Transcript Hardy-Weinberg Equation

In This Lesson:
Population
Evolution
(Lesson 2 of 3)
Today is Friday (!),
th
September 9 , 2016
Pre-Class:
What are three types of selection?
Today’s Agenda
• Population Evolution
• Hardy-Weinberg Equilibrium
• Other important dynamics in evolution across
a population.
• Where is this in my book?
– Chapter 23.
By the end of the lesson…
• You should be able to describe HardyWeinberg equilibrium and use its formula to
solve problems.
• You should be able to identify other dynamics
that can occur to populations and how they
will affect genetic diversity.
• You should be able to explain why places like
Hawaii, Australia, and Madagascar have such
weird life forms.
Quick Genetics Review
• Gene:
– A segment of DNA that codes for a particular protein.
• Allele:
– A version of a gene.
– We all have the eye color gene, but we have different eye
color alleles.
• Genotype:
– The underlying alleles (homozygous/heterozygous) behind
an individuals’ traits.
• Phenotype:
– The outward manifestation of an individual’s genotype.
– In other words, how an individual looks.
Quick Genetics Review
• Complete Dominance (Simple Inheritance)
– Purple flower + white flower = purple flower
• Incomplete Dominance
– Purple flower + white flower = pink flower
• Codominance
– Purple flower + white flower = purple/white flower
• Multiple Allele Inheritance
– More than two traits (eyes: hazel, brown, blue, etc.)
• Polygenic Inheritance
– More than one gene controls a trait.
Quick Genetics Review?
• Locus
– Where a gene is located within a chromosome.
• (it’s a location in the DNA)
– Plural: loci
Why populations?
• We study the evolution of populations because the
population is the smallest “unit” that can evolve.
– Mutations must be passed on, so evolution doesn’t
actually appear in individuals.
– Rather, the evolution is between generations.
– Evolution is therefore only viewed in aggregate.
• So how do you know if a population is evolving?
– The Hardy-Weinberg Theorem and Equation!
– Be ye warned: This is gonna get confusing before it gets
clear.
Hardy-Weinberg Theorem
• The Hardy-Weinberg Theorem was developed by
two separate individuals (independently).
• It is a way to determine whether evolution is
occurring in a population OR how many
individuals exhibit certain genotypes/phenotypes.
– If no evolution is occurring, allele frequencies should
be unchanging.
• Here’s the deal:
– Suppose we have a population of…
– …Blue-Footed Boobies.
http://www.duskyswondersite.com/wp-content/uploads/2010/07/blue-footed-booby-two.jpg
Hardy-Weinberg Equilibrium
• It’s not true, but for an example let’s also say
that blue-footed boobies can either have the
dominant allele for blue feet (B) or the
recessive allele for green feet (b).
– In other words, for feet, there are two possible
alleles in the gene pool – all the available alleles in
the population.
• Now, let’s also say that a particular booby
population is not evolving. It is therefore in
Hardy-Weinberg equilibrium.
– This allows us to make some broad statements
about the boo- er, “birds.”
https://lh3.googleusercontent.com/-d8McO_hqskg/ULI0QJLMvsI/AAAAAAAAyJM/5DulqEI35Gk/w506-h714/Blue-footed_Booby_Guard.jpg
Hardy-Weinberg Equilibrium
• Put bio on pause for a second.
• If I flip a fair coin, what’s the likelihood of
heads?
• 50%.
• If I flip a fair coin twice, what’s the likelihood
of heads both times?
• 50% * 50%, or 25%.
• Okay, back to bio.
Hardy-Weinberg Equilibrium
• Suppose, in the entire gene pool for foot color, B
(blue) alleles represent 70% of the population.
– That means b (green) alleles represent 30% of the
population.
• Therefore, those numbers should not change
generation-to-generation if this population is not
evolving.
• We can also determine the frequency of
genotypes (not just alleles) in the population, but
we need a concept or two first.
Hardy-Weinberg Equation
• To be BB, then, you are 70% likely to get B for
the first allele and 70% likely to get B again.
• 70% * 70% = 0.72 = 49%
• To be bb, it’s 30% the first time and 30% again.
• 30% * 30% = 0.32 = 9%
• To be Bb, however, you could be 30% or 70%
likely for the first allele, and then 70% or 30%
for the second allele.
