Hardy Weinberg Equations

population genetics

study of genetic variation within populations and the causes and consequences of this variation

evolution

change in allele and genotype frequencies over time

allele

one variant of a gene- Y or y

monomorphic

1 allele - no variation

mendel’s traits

2 alleles

polymorphic

more than 1 allele

polymorphism

a polymorphic gene has more than 1 allele

genotype

the genetic state/composition of an individual- YY or yy

genotype frequency

#of individuals with given genotype / total # of individuals in the population

example of genotype frequency

Gaa = N_AA/N_{AA +}N_Aa+ N_a

how to calculate allele frequencies with genotype counts

take the individual genotypes apart into their alleles

AA has twice the amount plus the amount from Aa

total # of alleles

2 times total # genotypes= 2N

p

freq of A allele

q

freq of a allele

genotype count

exact tally of individuals.- you sample 100 plants and find that 25 are AA, 50 are Aa, and 25 are aa, your genotype counts are 25, 50, and 25

p + q

allele frequencies

f(A) = f(AA) + ½ f(Aa)

f(A)= allele frequency

f(AA)= frequency of AA genotype (homo)

f(Aa)= frequency of Aa genotype

hardy weinberg equilibrium

p²+2pq+ q²= 1

p²

f(AA)

q²

f(aa)

heterozyous f(Aa)

2 x (p x q)

Uses of HWE

describes the expected genotype frequencies resulting from random mating among gametes

provides mathematical model for evaluating evidence for evolutionary change

What type of model is HWE

Null- need non changing population

Certain assumptions needed to be met for HWE

no mutation

no migration

no selection

random mating

large population size (no drift)

chi square test

a statistical method used to compare observed data with data you would expect to get by chance, specifically for categorical data (counts or frequencies).

chi square equation

• sum of all (O - E)^2 \ (div E):

when to reject statistical null

x² > 0.05

when to accept statistical null

x² < 0.05

the higher the x² value

the lower the p value

p value < 0.05

statistically significant

reject null hypothesis

signs of evolution

not in HWE

p value > 0.05

due to chance

fail to reject null

no signs of evolution

in HWE

evolution in an equation

change in allele frequency over generations

mutation

changes in nucleotide sequence of dna

causes of mutation

dna damage

dna replication errors

consequences of mutations

not all contribute to evolutionary change

random

have a bad effect

types of mutations

large scale

small scale

Large-Scale (Chromosomal) Mutations

• Deletion:

• Duplication:

• Inversion:

• Translocation:

Small Scale Mutations

• Substitution (Point Mutation): .

  • Silent Mutation:

  • Missense Mutation:

  • Nonsense Mutation:

• Insertion and Deletion (Indels):

• Frameshift Mutation

definition of small scale

These affect single nucleotides or small segments of a gene

definition of large scale

These alter large segments of a chromosome or the total number of chromosomes

mutation rate

μ

the fraction of alleles that mutate from one allele into another each generation

q^’ = q + μp

new frequency of a = old frequency of a + new a alleles created by mutation

new a from mutation

μp

mutations are happening to the A alleles and there are p of those

mutation selection balance

mutation adds an allele

selection removes it

BALANCE- hence q= square root of μ

equilibrium frequency

q = square root of μ

what happens to q at equilibrium

delta q = 0

genetic drift

changes in allele frequencies due to random sampling effects between generations

where is drift strongest

SMALL POPULATIONS

• bigger influence on the population if 5 out of 10 is affected then 5 out of 100

strength of drift

1 / 2N

n= population size

WITHIN POP- RGD () genetic variation

decreases

• causes alleles to become lost or fixed

AMONG POPS- RGD () genetic variation

increases

• each population can change in diff direction

RGD () inbreeding

increases

• as drift removes alleles individuals become genetically similar

• more sim are more like to mate

• increases homozygosity

three situations of genetic drift

bottleneck

founder

continuously small populations

bottle neck

populations suddenly becomes very small

founder effect

few individuals start new population

continuously small populations

if pop stays small for many gen

• drift stays strong

• variation keeps decreasing

• inbreeding increases

migration

movement of alleles or genotypes in and out of population

migration can be known as

gene flow

mirgation does what to allele frequencies

changes them

• introduces outside alleles

• make populations more similar

migration rate

m = # of migrants / total population size after migration

migration equation

delta p = m(p₂-p₁)

p₁₌ frequency of allele A in original population

p₂= frequency of allele A in migrant popuation

m= fraction of recipient population that is made up of migrants

natural selection

changes in allele frequencies due to differential survival and/or reproduction

types of ns

disruptive

directional

stablizing

distruptive selection

Favors both extreme phenotypes while selecting against intermediate or average forms.

Splits the peak of the trait distribution into two distinct peaks, potentially driving speciation or polymorphism

Stabilizing Selection

Favors intermediate phenotypes and selects against extreme variations

Narrows the bell curve and reduces overall genetic/phenotypic variance

Directional Selection

Favors individuals at one extreme of a phenotypic range, causing the population's trait distribution to shift in that single direction

Changes the average (mean) value of the trait over time

sexual selection

form of natural selection that occurs when there is competition for mating and or fertlization opportunity

sexual dimorphism

males and females of the same species look different

male vs female reproductive success

male- can i attract/ can i get mates

female- need resources to produce and care for offspring- HAVE LESS VARIATION IN REPRODUCTIVE SUCCESS

two types of sexual selection

intra

inter

intrasexual selection

within the same sex- competition

intersexual selection

between the sexes

primary sexual traits

needed for reproductive physiology, gametes, reproductive development

SEXUAL SELECTION DOES NOT ACT ON

secondary sexual traits

not essential for reproduction

not involved in gametes

competiton

SEXUAL SELECTION ACTS ON THIS

fitness

the relative likilhood that one genotype will contribute to the gene pool of the next generation compared with other genotypes

QUANTITATIVE MEASURE

relative fitness

absolute fitness / mean fitness population

mean absolute fitness of population

f(AA)W_AA + f(Aa)W_Aa+ f(aa)W_aa

W equals

the absolute fitness- highest amount of offspring

• everything else is divided by the largest number

process of allele frequency after selection

p₀ and q₀

HW

muliptly by fitness + calculate mean fitness

W with bar over

f₁(AA), f₁(Aa), f₁(aa)

calculate new allele frequency

p₁

compare old vs new

delta p = p1-p0