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2. Evolution, Ecology and Behavior: Basic Transmission Genetics
Poziom:
Temat: Nauka i technologia
Prof: Okay,
I'm going to start with an
example.
Isn't that a great shot of the
baby?
I mean, the Web is so great.
You can download pictures from
the Web that just look
fantastic.
So I want to start by posing
you a problem.
Jill and John are going to have
a baby, and Jill's got blue eyes
and John's got brown eyes.
Okay?
All of the other men whom Jill
knows have blue eyes.
The baby has blue eyes.
>
Should John be worried?
John's got brown eyes,
the baby's got blue eyes,
should John be worried?
Well, we can assume that brown
eyes are dominant to blue,
which roughly speaking is
correct.
The actual situation is a bit
more complex.
In fact, if you want to write a
paper on the evolution of eye
color and the genetics of eye
color, there's a lot out there.
But this is approximately
correct.
And John comes from an island
where one percent of the people
have blue eyes.
So that, just on the face of
it, would indicate that maybe
John ought to be worried.
But in fact just exactly how
worried should he be;
just based on genetics,
not based on behavior or rumors
or anything like that?
Well we'll come back to that.
I do that at the beginning just
to point out that there are
interesting issues here,
and that they are things that
touch our daily lives.
So now I'm going to run
through, as much as I can,
genetics, in the next forty
minutes.
And please speed me up or slow
me down, as you wish,
and don't hesitate to
interrupt.
Some of this may already be
very familiar to you.
So the genetic material is
deoxyribose nucleic acid.
We have known that since 1945,
and we've known its structure
since 1953.
And this is actually an
extremely important point:
Genes are solid particles that
are transmitted from parent to
offspring.
They are not fluid.
They're actually material stuff.
Okay?
And we know exactly what it is.
They encode information,
as sequences of nucleotides,
and in the DNA it's adenine,
thymine, guanine and cytosine.
So you can think of those as
four letters.
They string into a linear chain
to form a molecule,
and these, uh,
there are two strands that are
twisted around each other to
form a double helix.
So it looks like that.
The sugar phosphate strands
form the backbone,
and then the nucleotides are
glued onto the backbone and they
form pairs;
so adenine pairs with thymine,
and guanine pairs with
cytosine.
The sugar phosphate backbone is
the same in every DNA molecule
on the planet,
and the information in the
molecule is in the sequence of
nucleotides.
You can think of that as
letters forming words.
So these are big molecules.
If you were to put all the
chromosomes in your nuclei
together,
and just for one cell,
and string them together,
one haploid copy is exactly one
meter long.
So when they say it is a
macromolecule,
it is a serious macromolecule.
It is a big thing.
So just chop this piece of
measuring tape up into 26 pieces
and you get about the size that
you've got in each of your
chromosomes.
Okay?
When I first isolated DNA from
sugarcane,
and condensed it in ethanol,
it came out,
in the ethanol mixture,
as a bunch of white,
stringy strands,
and I could wrap it around a
glass rod.
This is big stuff.
So we're not talking about
tiny, weensy,
little molecules.
DNA is a biggie,
and it's very stable.
Now, how does this relate to
organisms?
Well that's the issue of
genotypes and phenotypes,
and that's a question of
information and matter.
So there's a general principle
here that's quite intriguing and
it has to do with how you turn
information into matter.
The genotype is basically the
info in the DNA,
and every cell in your body has
got all the information in it
that is needed to build a whole
organism.
That, by the way,
is an interesting statement,
because if we can overcome some
of the genetic programming of
the oocyte,
of the egg, we could,
in principle,
simply put a cotton swab into
your cheek and take one cell off
of your cheek and then do fancy
reproductive medicine and clone
you,
off of just the DNA in a cheek
cell.
Now it turns out that the
developmental machinery in the
egg is really critical,
and it's hard to do that.
But just from the point of view
of the information,
any cell in your body could be
used to make another you.
I can pull out a hair cell,
take a cell off of the root of
the hair, do the same thing.
The phenotype--basically you
should think of that as you.
Okay?
That's the material organism.
It's built according to
genotypic instructions.
So the genotype contains
information,
the phenotype contains matter,
and the transformation from
information into matter is done
by developmental biology.
Decoding that transformation is
one of the major research
agendas for the twenty-first
century in biology.
It's called the construction of
the genotype/phenotype map.
