Chpt. 23 The Evolution of Populations- Population Genetics

Individuals are selected …

Populations evolve

Individuals are selected …

Populations evolve

Populations

= unit of evolution

Natural selection

= mechanism of evolution

Gradualism

= accumulation of small changes in

gene pool

time over LONG periods of



Hardy-Weinberg Theorem



Hardy-Weinberg Theorem



examines the gene structure of a NON-evolving population



Hardy-Weinberg Theorem

examines the gene structure of a NON-evolving population.



Obviously, this is not common, however, gives a base-line / model

NULL HYPOTHESIS

for determining

if

and

why

populations evolve



Hardy-Weinberg Theorem

even though alleles are shuffled and recombined during meiosis and random fertilization.

This has no effect on the overall gene pool percentages.

A a A a A a a A A a A A a

Not SWIMMING pool…. a GENE POOL!!!



Hardy-Weinberg Theorem

Gene pool frequencies (percentages) will remain unchanged if no mechanism that can cause evolution to occur acts on a population.



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

Mutations are not occurring



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

Natural selection is not occurring



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

Population is LARGE



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

EVERYONE breeds…



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

EVERYONE randomly mates…



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

EVERYONE produces the same number of offspring



Hardy-Weinberg Theorem

Gene pool frequencies will remain unchanged if:

NOONE migrates in or out of the population… everyone stays



Hardy-Weinberg Theorem

5 Agents of evolutionary change:

Mutation Gene Flow (migration) Non-random mating Genetic Drift (same # of offspring) Selection



Hardy-Weinberg Theorem remember:

H.W. explains: the constant in a population… unless

Hardy-Weinberg Principle

Mathematical statement about the relative frequency of alleles (genotypes) in a population.

p +q = 1 p2 + 2pq + q2 = 1



Hardy-Weinberg Theorem



Frequency of alleles remains constant in a population,

unless acted upon by agents OTHER THAN sexual recombination.



Inheritance does not cause changes in allele frequency.

Hardy-Weinberg Principle

p = frequency of dominant allele

p + q = 1

Hardy-Weinberg Principle

q = frequency of recessive allele

p + q = 1

Hardy-Weinberg Principle

Mathematical statement about the relative frequency of alleles (genotypes) in a population.

in most cases, we only know the phenotypic frequencies

Hardy-Weinberg Principle

q 2 = frequency of homozygote recessive individuals

q 2 = # of aa individuals

Hardy-Weinberg Principle

p 2 = frequency of homozygote dominant individuals

p 2 = # of AA individuals

Hardy-Weinberg Principle

p = frequency of dominant allele

p = # of (AA) + 2 (# Aa)

Hardy-Weinberg Principle

q = frequency of recessive allele

q = # of (aa) + 2 (# Aa)

Hardy-Weinberg Principle

2pq = frequency of heterozygote individuals

2pq = # of Aa individuals

Hardy-Weinberg Principle

by comparing genotypic frequencies from one generation to the next, you can learn whether or not evolution has occurred…

Hardy-Weinberg Principle

if genotypic frequencies have changed from your original count… evolution has occurred!

Suppose there are 1,000 individuals in a population Genotype AA Aa aa

total

Number 490 420 90 1000 Genotypic Frequency 0.49

0.42

0.09

1.00

Suppose there are 1,000 individuals in a population Genotypic frequency population = the proportion of a particular genotype found in a Genotypic Frequency 0.49

AA 0.42

Aa 0.09

aa total 1.00

Suppose there are 1,000 individuals in a population Phenotype dominant recessive

total

Number 910 90 1000 Phenotypic Frequency 0.91

0.09

1.00

Suppose there are 1,000 individuals in a population Phenotypic frequency population = the proportion of a particular phenotype found in a Phenotypic Frequency 0.91

0.09

total 1.00

Suppose there are 1,000 individuals in a population Allele A a Number 1400 420 Allele Frequency 0.7

