Prof: Today we're going
to talk about Adaptive Genetic
Change.
 
And in order to set the stage
for this, before I get into the
slides, I would like you to
consider the following
proposition.
 
Every evolutionary change on
the planet,
that has ever led to something
that you think is cool and
interesting and is well
designed,
whether it is the brain of a
bat, or the vertebrate immune
system,
or the beautiful structure of
the ribosome,
or the precision of meiosis,
has occurred through a process
of adaptive genetic change.
A mutation has occurred that
had an effect on a process or a
structure and,
if it increased the
reproductive success of the
organism that it was in,
it was retained by evolution;
and if it did not,
it disappeared.
 
So what we're talking about
today is a look into a very
basic mechanism that is
operating in all of life and is
causing the accumulation of
information.
Now, these are the keys to the
lecture.
In the middle of the lecture
you're going to get a couple of
slides that have tables and
equations on them and stuff like
that,
and I'll lead you through one
of those tables,
and I'll ask you to go through
another one.
 
But they're not the point.
 
The point is this.
 
There are four major genetic
systems, and there are some
interesting exceptions to them.
 
But you can capture a big chunk
of the variation in the genetics
of the organisms on the planet
with just four systems.
Okay?
 
They are sexual versus asexual
and haploid versus diploid,
and those differences make a
big difference to how fast
evolution occurs.
 
You guys are sexual diploids
and you evolve slowly,
and your pathogens are asexual
haploids and they evolve fast.
That's important,
the kind of thing you ought to
know.
 
Now when we get into the
equations of population
genetics--
they're just algebra--the point
is that you can always go find
them in a book and you can
program them pretty easily,
even in simple spreadsheet
programs like Excel,
and you can understand their
basic properties by playing
around with them.
If you go on the web and go to
Google and type Hardy-Weinberg
equations,
you're going to get 20 websites
around the country where some
professor of population genetics
has put up some package for
students to play with and it's
going to generate all kinds of
beautiful pictures and stuff
like that.
 
It's real easy for you to lay
your hands on these tools now.
What's important for you to
know is (a) that they are there
and represent something
important;
(b) what their major
consequences are;
and (c) how to get a hold of
them when you need them.
I am not going to ask you to
repeat the derivation of the
Hardy-Weinberg equations on a
mid-term.
Okay?
 
But I do expect you to know why
they're important and what
they're about.
 
The third thing that I want you
to take home from this lecture
is that when adaptive genetic
change starts to occur,
it is virtually always slow at
the beginning,
fast in the middle and slow at
the end.
So that if you are looking at a
graph of gene frequencies over
time, it looks like an S;
and that's the third thing.
That's it, there's the lecture,
ta-da.
Now background to this decision.
 
When, in 1993,
Rolf Hoekstra and I began to
put together the first edition
of this book,
I asked Rolf to be my co-author
because he is a population
geneticist.
 
He has a marvelously clear mind.
 
He likes those kinds of
equations and he's really good
at them.
 
And we, Rolf and I,
went around and we asked about
fifteen of the leading
evolutionary biologists in the
world, "What's important?
 
What should every biologist
know about evolution?
This is for everybody.
 
This is for doctors and
molecular biologists and
developmental biologists,
everybody.
What should they know?"
 
And I said, "Rolf,
your job is to figure out the
part from population
genetics."
And he came back,
after about two weeks,
and he said,
"You know Steve,
I don't think there is
anything."
I was shocked.
 
I said, "Rolf,
you're a population geneticist.
This stuff is important,
right?"
And then he said,
"You know,
the way we normally teach
population genetics,
which is as a big bunch of
equations that are about drift
and frequency change under
selection and so forth,
most people end up not really
needing that.
What they need to know is that
there are four main genetic
systems and that genetic change
is slow, fast,
slow."
 
So that's where this lecture
came from.
It came from somebody thinking
deeply about that,
and asking lots of people.
 
Now if you like this,
there's a whole field there,
there's a whole bunch of
wonderful stuff that you can do.
But these are the things that
everybody I think should know.
So here's the outline.
 
I'm going to give you the
context, the historical context
that led to the concentration on
genetics in evolutionary
biology.
 
I'll talk a little about the
main genetic systems.
Then I'll run through changes
in gene frequencies under
selection and,
if I have time,
I'll get to selection on
quantitative traits.
If I don't get to selection on
quantitative traits,
it will be because I have
engaged in a dialog with you
about some interesting puzzles,
and that dialog is more
important to me than getting to
quantitative genetics.
Okay?
 