That's kind of modern jargon
for developmental biology.
So where does the DNA actually
sit in the cell?
Well here's some more
vocabulary.
I'm building vocabulary for
those of you who haven't been in
biology recently.
I'm going to say a few words
here.
The eukaryotes,
the things that have a real
nucleus--
which includes us and all other
multi-cellular organisms,
plus a whole bunch of
single-celled ones--
they have cells that have a
nucleus and the DNA in the
nucleus is contained in
chromosomes,
and these chromosomes are a
long structure that has kind of
a central scaffold,
it's got a central mirror.
That's labeled 2 here,
on the slide.
And the DNA itself is actually
wrapped around proteins in the
chromosome.
In the prokaryotes,
which are the things that lived
on this planet for about the
first two billion years of
life--
that is, bacteria and
archaea--they are single-celled
organisms,
and their DNA is basically not
in separate chromosomes,
but all in one circular loop.
So it's a circular chromosome;
it's attached to the cell wall.
So there's a big difference in
the way that eukaryotes and
prokaryotes are organized,
and in fact the eukaryotic
nucleus is very probably the
evolutionary residue of a
prokaryote;
that's where that organelle
probably came from.
Anybody know what the other
organelles are,
that used to be independent
organisms?
Student: Mitochondrion.
Prof: A mitochondrion is
one.
Student: Chloroplast.
Prof: Chloroplast is
another.
Student: Lysosomes.
Prof: Not isotopes.
Well, maybe lysosomes.
There's a little bit better
evidence though for another one.
Spindle apparatus;
the spindle apparatus that
pulls the chromosomes apart has
a little circular genome
associated with it.
Okay, a bit more on chromosomes.
The number of chromosomes is
usually constant,
within a species,
although there is some
variation.
You get 23 from your mom and 23
from your dad.
So you've got 46 sitting in
every cell of your body,
except your red blood cells
which don't have a nucleus.
That dual set,
one from mom and one from dad,
together it's called the
diploid condition.
Okay?
So d-i--2;
from Greek, diploid.
And in contrast to that,
your eggs and your sperm are
haploid.
So the gametes are haploid.
They have one set.
Haploid means one set of
chromosomes.
So the haploid number in humans
is 23.
The diploid number is 46.
World record for a eukaryotic
minimum chromosome number is 1.
Ascaris, a nematode that lives
in the gut of dogs,
has 1 chromosome.
World record for maximum number
of chromosomes?
Actually it's probably also in
ascaris, but in the somatic
condition.
That one chromosome falls into
about 1000 pieces when it
develops.
So chromosome number varies
widely.
They've got genes and other
things in them.
You can think of a chromosome
as being about 1000 genes,
and you can think of a gene as
having several thousand
nucleotides in it.
And you can think of a gene as
being a segment of DNA that
tells a cell to make a
particular protein,
a particular structural RNA,
and through splicing and other
things there are various other
classes of RNA that are now
important;
regulatory RNAs.
You're made out of proteins and
materials whose construction is
basically governed by the
actions of proteins.
And so the DNA in your genome
is a set of instructions on how
to make what kinds of proteins
at certain places and times to
control the construction of the
organism and determine the
uniqueness of the species.
This, uh, you know,
in a few words,
describes something which is
incredibly complicated and
beautiful.
And if you think about how
complicated your eyes or your
brains or your livers or
whatever else is,
and you think about that for
all of the ten to a hundred
million species of organisms on
earth,
the amount of information
stored in the genomes of the
organisms on earth is just
absolutely astounding.
And by the way,
when one goes extinct,
it's kind of like burning the
library at Alexandria,
and we lose all of that
information.
Okay, genes are in specific
locations and they come in
different forms.
So again, this is vocabulary
building.
We call the place that a gene
is found on a chromosome its
locus;
this is in classical genetics.
And genes can be found in
different versions.
We call those different
versions alleles.
So, for example,
the gene for eye color is
either blue or brown.
Those would be the allele for
blue or the allele for brown.
If you are carrying two
different versions of the gene--
you got one from your mom and
you got one from your dad and
they're different--
then you're a heterozygote,
and we call that condition the
heterozygous condition.
If you got the same one from
both parents,
then you're a homozygote,
and we call that the homozygous
condition.
What does a gene look like?
