1. HARDY WEINBERG EQUATIONS
MICROEVOLUTION
HARDY WEINBERG EQUATIONS
Ms.Kim
H. Biology

2. The Smallest Unit of Evolution
Darwin difficulty = what is the mechanism of natural selection?? How does it occur??
Genetic basis
After Darwin’s paper, Mendel inheritance was published (discrete, heritable characteristics “genes”)
By 1940’s modern synthesis combined ideas from different fields
Population is the unit of evolution
Natural selection is the main mechanism
Gradualism explained accumulation of small changes led to large ones over time

3. Population genetics Population:
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

4. “Individuals are selected, but populations evolve.”

5. Microevolution What is an Allele?
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
What is an Allele?
A complete gene contains 2 parts called alleles
An allele = a alternative form of a gene
You get 1 allele from “mom” and 1 from “dad”
Alleles are made up of DNA
Genotype = the genetic combination of 2 alleles

6. 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

7. 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

8. 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

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 population
In real populations, allele and genotype frequencies DO change over time

16. Causes of Microevolution
A change in the gene pool of a population over a succession of generations
We use 5 criteria for non-evolution to determine causes of microevolution
The Hardy Weinberg equations are used to determine the degree of microevolution that is occurring for a given allele

17. Cause #1: Small Populations
How can this happen? Genetic Drift
Genetic drift: changes in the gene pool of a SMALL population due to chance (usually reduces genetic variability)
2nd to last video

18. Genetic Drift Example #1
The Bottleneck Effect
Results from a reduction in population (natural disaster) such that the surviving population is no longer genetically representative of the original population
Reduced genetic variation means that the population may not be able to adapt to new selection pressures, such as climatic change or a shift in available resources, because that genetic variation that selection would act on may have already drifted out of the population.

19. Ex: NORTHERN ELEPHANT SEAL
Northern elephant seals have reduced genetic variation probably because of a population bottleneck humans inflicted on them in the 1890s. Hunting reduced their population size to as few as 20 individuals at the end of the 19th century. Their population has since rebounded to over 30,000—but their genes still carry the marks of this bottleneck: they have much less genetic variation than a population of southern elephant seals that was not so intensely hunted.
Ex: NORTHERN ELEPHANT SEAL

20. Genetic Drift Example #2
Founder Effect: a cause of genetic drift due to the colonization by a limited number of individuals from a parent population

21. Founder Effect in Amish
Causes dwarfism and polydactyly

22. Cause #2: Migration of Alleles
Gene Flow:
genetic exchange due to the migration of fertile individuals or gametes between populations (reduces differences between populations)

23. Cause #3: Mutations Mutations: a change in an organism’s DNA
original source of genetic variation (raw material for natural selection)
Mutations can immediately alter p and q in a population
Individual mutations are rare in a population, but there may be cumulative mutations that have an effect  cause evolution

24. Cause #4: “Picky” Mating
Nonrandom mating
“picky” mating
Unequal chances of each egg getting fertilized
Assortative mating - choosing individuals more like self

25. Sexual Selection
Sexual selection is natural selection for mating success
It can result in sexual dimorphism, marked differences between the sexes in secondary sexual characteristics

26. Intrasexual selection
competition among individuals of one sex for mates of opposite sex
Ex: Males competing for female attention
Intersexual selection
when individuals of one sex (usually females) are choosy in selecting their mates of the other sex
Selection may depend on the showiness of the male’s appearance

27. Sexual Dimorphism Males are usually more colorful and larger
Does NOT help cope with environment
DOES lead to reproductive success
Can be termed “Female Selection”

28. Cause #5: Natural Selection
differential reproductive success in reproduction due to variation
only form of microevolution that adapts a population to its environment
Phenotypes are selected FOR or AGAINST (not genotypes)
In a population at equilibrium, no phenotypes (therefore, alleles) are selected over other alleles

29. 3 Modes of Natural selection
Directional selection favors individuals at one end of the phenotypic range
Disruptive selection favors individuals at both extremes of the phenotypic range
Stabilizing selection favors intermediate variants and acts against extreme phenotypes

30. Directional Selection
This form of selection increases the expression of the extreme versions of a trait in a population.
For example: most of the moths had light-colored wings, but dark moths started to appear. Because moths live against tree barks, years later, most of the moths were dark. Thus, more dark moths survived, adding more genes for dark color to the population.

31. Disruptive Selection
Disruptive selection: a process that splits a population into two groups.
it tends to remove individuals with average traits but retain individuals expressing extreme traits at both ends of a continuum.
For Example, snakes that live on rocks and are grey will survive. Snakes that live on grass and are green will survive. Snakes that have an intermediate coloring would be disadvantaged because it would be more visible to predators.

32. Stabilizing Selection
It operates to eliminate extreme expressions of a trait when the average expression leads to higher fitness.
For example: human babies born with below-normal and above-normal birth weights have lower chances of survival than babies born with average weights.
Therefore, birth weight varies little in human populations.

33. LIGHT/DARK ROCK HABITAT MEDIUM COLOR ROCK HABITAT

34. Sources of Variations Mutations
At first the mutation may not be beneficial to the organism (resistance to antibiotics)
Once antibiotics are introduced the mutation is beneficial
2. Sexual recombination increases variation

35. Evolutionary Fitness
The phrases “struggle for existence”/“survival of the fittest” are commonly used to describe natural selection but can be misleading
Reproductive success is more subtle and depends on many factors
Fitness is determined by REPRODUCTIVE AND SURVIVAL success of individual
Variations & natural selection affect fitness
Sterile individuals even with a relatively fit allele will not be considered fit overall (=0)
Fitness is not determined by one trait but by the totality of traits in the organism

36. Practice Problem #1
Red color (R) is dominant to yellow color (r) in turtles.
In a population of 241 turtles, 34 are yellow.
What are the allele frequencies?
What percentage of each genotype are in this population?

37. ANSWER KEY R= Red r = yellow 34/241= 0.14 = yellow = rr= q2 √0.14=√q2
q = 0.37 then p = 0.63
RR = p2 = (0.63)2 = = 39.69%
Rr = 2pq = 2(0.63)(0.37) = = 46.62%
rr = q2 = (0.37)2 = = 13.69%

38. Practice Problem #2
Red color (R) is dominant to yellow color (r) in turtles.
In a population of 241 turtles, 85 are red.
What are the allele frequencies?
What percentage of each genotype are in this population?

39. ANSWER KEY R= Red r = yellow 156/241= 0.65 = yellow = rr= q2 √0.65=√q2
q = 0.80 then p = 0.20
RR = p2 = (0.20)2 = 0.04 = 4.0%
Rr = 2pq = 2(0.8)(0.2) = 0.32= 32.0%
rr = q2 = (0.8)2 = 0.64 = 64.0%

40. Practice Problem #3
ACTUAL-POPULATION IS GIVEN: CAN’T ASSUME HARDY-WEINBERG.
Red color (R) is dominant to yellow color (r) in turtles.
In a population of 241 turtles, 14 are rr, 200 are Rr and 27 are RR.
What are the allele frequencies?
What percentage of each genotype are in this population?

41. ANSWER KEY R= Red r = yellow gene pool= 482 alleles (241 turtles x 2)
R = p = = 254
AA Aa  p = 254/482 or 0.53
r = q = = 228
aa Aa  q = 228/482 or 0.47
RR = 27/241 = = 11.2%
Rr = 200/241 = 0.830= 83.0%
rr = 14/241 = = 5.81%