So here's how genetics became a
key element in evolutionary
thought.
 
Darwin did not have a plausible
genetic mechanism and he failed
to read Mendel's paper,
which came out six years after
he wrote The Origin,
but before he constructed some
of the later editions of his
book,
and so he reacted by
incorporating elements of
Lamarck into his later editions.
 
If you read the Sixth Edition
of The Origin of Species,
it's got some really Lamarckian
statements in it,
inheritance of acquired
characteristics.
Anybody here know what the
problem was with Darwin's
original model?
 
Anybody know how Darwin thought
genetics worked in 1859?
He had a model of blending
inheritance.
That meant that he thought that
when the gametes were formed,
gemmules from all over the
body, that had been out there
soaking up information about the
environment,
swam down into the gametes,
into the gonads,
carrying with them information
about the environment into the
gametes,
and that then when the zygote
was formed,
that the information from the
mother and the information from
the father blended together like
two liquids.
 
In other words,
he didn't think of genes as
distinct material particles.
 
He thought of them as fluids.
 
Now if I give you a glass of
red wine and a glass of white
wine, and I pour them together,
I get pink wine.
And if I take that glass of
pink wine and I pour it together
with another glass of white
wine, I get even lighter pink.
And you can see that if I
continue this,
pretty soon red disappears
completely.
The problem with blending
inheritance is that the parental
condition gets blended out and
there isn't really a
preservation of information.
 
That's why Darwin came under
attack.
And Mendel wasn't known,
and he resorted to
Lamarckianism,
and he was wrong.
So genetics became an issue.
 
In the year 1900 there was a
simultaneous rediscovery of
Mendel's Laws,
and at that point people went
back and they read Mendel's
paper,
and they realized that they had
missed this 35 years earlier.
Then the so-called 'fly group'
of Thomas Hunt Morgan and
Sturtevant and Bridges,
who were working at Cal-Tech,
demonstrated that genes are
carried on chromosomes.
And enough then was known about
cytology,
so that we knew that
chromosomes had an elaborate
kind of behavior,
at mitosis and meiosis,
and people then,
about 1915, showed that in fact
the behavior of chromosomes was
consistent with Mendel's Laws.
They didn't know at that point
what chromosomes were made out
of.
 
They had no notion of the
genetic code,
but they could establish
experimentally that genes were
on chromosomes;
and that was done by 1915.
However, there were still
issues about whether all of this
would actually work at the
population level.
It was not immediately clear
that you could take Mendelian
genetics and then construct
populations out of it,
that obeyed Mendel's Laws,
and have natural selection
work.
 
To do that actually required a
fair amount of math,
and the people who did it were
Ronald Fisher,
J.B.S. Haldane and Sewall
Wright, and they did it between
about 1918 and 1932.
 
In so doing,
they also invented much of what
is now regarded as basic
statistics.
So Fisher had to invent
analysis of variance in order to
understand quantitative
genetics,
and Wright had to invent path
coefficients in order to
understand how pedigrees
translate into patterns of
inheritance.
 
So these guys laid the
foundations.
As a result of that,
genetics really became regarded
as kind of the core of
evolutionary biology during the
twentieth century,
and there's been a tremendous
concentration on it.
 
And it is still true that many
people will not accept a claim
about any evolutionary process
unless it can be shown to be
consistent with genetics.
 
That's sort of a Gold Standard.
 
If you can't do it genetically,
if you can demonstrate it's
genetically illogical,
then a claim just falls
theoretically;
you don't even have to go out
and get the data.
 
Therefore, of course,
the Young Turks have great joy
in discovering cases that don't
fit and come up with epigenetics
and lots of stuff like that.
 
At any rate,
that's ahead of you;
that's not today.
 
The genetic system of a species
is really the basic determinant
of its rate of change.
 
So we have sexual versus
asexual species--there are
complications to this--and we
have haploid versus diploid,
and there are other ploidy
levels.
Can anybody name me asexual
vertebrates;
not sexual vertebrates but
asexual vertebrates?
Anybody ever heard of an
asexual vertebrate?
Fish, amphibians,
reptiles, birds,
mammals?
 
Student:  Wasn't there a
recent documentation of a shark?
You mentioned it.
 