Well there's a lot now that's
known about this,
and as a matter of fact I
encourage you to do things like
go on the Web and just type
gene structure,
and have a look at all the
diagrams that pop up.
Normally a gene has got a
codon--that is,
three nucleic acids--that say,
"This is where you're
going to start reading me
off."
And then it's got another one
down at the end that's a stop
codon, that says "That's
where you stop."
And then in between that you've
got a long string of DNA--
this is in eukaryotes,
not in prokaryotes--
a long string of DNA,
and some of it is going to end
up coding for protein and some
of it is not.
So the part that will code for
protein we call the exons;
the part that is going to be
cut out and spliced and put into
messenger RNA,
to go out and make protein.
And the part that is not we
call introns.
So not all the DNA is going to
go out and become protein.
The central dogma of molecular
biology, basically,
is that DNA makes RNA makes
protein.
And transcription is copying
the DNA into messenger RNA,
and that's done with
complementary pairing,
and in the process,
the thymine is replaced by
uracil in the messenger RNA.
The introns are cut out and
discarded.
The exons are spliced together
and the RNA is then translated
into protein in the ribosome.
There's a lot of activity here
for RNA.
RNA is doing a lot of stuff,
and in fact it's because of the
amount of engagement of RNA in
this very,
very basic process of life that
we think that RNA was probably
the original genetic molecule,
and that DNA evolved after RNA,
and then all of this process
developed after that.
The reason for that is that RNA
has a very high mutation rate;
DNA has a low mutation rate.
But RNA can be an enzyme and
DNA is not.
So RNA was a--both an
information storage molecule and
an enzyme, at the beginning,
close to the beginning,
of life, and then DNA came
along later.
So this is a picture of the
structure of genes and the
process that goes on when the
DNA is transcribed into RNA.
The RNA is spliced and
assembled into a molecule that
is then going to code for a
polypeptide;
or a big polypeptide is a
protein.
And that will then go through a
ribosome to make protein.
So the messenger RNA--and by
the way,
heh, when I was sitting in this
room in 1965,
I was taught about messenger
RNA and the faculty would laugh
and they would say,
"Nobody's ever seen
one."
That was forty years ago.
Now they are the basis of
high-tech genechips,
and people work with them all
the time.
But that's--you know--this kind
of ghost in the machine,
from forty years ago,
became very concrete by about
twenty-five years ago.
Transfer RNA is a much smaller
molecule.
Transfer RNA,
if you think of messenger RNA
as being that big,
transfer RNA is about that big.
And it is the molecule that
matches the genetic code,
that's sitting there in the
messenger RNA,
to a particular amino acid.
So you can think of--say if
this is the messenger RNA
sitting here,
the transfer RNA is coming
along and sitting down on the
messenger RNA and matching the
code on it,
and then on its other end it's
carrying--
like right here,
where I'm wiggling my finger--
it's carrying an amino acid.
And this whole process will get
fed through a ribosome,
and out at this end of it the
amino acids will get joined
together.
So the RNA will go out one part
of the ribosome,
and out of another part will
come the growing chain of the
protein.
So the transfer RNA is actually
the translation device--it is
what implements the genetic
code--which comes in units
called codons.
So it takes three nucleotides
to specify one amino acid.
And you can think of it like
this.
The DNA is a codon sequence.
It gets translated into an RNA,
and then in units of
three--okay, so in chunks of
three nucleotides,
the RNA gets translated into
protein.
Just to repeat this message,
RNA is playing a big role in
this whole process,
and there's good reason to
suspect that it was the original
genetic macromolecule.
There's an interesting
implication in this,
and I will not shy away from
telling stories like this during
the course.
Information is flowing out from
the genotype into the phenotype.
It doesn't go in the other
direction.
That's very important,
that it doesn't go in the other
direction.
Okay?
This is a re-statement of
something that August Weismann
said in the nineteenth century.
He said that there is a
distinction between the
genotype--the germline,
which is the genotype--and the
soma, which we now call the
phenotype.
And Weismann basically said in
the 1880s that information flows
from the genes out into the
organism and not back in the
other direction.
Now the implication of that is
that evolution of acquired
characteristics won't work.
In other words,
if during my lifespan I acquire
a healthy tan,
my child will not inherit it
because the information on
tanning isn't going to go back
into my genome and get
transmitted to my kids.
If I develop calluses on my
feet, they will not be
transmitted.
