1. The Evolution of Populations
HARDY WEINBERG EQUATIONS
Ms. Day
AP Biology
(Ch 23 Bioflix)

2. Population genetics- Vocab
Population genetics is the study of how populations change genetically over time
Population:
Group of the same species living in the same area that can interbred
Species:
a group of populations whose individuals have the potential to interbreed and produce fertile offspring
Gene pool:
the total combination of genes (alleles) in a population at any one time

3. “Individuals are selected for/against, but populations adapt and evolve.”

4. Microevolution
The change in the frequency of ALLELES (or how often a certain allele appears) in a population over time
The change in a population’s gene pool over time

5. Allele Frequencies
Each allele has a frequency in a population’s gene pool  a # of times it appears in a population A a A a a A

6. Allele Frequencies- EXAMPLE
In a population of wildflowers, the Red allele is A and white allele is a.
500 total plants in the population, 20 are white (aa), 320 are red (AA), 160 are pink (Aa)
How many total alleles for flower color are there in this population?
1000 (500 plants with 2 alleles EACH)
a= = 200 alleles
A = = 800 alleles

7. Allele Frequencies- EXAMPLE (Con’t)
What is the frequency of “A” allele and “a” allele? Always use a decimal for frequency!
800/1000  A = 0.8
200/1000  a = 0.2

9. How do we KNOW if a population is evolving?
Use the Hardy-Weinberg theorem (or equilibrium)
It is used to describe a population that is NOT evolving
Conditions in the population are completely RANDOM (null hypothesis)

10. Hardy Weinberg Theorem
Conditions for non-evolving (NOT CHANGING) population:
Very large population size
No migration
No mutations
Random mating
No natural selection
Since all is RANDOM, the null hypothesis is that the population is not evolving.
RARELY MET IN NATURE

11. 2 equations are used in the Hardy Weinberg Theorem p + q = 1
(1 means 100% of all alleles)
This means that there are only 2 possible alleles p and q
p = dominant allele frequency
q = recessive allele frequency
The equation that corresponds to the frequency of individuals regarding these 2 alleles:
p2 + 2pq + q2 = 1

12. (frequency of Aa plus aA genotype)
p2 + 2pq + q2 = 1
p2 = frequency of homozygous dominant individuals
2pq = frequency of heterozygous individuals
(frequency of Aa plus aA genotype)
q2 = frequency of homozygous recessive individuals
EXAMPLE
Round head is dominant to cone heads, 51% of the individuals in the population have round heads. What portion of this 51% are homozygous?
0.49 = q2 (recessive), Therefore q = 0.7, so p = 0.3
p2 is the frequency of homozygous dominant individuals = 0.09 or 9%

13. Hardy-Weinberg Theorem
States that…
the frequencies of alleles and genotypes will stay CONSTANT over generations UNLESS acted upon by agents or
It describes a population where allele frequencies do NOT change
p and q do NOT change over generations

14. Hardy-Weinberg Equation
When using this equation, we assume fertilization is RANDOM and all male/female combinations are likely

15. Conditions for Hardy-Weinberg Equilibrium
The Hardy-Weinberg theorem describes a hypothetical (IDEAL) population
All FIVE conditions are being met
Allele frequencies do NOT change over time
Genotype frequencies do NOT change over time
So…p and q values CAN be used (connected to) p2 + 2pq + q2 = 1

16. HOWEVER…p2 + 2pq + q2 and p + q will ALWAYS equal 1 (100%).
Real Life Populations
In real populations, allele and genotype frequencies DO change over time
All FIVE conditions are rarely met together!
So…p and q values can NOT be used (connected to) p2 + 2pq + q2 = 1
HOWEVER…p2 + 2pq + q2 and p + q will ALWAYS equal 1 (100%).