– This is trickier.
Hardy-Weinberg Equation
• Let’s suppose the sperm provides B and the
egg provides b:
• 70% * 30% = 21%.
• Suppose the opposite:
• 30% * 70% = 21%.
• That’s a total of 42%, so the chance of being
Bb is really B * b * 2.
Hardy-Weinberg Equation
• Therefore, 49% of individuals are BB, 42% are Bb,
and 9% are bb.
– That adds to 100% - not a coincidence.
• That’s just an example. As a formula, the HardyWeinberg Equation looks like this:
• p2 + 2pq + q2 = 1
2
p
+ 2pq +
2
q
=1
• WRITE THIS:
• p = frequency of dominant allele
• q = frequency of recessive allele
– Therefore, p + q = 1.
• p2 = frequency of homozygous dominant individuals
• 2pq = frequency of heterozygous individuals
• q2 = frequency of homozygous recessive individuals
• Again, what’s the point?
– Either to determine if evolution is occurring, or to determine how
many individuals exhibit certain traits or have certain genotypes.
Wait…what?
• What’s the difference between “alleles” and
“individuals?”
– AKA what’s the difference between “q” and “q2?”
• Let’s explain it with an example – eye color.
– Suppose you can either have brown eyes (B) or blue eyes
(b), and brown eyes are dominant.
– I can look at a room of people and determine the
frequency of people with blue eyes (that’s q2).
– However, I can’t look at the room and determine how
many blue alleles are out there (that’d be q).
• Some people with brown eyes could be heterozygous, and
therefore carry a blue allele without showing it.
– This is why we need the equation, and it only works if the
population is at equilibrium.
Hardy-Weinberg Equation
• We’re going to practice, but first, some
assumptions of Hardy-Weinberg equilibrium.
• To be at H-W equilibrium, a population must:
– Not have mutation (no DNA changes).
– Have random mating (no sexual selection).
– Not have natural selection (no “fitter” genotypes).
– Be large (smaller ones fluctuate through genetic drift).
– Not have gene flow (no individuals come in or out).
• Any violation of these conditions indicates
evolution.
Hardy-Weinberg Equation
• Let’s start with a real world example.
• We’re going to test THIS CLASS for a certain trait.
– So we’ll see who has the dominant trait and the recessive
trait, but importantly, among the dominant folks, we
won’t know who is homozygous dominant and who is
heterozygous.
• Using the Hardy-Weinberg equation, we can figure
out what percentage of our class is homozygous
dominant, heterozygous, and homozygous recessive.
– Then we’ll practice more.
• Lab 8 begins!
H-W Practice Problem
• The frequency of the “not caring” allele (N) in
honey badgers is 95%.
• If the population is at Hardy-Weinberg equilibrium,
how many honey badgers don’t care in a
population of 5000?
–
–
–
–
If 95% of alleles in the gene pool are N, 5% are n.
p2 + 2pq + q2 = 1.
(0.95)2 + 2(0.95)(0.05) + (0.05)2 = 1
90.25% are NN, 9.5% are Nn, 0.25% are nn, or in other
words, 90.25% + 9.5% = 99.75% don’t care.
– 99.75% of 5000 is 4987 badgers.
H-W Practice Problem 2
• This one’s adapted from your textbook (p.
486).
• Phenylketonuria (PKU) is a rare disease caused
by a recessive allele. It can cause mental
disability and other symptoms as a result of
being unable to metabolize the amino acid
phenylalanine, but is relatively easily treated.
• If 1 in 10,000 births in the USA is
phenylketonuric, what percent of the
population are carriers of the allele?
H-W Practice Problem 2
• Okay, this is a bit of a weird one.
• First, let’s make sure we can even use HardyWeinberg:
–
–
–
–
–
Are new PKU mutations being introduced? Nope.
Do people mate with others based on PKU? Nope.
Are people with PKU dying off? Nope.
Is there a large population size? Yep.
Is there gene flow? Yes, but other populations have
similar PKU rates.
• Proceed.
What percent of people are
heterozygous (carriers) for PKU?
• Since PKU is recessive, q2 represents the frequency of
PKU-positive individuals.
