Inverse trig functions: arcsin

WEBVTT
Kind: captions
Language: en

00:00:00.340 --> 00:00:03.360
If I were to walk up to you on
the street and say you, please

00:00:03.360 --> 00:00:07.450
tell me what-- so I didn't want
to write that thick --please

00:00:07.450 --> 00:00:11.710
tell me what sine
of pi over 4 is.

00:00:11.710 --> 00:00:14.950
And, obviously, we're assuming
we're dealing in radians.

00:00:14.950 --> 00:00:17.510
You either have that memorized
or you would draw the

00:00:17.510 --> 00:00:19.920
unit circle right there.

00:00:19.920 --> 00:00:21.360
That's not the best
looking unit circle,

00:00:21.360 --> 00:00:23.080
but you get the idea.

00:00:23.080 --> 00:00:26.960
You'd go to pi over 4
radians, which is the

00:00:26.960 --> 00:00:29.760
same thing as 45 degrees.

00:00:29.760 --> 00:00:31.840
You would draw that
unit radius out.

00:00:31.840 --> 00:00:35.130
And the sine is defined
as a y-coordinate

00:00:35.130 --> 00:00:36.250
on the unit circle.

00:00:36.250 --> 00:00:38.910
So you would just want to
know this value right here.

00:00:38.910 --> 00:00:40.210
And you would
immediately say OK.

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This is a 45 degrees.

00:00:42.630 --> 00:00:45.530
Let me draw the triangle
a little bit larger.

00:00:45.530 --> 00:00:47.530
The triangle looks like this.

00:00:47.530 --> 00:00:49.210
This is 45.

00:00:49.210 --> 00:00:50.900
That's 45.

00:00:50.900 --> 00:00:53.790
This is 90.

00:00:53.790 --> 00:00:57.330
And you can solve a
45 45 90 triangle.

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The hypotenuse is 1.

00:00:59.040 --> 00:00:59.960
This is x.

00:00:59.960 --> 00:01:00.640
This is x.

00:01:00.640 --> 00:01:01.930
They're going to be
the same values.

00:01:01.930 --> 00:01:04.920
This is an isosceles
triangle, right?

00:01:04.920 --> 00:01:06.960
Their base angles are the same.

00:01:06.960 --> 00:01:10.690
So you say, look. x squared
plus x squared is equal to 1

00:01:10.690 --> 00:01:12.960
squared, which is just 1.

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2x squared is equal to 1.

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x squared is equal to 1/2.

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x is equal to the square root
of 1/2, which is one over

00:01:20.840 --> 00:01:22.780
the square root of 2.

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I can put that in rational form
by multiplying that by the

00:01:25.960 --> 00:01:27.330
square root of 2 over 2.

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And I get x is equal to the
square root of 2 over 2.

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So the height here is
square root of 2 over 2.

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And if you wanted to know
this distance too, it would

00:01:40.400 --> 00:01:41.710
also be the same thing.

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But we just cared
about the height.

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Because the sine value,
the sine of this, is just

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this height right here.

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The y-coordinate.

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And we got that as the
square root of 2 over 2.

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This is all review.

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We learned this in the
unit circle video.

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But what if someone else--
Let's say on another day, I

00:02:02.290 --> 00:02:08.850
come up to you and I say you,
please tell me what the

00:02:08.850 --> 00:02:14.820
arcsine of the square
root of 2 over 2 is.

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What is the arcsine?

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And you're stumped.

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You're like I know what the
sine of an angle is, but this

00:02:19.180 --> 00:02:24.480
is some new trigonometric
function that Sal has devised.

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And all you have to realize,
when they have this word arc in

00:02:27.770 --> 00:02:29.455
front of it-- This is also
sometimes referred to

00:02:29.455 --> 00:02:30.810
as the inverse sine.

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This could have just as easily
been written as: what is

00:02:33.960 --> 00:02:38.420
the inverse sine of the
square root of 2 over 2?

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All this is asking is what
angle would I have to take the

00:02:42.900 --> 00:02:48.310
sine of in order to get the
value square root of 2 over 2.

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This is also asking what angle
would I have to take the sine

00:02:52.000 --> 00:02:54.610
of in order to get square
root of 2 over 2.

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I could rewrite either of
these statements as saying

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square-- Let me do it.

00:03:02.260 --> 00:03:06.890
I could rewrite either of these
statements as saying sine

00:03:06.890 --> 00:03:11.200
of what is equal to the
square root of 2 over 2.

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And this, I think, is a
much easier question

00:03:14.910 --> 00:03:15.820
for you to answer.

00:03:15.820 --> 00:03:18.400
Sine of what is square
root of 2 over 2?

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Well I just figured out that
the sine of pi over 4 is

00:03:21.950 --> 00:03:24.080
square root of 2 over 2.

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So, in this case, I know that
the sine of pi over 4 is equal

00:03:28.560 --> 00:03:30.630
to square root of 2 over 2.

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So my question mark is
equal to pi over 4.

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Or, I could have rewritten
this as, the arcsine-- sorry

00:03:42.400 --> 00:03:51.940
--arcsine of the square root of
2 over 2 is equal to pi over 4.

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Now you might say so, just as
review, I'm giving you a value

00:03:56.120 --> 00:03:58.630
and I'm saying give me an angle
that gives me, when I take the

00:03:58.630 --> 00:04:01.490
sine of that angle that
gives me that value.

00:04:01.490 --> 00:04:03.030
But you're like hey Sal.

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Look.

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Let me go over here.

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You're like, look
pi over 2 worked.

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45 degrees worked.

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But I could just keep adding
360 degrees or I could

00:04:11.560 --> 00:04:13.130
keep just adding 2 pi.

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And all of those would work
because those would all get

00:04:15.330 --> 00:04:18.870
me to that same point of
the unit circle, right?

00:04:18.870 --> 00:04:19.960
And you'd be correct.

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And so all of those values, you
would think, would be valid

00:04:23.350 --> 00:04:25.290
answers for this, right?

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Because if you take the sine of
any of those angles-- You could

00:04:27.700 --> 00:04:29.720
just keep adding 360 degrees.

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If you take the sine of any
of them, you would get

00:04:31.740 --> 00:04:33.540
square root of 2 over 2.

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And that's a problem.

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You can't have a function where
if I take the function-- I

00:04:37.070 --> 00:04:40.340
can't have a function, f
of x, where it maps to

00:04:40.340 --> 00:04:42.230
multiple values, right?

00:04:42.230 --> 00:04:47.490
Where it maps to pi over 4, or
it maps to pi over 4 plus 2

00:04:47.490 --> 00:04:52.280
pi or pi over 4 plus 4 pi.

00:04:52.280 --> 00:04:55.320
So in order for this to be a
valid function-- In order for

00:04:55.320 --> 00:04:58.450
the inverse sine function to
be valid, I have to

00:04:58.450 --> 00:05:00.340
restrict its range.

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And the way that-- We'll
just restrict its range to

00:05:02.660 --> 00:05:04.710
the most natural place.

00:05:04.710 --> 00:05:06.990
So let's restrict its range.

00:05:06.990 --> 00:05:08.910
Actually, just as a
side note, what's its

00:05:08.910 --> 00:05:10.120
domain restricted to?

00:05:10.120 --> 00:05:13.160
So if I'm taking the
arcsine of something.

00:05:13.160 --> 00:05:18.320
So if I'm taking the arcsine of
x, and I'm saying that that is

00:05:18.320 --> 00:05:21.900
equal to theta, what's the
domain restricted to?

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What are the valid values of x?

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x could be equal to what?

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Well if I take the sine of
any angle, I can only get

00:05:30.770 --> 00:05:33.840
values between 1 and
negative 1, right?

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So x is going to be greater
than or equal to negative 1 and

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then less than or equal to 1.

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That's the domain.

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Now, in order to make this
a valid function, I have

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to restrict the range.

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The possible values.

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I have to restrict the range.

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Now for arcsine, the convention
is to restrict it to the

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first and fourth quadrants.

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To restrict the possible angles
to this area right here

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along the unit circle.

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So theta is restricted to being
less than or equal to pi over

00:06:03.840 --> 00:06:11.180
2 and then greater than or
equal to minus pi over 2.

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So given that, we now
understand what arcsine is.

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Let's do another problem.

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Clear out some space here.

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Let me do another arcsine.

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So let's say I were to ask you
what the arcsine of minus the

00:06:30.450 --> 00:06:32.390
square root of 3 over 2 is.

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Now you might have
that memorized.

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And say, I immediately know
that sine of x, or sine

00:06:40.100 --> 00:06:41.420
of theta is square
root of 3 over 2.

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And you'd be done.

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But I don't have
that memorized.

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So let me just draw
my unit circle.

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And when I'm dealing with
arcsine, I just have to

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draw the first and fourth
quadrants of my unit circle.

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That's the y-axis.

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That's my x-axis.

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x and y.

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And where am I?

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If the sine of something is
minus square root of 3 over 2,

00:07:04.360 --> 00:07:07.760
that means the y-coordinate on
the unit circle is minus

00:07:07.760 --> 00:07:09.320
square root of 3 over 2.

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So it means we're
right about there.

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So this is minus the
square root of 3 over 2.

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This is where we are.

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Now what angle gives me that?

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Let's think about
it a little bit.