Prof: I could imagine
that a shark might be capable of
being asexual.
 
I haven't heard of that case.
 
Student:  I think it was
kind of a
>
 
Prof: Yes,
there are some.
There are some asexual lizards.
 
There are some interestingly
asexual fish.
There are some frogs that
manage to be kind of
quasi-asexual by using male
sperm but then not incorporating
it into gametes--
excuse me, in the developing
baby.
 
So they use it just to
stimulate development.
There's one case in captivity
of an asexual turkey.
But asexual types are not
frequent among vertebrates.
They are common in plants.
 
Of course, most bacterial sex
is asexual, although bacteria do
have a bit of sex.
 
You're diploid;
your adult large form is
diploid.
 
Anybody know what group of
plants is haploid in the state
in which you normally see them
in nature, where the big
recognizable thing is haploid?
 
I'll show you one in a minute.
 
I just wanted to check.
 
Mosses;
mosses are haploid.
Okay, so this is what's going
on with these four systems.
Basically the difference
between sexual haploids and
sexual diploids is the point in
the lifecycle where meiosis
occurs.
 
If the adult is diploid and
meiosis occurs in gonads in the
adults that produce gametes,
and then the zygote form
develops so that all of the
cells in the developing organism
are diploid,
you get the diploid cycle.
If you have the zygote having
meiosis immediately,
or shortly after being formed,
so that the developing young
are haploid,
then you get a haploid adult.
So this is what moss do and
this is what we do.
Then we have asexual haploids
and asexual diploids,
and at least in outline they
look pretty simple.
Asexual diploid,
just makes a copy of itself;
just goes through mitosis,
makes babies.
Asexual haploid,
same kind of thing.
So those are the four major
genetic systems.
There are many,
many variations on them.
So the asexual haploids are
things like the tuberculosis
pathogen,
blue-green algae,
the bread mould,
the penicillin fungus,
cellular slime moulds,
and they constitute the bulk of
the organisms on the planet.
 
Sexual haploids are things like
moss, and red algae;
most fungi are sexual haploids.
 
In this case you can see that's
where the haploid adult is in
the lifecycle.
 
There are where the gametes are
formed.
They are formed up on the head
of the adult.
You can see the pink and the
blue are coding for the male and
the female gametes,
on different parts of the
gametophyte.
 
Then the zygote forms where the
sperm gets into an ovule,
on the tip of the plant,
and then the young actually
develop up here.
 
So this is haploid up here and
then the spores go out--meiosis
has occurred in here and the
spores go out as haploid spores.
So that is a sexual haploid
lifecycle.
The asexual diploids include
the dynoflagelates;
there are about ten groups of
the protoctists--
that's the modern name for what
you think of as protozoa,
but it also includes some
single-celled organisms that
have chloroplasts in them--
the unicellular algae,
some protozoa,
some unicellular fungi.
There are a lot of
multi-cellular animals that are
asexual diploids,
and this one here,
the bdelloid rotifer is one of
them.
It is called a scandalous
ancient asexual.
Anybody know why the word
'scandalous' is used in this
context?
 
Yes?
 
What?
 
Student:  No males.
 
Prof: There are no males;
bdelloid rotifers do not have
any males, nobody's ever seen a
male bdelloid rotifer.
But that's not the scandal;
I mean, if you're a male you
might think it was scandalous.
 
Right?
 
>
 
But for an evolutionary
biologist, no,
that's not scandalous.
 
Well it actually has to do with
this part of it right here.
Almost all asexual organisms on
the planet,
that are
multi-cellular--leaving out the
bacteria--
but all the multi-cellular ones
are derived from sexual
ancestors and originated
relatively recently,
with a few exceptions,
and this is one of the
exceptions.
There is a whole huge body of
literature on the evolution of
sex that says one of the things
that sex is good for is that it
allows long persistence.
 
We see that sexual things have
been in a sexual state on the
Tree of Life for a long time,
and the asexual things have
branched off of it,
and we don't see very many
ancient ones.
 
The reason for that--we'll come
to that,
when we get to the evolution of
sex--
is that both because of
mutations and because of
pathogens,
sex repairs damage and defends
the organism against attack.
 
So this is a low maintenance,
poorly defended organism,
and it looks like it's been
around without sex for perhaps
300 million years.
 
The scandal is we don't know
how it did it.
Okay?
 