• q2 = 1/10,000 = 0.0001
• q = √0.0001 = 0.01 (1% of all alleles are PKU)
• Therefore, the non-PKU dominant allele has a 99%
frequency.
• p2 + 2pq + q2 = 1
• (0.99)2 + 2(0.99)(0.01) + (0.01)2 = 1
• We care about the highlighted part because those are
the carriers.
• 2(0.99)(0.01) = 0.0198, or 1.98% of the population carries
PKU.
H-W Practice Problem 3
• In a population of 1000 Polish Frizzle chickens, 342 have a
recessive phenotype for tan feathers. Determine how many
chickens are homozygous dominant and heterozygous.
• 342 out of 1000 is 34.2%, or 0.342 (q2).
• q = 0.585 (√q2).
• p = 0.415 (p + q = 1)
• p2 = 0.172; 2pq = 0.486; q2 = 0.342.
• But! That’s not good enough. They gave us a starting
population size (1000 individuals).
– So 0.172, or 17.2%, is 172 chickens homozygous dominant. 2pq =
0.486 (or 48.6%) means 486 chickens are heterozygous.
http://memberfiles.freewebs.com/00/26/41242600/photos/Diane-Spisak/cwhfriz.JPG
Hardy-Weinberg Takeaways
• A gene pool is the sum of all the individual alleles
(“gene letters”) in a population.
• In order to have no evolution, you need the five
assumptions of Hardy-Weinberg equilibrium.
• If there is no evolution, allele frequencies in the gene
pool are unchanging.
• When allele changes are in equilibrium, we can
estimate genotypes in a population.
• If actual numbers show considerable difference from
Hardy-Weinberg probabilities, evolution is occurring.
• Letters are allele frequencies; terms in the equation
are genotype frequencies.
Hardy-Weinberg Tips
• Because heterozygous individuals “hide”
recessive alleles, start your analysis with the
homozygous recessive genotype/phenotype.
• Frequently, but not always, problems require
you to find q2, then q, then p, and then use
the Hardy-Weinberg equation.
• Keep your allele frequencies as decimals
unless percentages are specifically required by
the problem.
Final Hardy-Weinberg Note
• Polymorphism…what’s that?
– Think root words!
• Poly- = many.
• -morph = form.
• So polymorphisms are different forms of an
organism within a population.
– For example, white-handed gibbons can be
either black or blond (not related to gender).
– That’s a color polymorphism.
– There can even be single nucleotide
polymorphisms (SNPs), which are when DNA
bases change at certain points (loci).
http://blogs.ucl.ac.uk/museums/files/2012/05/White-handed-gibbons-showing-colour-morphs.jpg
Practice
• Let’s first try another way of measuring allele
frequencies:
– Lab 8 – Population Genetics and Evolution
• Followed by:
– Hardy-Weinberg Practice Problems (odd numbers)
Onward!
• Now that that’s done, let’s look at some broad
population-level evolutionary trends:
– Genetic Drift
• Bottleneck Effect
• Founder Effect
– Gene Flow
– Mutations
– Natural Selection
• Directional Selection
• Diversifying Selection
• Stabilizing Selection
– Sexual Selection
Genetic Drift
• Genetic drift has occurred when allele
frequencies have changed due to chance.
• Prevalent in small populations.
• Decreases variation and thus adaptability.
• Non-biology example:
– If you flip a coin 1000 times, what percent of flips will
be heads?
• About 50%, or maybe slightly more. It’s unlikely to be that
far off.
– If you flip a coin 5 times, what percent of flips will be
heads?
• Well, it should be 50%, but with fewer flips it’s not entirely
unlikely you could even get 100% heads. Or 0%.
Small Populations
• So how do populations shrink, leading to
genetic drift?
1. Bottleneck Effect
• Disaster, famine, loss of habitat shrinks population.
• Importantly, genetic fitness has no correlation with the
alleles lost from gene pool. It’s chance only.
Bottleneck Effect Case in Point
• Cheetahs:
– Very small number of alleles in
the cheetah gene pool.
• Caused by a bottleneck during
the last ice age (~10,000 years
ago) and more recently from
poaching.
– Zoo populations and other
captive cheetahs must be
managed carefully to outcross
(avoid inbreeding).