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My y-coordinate is minus
square root of 3 over 2.

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This is the angle.

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It's going to be a negative
angle because we're going

00:07:36.110 --> 00:07:39.130
below the x-axis in the
clockwise direction.

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And to figure out-- Let me just
draw a little triangle here.

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Let me pick a better
color than that.

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That's a triangle.

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Let me do it in
this blue color.

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So let me zoom up
that triangle.

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Like that.

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This is theta.

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That's theta.

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And what's this
length right here?

00:08:00.660 --> 00:08:03.120
Well that's the same as
the y-height, I guess

00:08:03.120 --> 00:08:03.890
we could call it.

00:08:03.890 --> 00:08:06.020
Which is square
root of 3 over 2.

00:08:06.020 --> 00:08:07.560
It's a minus because
we're going down.

00:08:07.560 --> 00:08:08.850
But let's just figure
out this angle.

00:08:08.850 --> 00:08:11.960
And we know it's a
negative angle.

00:08:11.960 --> 00:08:14.540
So when you see a square root
of 3 over 2, hopefully you

00:08:14.540 --> 00:08:16.870
recognize this is a
30 60 90 triangle.

00:08:16.870 --> 00:08:17.980
The square root of 3 over 2.

00:08:17.980 --> 00:08:19.950
This side is 1/2.

00:08:19.950 --> 00:08:21.250
And then, of course,
this side is 1.

00:08:21.250 --> 00:08:22.880
Because this is a unit circle.

00:08:22.880 --> 00:08:24.630
So its radius is 1.

00:08:24.630 --> 00:08:27.415
So in a 30 60 90 triangle, the
side opposite to the square

00:08:27.415 --> 00:08:30.500
root of 3 over 2 is 60 degrees.

00:08:30.500 --> 00:08:32.610
This side over here
is 30 degrees.

00:08:32.610 --> 00:08:35.140
So we know that our theta
is-- This is 60 degrees.

00:08:35.140 --> 00:08:36.100
That's its magnitude.

00:08:36.100 --> 00:08:37.325
But it's going downwards.

00:08:37.325 --> 00:08:39.970
So it's minus 60 degrees.

00:08:39.970 --> 00:08:43.180
So theta is equal to
minus 60 degrees.

00:08:43.180 --> 00:08:44.630
But if we're dealing
in radians, that's

00:08:44.630 --> 00:08:45.210
not good enough.

00:08:45.210 --> 00:08:52.350
So we can multiply that times
100-- sorry --pi radians

00:08:52.350 --> 00:08:54.540
for every 180 degrees.

00:08:54.540 --> 00:08:56.070
Degrees cancel out.

00:08:56.070 --> 00:08:59.500
And we're left with
theta is equal to minus

00:08:59.500 --> 00:09:04.090
pi over 3 radians.

00:09:04.090 --> 00:09:10.630
And so we can say-- We can now
make the statements that the

00:09:10.630 --> 00:09:16.780
arcsine of minus square root
of 3 over 2 is equal to

00:09:16.780 --> 00:09:19.980
minus pi over 3 radians.

00:09:19.980 --> 00:09:24.680
Or we could say the inverse
sign of minus square root

00:09:24.680 --> 00:09:30.840
of 3 over 2 is equal to
minus pi over 3 radians.

00:09:30.840 --> 00:09:34.290
And to confirm this, let's
just-- Let me get a

00:09:34.290 --> 00:09:35.310
little calculator out.

00:09:35.310 --> 00:09:38.200
I put this in radian
mode already.

00:09:38.200 --> 00:09:39.370
You can just check that.

00:09:39.370 --> 00:09:41.060
Per second mode.

00:09:41.060 --> 00:09:43.040
I'm in radian mode.

00:09:43.040 --> 00:09:45.490
So I know I'm going to get,
hopefully, the right answer.

00:09:45.490 --> 00:09:47.840
And I want to figure
out the inverse sign.

00:09:47.840 --> 00:09:51.610
So the inverse sine-- the
second and the sine button

00:09:51.610 --> 00:09:59.790
--of the minus square
root of 3 over 2.

00:09:59.790 --> 00:10:03.800
It equals minus 1.04.

00:10:03.800 --> 00:10:11.040
So it's telling me that this is
equal to minus 1.04 radians.

00:10:11.040 --> 00:10:13.970
So pi over 3 must
be equal to 1.04.

00:10:13.970 --> 00:10:16.030
Let's see if I can
confirm that.

00:10:16.030 --> 00:10:25.180
So if I were to write minus pi
divided by 3, what do I get?

00:10:25.180 --> 00:10:26.670
I get the exact same value.

00:10:26.670 --> 00:10:28.710
So my calculator gave me the
exact same value, but it might

00:10:28.710 --> 00:10:31.240
have not been that helpful
because my calculator doesn't

00:10:31.240 --> 00:10:34.520
tell me that this is
minus pi over 3.


Hardy-Weinberg Principle

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:03.220
I've already started with the
eye color example so I figured

00:00:03.220 --> 00:00:05.150
no harm in continuing it.

00:00:05.150 --> 00:00:09.170
Let's say we live on a planet
or we're a species where

00:00:09.170 --> 00:00:18.090
there's only two possible eye
colors: either blue-- and the

00:00:18.090 --> 00:00:21.270
genotype or the allele for blue
I'll abbreviate with a

00:00:21.270 --> 00:00:26.590
lowercase b --or you could
have brown eyes.

00:00:26.590 --> 00:00:28.960
I'm doing it in this salmon
color just because I got tired

00:00:28.960 --> 00:00:29.900
of the brown.

00:00:29.900 --> 00:00:32.049
We'll do an uppercase B.

00:00:32.049 --> 00:00:34.620
And I'll make a few other
simplifying assumptions.

00:00:34.620 --> 00:00:39.780
First of all, let's assume that
the expression of this

00:00:39.780 --> 00:00:44.900
gene is very simple, that brown
is dominant to blue.

00:00:44.900 --> 00:00:46.405
So if you have one of
each, you're going

00:00:46.405 --> 00:00:47.420
to see brown eyes.

00:00:47.420 --> 00:00:50.180
The only way you're going to see
blue eyes is if you have a

00:00:50.180 --> 00:00:53.380
blue allele from each
of your parents.

00:00:53.380 --> 00:00:56.210
And the other assumptions I'm
going to make is that this

00:00:56.210 --> 00:01:01.680
population essentially has a
stable gene pool with respect

00:01:01.680 --> 00:01:03.300
to the eye color gene.

00:01:03.300 --> 00:01:04.569
What do I mean by that?

00:01:04.569 --> 00:01:11.400
No selection is taking place, no
natural selection based on

00:01:11.400 --> 00:01:12.100
this trait.

00:01:12.100 --> 00:01:16.030
So, for example, you're not more
or less likely to be able

00:01:16.030 --> 00:01:18.850
to reproduce, or the number of
children you have is not going

00:01:18.850 --> 00:01:23.290
to be larger or greater
dependent on what your eye

00:01:23.290 --> 00:01:25.120
color is in this population.

00:01:25.120 --> 00:01:27.005
I'm also going to assume that
there's no mutations.

00:01:30.130 --> 00:01:33.450
So for whatever reason, a
chromosome that has a blue

00:01:33.450 --> 00:01:36.130
allele can't randomly turn into
a brown or vice versa or

00:01:36.130 --> 00:01:37.650
turn into a third color.

00:01:37.650 --> 00:01:39.190
I'm also going to assume that
I'm going to have a large

00:01:39.190 --> 00:01:40.440
population.

00:01:43.550 --> 00:01:45.960
The reason why I'm making all
of these assumptions is

00:01:45.960 --> 00:01:49.400
because I essentially want to
have a stable gene pool, at

00:01:49.400 --> 00:01:53.420
least relative to this gene.

00:01:53.420 --> 00:01:56.450
Relative to the eye color gene,
I want to be stable.

00:01:56.450 --> 00:01:59.530
I want to have a stable
allele frequency.

00:01:59.530 --> 00:02:01.540
What do I mean by allele
frequency?

00:02:08.110 --> 00:02:10.400
I said a large population, but
let's take a very small

00:02:10.400 --> 00:02:10.960
population.

00:02:10.960 --> 00:02:16.890
Let's say that there's two
people in the population, and

00:02:16.890 --> 00:02:27.460
one guy right here, his
genotype is big B and

00:02:27.460 --> 00:02:31.050
lowercase B, and let's say that
the other guy has blue

00:02:31.050 --> 00:02:33.280
eyes, so he has to be homozygous
recessive.

00:02:33.280 --> 00:02:35.230
Let's say this is the
entire population.

00:02:35.230 --> 00:02:37.840
Of course, a population of two
can't apply to what I'm about

00:02:37.840 --> 00:02:41.010
to do, but I just want explain
allele frequency.

00:02:41.010 --> 00:02:45.960
The allele frequency here of the
blue eyes, the blue-eyed

00:02:45.960 --> 00:02:49.140
allele frequency
here, is what?

00:02:49.140 --> 00:02:52.300
Well, in this population, I
have exactly four alleles.

00:02:52.300 --> 00:02:54.150
I only have two individuals,
but they

00:02:54.150 --> 00:02:55.700
each have two alleles.

00:02:55.700 --> 00:02:58.810
So it's going to be 75%.