That's why it's called a
scandalous ancient asexual.
Yes, that's a very intellectual
definition of scandal;
I agree.
 
Okay, sexual diploids.
 
You guys are sexual diploids,
this bee is a sexual diploid,
and that flower is a sexual
diploid.
They have this kind of
lifecycle, as is sketched here,
the one that I talked about
earlier.
So about twenty animal phyla
are sexual diploids.
Many plants,
most multi-cellular plants are,
and there are some algae
protozoa and fungi that are
sexual diploids.
 
They include the malaria and
sleeping sickness pathogens.
There are some things that
don't fit;
the sexual diploid part doesn't
fit, for malaria and sleeping
sickness.
 
The things that are alternating
between being haploid and
diploid,
with neither one dominating,
are mushrooms,
microsporidian parasites,
which are things that are
actually quite common in many
insects,
and the malaria--malaria has a
very complex lifecycle.
 
So it is haploid inside your
red blood cells,
it's diploid at a certain point
in a mosquito,
and it's moving back and forth.
 
The things that alternate
sexual and asexual reproduction:
there are some rotifers,
some cnidarians,
some water fleas,
some annelids.
There's a great little annelid
that lives in the bottom of the
Harbor of Naples in Italy,
and it actually does
everything.
 
It can be asexual--the same
species--it can be asexual;
it can be born as a female and
turn into a male;
it can be born as a male and
turn into a female;
and it can be born as both and
do both.
So some things are really
flexible, but most things
aren't.
 
And the timing of sexuality and
asexuality is an important part
of the lifecycle of all of these
things.
Last fall, for example,
there were huge jellyfish
blooms over much of the world's
oceans,
and that's part of a complex
lifecycle in which there is an
asexual phase on the floor of
the ocean,
that builds up what looks like
a stack of dinner plates,
and then the top plate flips
off and turns into a jellyfish.
It goes off as a jellyfish and
has sex and makes larvae,
and then goes down and turns
into an asexual thing on the
bottom that makes stacks of
dinner plates.
So there's a lot of variety out
there.
All of these things probably
evolved from an asexual haploid;
and we say that because we
believe that the bacterial state
was the ancestral condition.
 
Okay, now genetics constrains
evolution,
and genetics is doing something
to evolutionary thought which is
about what chemistry does to
metabolism and structure,
and is about what physics does
to chemistry.
Okay?
 
There's a broad analogy there.
 
If you want to understand
molecular and cell biology,
you learn a lot of chemistry.
 
If you want to understand some
evolution, then you need to
learn a little bit about how
genetics constrains evolution,
and so you need a little math.
 
So I'm going to give you some
simple math, and here's some
terminology to soak up.
 
So we're going to represent
these ideas by symbols.
We're going to call alleles Aa.
 
So those are two alleles at one
locus;
a little exercise of genetic
terminology.
We're going to let p be the
frequency of A1,
and q the frequency of A2.
 
And frequency just means the
following: some traits are
Mendelian, which means that
they're easily recognized in the
phenotype.
 
One of the Mendelian traits in
humans is the ability to curl
your tongue.
 
I am a tongue curler.
 
Okay?
 
How many of you can curl your
tongues?
Okay, let's say it's about 45.
 
How many of you cannot curl
your tongues?
Let's say it's about 30.
 
So the frequency of tongue
curling is going to be--I'm just
making up the numbers,
right?--45 divided by 75.
That's how we get the number.
 
And by the way,
the frequency of the other one
is going to be 1 minus that
frequency, because p plus q is
equal to 1;
and we'll let s be the
selection coefficient,
which is measuring the
reproductive success of the
organism carrying this trait,
the difference that it makes.
 
And if we look at the genetic
change in asexual haploids,
basically what one does is make
a table of the process;
and it is moving from young,
in the present generation,
through the adult stage,
to young in the next
generation.
 
So we try to go through one
generation.
This is an active Cartesian
reduction.
We're taking a complex process
and breaking it down into the
parts that are essential for the
thing that we're thinking about.
We have genotype
frequencies--for genotypes A1
and A2 they're p and q--and we
have relative fitnesses up here.
The only place that selection
is making any difference,
on this whole page that's in
front of you,
is right here.
 
And basically what--our placing
that there is an act that means
the following.
 
We are only going to think
about the case in which there is
some difference in the juvenile
survival of A2;
it's different from A1.
 