Founder Effect
2. The founder effect occurs
when a new population is
started with a small group of
individuals (founders).
– The new gene pool may not
resemble the old gene pool.
– This frequently leads to
microevolution.
• This is much like a small sample
size in an experiment.
– A small group leads to sampling
error.
About sampling error…
• Suppose I wanted to poll the school on which sport
we all like the best.
• I ask only the football team.
• I then conclude that football is our school’s favorite.
Fair?
– Nope, this is sampling error.
– Similarly, if a group of birds settles on an island and starts a
new population, but their gene pool does not have the
same allele frequency as the “starting” gene pool, we may
experience sampling error as the birds all appear “red” for
example.
– It’s sampling error because we end up with a different gene
pool composition from the “previous” gene pool.
Founder Effect Example
• Amish people have higher-thanaverage rates of polydactyly
(extra digits).
• It has nothing to do with being
Amish – it’s just that the Amish
community was founded by a
relatively small group with
higher-than-average polydactyly
rates.
• Since the Amish usually do not
reproduce outside the
community, the skewed allele
frequency is maintained.
http://www.whodiscoveredit.com/wp-content/uploads/2010/06/Polydactyly.jpg
Genetic Drift: Alternate Example
• Here’s something weird:
– We all know DNA can be mutated by UV radiation.
– UV radiation doesn’t just harm our DNA. It can also
mutate viral DNA.
– Some research suggests that UV radiation might cause
the mutations that lead to pandemics.
– The crazy part? In the 20th century, 6 out of 9 massive
flu outbreaks were accompanied by increased sunspot
activity – when the sun releases a bunch more
radiation than normal.
• The acquisition of these novel genes by viruses is
known as antigenic drift.
Okay, next…
• Another population-level pattern in evolution: gene
flow.
• When a population’s alleles are spread to another
population, gene flow has occurred.
• For most of human history, for example, people tended
to not move very far.
• Once modern transportation came about, however,
populations that would never have come in contact
with one another now are.
• When these formerly-isolated groups reproduce,
alleles from each “flow” into the other population.
Gene Flow Example
• GMO Plants
• Some of the fear around
genetically-modified
organisms, plants in this
example, is that their pollen,
seeds, et cetera, will spread
into the wild.
• You might say the fear is of
GMOGF, or geneticallymodified organism gene
flow.
http://sustainablepulse.com/2013/11/12/spread-of-gm-crops-out-of-control-in-many-countries-breaking-news/#.U8mhoFbqsWY
Mutations
• Any time DNA is copied or transcribed (to
RNA), there are always mistakes.
– Many are fixed but some slip through.
– About one typo in every billion DNA bases goes
uncorrected.
• These mutations, over millions of years and
coupled with genetic drift and/or natural
selection, can ultimately lead to evolution.
– They are not always positive. They are random*.
*Random Mutations
• Recent research suggests that not all mutations are
random.
• Jumping genes have been documented across the
biological world, but they were first found in corn by
Barbara McClintock in the 1950s.
• When corn plants were stressed by heat or drought,
mutation rates soared. Entire genes were moving!
– The movements were not random, however.
– Genes went certain places significantly more frequently
than others and their movement occurred as a result of
environmental stimuli.
Natural Selection
• We’ve covered this one, but obviously natural
selection is usually applied at the population
level, not just for the individual.
• Note that there will never be a “perfect”
individual produced through natural selection:
– There are historical constraints (like the existence of
vestigial structures – old adaptations now unneeded).
– Mutations must occur for new and fitter phenotypes
to occur than those already in existence.
– Adaptations frequently represent compromises. One
trait often can’t suit every possible use.
Types of Selection
• Here’s the thing…selection manifests across a
population in a few different ways:
A. Directional Selection
B. Diversifying/Disruptive Selection
C. Stabilizing Selection
• Remember, these are responses to selective
pressures.
Types of Selection
Arrows represent
selective pressures.
Directional Selection
• When a population’s genetics
shift in one direction toward
an extreme phenotype.
• Example: Male house
sparrow’s black “bibs” are
preferred by females. Over
time, we would expect the bibs
to become bigger and bigger.
http://www.sparrowdove.com/wp-content/uploads/2012/07/house_sparrow.jpg
Diversifying/Disruptive Selection
• When both extremes of a
phenotype are preferred over
the middle ground.