00:02:58.810 --> 00:03:03.800
75% of the alleles in this
population are blue, right?

00:03:03.800 --> 00:03:06.010
There's one, two, three,
four alleles, and

00:03:06.010 --> 00:03:07.650
three of them are blue.

00:03:07.650 --> 00:03:13.640
The frequency of the brown
allele is 25%.

00:03:13.640 --> 00:03:16.060
And this is different than
the actual expression.

00:03:16.060 --> 00:03:19.390
If I asked you the frequency
of brown eyes versus blue

00:03:19.390 --> 00:03:22.780
eyes-- So this is allele
frequency.

00:03:22.780 --> 00:03:24.880
Let me write that down.

00:03:24.880 --> 00:03:27.050
That's allele frequency
right there.

00:03:27.050 --> 00:03:37.580
If I were ask you phenotype
frequency, if I said how

00:03:37.580 --> 00:03:42.420
frequent are blue eyes seen
in my population?

00:03:42.420 --> 00:03:44.970
Well, it's only one out of the
two people in my population,

00:03:44.970 --> 00:03:48.020
so you'd say it's 50%, and then
for brown eyes, you would

00:03:48.020 --> 00:03:52.790
say it's 50%.

00:03:52.790 --> 00:03:54.490
So I want to make this
distinction very clear because

00:03:54.490 --> 00:03:55.930
it can be very confusing
when people talk

00:03:55.930 --> 00:03:57.310
about allele frequency.

00:03:57.310 --> 00:03:59.790
Allele frequency is literally
if you were able to go and

00:03:59.790 --> 00:04:02.950
look at the actual genotype,
the actual chromosomes of

00:04:02.950 --> 00:04:05.230
every person in the population,
and count how many

00:04:05.230 --> 00:04:07.950
of them had the blue allele
versus the brown allele, you

00:04:07.950 --> 00:04:09.400
would come up with
this number.

00:04:09.400 --> 00:04:12.680
This is different than the
actual phenotype frequency.

00:04:12.680 --> 00:04:17.940
Now, all of that is just as a
background, because if these

00:04:17.940 --> 00:04:23.165
set of assumptions are true and
my population isn't in any

00:04:23.165 --> 00:04:26.360
way evolving, then my allele
frequency is going to be

00:04:26.360 --> 00:04:27.860
roughly constant.

00:04:27.860 --> 00:04:29.800
I have to assume a large
population, because a small

00:04:29.800 --> 00:04:32.260
population, just from random
chance, my allele frequency

00:04:32.260 --> 00:04:33.710
could start to change.

00:04:33.710 --> 00:04:36.210
But let's say my allele
frequency is constant, then

00:04:36.210 --> 00:04:38.170
I'm in a Hardy-Weinberg
equilibrium.

00:04:48.090 --> 00:04:50.070
All this is a situation
where the allele

00:04:50.070 --> 00:04:51.320
frequency isn't changing.

00:04:54.500 --> 00:04:56.390
The reason why we're making all
of those assumptions is

00:04:56.390 --> 00:05:00.450
because, if we can assume this,
we can start to deduce

00:05:00.450 --> 00:05:04.230
some things about what we
observe, what must be the

00:05:04.230 --> 00:05:06.810
genotypes in the population or
the frequencies of different

00:05:06.810 --> 00:05:08.870
phenotypes and whatever else.

00:05:08.870 --> 00:05:15.360
So, for example, if p is the
frequency of blue eyes, so let

00:05:15.360 --> 00:05:20.940
me say p is equal to the
frequency of blue eyes, and q

00:05:20.940 --> 00:05:26.300
is equal to the frequency of
brown eyes, what's p plus q

00:05:26.300 --> 00:05:27.930
going to be?

00:05:27.930 --> 00:05:29.900
What's p plus q?

00:05:29.900 --> 00:05:32.800
Well, everything is either going
to have blue eyes or

00:05:32.800 --> 00:05:33.420
brown eyes.

00:05:33.420 --> 00:05:37.305
If this is 20%-- And anyway,
this is the allele.

00:05:37.305 --> 00:05:39.490
Let me make that b allele.

00:05:39.490 --> 00:05:40.720
Let me make that very clear.

00:05:40.720 --> 00:05:42.500
This isn't necessarily
what you observe.

00:05:42.500 --> 00:05:44.650
This is the allele itself.

00:05:44.650 --> 00:05:47.300
This is the allele frequency, if
you were actually to count

00:05:47.300 --> 00:05:51.920
the chromosomes and see what
percentage have the blue

00:05:51.920 --> 00:05:53.330
allele and what percentage
have the

00:05:53.330 --> 00:05:55.170
uppercase brown allele.

00:05:55.170 --> 00:05:58.520
Well, every chromosome has to
have either of those, so these

00:05:58.520 --> 00:06:03.140
are going to add up to
100%, or equal to 1.

00:06:03.140 --> 00:06:08.210
For example, if 30% of the
alleles are blue, then 70% are

00:06:08.210 --> 00:06:10.090
going to have to be brown
because, I already told you at

00:06:10.090 --> 00:06:12.590
the beginning of this video,
that we're in a world where

00:06:12.590 --> 00:06:15.650
you either have a blue allele
or a brown allele.

00:06:15.650 --> 00:06:17.450
Now, what if we don't care about
alleles, we actually

00:06:17.450 --> 00:06:22.710
care about the frequency
of the genotypes?

00:06:22.710 --> 00:06:24.010
So there's a couple of
things we could do.

00:06:24.010 --> 00:06:26.860
We could literally just square
both sides of this and then

00:06:26.860 --> 00:06:28.070
think about what
that gives us.

00:06:28.070 --> 00:06:31.350
If we square both sides as this
equation, you get what? p

00:06:31.350 --> 00:06:36.570
plus q squared is p squared plus
2pq plus q squared, and

00:06:36.570 --> 00:06:40.370
you square the other side and
it's equal to 1 as well.

00:06:40.370 --> 00:06:42.180
What does this tell us?

00:06:42.180 --> 00:06:44.950
What is p squared?

00:06:44.950 --> 00:06:48.090
Well, it's the probability
that I get two of the

00:06:48.090 --> 00:06:49.960
lowercase blue alleles, right?

00:06:49.960 --> 00:06:54.270
What's the probability that I
get two, that I end up with

00:06:54.270 --> 00:06:57.430
lowercase b, lowercase
b as my genotype?

00:06:57.430 --> 00:07:00.320
Well, I have to get a lowercase
b from my first

00:07:00.320 --> 00:07:03.650
parent, and that's with a
probability of p, and then a

00:07:03.650 --> 00:07:05.380
lowercase b from my second
parent with a

00:07:05.380 --> 00:07:07.300
probability of p.

00:07:07.300 --> 00:07:10.610
So it's p times p, so
that's p squared.

00:07:10.610 --> 00:07:12.800
What's q squared?

00:07:12.800 --> 00:07:15.800
Well, that's the probability
that I get a big B, a

00:07:15.800 --> 00:07:18.180
brown-eyed allele from each
parent, because the

00:07:18.180 --> 00:07:21.970
probability from parent 1 is q
and then the probability from

00:07:21.970 --> 00:07:24.400
parent 2 is also q.

00:07:24.400 --> 00:07:27.320
So that's q squared
right there.

00:07:27.320 --> 00:07:28.570
Now, what's 2pq?

00:07:31.140 --> 00:07:33.990
Well, essentially, this
entire term is the

00:07:33.990 --> 00:07:37.880
frequency that I'm a hybrid.

00:07:37.880 --> 00:07:40.010
I have a heterozygous
genotype.

00:07:40.010 --> 00:07:41.260
And why is that?

00:07:41.260 --> 00:07:43.840
Because there's two ways that
I can be a heterozygote.

00:07:46.580 --> 00:07:49.590
I could be like this.

00:07:49.590 --> 00:07:52.000
I want to do that other blue.

00:07:52.000 --> 00:07:56.200
I could get blue eyes from one
parent and brown eyes from the

00:07:56.200 --> 00:07:58.900
other or I could get brown eyes
from the first parent and

00:07:58.900 --> 00:08:00.200
blue eyes from the second.

00:08:00.200 --> 00:08:04.390
I don't know anything about
these parents, so if I'm

00:08:04.390 --> 00:08:06.210
making no assumptions, then I
just have to assume that the

00:08:06.210 --> 00:08:09.760
probability that I get an allele
from either one of them

00:08:09.760 --> 00:08:14.650
is equal to the frequency
in the population.

00:08:14.650 --> 00:08:16.540
So there's two ways
of getting these.

00:08:16.540 --> 00:08:18.780
The probability of each of these
ways, the probability of

00:08:18.780 --> 00:08:21.450
this combination,
is p times q.

00:08:21.450 --> 00:08:23.630
The probability of this is q
times p, which is the same

00:08:23.630 --> 00:08:26.960
thing, and you add them together
and you get 2pq.

00:08:26.960 --> 00:08:30.000
So this is essentially the
frequency of the hybrids in

00:08:30.000 --> 00:08:32.140
the population.

00:08:32.140 --> 00:08:33.929
I've been kind of
abstract so far.

00:08:33.929 --> 00:08:37.500
Let's see if we can apply this
to a real world problem, and

00:08:37.500 --> 00:08:40.320
obviously, I'm making some
simplifying assumptions.