If it makes it to adulthood,
there's no difference;
we don't put that down in the
table.
So this is a case where we're
just--you know,
it's a special case--we're just
looking at the juvenile survival
difference between A1 and A2.
 
What happens?
 
Well it changes the frequencies
of A1 and A2 in the adults.
Basically it changes them by
reducing the number of A2s.
Some of them have died out;
that's 1 minus s,
that's what the 1 minus s is
doing.
You can take these expressions
here and you can simplify them
so they look like this--
it's just a little bit of
algebra--and because these are
the frequencies in the adults,
the young in the next
generation have exactly those
frequencies,
because there is no selective
difference in the adult stage.
 
Okay?
 
That's what that table means.
 
Now a little bit about this.
 
This little process that I've
gone through,
which probably looks like
remarkably simplistic
bookkeeping to you,
is actually the part of doing
applied mathematics which is the
most difficult.
It is the translation of a
process into something
analytically simple,
that you can deal with.
In the act of doing it,
you make certain assumptions to
simplify the situation,
and by writing them down it
helps you to remember what
assumptions you made and what
thing you're actually looking
at.
We're not looking at all of
evolution here,
we're looking at a very special
case;
we're looking at asexual
haploids where selective
differences only occur in
juveniles.
What happens is you get a
change in the gene frequencies
of the adults that result from
that process,
and then that exact change is
passed on to the next
generation.
 
So that's the part of this
process that I want you to
remember.
 
You can go look this stuff up
any time.
You don't need to memorize that.
 
You can program this as
recursion equations and apply
them repeatedly.
 
Okay?
 
Now let's do it for sexual
diploids.
In the sexual diploids,
you've already been exposed to
the Hardy-Weinberg Law,
this p^(2) 2pq q^(2) law.
In order to get it,
we have to assume random mating
in a big population.
 
The reason you need the big
population is so that those p's
and q's are actually accurate
measures.
In a small population they're
noisy, but in a big population
they are good stable estimates.
 
And if there's random mating,
that means that matings are
occurring in proportion to the
frequency of each type.
So you get a Punnet diagram
like this.
You have the probability of one
of these alleles occurring;
and one parent is going to p,
the other allele in that parent
q.
 
Same for the other parent.
 
These are the possible zygotes
that will result from that.
This one has probability p^(2;
)this one has probability q^(2);
and these two together have
probability 2pq.
That's just simple basic
probability theory.
Now, the important thing about
the Hardy-Weinberg Law is that
it implies that there's no
change from one generation to
the next.
 
The gene frequencies under
Hardy-Weinberg don't change.
That means that the information
that's been accumulated on what
works in the population doesn't
change for random reasons.
If it's going to change,
it's going to change because
that big population is going to
come under selection.
Okay?
 
That means that replication is
accurate and fair,
at the level of the population,
just as it is at the level of
the cell.
 
Now, of course,
gene drift is going on,
but we're not so worried here
about gene drift,
because gene drift is affecting
things that aren't making a
difference to selection,
and we're building models of
selection.
 
What Hardy-Weinberg does is
tell you if there isn't any
drift,
if there isn't any mutation,
if there isn't any selection,
if there isn't any migration in
the population,
and if you don't have a high
mutation rate,
things are going to stay the
same.
 
So if they're changing,
one of those things is making a
difference.
 
Okay?
 
And that gives us a baseline.
 
So it gives us a baseline to
see the process of selection
occurring,
but it also means that random
mating in large populations
preserves information on what
worked in the past.
 
So you don't have to invent
everything all over again.
And a note for future lectures,
these are also the conditions
that remove conflict by
guaranteeing fairness.
So basically the Hardy-Weinberg
situation is one in which
everything that was in the
population last generation has
exactly the same chance of
getting into the next
generation,
in proportion to its frequency;
nothing is going to change.
 
Okay, here's a genetic
counseling problem,
and I'm going to take a little
time on this.
We go back to John and Jill.
 
They've fallen in love,
they want to get married,
but they're worried.
 
John's brother died of a
genetic disease,
and that is a nasty one.
 
It's recessive,
it's lethal,
it kills anybody that carries
it before they can reproduce.
That's fact one.
 
Jill doesn't have any special
history of this disease in her
family,
but that history's not well
known, and so we estimate the
probability that Jill carries
the disease from the frequency
of deaths in the general
population,
and that frequency is 1%;
to make it easier for you to
calculate.
Okay?
 