• Example: Oysters. Being
relatively light-colored helps
blend in with rocks. Being
dark-colored helps blend in
with shadows. Being mediumcolored helps you get eaten.
http://bivalves.teacherfriendlyguide.org/index.php?option=com_content&view=article&id=42:ty
pes-of-natural-selection&catid=27&Itemid=124
Stabilizing Selection
• When both extremes of a
phenotype are not preferred
over the middle ground (being
in the middle is best).
• Example: Birth weight. Being
underweight or a big ol’ baby
are not good. A middle-weight
infant has the best chance of
survival.
http://circ.ahajournals.org/content/114/16/1687.figures-only
Sexual Selection
• Where natural selection is all about being able to
survive well enough to reproduce, this one’s
about being able to win over the opposite sex.
• Sexual selection is a process by which individuals
more readily survive to reproduce because they
have traits desired by mates.
– …sometimes.
– I know, we talked about this before. More details
now; types and examples on the next slides…
Sexual Selection
• Intrasexual selection occurs
when individuals of the same
sex (usually males) compete for
the opportunity to mate.
– Example: Young male lions that
must oust an older male from his
pride in order to win the harem.
– Example: Buck Fight!
– Example: Koala Fight!
• By the way, the male lion’s mane
serves as a way to defend against
another male’s “neck bite” attempt.
http://blog.londolozi.com/wp-content/uploads/2012/02/Pic2.jpg
Sexual Selection
• Intersexual selection occurs
when individuals of the
opposite sex select mates
based on certain desirable
traits.
– Example: Female zebra
finches that select the males
with the reddest beaks and
legs, and biggest cheek
patches.
http://www.mpg.de/663248/zoom.jpeg
Sexual Selection Key Points
• Sexual selection is a form of nonrandom mating.
• It can lead to sexual dimorphism
– when males and females differ
visibly.
• For intersexual selection, females
are using some kind of visual
assessment as a proxy for good
genes.
– “If that stud can keep his beak so
red, he must be good at securing
food. He’ll be a great father.”
http://media-cache-ec0.pinimg.com/236x/8a/55/1e/8a551eee45902d4c2de140f76b5903a5.jpg
Balancing Selection
• Balancing selection is a form of selection that acts
to preserve variation, or in other words, preserve
allele variety:
– Heterozygote advantage occurs when the
heterozygote genotype is favored, thus preserving
both alleles.
• Example: Cystic Fibrosis has been shown to prevent Cholera.
– Frequency-dependent selection is a condition when
individuals with uncommon characteristics are favored:
• Book example: Scale-eating fish in Lake Tanganyika (Africa)
have mouths facing left or right (not both).
• When most scale-eating fish have left-facing mouths, being
able to attack from the opposite side is advantageous.
Frequency-Dependent Selection
Example
• It’s subtle, but look at the mouth directions:
http://gcoe.biol.sci.kyoto-u.ac.jp/gcoe/jpn/report/TakahashiTfig1.jpg
Heterozygote Advantage Example
• Take a look at these maps and tell me if you
think it’s just a coincidence.
– (The HbS allele leads to sickle-cell anemia)
http://media-2.web.britannica.com/eb-media/84/126284-004-86317AFD.jpg
Last Thing: Clines
• This is a “kitchen-sink” type vocabulary word:
• A cline is a “gradient” of phenotypes.
– For example, suppose polar bears get thicker coats
as you go further north.
– North Pole bears would have thick blubber and
mid-range Canada bears, if any, would have thin
blubber.
– Thus, a gradient.
Closure
• I want you to remember this important phrase
in biology:
– “Form follows function.”
• This should make sense to you now:
– Evolution guides the development of the
phenotypes we see around us by selecting for
certain alleles.
– No “form” exists apart from its “function.”
– Everything either serves a purpose or did so
previously.
Closure Deux
• So why do islands have weird life forms?
– Islands often have unique selective pressures and
their small sizes lead to increased genetic drift.
– As we’ll see next unit, some islands with lower
biodiversity also have fragile ecosystems that may
not hold up well in the face of change or invasive
species.