00:08:40.320 --> 00:08:42.310
Let's say that we go
into a population.

00:08:42.310 --> 00:08:45.270
Let's say it's a population of
a million people, reasonably

00:08:45.270 --> 00:08:53.720
large, and we observe that
9% have blue eyes.

00:08:53.720 --> 00:08:55.940
This is their phenotype.

00:08:55.940 --> 00:09:02.300
This is the frequency of the
genotype lowercase b,

00:09:02.300 --> 00:09:04.840
lowercase b, right?

00:09:04.840 --> 00:09:07.930
I started with this phenotype
blue eyes, but I know, since

00:09:07.930 --> 00:09:13.440
blue is a recessive trait, that
they must have two copies

00:09:13.440 --> 00:09:15.080
of the recessive allele.

00:09:15.080 --> 00:09:18.280
So this is the frequency.

00:09:18.280 --> 00:09:22.780
The frequency of having two
lowercase b's is 9%.

00:09:22.780 --> 00:09:24.920
Well, if you just look here, I
just showed you that that's

00:09:24.920 --> 00:09:27.860
also equal to p squared.

00:09:27.860 --> 00:09:30.000
p squared is equal to 9%.

00:09:30.000 --> 00:09:31.210
And how do you think
about that?

00:09:31.210 --> 00:09:33.040
Well, p is the probability
of getting a blue allele.

00:09:33.040 --> 00:09:35.850
It's the frequency of the blue
allele in the population.

00:09:35.850 --> 00:09:38.430
In order to get two of them,
you have to multiply p by

00:09:38.430 --> 00:09:39.910
itself twice.

00:09:39.910 --> 00:09:43.220
So what's the frequency of the
blue allele in the population?

00:09:43.220 --> 00:09:48.680
p is equal to the square root
of 0.09, which is 0.3.

00:09:48.680 --> 00:09:51.950
So if you went and actually
counted all of the alleles in

00:09:51.950 --> 00:09:56.930
the population, you would
actually find that 30% of them

00:09:56.930 --> 00:09:59.410
are the lowercase blue.

00:09:59.410 --> 00:10:02.740
Now, a much smaller percentage
of people, only 9%, showed the

00:10:02.740 --> 00:10:04.340
blue eyes because you
need two of them.

00:10:04.340 --> 00:10:07.000
You have a 30% chance of getting
it from your mom and a

00:10:07.000 --> 00:10:09.550
30% chance of getting
it from your dad.

00:10:09.550 --> 00:10:16.110
So what's the frequency of
a brown-eyed allele?

00:10:19.130 --> 00:10:21.890
Well, we know that the frequency
of the blue eyes

00:10:21.890 --> 00:10:25.770
plus the brown eyes is 100%,
so that's going to be 70%.

00:10:25.770 --> 00:10:31.100
If 30% of all of the chromosomes
or of all of the

00:10:31.100 --> 00:10:34.180
alleles in the population are
blue, the other 70% are going

00:10:34.180 --> 00:10:36.020
to have to be brown.

00:10:36.020 --> 00:10:39.090
So what percentage of my
population are going to be--

00:10:39.090 --> 00:10:40.750
Well, there's a couple
of things we can do.

00:10:40.750 --> 00:10:43.720
What percentage of my population
are going to have--

00:10:43.720 --> 00:10:44.480
Well, I'll do an easy one.

00:10:44.480 --> 00:10:46.210
What percentage of my population
are going to have

00:10:46.210 --> 00:10:50.050
brown eyes, so if I just look
at the phenotype brown eyes?

00:10:50.050 --> 00:10:51.170
I don't even have to
use any of these

00:10:51.170 --> 00:10:53.530
formulas for this one.

00:10:53.530 --> 00:10:56.640
I already told you 9% have blue
eyes, so the rest must

00:10:56.640 --> 00:10:58.280
have brown eyes.

00:10:58.280 --> 00:11:01.880
So 91% percent have
brown eyes.

00:11:05.700 --> 00:11:11.070
Now, we just said we have 9% who
have blue eyes, 91% have

00:11:11.070 --> 00:11:11.940
brown eyes.

00:11:11.940 --> 00:11:14.380
What percentage of the
population are going to be

00:11:14.380 --> 00:11:17.640
homozygous for brown eyes?

00:11:17.640 --> 00:11:21.760
So they need to have the capital
B from both parents.

00:11:21.760 --> 00:11:24.320
Well, we know that the frequency
of the capital B

00:11:24.320 --> 00:11:28.380
allele is 70%, so what
percent are going to

00:11:28.380 --> 00:11:29.830
be homozygous dominant?

00:11:29.830 --> 00:11:32.330
Let me draw that.

00:11:32.330 --> 00:11:34.910
Homozygous dominant.

00:11:34.910 --> 00:11:38.410
Well, the frequency is going
to be q squared.

00:11:38.410 --> 00:11:40.070
They're going to have
to get a q.

00:11:40.070 --> 00:11:43.040
They're going to have to get
an uppercase B from each

00:11:43.040 --> 00:11:46.320
parent, so that's going to be
0.7 squared, which is equal to

00:11:46.320 --> 00:11:52.210
0.49, or 49%.

00:11:52.210 --> 00:11:56.120
So just starting already from
that one idea, from that one

00:11:56.120 --> 00:12:02.940
idea that 9% have blue eyes,
we've already been able deduce

00:12:02.940 --> 00:12:08.460
that 91% must have brown eyes.

00:12:08.460 --> 00:12:12.000
And of the 91% of the brown eyes
of the whole population,

00:12:12.000 --> 00:12:15.230
49%-- this isn't
49% of the 91%.

00:12:15.230 --> 00:12:17.780
This is 49% of the population.

00:12:17.780 --> 00:12:21.060
49% percent are homozygous
dominant.

00:12:25.730 --> 00:12:28.760
And then what percentage
of the population

00:12:28.760 --> 00:12:30.350
are going to be hybrids?

00:12:30.350 --> 00:12:32.750
Well, hybrids also have brown
eyes, but they're not

00:12:32.750 --> 00:12:35.340
homozygous dominant, so
the remainder here.

00:12:35.340 --> 00:12:36.690
So what is that?

00:12:36.690 --> 00:12:42.020
That's 42%.

00:12:42.020 --> 00:12:49.020
42% are going to be hybrids.

00:12:49.020 --> 00:12:52.540
And if we go back to
the Hardy-Weinberg

00:12:52.540 --> 00:12:53.770
equation, we see that.

00:12:53.770 --> 00:13:01.110
So we get p plus q has to be
equal to 100%, or I could just

00:13:01.110 --> 00:13:02.600
write equal to 1.

00:13:02.600 --> 00:13:06.400
And we figured out
that p was 30%.

00:13:06.400 --> 00:13:09.450
That's the frequency of the
blue-eyed allele, the actual

00:13:09.450 --> 00:13:12.980
trait, not the observation
of it or the genotype.

00:13:12.980 --> 00:13:16.060
And the frequency of the
brown eyes was 70%.

00:13:16.060 --> 00:13:18.080
And then this is actually a
breakdown when you square

00:13:18.080 --> 00:13:23.820
that, so we also know that
p squared plus 2pq plus q

00:13:23.820 --> 00:13:26.090
squared is equal to 1.

00:13:26.090 --> 00:13:29.610
This is the percentage of the
population that has blue eyes.

00:13:29.610 --> 00:13:33.810
They have two blue alleles,
so that's 9%.

00:13:33.810 --> 00:13:36.880
This is the percentage of the
population that has two brown

00:13:36.880 --> 00:13:42.450
alleles, homozygous dominant,
so that is 49%.

00:13:42.450 --> 00:13:46.120
And then the remainder, this
2pq, this whole term right

00:13:46.120 --> 00:13:47.340
here is what's left over.

00:13:47.340 --> 00:13:52.950
So 9 plus this 58, this
is going to be 42%.

00:13:52.950 --> 00:13:55.750
42% are hybrids.

00:13:55.750 --> 00:13:59.620
And if I just talked about
phenotypes, I'd say 9% have

00:13:59.620 --> 00:14:02.950
blue eyes and then
the remainder,

00:14:02.950 --> 00:14:06.050
91%, have brown eyes.

00:14:06.050 --> 00:14:08.000
Hopefully, you found that
reasonably useful.

00:14:08.000 --> 00:14:14.420
Just from very simple
deductions, it's almost kind

00:14:14.420 --> 00:14:17.120
of silly that this is almost a
separate principle, because

00:14:17.120 --> 00:14:20.250
you can kind of deduce this from
very basic ideas, and you

00:14:20.250 --> 00:14:21.780
can square both sides of that.

00:14:21.780 --> 00:14:24.730
But you can come up with some
fairly fascinating results

00:14:24.730 --> 00:14:27.400
about what's going on in a
population because we can

00:14:27.400 --> 00:14:30.185
observe maybe the frequency of,
let's say, some disease

00:14:30.185 --> 00:14:35.250
that only happens when someone
is homozygous recessive.

00:14:35.250 --> 00:14:37.410
So you can go and see, OK,
what percentage of the

00:14:37.410 --> 00:14:40.260
population has that disease, but
then doing the math that

00:14:40.260 --> 00:14:42.600
we just did in this video, you
can figure out what percentage

00:14:42.600 --> 00:14:46.530
of the population have the
allele for the disease.

