1. Evolution and Genetic Equilibrium
and the Hardy-Weinberg Principle

2. Another way to look at evolution
Evolution is not only the development of new species from older ones, as most people assume…

3. It is also the minor changes within a species from generation to generation over long periods of time that can result in species. 

4. It is clear that the effects of evolution are felt by individuals, but it is the population as a whole that actually evolves.

5. Causes of Variation in Traits
Mutation – random changes in genes passed to offspring
Recombination – reshuffling of genes in a diploid organism (occurs during crossing-over in prophase 1 of meiosis)
Random pairing of gametes – Each organism produces a large number of gametes; so the union of a particular pair of gametes is a matter of chance

6. The biological sciences now generally define evolution as being the sum total of the genetically inherited changes in the individuals who are the members of a population's gene pool. 

7. All the genes of a population are referred to the gene pool
All the genes of a population are referred to the gene pool The percentage of any allele in that pool is the allele frequency.
If there are no changes in the allele frequencies, then there is genetic equilibrium evolution does not occur.

8. Calculating allele frequency
Allele frequency is determined by dividing the number of a certain allele by the total number of alleles of all types in the population.
Example: There are two alleles A and a in a set of 10 gametes. If 5 gametes carry allele A , we say the allele frequency of A is 0.5 or 50%.
Modern Biology – Holt, Rhinehart & Winston pg 318
Next: The Dancing Alleles

9. Phenotypic frequencies
A phenotypic frequency is equal to the number of individuals with a particular phenotype divided by the total number of individuals in the population.
Examples: Calculated phenotypic frequencies of four-o’ clock flowers. Modern Biology – Holt, Rhinehart & Winston pg 319
4/8 = .5
4/8 = .5
Allele Frequency Calculations:

10. Although the four-o’clock flowers differ phenotypically from generation to generation, the allele frequencies tend to remain the same.

11. Evolution is simply a change in frequencies of alleles in the gene pool of a population.

12. Let us assume that there is a trait that is determined by the inheritance of a gene with two alleles “ ” and “ ” If the parent generation has 92% B and 8% b and their offspring have 90% B and 10% b, evolution has occurred between generations. B b

13. The entire population’s gene pool has evolved in the direction of a higher frequency of the b allele --- it was not those individuals who inherited the b allele who evolved.

14. This definition of evolution was developed largely as a result of independent work in the early 20th century by Godfrey Hardy, an English mathematician, and Wilhelm Weinberg, a German physician. 

15. Gene shuffling during sexual reproduction produces many gene combinations. But a century ago, researchers realized that meiosis and fertilization, by themselves, do not change allele frequencies.
So hypothetically, a population of sexually reproducing organisms could remain in genetic equilibrium. “Biology” Miller and Levine (pg 491)

16. If a population is not evolving, allele frequencies in its gene pool do not change, which means that the population is in genetic equilibrium.
“Biology” Miller and Levine (pg 491)

17. mutation is not occurring natural selection is not occurring
Hardy, Weinberg, and the population geneticists who followed them, came to understand that evolution will not occur in a population if seven conditions are met:
mutation is not occurring
natural selection is not occurring
the population is infinitely large
all members of the population breed
all mating is random
everyone produces the same number of offspring
There is no migration in or out of the population

18. However, since it is highly unlikely that any of these seven conditions, let alone all of them, will happen in the real world, evolution is the inevitable result.

19. Hardy-Weinberg Equilibrium Equation
Hardy & Weinberg developed a simple equation which was helpful in discovering the probable genotype frequencies in a population and help track their changes from generation to generation.

20. By the outset of the 20th century, Punnett squares were used to predict the probability of offspring genotypes for particular traits based on genotypes of their two parents when the traits followed simple Mendelian rules of dominance and recessiveness. 
The Hardy-Weinberg equation essentially allowed geneticists to do the same thing for entire populations.

21. In this equation (p² + 2pq + q² = 1), p is defined as the frequency of the dominant allele and q as the frequency of the recessive allele for a trait controlled by a pair of alleles (A and a).  
(and p + q = 1)

22. Let’s do a sample problem
Albinism is due to an autosomal recessive allele. The average human frequency of albinism in North America is only 1 in 20,000.
The frequency of homozygous recessive individuals (aa) in a population is q²
so q² = 1/20,000 =
the square root of = .007
so q = .007
If p + q = 1 ,
then p = 1 -q
p =
p = .993

23. The frequency of the dominant, normal allele (A) is, therefore,
The frequency of the dominant, normal allele (A) is, therefore, .993 or about 99 in 100.
The next step is to plug the frequencies of p and q into the Hardy-Weinberg equation:
p² pq q² = 1
(.993)² + 2 (.993)(.007) + (.007)² = 1
= 1

24. This gives us the frequencies for each of the three genotypes for this trait in the population:

25. With a frequency of .005% (about 1 in 20,000), albinos are extremely rare.  However, heterozygous carriers for this trait, with a predicted frequency of 1.4% (about 1 in 72), are far more common than most people imagine. 
There are roughly 278 times more carriers than albinos. 
Clearly, though, the vast majority of humans (98.6%) probably are homozygous dominant and do not have the albinism allele.