If a giraffe stretches its neck
on the savanna to try to get to
the top of the tree,
and thereby actually does
physically lengthen its neck by
a couple of centimeters,
that will not get transmitted
to the next generation.
Okay?
So that would be evolution of
acquired characteristics-
-characteristics acquired during
the lifetime of the parent--and
it doesn't work;
that's not how evolution works.
You're probably sitting there
wondering, well how does it
work?
Hey, that's what this course is
about;
you're going to find out,
don't worry.
Now there was a guy named
Trofim Lysenko,
who was a demagogue and a
corrupt guy;
a pretty evil man.
He claimed that evolution by
acquired characteristics would
work, and it would work very
rapidly.
This would allow crop selection
to go on in a period of one
generation,
rather than ten or a hundred
generations,
and that therefore in Russia
Stalin would be able to move
people into Siberia and into
areas where crops were not
currently grown;
and Lysenko said,
"And we can guarantee you,
scientifically,
that these crops will
work."
The science was wrong and
millions of people died,
because they starved to death.
Communist China was influenced
by Stalin,
and in fact Mao bought this
stuff for awhile and carried out
some similar policies during the
Great Leap Forward,
in the 1950s,
and millions of people starved
to death in China as well.
The Chinese found it a little
bit easier to get rid of this
incorrect, this bad science,
because after all it was a
Russian import.
Right?
So you could throw it out a bit
more easily than the Russians
could.
Lysenko, in fact,
persisted for quite a while in
Russia,
and when he was denounced by
geneticists who told--
were trying to tell Stalin that
it was bad science,
Lysenko arranged to have them
killed;
and they were killed,
they were executed.
Vavilov died in the gulag in
1943;
one of the greatest
evolutionary geneticists of the
twentieth century.
So the point of this is that
there's some important stuff
about genetics,
and it's not just abstract.
It's affected science policy,
it's affected international
relationships,
and it's affected the ability
of agricultural practices to
support human populations.
Ideas have very important
consequences,
and this is just one of the
first that you're going to run
into, in this course.
Okay, back to genetics.
Whoosh.
When the cells divide,
the DNA replicates and each
daughter cell gets a complete
copy.
This is how inheritance works.
Okay?
This is why you look like your
parents.
During replication the ends of
the DNA strand are loosened and
opened up so that in the notch
between the two strands the
nucleotides can be inserted.
And all of this is done with
complex enzymatic machinery and
it's done extremely precisely.
Only one mistake in about a
billion nucleotides occurs in
DNA.
It's almost impossible for
humans to construct a system
that has that degree of
reliability.
Obviously this precision has
been an extremely important
thing.
Natural selection has worked
very hard to get those enzymes
that precise.
When a mistake does occur,
that is one source of mutation.
And, in fact,
the more frequently DNA is
copied, the higher the mutation
rate.
So that's one place where
mutations come from.
When this is going on,
this copying is going on in the
process of the development of,
uh, a multi-cellular eukaryote,
like yourselves,
or when it's going on in an
asexual,
uh, eukaryote,
basically what happens is the
chromosomes go through the
process of mitosis.
And in mitosis what--what's
going on is that the chromosomes
will be duplicated,
they will line up at a plate,
at the center of the cell;
spindles will form.
So these are proteins,
these react in the fibrils
here,
and they are anchored to an
organizing center,
which is at the poles of the
cell, and they attach to the
centromeres of the chromosomes,
and they pull one copy into
each cell,
and then the cell splits.
So that's physically how the
copying occurs at the DNA level
and then at the chromosomal
level, in the cell.
And the picture basically is a
stained mitosis caught in an
onion root tip cell;
which is sort of the classical
place to observe this.
The important result of this is
that if you've got two genes,
A and a, that are alleles at
the same locus,
the two versions of the gene at
the same place on the
chromosome,
mitosis basically consists of a
doubling--
of first a doubling of the
chromosome,
so you have enough copies to
end up with.
They line up at the middle of
the cell,
and then the spindle apparatus
pulls one copy of the A and one
copy of the a--
in this slide they're on
different chromosomes--
into each of the daughter cells.
What about meiosis?
Meiosis is the process that
produces gametes.
So it takes the diploid parent
down into a haploid gamete.
So it's a reduction division.
The process is more
complicated, and in fact it is
like sticking two mitoses
together in a sequence,
but with a bit of additional
machinery.