00:14:46.530 --> 00:14:49.110
They're carriers for the
disease, but they don't

00:14:49.110 --> 00:14:50.750
actually show it, and
that would be the

00:14:50.750 --> 00:14:52.680
hybrids right there.

00:14:52.680 --> 00:14:54.300
So this is actually
a pretty powerful

00:14:54.300 --> 00:14:56.390
tool you've just learned.


Punnett square fun

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:04.750
In the last video, I drew this
grid in order to understand

00:00:04.750 --> 00:00:07.180
better the different
combinations of alleles I

00:00:07.180 --> 00:00:09.400
could get from my
mom or my dad.

00:00:09.400 --> 00:00:12.310
And this grid that I drew is
called a Punnett square.

00:00:17.000 --> 00:00:20.650
And I looked up what Punnett
means, and it turns out, and

00:00:20.650 --> 00:00:24.050
this might be the biggest
takeaway from this video, that

00:00:24.050 --> 00:00:26.370
when you go to the farmers'
market or you go to the

00:00:26.370 --> 00:00:29.840
produce and you see those little
baskets, you see those

00:00:29.840 --> 00:00:33.370
little baskets that often you'll
see maybe strawberries

00:00:33.370 --> 00:00:35.760
or blueberries sitting in, they
have this little grid

00:00:35.760 --> 00:00:36.760
here, right there.

00:00:36.760 --> 00:00:39.150
Sometimes grapes are in them,
and you have a bunch of

00:00:39.150 --> 00:00:42.530
strawberries in them
like that.

00:00:42.530 --> 00:00:45.770
That green basket
is a punnett.

00:00:45.770 --> 00:00:46.590
That's a punnett.

00:00:46.590 --> 00:00:48.500
Apparently, in some countries,
they call it a punnett.

00:00:48.500 --> 00:00:53.460
I think England's one of them,
and you UK viewers can correct

00:00:53.460 --> 00:00:54.190
me if I'm wrong.

00:00:54.190 --> 00:00:56.640
And so I guess that's where
the inspiration comes for

00:00:56.640 --> 00:00:59.300
calling these Punnett squares,
that these are kind of these

00:00:59.300 --> 00:01:02.380
little green baskets that
you can throw different

00:01:02.380 --> 00:01:04.640
combinations of genotypes in.

00:01:04.640 --> 00:01:07.140
And these Punnett squares
aren't just useful.

00:01:07.140 --> 00:01:10.780
If you're talking about crossing
two hybrids, this is

00:01:10.780 --> 00:01:14.140
called a monohybrid cross
because you are crossing two

00:01:14.140 --> 00:01:15.970
hybrids for only one trait.

00:01:15.970 --> 00:01:19.370
It could be useful for a whole
set of different types of

00:01:19.370 --> 00:01:25.000
crosses between two reproducing
organisms. It

00:01:25.000 --> 00:01:27.450
doesn't even have to be a
situation where one thing is

00:01:27.450 --> 00:01:28.420
dominating another.

00:01:28.420 --> 00:01:31.310
Let's do a bunch of these,
just to make you

00:01:31.310 --> 00:01:32.600
familiar with the idea.

00:01:32.600 --> 00:01:34.730
So let's say you have a mom.

00:01:34.730 --> 00:01:38.910
So instead of doing two hybrids,
let's say the mom--

00:01:38.910 --> 00:01:43.160
I'll keep using the blue-eyed,
brown-eyed analogy just

00:01:43.160 --> 00:01:45.830
because we're already reasonably
useful to it.

00:01:45.830 --> 00:01:48.670
Let's say that she's homozygous
dominant.

00:01:48.670 --> 00:01:56.160
And let's say that the dad is a
heterozygote, so he's got a

00:01:56.160 --> 00:01:59.020
brown and he's got a blue.

00:01:59.020 --> 00:02:01.370
And we want to know the
different combinations of

00:02:01.370 --> 00:02:04.400
genotypes that one of their
children might have. So what

00:02:04.400 --> 00:02:07.392
we do is we draw a Punnett
square again.

00:02:07.392 --> 00:02:13.550
Let me draw a grid here and
draw a grid right there.

00:02:13.550 --> 00:02:16.720
And up here, we'll write the
different genes that mom can

00:02:16.720 --> 00:02:19.510
contribute, and here, we'll
write the different genes that

00:02:19.510 --> 00:02:21.960
dad can contribute, or the
different alleles.

00:02:21.960 --> 00:02:22.770
I didn't want to write gene.

00:02:22.770 --> 00:02:26.160
I wanted to write dad.

00:02:26.160 --> 00:02:30.610
So the mom in either case is
either going to contribute

00:02:30.610 --> 00:02:35.150
this big B brown allele from
one of the homologous

00:02:35.150 --> 00:02:37.320
chromosomes, or on the other
homologous, well, they have

00:02:37.320 --> 00:02:39.430
the same allele so she's
going to contribute

00:02:39.430 --> 00:02:41.840
that one to her child.

00:02:41.840 --> 00:02:48.900
The dad could contribute this
one, that big brown-eyed-- the

00:02:48.900 --> 00:02:54.230
capital B allele for brown eyes
or the lowercase b for

00:02:54.230 --> 00:02:55.970
blue eyes, either one.

00:02:55.970 --> 00:02:58.730
So the different combinations
that might happen, an

00:02:58.730 --> 00:03:03.080
offspring could get both of
these brown alleles from one

00:03:03.080 --> 00:03:05.210
copy from both parents.

00:03:05.210 --> 00:03:08.060
This could also happen where you
get this brown allele from

00:03:08.060 --> 00:03:11.750
the dad and then the other brown
allele from the mom, or

00:03:11.750 --> 00:03:15.820
you could get a brown allele
from the mom and a blue-eyed

00:03:15.820 --> 00:03:19.080
allele from the dad, or you
could get the other brown-eyed

00:03:19.080 --> 00:03:22.240
allele from the mom, right?

00:03:22.240 --> 00:03:25.240
When the mom has this, she has
two chromosomes, homologous

00:03:25.240 --> 00:03:25.800
chromosomes.

00:03:25.800 --> 00:03:29.140
Each of them have the same
brown allele on them.

00:03:29.140 --> 00:03:32.010
They both have that same brown
allele, so I could get the

00:03:32.010 --> 00:03:35.410
other one from my mom and
still get this blue-eyed

00:03:35.410 --> 00:03:37.000
allele from my dad.

00:03:37.000 --> 00:03:39.070
So if you said what's the
probability of having a

00:03:39.070 --> 00:03:44.140
blue-eyed child, assuming that
blue eyes are recessive?

00:03:44.140 --> 00:03:45.820
And remember, this
is a phenotype.

00:03:45.820 --> 00:03:48.330
These particular combinations
are genotypes.

00:03:48.330 --> 00:03:50.860
Well, in order to have blue
eyes, you have to be

00:03:50.860 --> 00:03:52.250
homozygous recessive.

00:03:52.250 --> 00:03:54.440
You have to have two
lowercase b's.

00:03:54.440 --> 00:03:56.490
So what's the probability
of having this?

00:03:56.490 --> 00:03:58.410
Well, there are no combinations
that result in

00:03:58.410 --> 00:04:02.330
that, so there's a 0%
probability of having two

00:04:02.330 --> 00:04:03.510
blue-eyed children.

00:04:03.510 --> 00:04:08.170
What's the probability
of having a

00:04:08.170 --> 00:04:09.850
homozygous dominant child?

00:04:09.850 --> 00:04:10.600
Let me write that.

00:04:10.600 --> 00:04:17.089
A homozygous dominant.

00:04:17.089 --> 00:04:18.860
And now we're looking
at the genotype.

00:04:18.860 --> 00:04:20.589
We care about the
specific alleles

00:04:20.589 --> 00:04:22.740
that that child inherits.

00:04:22.740 --> 00:04:24.880
Well, which of these are
homozygous dominant?

00:04:24.880 --> 00:04:27.530
Well, you have this one right
here and you have that one

00:04:27.530 --> 00:04:31.200
right there, and so two of
the four equally likely

00:04:31.200 --> 00:04:33.770
combinations are homozygous
dominant, so

00:04:33.770 --> 00:04:37.090
you have a 50% shot.

00:04:37.090 --> 00:04:38.440
And we can do these
Punnett squares.

00:04:38.440 --> 00:04:42.800
They don't even have to be for
situations where one trait is

00:04:42.800 --> 00:04:45.240
necessarily dominant
on the other.

00:04:45.240 --> 00:04:47.630
For example, you could have the
situation-- it's called

00:04:47.630 --> 00:04:48.880
incomplete dominance.

00:04:59.330 --> 00:05:05.650
Let's say you have two traits
for color in a flower.

00:05:05.650 --> 00:05:10.260
You could have red flowers or
you could have white flowers.

00:05:14.160 --> 00:05:23.170
And let's say I were to cross
a parent flower that has the

00:05:23.170 --> 00:05:28.130
genotype capital R-- I'll just
make it in a capital W.

00:05:28.130 --> 00:05:31.110
So that could be the mom or the
dad, although the analogy

00:05:31.110 --> 00:05:32.800
breaks down a little bit with
parents, although there is a

00:05:32.800 --> 00:05:36.170
male and female, although
sometimes on the same plant.