What's the probability that
they will have a child that dies
from this disease in childhood?
 
The probability is .03.
 
Your problem is not to tell me
.03, your problem is to tell me
why did I use that equation?
 
Okay?
 
So take a look at that equation
for a minute,
take a look at that problem,
and let's go through and pull
it apart.
 
Can anybody see why either the
two-thirds or the one-quarter is
in the equation?
 
Student:  We know that
his brother has a recessive
version of the lethal gene,
and therefore John is either
heterozygous-- doesn't look like
it's dominant,
looks like it's recessive.
 
So if he is heterozygous or
homozygous recessive,
then he's carrying the gene;
which is what we're worried
about.
 
So there's a two-thirds chance
that he is either carrying it or
actually has the disease.
 
Prof: That's correct.
 
The only slip you made in
expressing that is that we know
that if they are going to have a
child that has the defect,
they both must be heterozygous,
and so we're concentrating
specifically on what's the
probability that they're
heterozygous.
 
You then gave me that
probability.
Does anybody have a problem
seeing why the probability that
John is a heterozygote is
two-thirds, rather than 50%;
excuse me, that the baby is a
heterozygote is two-thirds?
Yes?
 
Student: So we're going
to keep him as a
>.
 
Prof: Yes, you do.
 
Okay.
 
This is for the baby.
 
Okay?
 
If John is a heterozygote and
if Jill is a heterozygote,
they can have either a
homozygous recessive,
and that one will die before
birth;
they can have a homozygous
dominant, perfectly healthy;
or they can have a heterozygote.
 
The probability of the
homozygote recessive is 25%,
the probability of the
homozygous dominant is 25%,
and the probability of the
heterozygote is 50%.
But, the probability that John
and Jill will have a baby that
dies from this disease in
childhood is going to be
therefore this one-quarter.
 
This two-thirds is going to be
the probability that John is a
heterozygote.
 
How do we know that
John--John's parents were both
heterozygotes?
 
Student:  They had a
recessive son.
Prof: They had a
recessive son.
John's parents had to be
heterozygotes.
Therefore, given that John's
parents were heterozygotes,
his probability is two-thirds.
 
We know he survived to
adulthood;
the other 25% died.
 
So of those who survived to
adulthood, two-thirds are
heterozygotes and one-third are
homozygotes.
Student:  Why can't one
be homozygote recessive and the
other one be heterozygous?
 
>.
 
Prof: Because if one,
the parent--if one parent was a
homozygote,
it could only have been
homozygous dominant,
because it survived to
adulthood, to have a child.
 
And if the other parent was a
heterozygote,
the only possibilities for the
children are both heterozygotes;
and that wasn't the case,
because John's brother died.
Okay?
 
So this is the probability that
John is a heterozygote.
This is the probability that if
John and Jill have a baby,
it will have the problem.
 
What's this thing in the
middle--2 times 0.9 times 0.1?
Student:
>
Prof: Right.
 
That's the probability that
Jill is a heterozygote,
and we get that from here.
 
The square root of 1% is .1.
 
1 minus .1 is .9.
 
This is q and this is p and
this is 2pq.
Okay?
 
Where did we get this from?
 
That's in Jill's part of the
population.
Those are the baby--oh you've
got it.
Student:  The
probability has to be out of the
entire population,
and the long-term population,
they can't reproduce--
>.
Prof: Right.
 
So we have to correct the
percentages for the ones that
have died.
 
Yes, you got it.
 
Do you see how much goes into
dissecting an equation like
that?
 
But because we've set up the
logical apparatus,
we can go through a sequence of
steps and say,
"Okay, first we know they
both have to be heterozygous.
Then, if they are both
heterozygous,
the probability that Jack is,
is two-thirds;
the probability that Jill is,
is 2pq, corrected for the fact
that 1% have died.
 
She has survived,
so we have to correct for that.
Then this is the probability
that their baby has the
disease."
 
That's the kind of process that
one goes through when thinking
about population genetics.
 
This is the table for sexual
diploids that reflects this kind
of thinking.
 
It is more complicated because
now we have to keep track of
both the haploid and the diploid
condition.
So we have these haploid
gametes, with frequencies p and
q.
 
We have the diploid zygotes.
 
Then another process comes in.
 
We can have a selective
difference--I made a S here;
I made a -S in the last one.
 
