MICROEVOLUTION
HARDY
WEINBERG
EQUATIONS
Ms.Kim
H. Biology
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
Population genetics
• 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
“Individuals are selected,
but populations evolve.”
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
What is an Allele?
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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
Allele Frequencies
• Each allele has a frequency in a
population’s gene pool  a # of
times it appears in a population
A
A
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= 20 + 20 + 160 = 200 alleles
• A = 320 + 320 + 160 = 800 alleles
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
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
Hardy Weinberg Theorem
• Conditions for non-evolving (NOT
CHANGING) population:
– Very large population size
– No migration
– No mutations
RARELY MET IN
– Random mating
NATURE
– No natural selection
Since all is RANDOM, the null
hypothesis is that the population is
not evolving.
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
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%
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
Hardy-Weinberg Equation
When using this
equation, we assume
fertilization is RANDOM
and all male/female
combinations are likely
Conditions for HardyWeinberg Equilibrium
• The Hardy-Weinberg theorem
describes a hypothetical population
• In real populations, allele and
genotype frequencies DO change
over time
•
http://www.hippocampus.org/Biology;jsessionid=6E6D9D7721EBDBFE9BD00616517846DD
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
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)
•
•
http://highered.mcgrawhill.com/sites/0072835125/student
_view0/animations.html#
2nd to last video
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.
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
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
http://bcs.whfreeman.com/thelifewire/conten
t/chp24/2402002.html
Founder Effect in Amish
Causes dwarfism and polydactyly
http://www.mhhe.com/biosci/esp/2001_gbio/folder_structure/ev/m2/s4/evm2s4_7.ht
m
Cause #2: Migration of Alleles
Gene Flow:
genetic exchange
due to the
migration of
fertile individuals or
gametes between
populations
(reduces
differences
between
populations)
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
Cause #4: “Picky” Mating
Nonrandom
mating
• “picky” mating
• Unequal
chances of each
egg getting
fertilized
• Assortative
mating choosing
individuals
more like self
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
• 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
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”
Cause #5: Natural Selection
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
•
http://www.mhhe.com/biosci/esp/2001_gbio/folder_structure/ev/m2/s1/evm2s1_6.htm
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
•
http://wps.pearsoncustom.com/wps/media/objects/3014/3087289/Web_Tutorials/17_A02.swf
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.
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.
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.
DARK ROCK HABITAT
LIGHT/DARK ROCK HABITAT
MEDIUM COLOR ROCK HABITAT
Sources of Variations
1. 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
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
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?
ANSWER KEY
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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 = 0.3969 = 39.69%
Rr = 2pq = 2(0.63)(0.37) = 0.4662= 46.62%
rr = q2 = (0.37)2 = 0.1369 = 13.69%
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?
ANSWER KEY
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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%
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?
ANSWER KEY
• R= Red
r = yellow
• gene pool= 482 alleles (241 turtles x 2)
• R = p = 27 + 27 + 200 = 254
AA
Aa  p = 254/482 or 0.53
• r = q = 14 + 14 + 200 = 228
aa
Aa  q = 228/482 or 0.47
• RR = 27/241 = 0.112 = 11.2%
• Rr = 200/241 = 0.830= 83.0%
• rr = 14/241 = 0.0581= 5.81%