0.3

total

2000 1.00

q = frequency of recessive allele However, we do not know how many a’s there are just by looking at phenotype

Allele frequency

Pssst…(There are 1,000 copies of the flower color gene in this population of 500 total flowers…)

q =

480

q2 = frequency of recessive genotype

480 Genotypic frequency

q 2 = 20/500

q2 = frequency of recessive genotype

480 Genotypic frequency

q 2 = .04

q = frequency of recessive allele

480 Allele frequency

q =  .04

q = frequency of recessive allele

480 Allele frequency

q = .2

q = frequency of recessive allele p = frequency of dominant allele

480

q = .2

Allele frequency

p + q = 1 p + .2 = 1 p = 1 - .2

p = .8

480

p = .8 q = .2

Some of the pink flowers will be AA and some will be Aa p2 + 2pq + q2 = 1

480 Some of the pink flowers will be AA and some will be Aa .64 + .32 + .04 = 1

480 How many of the pink flowers will be AA and how many will be Aa .64 X 500 individuals 320 individuals are AA

480 How many of the pink flowers will be AA and how many will be Aa .32 X 500 individuals 160 individuals are Aa

480 320 are AA 160 are Aa 480 total

.8 x .8 = .64

Genetic structure of next generation

.2 x .2 = .04

Genetic structure of next generation

.2 x .8 = .16

.8 x .2 = .16

.32

aA Aa Genetic structure of next generation

Hardy-Weinberg Principle



Under ideal conditions, the relative allele frequencies are the same in the offspring generation as in the parent generation.

p 2 + 2pq + q 2 = 1

IF

:

frequencies in a population

deviate

Hardy-Weinberg (these are set numbers)… from THEN

:

we know the population is evolving.

Oh Hardy, why did you quit your job at ABERCRO MBIE?

Weinburg, I keep telling you, I got sick of changing genes!!!

change over time is a result of changes in a population’s frequency of genotypes /

genetic

Lets Hardy!!

What percentage of the human population are carriers for the allele for PKU?

1 out of 10,000 babies are born with this recessive

Most of the time you will begin by determining the frequency of the homozygous recessive genotype Find q2 (frequency of homo recessive)

Lets Hardy!!

What percentage of the human population are carriers for the allele for PKU?

1 out of 10,000 babies are born with this recessive

Hint: q2 = 1 / 10,000 (frequency of aa) 

Find q



Find p



Find pq

AP Problems Using Hardy-Weinberg

•

Solve for q 2 (% of total)

•

Solve for q (equation)

•

Solve for p (1- q)

•

H-W is always on the national AP Bio exam (but no calculators are allowed).

AP Problems Using Hardy-Weinberg

•

Solve for q 2 (% of total)

•

Solve for q (equation)

•

Solve for p (1- q)

•

H-W is always on the national AP Bio exam (but no calculators are allowed).

AP Problems Using Hardy-Weinberg

•

Solve for q 2 (% of total)

•

Solve for q (equation)

•

Solve for p (1- q)

•

H-W is always on the national AP Bio exam (but no calculators are allowed).

AP Problems Using Hardy-Weinberg

•

Solve for q 2 (% of total)

•

Solve for q (equation)

•

Solve for p (1- q)

•

H-W is always on the national AP Bio exam (but no calculators are allowed)

AP Problems Using Hardy-Weinberg population: 100 cats 84 black, 16 white How many of each genotype?

q

2 (bb): 16/100 = .16

q

(b): √.16 = 0.4

p

(B): 1 - 0.4 = 0.6

p

2 =.36

BB 2pq=.48

Bb

q

2 =.16

bb

AP Problems Using Hardy-Weinberg Assuming H-W equilibrium

p

2 =.36

BB 2pq=.48

Bb

q

2 =.16

bb Null hypothesis Sampled data How do you explain the data?

p

2 =.20

BB 2pq=.64

Bb

q

2 =.16

bb