00:05:36.170 --> 00:05:38.680
And let's say the other plant
is also a red and white.

00:05:38.680 --> 00:05:42.490
The other plant has
a red allele and

00:05:42.490 --> 00:05:45.020
also has a white allele.

00:05:45.020 --> 00:05:46.870
So what are the different
possibilities?

00:05:46.870 --> 00:05:50.200
Well, we just draw our
Punnett square again.

00:05:50.200 --> 00:05:53.830
Let me draw our little grid.

00:05:53.830 --> 00:05:58.711
So the child could inherit both
of these red alleles.

00:05:58.711 --> 00:06:02.690
He could inherit this white
allele and then this red

00:06:02.690 --> 00:06:06.720
allele, so this red one and then
this white one, right?

00:06:06.720 --> 00:06:09.050
That's that right there
and that red one

00:06:09.050 --> 00:06:10.290
is that right there.

00:06:10.290 --> 00:06:14.190
Or it could inherit this red one
from-- let's say this is

00:06:14.190 --> 00:06:18.810
the mom plant and then the
white allele from the dad

00:06:18.810 --> 00:06:21.990
plant, so that's that
one right there.

00:06:21.990 --> 00:06:24.660
Or you could inherit
both white alleles.

00:06:24.660 --> 00:06:26.710
What I said when I went into
this, and I wrote it at the

00:06:26.710 --> 00:06:29.570
top right here, is we're
studying a situation dealing

00:06:29.570 --> 00:06:32.300
with incomplete dominance.

00:06:32.300 --> 00:06:33.660
So what does that mean?

00:06:33.660 --> 00:06:36.540
Well, that means you might
actually have mixing or

00:06:36.540 --> 00:06:41.120
blending of the traits when
you actually look at them.

00:06:41.120 --> 00:06:43.800
So if this was complete
dominance, if red was dominant

00:06:43.800 --> 00:06:46.330
to white, then you'd say, OK,
all of these guys are going to

00:06:46.330 --> 00:06:49.770
be red and only this guy right
here is going to be white, so

00:06:49.770 --> 00:06:52.260
you have a one in four
probability to being white.

00:06:52.260 --> 00:06:57.130
But let's say that a
heterozygous genotype-- so let

00:06:57.130 --> 00:06:59.530
me write that down.

00:06:59.530 --> 00:07:05.360
Let's say when you have one R
allele and one white allele,

00:07:05.360 --> 00:07:07.150
that this doesn't
result in red.

00:07:07.150 --> 00:07:08.400
This results in pink.

00:07:12.660 --> 00:07:13.860
So this is what blending is.

00:07:13.860 --> 00:07:15.320
It's kind of a mixture
of the two.

00:07:15.320 --> 00:07:19.650
So if I said if these these two
plants were to reproduce,

00:07:19.650 --> 00:07:24.060
and the traits for red and white
petals, I guess we could

00:07:24.060 --> 00:07:28.170
say, are incomplete dominant,
or incompletely dominant, or

00:07:28.170 --> 00:07:32.840
they blend, and if I were to say
what's the probability of

00:07:32.840 --> 00:07:35.650
having a pink plant?

00:07:35.650 --> 00:07:37.580
And now when I'm talking
about pink, this, of

00:07:37.580 --> 00:07:39.140
course, is a phenotype.

00:07:39.140 --> 00:07:41.490
So the probability of pink,
well, let's look at the

00:07:41.490 --> 00:07:42.940
different combinations.

00:07:42.940 --> 00:07:45.550
How many of these are pink?

00:07:45.550 --> 00:07:47.750
This one is pink and
this is pink.

00:07:47.750 --> 00:07:52.580
So two are pink of a total
of four equally likely

00:07:52.580 --> 00:07:59.120
combinations, so it's a 50%
chance that we're pink.

00:07:59.120 --> 00:08:01.970
And we could keep doing this
over multiple generations, and

00:08:01.970 --> 00:08:04.170
say, oh, what happens in the
second and third and the

00:08:04.170 --> 00:08:05.830
fourth generation?

00:08:05.830 --> 00:08:07.830
Actually, we could even have
a situation where we have

00:08:07.830 --> 00:08:11.180
multiple different alleles, and
I'll use almost a kind of

00:08:11.180 --> 00:08:12.690
a more realistic example.

00:08:12.690 --> 00:08:15.690
I'll use blood types
as an example.

00:08:15.690 --> 00:08:19.526
So there's three potential
alleles for blood type.

00:08:22.150 --> 00:08:26.880
You can have a blood type A, you
could have a blood type B,

00:08:26.880 --> 00:08:28.655
or you could have
a blood type O.

00:08:32.580 --> 00:08:35.230
What happens is you have a
combination here between

00:08:35.230 --> 00:08:37.840
codominance and recessive
genes.

00:08:37.840 --> 00:08:40.440
And I'm going to show you what
I talk about when we do the

00:08:40.440 --> 00:08:41.260
Punnett squares.

00:08:41.260 --> 00:08:43.230
Maybe I'll stick to one color
here because I think you're

00:08:43.230 --> 00:08:44.530
getting the idea.

00:08:44.530 --> 00:08:47.430
So let's say I have a
parent who is AB.

00:08:47.430 --> 00:08:50.820
So that means that they have
on one of their homologous

00:08:50.820 --> 00:08:53.980
chromosomes, they have the A
allele, and on the other one,

00:08:53.980 --> 00:08:55.160
they have the B allele.

00:08:55.160 --> 00:08:56.720
That's what AB means.

00:08:56.720 --> 00:08:59.240
So the phenotype is
the genotype.

00:08:59.240 --> 00:09:00.270
They're codominant.

00:09:00.270 --> 00:09:02.230
They both express themselves.

00:09:02.230 --> 00:09:03.370
They don't necessarily blend.

00:09:03.370 --> 00:09:04.300
They both express.

00:09:04.300 --> 00:09:06.570
That's an AB blood type.

00:09:06.570 --> 00:09:07.390
Let me write this right here.

00:09:07.390 --> 00:09:10.740
This is AB blood type.

00:09:13.490 --> 00:09:23.200
And then the other parent is--
let's say that they are fully

00:09:23.200 --> 00:09:25.420
an A blood type.

00:09:25.420 --> 00:09:28.050
Let's say they're
an A blood type.

00:09:28.050 --> 00:09:30.970
Let's say their phenotype is an
A blood type-- I hope I'm

00:09:30.970 --> 00:09:34.190
not confusing you-- but their
genotype is that they have one

00:09:34.190 --> 00:09:37.350
allele that's an A and their
other allele that's an O.

00:09:37.350 --> 00:09:39.200
So this is what's interesting
about blood types.

00:09:39.200 --> 00:09:40.220
It's a mixture.

00:09:40.220 --> 00:09:43.710
O is recessive.

00:09:43.710 --> 00:09:47.050
O is recessive, while these
guys are codominant.

00:09:47.050 --> 00:09:48.650
So if you have either of
these guys with an

00:09:48.650 --> 00:09:50.510
O, these guys dominate.

00:09:50.510 --> 00:09:53.140
If you have them together, then
your blood type is AB.

00:09:53.140 --> 00:09:56.180
So what are all the different
combinations for these for

00:09:56.180 --> 00:09:57.580
this couple here?

00:10:02.360 --> 00:10:06.570
Well, you could get this A and
that A, so you get an A from

00:10:06.570 --> 00:10:10.990
your mom and you get an A from
your dad right there.

00:10:10.990 --> 00:10:15.020
And clearly in this case, your
phenotype, you will have an A

00:10:15.020 --> 00:10:17.000
blood type in this situation.

00:10:17.000 --> 00:10:20.960
You could get the A from your
dad and you could get the B

00:10:20.960 --> 00:10:25.580
from your mom, in which case
you have an AB blood type.

00:10:25.580 --> 00:10:31.030
You could get the A from your
mom and the O from your dad,

00:10:31.030 --> 00:10:34.360
in which case you have an A
blood type because this

00:10:34.360 --> 00:10:35.930
dominates that.

00:10:35.930 --> 00:10:40.770
Or you could get the B from
your-- I dont want to

00:10:40.770 --> 00:10:42.080
introduce arbitrary colors.

00:10:42.080 --> 00:10:49.300
You could get the B from your
mom, that's this one, or the O

00:10:49.300 --> 00:10:51.490
from your dad.

00:10:51.490 --> 00:10:53.490
No, once again, I introduced
a different color.

00:10:53.490 --> 00:10:54.920
And this is a B blood type.

00:10:54.920 --> 00:11:02.650
So if I said what's the
probability of having an AA

00:11:02.650 --> 00:11:05.980
blood type?

00:11:05.980 --> 00:11:08.460
And once again, we're talking
about a phenotype here.

00:11:08.460 --> 00:11:10.220
So which of these are
an A blood type?

00:11:10.220 --> 00:11:13.800
This one definitely is,
because it's AA.

00:11:13.800 --> 00:11:16.640
If you have two A alleles,
you'll definitely have an A

00:11:16.640 --> 00:11:20.750
blood type, but you also have
an A blood type phenotype if

00:11:20.750 --> 00:11:23.020
you have an A and then an O.

00:11:23.020 --> 00:11:24.430
O is recessive.

