are termed inbred.
Coefficient of relationship (R) is a measure of the proportion of genes shared
by two relatives that are identical by descent
Coefficient of Inbreeding (F) is a measurement of the probability that a
person that person is homozygous for a trait with alleles that are identical by
descent.
 R=(1/2) n
 F=(1/2)n+1
 n=the number of matings that divide the two people being
compared
 Ratio only works when there is a low rate of inbreeding (ie not West
Virginia or Idaho or lab rats)
Inbred animal strains
 20 or more generations of brother sister mating will make 99% of
loci homozygous.
Risk Assessment
10/30/2008 9:23:00 AM
Probability Calculation
 Two types of events are possible
o Mutually exclusive—either one outcome or another will occur.
This uses the additive property of probabilities
o Independent—one event does not affect the probability of
another event. This uses the multiplicative property of
probabilities
Baysian Analysis
 Prior Probability-initial probability
 Conditional Probability-probabilities determined by observation or
prior information (statistics and such)
 Joint Probability-product of the prior and conditional probabilities
 Relative Probability-joint probability of an event divided by the
Auto Recessive
 Probability that a child will be affected is:
Pchild=(P father is a carrier)(P father will pass on allele)
multiplied by the (P mother carrier)(Pmother pass)
 If a person is an obligate heterozygote, then the P that the person
is a carrier=1.