What is Evolution and What is Required?

When does evolution NOT occur?

I)  Random Segregation of Chromosomes and Independent Assortment of Genes

A)  Random Segregation of Chromosomes

a)  Homologous chromosomes are randomly proportioned to gametes in Meiosis I

B)  Independent Assortment of Alleles of Different Genes

1) Alleles at one locus are proportioned into gametes without regard for alleles at other loci (i.e., unlinked)

II)  Basic Probability

In a tossing a coin and assuming it is a FAIR coin, I can expect:

P(heads) = 0.5
P(tails) = 0.5

A) Multiplicative (AND) Rule - the combined probability that two independent events will occur together is the product of the individual probabilities.

In two tosses what is the probability of getting two heads?

P(head & head) = P(head) X P(head)

      = 0.5 x 0.5

      = 0.25

B) Additive (OR) Rule c the combined probability that either of two independent events will occur is the sum of the individual probabilities.

In two tosses what is the probability of getting one head and one tail?

P(head & tail)  = P(head) X P(tail)

= 0.5 x 0.5

= 0.25

AND               P(tail & head) =P(tail) X P(head)

= 0.5 x 0.5

= 0.25

Therefore the probability of getting one head and one tail is:

P(head & tail) + P(tail  & head)

= 0.25 + 0.25 = 0.5

III) Genotype and Allele Frequencies

A) Basic Frequency - 0 to 100%

1) frequency of something is the number of times that you observed that something divided by the total number of times that you could have observed it

F(red cars passing 56th street on Fowler) =

F(of men in this class) =

F(of arms with watches) =

OR

F(of arms with watches) =

B) Genotype Frequencies

1) 1 locus with two alleles

N = total number of individuals in the population

A1 = allele 1, A2 = allele 2

F(A1A1) = = 0.928

F(A1A2) = = 0.070

F(A2A2) = = 0.002

C)Calculation of Allele Frequencie

1) Based on number of individuals

F(A1) = = = 0.963

F(A1) == = 0.963      (p)

F(A2) = == 0.037             (q)

2) Based on frequency of Genotypes

F(A1)  = F(A1A1) + F(A1A2)

F(A2) = F(A1A2) + F(A2A2)

IV) Hardy-Weinberg Genotype Frequency Equilibrium
AKA When things don t change.

A)   Assumptions

1)  All individuals, regardless of genotype, mate randomly.
2)  No natural selection.
3)  everyone has the same number of offspring
4)    everyone is equally fit
5)  Populations are infinitely large (or just really big).
6)  No individuals enter or leave the population.
7)  No mutation.

If these assumptions are true, we can show that the frequency of an allele in the parent population will not change from one generation to the next c i.e., there is no evolution

A1A1 individuals produce gametes that all carry the A1 allele

A1A2 individuals produce gametes:   half of which carry the A1 allele

    half of which carry the A2 allele

A2A2 individuals produce gametes that all carry the A2 allele

In a gamete pool:

F(A1) = F(A1A1 adults) + F(A1A2 adults)

AND

F(A2)  = F(A1A2 adults) + F(A2A2 adults)

If Hardy-Weinberg Assumptions are met, then in the zygote pool:

F(A1A1)  = probability that two A1 gametes form a zygote

      = F(A1) x F(A1)

      = F(A1) x 2

F(A1A2)  = probability that one A1 and one A2 gametes form a zygote

= F(A1) x F(A2) + F(A2) x F(A1)

= 2[F(A1) x F(A2)]

 

F(A2A2)  = probability that two A2 gametes form a zygote

= F(A2) x 2

 

Genotype Frequency with Random Mating and Autosomal Genes

 

Define:  F(A1A1) = U

F(A1A2) = V

F(A2A2) = W

U = U2 + UV + 1/4V2

    = (U + 1/2V)2 = F(A1)2

V = UV + 2UW + 1/2V2 + VW

    = 2[(U + 1/2V)(W + 1/2V)] = 2[F(A1)F(A2)]

U = W2 + VW + 1/4V2

    = (W + 1/2V)2 = F(A2)2

REMARKABLE! If HW assumptions are met we know a lot of things!