00:11:24.430 --> 00:11:28.690
So this is also going to
be an A blood type.

00:11:28.690 --> 00:11:36.010
So these are both A blood, so
there's a 50% chance, because

00:11:36.010 --> 00:11:40.880
two of the four combinations
show us an A blood type.

00:11:40.880 --> 00:11:42.570
And you could do all of the
different combinations.

00:11:42.570 --> 00:11:44.950
You say, well, how do you
have an O blood type?

00:11:44.950 --> 00:11:48.450
Well, both of your parents
will have to carry

00:11:48.450 --> 00:11:49.520
at least one O.

00:11:49.520 --> 00:11:54.300
So, for example, to have a--
that would've been possible if

00:11:54.300 --> 00:11:58.090
maybe instead of an AB, this
right here was an O, then this

00:11:58.090 --> 00:12:00.380
combination would've been
two O's right there.

00:12:00.380 --> 00:12:02.660
So hopefully, that gives you
an idea of how a Punnett

00:12:02.660 --> 00:12:05.960
square can be useful, and it can
even be useful when we're

00:12:05.960 --> 00:12:09.110
talking about more
than one trait.

00:12:09.110 --> 00:12:12.970
So let's go to our situation
that I talked about before

00:12:12.970 --> 00:12:18.040
where I said you have little b
is equal to blue eyes, and

00:12:18.040 --> 00:12:21.790
we're assuming that that's
recessive, and you have big B

00:12:21.790 --> 00:12:25.530
is equal to brown eyes,
and we're assuming

00:12:25.530 --> 00:12:26.780
that this is dominant.

00:12:29.980 --> 00:12:31.346
And let's say we have
another trait.

00:12:34.820 --> 00:12:37.750
I introduced that tooth
trait before.

00:12:37.750 --> 00:12:40.780
So let's say little t is
equal to small teeth.

00:12:43.790 --> 00:12:46.290
I don't know what type of
bizarre organism I'm talking

00:12:46.290 --> 00:12:48.310
about, although I think
I would fall into

00:12:48.310 --> 00:12:49.830
the big tooth camp.

00:12:49.830 --> 00:12:52.330
Let's say big T is equal
to big teeth.

00:12:56.010 --> 00:13:00.330
So an individual can have--
for example, I might be

00:13:00.330 --> 00:13:05.050
heterozygous brown eyes, so my
genotype might be heterozygous

00:13:05.050 --> 00:13:10.740
for brown eyes and then
homozygous dominant for teeth.

00:13:10.740 --> 00:13:12.500
So this might be my genotype.

00:13:12.500 --> 00:13:15.680
And the phenotype for this one
would be a big-toothed,

00:13:15.680 --> 00:13:17.810
brown-eyed person, right?

00:13:17.810 --> 00:13:18.820
Let me make that clear.

00:13:18.820 --> 00:13:20.160
This is big tooth phenotype.

00:13:23.260 --> 00:13:25.120
And this is the phenotype.

00:13:25.120 --> 00:13:27.760
What you see is brown eyes.

00:13:27.760 --> 00:13:30.690
A big-toothed, brown-eyed
person.

00:13:30.690 --> 00:13:35.790
Now if we assume that the genes
that code for teeth or

00:13:35.790 --> 00:13:39.630
eye color are on different
chromosomes, and this is a key

00:13:39.630 --> 00:13:44.160
assumption, we can say that
they assort independently.

00:13:44.160 --> 00:13:46.915
Let me write that down:
independent assortment.

00:14:00.060 --> 00:14:05.310
So this is a case where if I
were look at my chromosomes,

00:14:05.310 --> 00:14:09.230
let's say this is one homologous
pair, maybe we call

00:14:09.230 --> 00:14:12.060
that homologous pair 1, and
let's say I have another

00:14:12.060 --> 00:14:16.270
homologous pair, and obviously
we have 23 of these, but let's

00:14:16.270 --> 00:14:23.840
say this is homologous pair 2
right here, if the eye color

00:14:23.840 --> 00:14:30.270
gene is here and here, remember
both homologous

00:14:30.270 --> 00:14:32.360
chromosomes code for
the same genes.

00:14:32.360 --> 00:14:34.060
They might have different
versions.

00:14:34.060 --> 00:14:35.160
Those are alleles.

00:14:35.160 --> 00:14:41.720
And if teeth are over here,
they will assort

00:14:41.720 --> 00:14:42.520
independently.

00:14:42.520 --> 00:14:46.910
So after meiosis occurs to
produce the gametes, the

00:14:46.910 --> 00:14:51.370
offspring might get this
chromosome or a copy of that

00:14:51.370 --> 00:14:55.170
chromosome for eye color and
might get a copy of this

00:14:55.170 --> 00:14:59.060
chromosome for teeth
size or tooth size.

00:14:59.060 --> 00:15:00.410
Or it could go the other way.

00:15:00.410 --> 00:15:05.220
Maybe another offspring gets
this one, this chromosome for

00:15:05.220 --> 00:15:07.590
eye color, and then this
chromosome for teeth color and

00:15:07.590 --> 00:15:09.570
gets the other version
of the allele.

00:15:09.570 --> 00:15:13.680
So because they're on different
chromosomes, there's

00:15:13.680 --> 00:15:16.890
no linkage between if you
inherit this one, whether you

00:15:16.890 --> 00:15:19.990
inherit big teeth, whether
you're going to inherit small

00:15:19.990 --> 00:15:21.850
brown eyes or blue eyes.

00:15:21.850 --> 00:15:24.120
Now, if they were on the same
chromosomee-- let's say the

00:15:24.120 --> 00:15:26.410
situation where they are
on the same chromosome.

00:15:26.410 --> 00:15:30.350
So let me pick another
trait: hair color.

00:15:34.130 --> 00:15:38.180
Let's say the gene for hair
color is on chromosome 1, so

00:15:38.180 --> 00:15:41.250
let's say hair color, the
gene is there and there.

00:15:41.250 --> 00:15:43.060
These might be different
versions of hair color,

00:15:43.060 --> 00:15:44.950
different alleles, but the
genes are on that same

00:15:44.950 --> 00:15:45.860
chromosome.

00:15:45.860 --> 00:15:50.520
In this situation, if someone
gets-- let's say if this is

00:15:50.520 --> 00:15:55.200
blue eyes here and this is blond
hair, then these are

00:15:55.200 --> 00:15:56.910
going always travel together.

00:15:56.910 --> 00:15:59.370
You're not going to have these
assort independently.

00:15:59.370 --> 00:16:02.010
And these are called
linked traits.

00:16:02.010 --> 00:16:03.560
Let me highlight that.

00:16:03.560 --> 00:16:07.730
So these right there, those
are linked traits.

00:16:07.730 --> 00:16:10.180
But for a second, and we'll talk
more about linked traits,

00:16:10.180 --> 00:16:13.140
and especially sex-linked traits
in probably the next

00:16:13.140 --> 00:16:15.520
video or a few videos from now,
but let's assume that

00:16:15.520 --> 00:16:19.000
we're talking about traits that
assort independently, and

00:16:19.000 --> 00:16:21.150
we cross two hybrids.

00:16:21.150 --> 00:16:23.350
So this is called a
dihybrid cross.

00:16:23.350 --> 00:16:26.600
Very fancy word, but it just
gives you an idea of the power

00:16:26.600 --> 00:16:28.170
of the Punnett square.

00:16:28.170 --> 00:16:35.490
So let's say both parents are--
so they're both hybrids,

00:16:35.490 --> 00:16:41.730
which means that they both have
the dominant brown-eye

00:16:41.730 --> 00:16:46.410
allele and they have the
recessive blue-eye allele, and

00:16:46.410 --> 00:16:51.360
they both have the dominant
big-tooth gene and they both

00:16:51.360 --> 00:16:53.570
have the recessive little
tooth gene.

00:16:53.570 --> 00:16:57.300
So this is the genotype
for both parents.

00:16:57.300 --> 00:17:00.440
Both parents are dihybrid.

00:17:00.440 --> 00:17:03.980
They're hybrids for both
genes, both parents.

00:17:03.980 --> 00:17:04.980
What are all the different

00:17:04.980 --> 00:17:06.920
combinations for their children?

00:17:06.920 --> 00:17:09.300
And I could have done this
without dihybrids.

00:17:09.300 --> 00:17:12.490
I could have made one of them
homozygous for one of the

00:17:12.490 --> 00:17:15.000
traits and a hybrid for the
other, and I could have done

00:17:15.000 --> 00:17:17.200
every different combination,
but I'll do the dihybrid,

00:17:17.200 --> 00:17:19.780
because it leads to a lot of our
variety, and you'll often

00:17:19.780 --> 00:17:22.630
see this in classes.

00:17:22.630 --> 00:17:29.160
So if I'm talking about the mom,
what are the different

00:17:29.160 --> 00:17:32.930
combinations of genes that
the mom can contribute?

00:17:32.930 --> 00:17:37.770
Well, the mom could contribute
the brown-- so for each of

00:17:37.770 --> 00:17:41.390
these traits, she can only
contribute one of the alleles.

00:17:41.390 --> 00:17:46.660
So she could contribute this
brown right here and then the

00:17:46.660 --> 00:17:51.670
big yellow T, so this is one
combination, or she could

00:17:51.670 --> 00:17:59.140
contribute the big brown and
then the little yellow t, or

00:17:59.140 --> 00:18:01.670
she can contribute
the blue-eyed

00:18:01.670 --> 00:18:04.160
allele and the big T.