So the first thing that happens
is that the chromosomes are
duplicated and they are then
actually duplicated again.
Then out of,
uh, out of the original
chromosome there are two--out of
the original cell.
You're going to go through a
process first of duplication,
another duplication,
and you're going to reduce them
each twice by going through two
mitoses in, uh,
in sequence.
And as a result of that,
each haploid gamete is getting
one original chromosome,
or the other,
but not both.
That's a cartoon of meiosis.
Meiosis is actually much more
complicated than that,
and is much more precise than
I'm able to indicate with these
kinds of stick diagrams.
But for today's purposes the
main thing to remember about it
is that meiosis takes a diploid
parent and from the diploid
parent generates haploid
gametes,
and each haploid gamete is
getting one original chromosome,
or the other,
but it doesn't get both.
There's a great paper that was
written back in 1907 by a
geneticist on this issue:
Does the behavior of
chromosomes explain Mendel's
Laws?
And it does.
So Mendel's First Law is that
if you have two alleles,
two members of a gene pair,
when they segregate into the
gametes, one goes into each
gamete;
that's Mendel's Law of
Segregation.
So half of the gametes from a
heterozygous Aa,
will carry the A allele,
and half of them will have a
little a allele.
So this is the law that allows
us to predict what the genotype
ratio should be in the
offspring,
and that allows us to notice
any deviations from that
genotype ratio.
So I'm jumping ahead a little
bit here to Punnett diagrams.
Just make a note in your head
that this fact of segregation is
the basis for our being able to
predict what the offspring will
be like if we know what the
parents are like;
at least it's part of it.
So if you have two
heterozygotes who are mating
with each other--
so the male gametes have either
A or a,
and the female gametes have
either A or a,
it is Mendel's Law of
Segregation which tells us that
we can expect those gametes to
be equally likely.
The probability is 50% in each
case.
When they then come together to
make a zygote that's going to
grow up to be the offspring,
then these--we just multiply
these probabilities together.
So .5 times .5 gives us .25,
and each of these kinds of
zygotes is equally likely;
25%.
However there was a reason that
we wrote A and a.
If A is dominant,
that is say it's brown eyes,
and a is recessive,
say it's blue eyes--and
remember our baby with
issues--then the ratio here is
3:1.
That's only true because--it's
3:1 because in these three cases
we have a A, and in this one
case we don't.
So the ratio is 3:1.
It was this observation of 3:1
ratios in the offspring of
heterozygote crosses that caused
Mendel to postulate the idea
that hey,
some genes are dominant and
some genes are recessive.
If a gene's dominant,
you can see that fact in the
phenotype;
you can see that the allele is
present in the phenotype.
If it's recessive,
you can't see the presence of
the gene in the heterozygote.
Its presence is covered up by
the dominant one.
Mendel's Second Law:
What happens when we're looking
at two genes and they're on
different chromosomes?
Well Mendel's Second Law
basically says that the events
that occur at the different
chromosomes are independent of
each other.
So genes that are sitting on
one chromosome are going to be
assorting independently to genes
that are sitting on other
chromosomes.
So in this picture you can see
that if we have Aa--and this
would be a Aa heterozygote;
this is a Bb heterozygote.
They are depicted as already
having been copied.
Okay?
So they've been duplicated so
that they can start going
through the process of meiosis.
And what's going to happen is
that we're going to pull them
apart.
We're going to make four
gametes out of each of the
chromosomes.
This combination,
where you get AB and ab,
is just as likely as this
combination, where you get Ab
and aB.
Okay?
So that's tracking what happens
when you have genes on two
different chromosomes that are
forming gametes.
That's Mendel's Second Law.
So meiosis is capable of
producing genotypes that are
different from the parental
genotype.
I'll pause for a moment
there--I'm not just going to
keep running through this
slide--
because I want to tell you that
this is the essence of sexual
reproduction.
The fact that the offspring
gene--genotypes are different
from the parental genotypes is
the essential evolutionary fact
about sex.
It can be achieved in a lot of
different ways,
but it means that sex produces
offspring that are not copies of
the parent;
they are all different from the
parent.
And there are two genetic
mechanisms that do it.
I just showed you the first one.
If you've got the genes on
different chromosomes,
they assort independently.
If they're on the same
gene--chromosome,
you can have crossing over.
Okay?
So crossing over means that
chromosome parts are exchanged
during meiosis,
and it produces new
combinations.