I made that change
deliberately,
just so that you'd see it as
arbitrary;
because we can make S negative
or positive itself.
Right?
 
S doesn't have to be a positive
number;
neither does H.
 
Anybody have an idea what H
might be in there for?
It's in there to represent
something that's going on in
genetics.
 
Yes?
 
Student:  Is it
heritability?
Prof: No it's not
heritability,
in this context.
 
Okay?
 
Yes?
 
Student:  Is it the
Marsh's coefficient for being
heterozygous?
 
>
 
Prof: Not in this
context.
Good idea, but no.
 
What is it about that
heterozygote that doesn't
necessarily have anything to do
with selection?
H expresses dominance.
 
It expresses the degree to
which A1 is covering up A2 in
the phenotype.
 
Dominance itself is not
something that's always there.
If there isn't any dominance,
then the heterozygote is just
exactly halfway in the phenotype
between the two homozygotes.
So H is a little mathematical
symbol that allows us to deal
with situations in which either
there's a lot of dominance or
none at all.
 
If H = 0, there's no dominance.
 
Okay?
 
No excuse me,
the way it's set up,
if H = 0, then A1,
A2 is just exactly like A1,
A1, and there is dominance.
 
So we have to make H something
non-zero, in order to express
deviations from dominance,
the way this one is set up.
At any rate,
the--what's going on here is
essentially the same kind of
selection process.
There is a selective
difference, which is
disadvantaging A2.
 
So A2 doesn't survive as well
as A1.
When it is in the heterozygous
form, it may do better,
if there's some dominance.
 
And that results in a more
complicated set of equations.
W here is defined as this big
term.
We have basically the adults
being p^(2), 2 pq times 1 plus
hs.
 
And A2, A2 has a frequency of
q^(2) times 1 plus s,
which is the selection
coefficient over here.
So q is changing the most,
and to the degree that A2 can
be seen in the heterozygote,
it will also be affected by s,
but it won't be affected if
there is complete dominance.
Okay?
 
So if h is zero,
there's no effect of selection
on the heterozygote;
this term cancels out.
The result of that is that you
get these frequencies forming
the next generations.
 
Now there a couple of ways of
setting up this whole
derivation,
and in the Second Edition of
the book,
Box 4.1 and Box 4.2 do it a
little bit differently.
 
You might want to just step
through those things in section.
The goal here is not to
memorize how to derive the
equations, or to memorize the
equations.
Because, as I've said,
you can always pick them up in
a book, or pull them off the
web, and you can find programs
that will do it all the time.
 
The goal is to understand what
it is that population
geneticists are thinking about
when they set it up this way,
and what power it gives them.
 
So let me just show you what
happens when you program these
recursion equations.
 
By the way, they're called
recursion equations because they
give us the frequency in the
next generation as a function of
the frequency in this
generation.
So they form kind of a Markov
chain.
They allow us to calculate next
time from this time;
that's something computers are
really good at.
So this is the take-home
message of all that analysis:
you look at genetic change,
in asexual haploids,
sexual diploids,
and it's slow at the beginning,
fast in the middle;
it's slow at the end.
The haploids change faster than
the diploids,
and the dominants change faster
than the recessives.
So let's step through that and
see if you can tell me why this
is the case.
 
First let's take the asexual
haploids, or haploids of any
kind.
 
Why is it that haploids change
gene frequencies faster,
for given selection pressures,
than do diploids?
Yes?
 
Student: The entire
gene--all the genes are
inherited.
 
It's not all
>;
it's sort of a complete
replication of them,
the order.
 
Prof: Well that is what
a haploid is,
but that doesn't explain why
it's faster.
The statement is true,
but it's not an answer to my
question.
 
Another try.
 
Yes?
 
Student:  Well all the
>
, the bad genes die off.
 
>
 
Prof: Okay,
that's going in the right
direction, but I think it can be
expressed even more clearly.
Yes?
 
Student: 
>
Prof: That's interesting.
 
That actually gets into the
evolution of sex.
I'm actually thinking though
about an answer that has more to
do with developmental biology
and not so much to do with sex,
at this point.
 
Um, actually I think that,
uh, your answer is partially
correct, but it's more
complicated than what I was
looking for.
 
>
 
Yes?
 
Student:  Is it that all
asexuals can reproduce?
Prof: No,
it's not that all of the
asexuals can reproduce.
 
Many of them die as juveniles.
 