Like this.
It's easiest to show you just
with a diagram,
rather than with words.
So when we've made the copies
of the chromosomes and they are
lined up--
I think this is in Prophase 1,
if I've got my phases right in
meiosis--
it is possible that there will
be a break and then a rejoining
at a certain spot,
and this will be done where the
DNA sequences are very similar.
So the chromosomes can break
and be rejoined,
and the product of that is
gametes that are different.
These are recombinant gametes
generated by crossing over.
These combinations,
this kind of genetic variation,
is something that's going on in
every generation.
The estimate for the human
genome is that actually in order
to go through meiosis,
there must be a crossing-over
event,
and it is thought that every
human chromosome experiences one
crossing-over event every
generation, roughly;
probably true for most
organisms.
So these things are continually
being shuffled.
And the point of that is that
there are two mechanisms of
recombination.
Remember this.
Okay?
When we say that the genes
recombine, they do it both
because the chromosomes get
shuffled, and because there is
crossing over.
The crossing over generates new
combinations within chromosomes
and the chromosome assortment
generates new combinations
within the genome;
both things are going on.
Now mutations are also going on
in every generation,
and they produce changes in DNA
sequences.
Some of them make genes that
are functional.
Some mutated genes have
improved.
Many don't, many have worse
function.
A lot of them are neutral.
And it's mutations that occur
in the germline--that is,
in the cells that will form
eggs and sperm--that get
transmitted to offspring.
They have evolutionary
significance.
So they change the information
that's transmitted over
evolutionary time.
Mutations that occur in somatic
cells are things that lead to
cancer.
Cancer is a mutational process,
and every cancer is a little
evolutionary process that occurs
just within the lifetime of the
person who has it.
Ultimately, if you go back,
through the history of life,
mutations are where all genetic
variation came from.
So it's important to understand
basically what's going on here.
We refer, on the one hand,
to point mutations.
That's where you just change
one nucleotide,
and there's a category--there
are categories of point
mutations.
You can have substitutions,
you can have deletions,
and you can have--a deletion of
an entire codon will not cause a
change in the downstream amino
acids.
So if you take out three
nucleotides at once,
there won't be any change in
the coding for the remaining
amino acids.
But if you take out one or two,
you're shifting the reading
frame.
So if you have a deletion of
one nucleotide or two
nucleotides, it changes
everything downstream,
from that point.
So one or two deletions can
have really big effects on the
information content of the whole
genome.
We call those frameshift
mutations.
Mutations also occur at higher
levels.
You can have chromosomal
mutations where you delete
entire genes.
So if I say we delete B,
I want you to think now that
we're taking out maybe 3000
nucleotides.
The whole gene disappears;
everything from the start codon
to the stop codon.
We can duplicate a gene,
so we get two copies,
or we can invert them.
These are very important
evolutionary processes.
If you duplicate a gene,
you can use the old copy to
keep things working while you
innovate with a new copy.
So gene duplications are really
important.
Your genome has been completely
duplicated twice.
We can see that in the HOX
genes;
you'll see that in a few
lectures.
But in the course of vertebra
evolution,
once back about with the
hagfishes,
in the Agnatha,
and then once between the
Agnatha and the higher fishes,
the entire genome was
duplicated, and it is thought
that this duplication of
information may very well have
been associated with the fact
that there was radiation and a
generation of a lot of
morphological complexities,
because we had duplicated the
entire library.
You could keep one of them
going, to keep everything
running, and you could use the
other one for innovation.
So duplications are important.
Now, to get back to John,
Jill, and the baby with issues.
Remember I said that John came
from an island where the
population had a 1% gene
frequency.
Well we need to think about the
whole population then.
Now I want you to think about
an out-crossing,
sexual diploid population that
produces haploid gametes--
it could be the population of
Connecticut,
it could be the population of
New Haven,
the population of Pitcairn
Island--and focus on one gene
that occurs as two alleles.
Okay?
We'll call them A and a.
We've got Mendel's Laws going
on.
So we have random fair
assort--assortment of alleles
into gametes,
we have random fusion of
gametes into zygotes,
and we can put that into a
Punnett diagram.
So this would be for
heterozygotes,
Aa, mating with Aa.
If we look at it as a
population diagram,
then the frequencies can be
anything.
It doesn't have to be
heterozygote frequencies.