It has to do with haploidy
versus diploidy.
Yes?
 
Student:  Then if the
organism has the allele that's
different, it's going to best.
 
Prof: Yes.
 
Student: And that's when
this other comes along.
Prof: Every gene is
expressed, and there's no
dominance covering up any hidden
genetic information.
The genes are exposed to
selection, in haploids.
Yes?
 
Student:  So why is that
faster than a dominant zygote,
>?
 
Prof: Good.
 
We'll find out as we go through
the next questions.
Okay?
 
So the haploids are faster than
a dominant diploid because--?
Student:
>.
That's why it's a recessive
gene.
Prof: Basically, yes.
 
The heterozygotes react like
the dominant,
but contain the recessive.
 
And so if you're measuring the
rate of evolution as the rate at
which the dominant takes over
the population,
it's carrying along in the
heterozygotes a bunch of
recessives.
 
Okay?
 
They're doing just as well as
it is.
So development,
which is covering up the
difference between the two,
is actually giving the
recessives an advantage and
slowing down the rate at which
the dominant can take over.
 
Okay?
 
Recessive diploid;
I think that you now see why
that would be the slowest.
 
If we have an advantageous
recessive gene,
it gets slowed down by the fact
that when it's in the
heterozygote,
its effects are being covered
up by the other allele.
 
Okay, why is it S-shaped?
 
Why is the trait--let's do it
for a dominant diploid sexual.
Okay?
 
Slow at the beginning,
fast in the middle,
really slow at the end.
 
Let's concentrate on first why
this is really slow at the end,
and then we can also look at
why a recessive diploid sexual
is really slow at the beginning.
 
What do you have to think about
in order to pull the answer out
of that diagram?
 
What proportion of the
population is in heterozygous
form, as you get near the end?
 
If you're a dominant diploid
sexual and you're at a frequency
of .9,81% of you are going to be
dominant homozygotes;
18% of you are going to be
heterozygotes;
and 1% of you are going to be
recessive.
There are eighteen times as
many heterozygotes as there are
recessive homozygotes.
 
Selection, at that point,
is trying to eliminate that 1%
of recessive homozygotes.
 
It can't touch the 18%.
 
If you carry that process over,
where we're dealing with .01
and .99, it gets even more
extreme.
A tinier and tinier fraction of
that population is a recessive
homozygote.
 
A larger and larger fraction of
the remaining recessive alleles
are tied up in heterozygotes,
where selection can't operate.
So this thing just slows way
down.
It gets harder and harder to
get rid of the disadvantageous
alleles,
because a larger and larger
proportion of them--
not an absolute number but a
larger proportion of them--
are hidden in the heterozygotes.
The same thinking describes why
evolutionary change in a
recessive diploid,
where the recessive gene has
the advantage,
is very slow at the beginning.
If a new recessive mutation
comes into the population,
it's a very low frequency.
 
Its frequency is 1 divided by
the number of individuals in the
population.
 
The only things it can mate
with are dominant forms.
All of its babies are
heterozygotes.
So at the beginning selection
can't operate on it at all.
Only after two heterozygotes
manage to get together and mate,
which means they must have come
to fairly high frequency,
will they have a baby that is a
recessive homozygote that
selection will operate on.
 
So it takes awhile to get this
going.
And because of dominance,
it takes a long time to build
up to the point where it
accelerates.
But then at the end it's fast,
because at the end the thing
that's being selected is the
recessive, and it speeds up as
it goes through.
 
Okay, I thought this would
happen,
uh, it's time for class to end,
and I'm just getting to
quantitative genetics,
and so I'm going to let you
pick up quantitative genetics
from the lecture notes and from
the reading.
 
I do want to indicate as
potential paper topics though
that quantitative genetics has
got some of the most interesting
questions that we encounter in
evolutionary biology,
and that it includes questions
like the heritability of
intelligence,
the heritability of SAT
scores--those are all things
where the apparatus you need to
analyze the issue is given to
you by quantitative genetics.
And there is a good paper on
this, and I have put it up on
the course website,
under Recommended Readings;
there's now a folder called
Recommended Readings,
PDFs of Recommended Readings.
 
You can find this paper and
some other ones in there,
if that's something that
strikes your fancy.
Go take a look at the title and
abstract.
So this is the summary of
today's lecture.
And the next time we're going
to talk about the origin and the
maintenance of genetic
variation.