We can just say if there's
random mating of individuals in
this population;
some of them are homozygote,
some of them are heterozygotes.
We have a population of eggs
and a population of sperm,
and the frequency of A we will
call p, and the frequency of a
we'll call q.
And it's important to
remember--and this is a place
where people just getting into
it often get fouled up--p and q
can be anything between 0 and 1.
They're not 50%.
Okay?
They can be anything between 0
and 1.
These genes can occur at
arbitrary different frequencies;
in the general case.
Well p plus q has got to equal
1, because we only have two
possibilities;
and that's just the definition
of frequencies.
The frequencies of the kinds of
zygotes they will form are
p^(2), 2pq and q^(2),
and those frequencies also add
up to 1.
The assumptions behind those
statements are that meiosis is
fair--
so it's just like flipping a
coin, it's 50% probability
whether you'll get one or the
other allele in any particular
mating--
that mating is random,
that there are large
populations,
and that there's no selection
and there's no migration.
So this is kind of an ideal Gas
Law for biology,
and such laws are very useful
in physics and chemistry,
and this one is particularly
useful in evolution.
It tells us that if these
assumptions hold,
then in every generation you
can expect those proportions of
genotypes;
no mutation.
Well what does it mean?
It means that if you start in
one generation with frequencies
p and q,
and you go through that kind of
mating,
you get zygotes with these
frequencies,
and in the next generation you
get the same gamete frequencies;
nothing changes.
It's kind of funny that you
would place a lot of emphasis on
a law that says that nothing
changes.
But in fact it's extremely
important, because it means
that, at the level of a
population, genetic information
doesn't disappear.
Gene frequencies stay the same,
and that means that the
population gets replicated,
the whole population gets
replicated.
That allows information to
accumulate.
If this were not true,
then the information that had
been accumulated would get
eroded by just the basic process
of genetics.
It turns out that genetics and
random mating,
and, uh, the whole structure of
the Hardy-Weinberg assumptions,
is set up in such a way that
information is preserved at the
level of the population.
That makes evolution possible.
If we didn't have that
retention of information,
then you couldn't tweak it;
it would get eroded by
processes other than natural
selection.
So it's kind of an inheritance
mechanism at the whole
population level.
And, by the way,
it minimizes conflicts among
genes about who gets into the
next generation.
And genetic conflict will be
something that we examine in
more detail later on;
particularly interesting in the
context of evolutionary medicine
and reproductive biology.
Okay, let's go back to our
problem.
Jill and John have this baby,
and the baby is at issue.
So Jill's got--Jill is a--I'm
now going to use the words,
to drive them home--Jill is a
recessive homozygote.
She's got two copies of a.
John could be either a dominant
homozygote, or he could be a
heterozygote;
he's got brown eyes.
The baby's got blue eyes,
and is a recessive homozygote.
Should John be worried?
Well here's the hint.
This is the one new piece of
information I'm going to give
you.
We're going to assume that
John's genotype is a random
sample of those on the island,
and therefore that
q^(2)--that's the frequency of
aa-- is 0.01.
So if q^(2) is 0.01,
what is q?
.1.
Right; 10% probability.
What's the probability that
John is a heterozygote?
This requires having picked up
information very rapidly.
It's 2pq.
Okay?
Those are the heterozygotes.
The probability that John is a
dominant homozygote is p^(2);
p is .9;
p^(2) is .81;
81% probability that John is a
homozygote.
Should John be worried;
I mean, just on genetic
grounds, heh?
The only way that that baby
could be John's child is if he
is a heterozygote.
2pq is 18%;
p^(2) is 81%.
Okay?
So I did that just to give you
a problem that has a little bit
of human content to it,
that is answered by genetics
and by the concepts that we were
playing with today.
Yes?
Student: The 81%,
does that just mean it's not,
there's no way,
or there's a high probability
that there's no way?
Prof: Well if he,
in fact, is a homozygote,
there is no way that that child
is his, unless he--no,
there is a way.
He could've had a mutation in
the gene that turned it from a
brown into a blue gene,
and that could've found its way
into the sperm that fathered the
child;
and the probability of that
happening is about 10^(-9).
Okay.
See if you can explain that.
Take--print this list out.
Sit down at lunch with a
colleague from class and see
what you can't explain.
Take that term into section and
get it explained.
Okay?
Next time, Adaptive Evolution.