00:18:04.160 --> 00:18:06.040
So these are all the different
combinations that she could

00:18:06.040 --> 00:18:07.000
contribute.

00:18:07.000 --> 00:18:10.210
And then the final combination
is this allele and that

00:18:10.210 --> 00:18:16.370
allele, so the blue eyes
and the small teeth.

00:18:16.370 --> 00:18:18.180
So that's from mom.

00:18:18.180 --> 00:18:21.050
And, of course, dad could
contribute the same different

00:18:21.050 --> 00:18:23.900
combinations because dad
has the same genotype.

00:18:23.900 --> 00:18:27.060
Let me write that down.

00:18:27.060 --> 00:18:29.250
Let me just write it like this
so I don't have to keep

00:18:29.250 --> 00:18:32.130
switching colors.

00:18:32.130 --> 00:18:33.850
Actually, I want to make them
a little closer together

00:18:33.850 --> 00:18:37.490
because I'm going to run
out of space otherwise.

00:18:37.490 --> 00:18:38.870
Nope.

00:18:38.870 --> 00:18:40.400
Let me do it like that.

00:18:40.400 --> 00:18:46.320
OK, brown eyes, so the dad could
contribute the big teeth

00:18:46.320 --> 00:18:50.190
or the little teeth, z along
with the brown-eyed gene, or

00:18:50.190 --> 00:18:54.510
he could contribute the
blue-eyed gene, the blue-eyed

00:18:54.510 --> 00:18:58.710
allele in combination with the
big teeth or the yellow teeth.

00:18:58.710 --> 00:19:00.940
Not the yellow teeth,
the little teeth.

00:19:00.940 --> 00:19:02.940
That would be a different gene
for yellow teeth or maybe

00:19:02.940 --> 00:19:04.600
that's an environmental
factor.

00:19:04.600 --> 00:19:07.270
So these are all the different
combinations that can occur

00:19:07.270 --> 00:19:08.530
for their offspring.

00:19:08.530 --> 00:19:12.790
So let's draw-- call this maybe
a super Punnett square,

00:19:12.790 --> 00:19:14.250
because we're now dealing
with, instead of four

00:19:14.250 --> 00:19:20.030
combinations, we have
16 combinations.

00:19:20.030 --> 00:19:24.160
It looks like I ran out
of ink right there.

00:19:24.160 --> 00:19:28.230
It's strange why--
16 combinations.

00:19:28.230 --> 00:19:32.080
Let me write that out.

00:19:32.080 --> 00:19:33.860
Something's wrong
with my tablet.

00:19:33.860 --> 00:19:34.790
Maybe there's something weird.

00:19:34.790 --> 00:19:38.350
OK, so there's 16 different
combinations, and let's write

00:19:38.350 --> 00:19:40.870
them all out, and I'll just
stay in one maybe neutral

00:19:40.870 --> 00:19:42.490
color so I don't have
to keep switching.

00:19:42.490 --> 00:19:47.500
I could get this combination,
so this brown eyes from my

00:19:47.500 --> 00:19:51.410
mom, brown eyes from my dad
allele, so its brown-brown,

00:19:51.410 --> 00:19:53.510
and then big teeth from both.

00:19:53.510 --> 00:19:56.870
I could have this combination,
so I have capital B

00:19:56.870 --> 00:19:58.830
and a capital B.

00:19:58.830 --> 00:20:02.580
And then I have a capital
T and a lowercase t.

00:20:02.580 --> 00:20:05.000
And then let's just keep
moving forward.

00:20:05.000 --> 00:20:09.630
So I could get a capital B and a
lowercase B with a capital T

00:20:09.630 --> 00:20:16.070
and a capital T, a big B,
lowercase B, capital T

00:20:16.070 --> 00:20:17.350
lowercase t.

00:20:17.350 --> 00:20:18.780
And I'm just going to go through
these super-fast

00:20:18.780 --> 00:20:21.920
because it's going to take
forever, so capital B from

00:20:21.920 --> 00:20:26.130
here, capital B from there;
capital T, lowercase t from

00:20:26.130 --> 00:20:32.150
here; capital B from each and
then lowercase t from each.

00:20:32.150 --> 00:20:35.220
You have a capital B and then
a lowercase b from that one,

00:20:35.220 --> 00:20:39.760
and then a capital T from the
mom, lowercase t from the dad.

00:20:39.760 --> 00:20:42.070
Hopefully, you're not getting
too tired here.

00:20:42.070 --> 00:20:45.730
And so then you have the capital
B from your dad and

00:20:45.730 --> 00:20:48.060
then lowercase b
from your mom.

00:20:48.060 --> 00:20:50.980
Two lowercase t's-- actually
let me just pause and fill

00:20:50.980 --> 00:20:53.320
these in because I don't want
to waste your time.

00:20:53.320 --> 00:20:56.400
There I have saved you some time
and I've filled in every

00:20:56.400 --> 00:20:59.750
combination similar to what
happens on many cooking shows.

00:20:59.750 --> 00:21:01.290
But now that I've filled
in all the different

00:21:01.290 --> 00:21:03.850
combinations, we can talk a
little bit about the different

00:21:03.850 --> 00:21:06.000
phenotypes that might
be expressed from

00:21:06.000 --> 00:21:07.860
this dihybrid cross.

00:21:07.860 --> 00:21:11.990
For example, how many of these
are going to exhibit brown

00:21:11.990 --> 00:21:13.620
eyes and big teeth?

00:21:13.620 --> 00:21:15.780
So big teeth, brown-eyed kids.

00:21:19.340 --> 00:21:21.110
Let me write this down here.

00:21:21.110 --> 00:21:27.190
So if I want big teeth
and brown eyes.

00:21:31.590 --> 00:21:35.480
All of a sudden, my pen
doesn't-- brown eyes.

00:21:35.480 --> 00:21:36.500
So how many are there?

00:21:36.500 --> 00:21:37.880
Big teeth and brown eyes.

00:21:37.880 --> 00:21:42.450
So they're both dominant, so if
you have either a capital B

00:21:42.450 --> 00:21:45.490
or a capital T in any of them,
you're going to have big teeth

00:21:45.490 --> 00:21:49.410
and brown eyes, so this is
big teeth and brown eyes.

00:21:49.410 --> 00:21:52.820
Big teeth right here,
brown eyes there.

00:21:52.820 --> 00:21:54.700
Or maybe I should just say
brown eyes and big teeth

00:21:54.700 --> 00:21:56.250
because that's the order that
I wrote it right here.

00:21:56.250 --> 00:21:59.780
Brown eyes and big teeth, brown
eyes and big teeth.

00:21:59.780 --> 00:22:01.370
Even though I have a recessive
trait here,

00:22:01.370 --> 00:22:02.620
the brown eyes dominate.

00:22:02.620 --> 00:22:05.350
I had a small teeth here, but
the big teeth dominate.

00:22:05.350 --> 00:22:07.820
This is brown eyes
and big teeth.

00:22:07.820 --> 00:22:10.200
This is brown eyes
and big teeth.

00:22:10.200 --> 00:22:13.700
Let's see, this is brown eyes
and big teeth, brown eyes and

00:22:13.700 --> 00:22:18.660
big teeth, and let me see,
is that all of them?

00:22:18.660 --> 00:22:19.360
Well, no.

00:22:19.360 --> 00:22:21.180
This is brown eyes
and little teeth.

00:22:21.180 --> 00:22:24.850
This is brown eyes and big teeth
right there, and this is

00:22:24.850 --> 00:22:26.160
also brown eyes and big teeth.

00:22:26.160 --> 00:22:29.450
They're heterozygous for each
trait, but both brown eyes and

00:22:29.450 --> 00:22:32.720
big teeth are dominant, so these
are all phenotypes of

00:22:32.720 --> 00:22:33.890
brown eyes and big teeth.

00:22:33.890 --> 00:22:35.160
So how many of those
do we have?

00:22:35.160 --> 00:22:37.740
We have one, two, three,
four, five, six, seven,

00:22:37.740 --> 00:22:40.430
eight, nine of those.

00:22:40.430 --> 00:22:43.030
So we have nine.

00:22:43.030 --> 00:22:45.840
Nine brown eyes and big teeth.

00:22:45.840 --> 00:22:49.810
Now, how many do we
have of big teeth?

00:22:52.630 --> 00:22:55.350
Let me write in a different
color, so let me write brown

00:22:55.350 --> 00:22:59.880
eyes and little teeth.

00:23:02.820 --> 00:23:04.350
Something on my pen tablet
doesn't work

00:23:04.350 --> 00:23:05.560
quite right over there.

00:23:05.560 --> 00:23:07.970
So brown eyes and
little teeth.

00:23:07.970 --> 00:23:09.500
So let's see, this
is brown eyes and

00:23:09.500 --> 00:23:11.100
little teeth right there.

00:23:11.100 --> 00:23:14.270
This is brown eyes and little
teeth right there.

00:23:14.270 --> 00:23:17.280
This is brown eyes and little
teeth right there.

00:23:17.280 --> 00:23:19.070
So there's three combinations
of brown

00:23:19.070 --> 00:23:22.010
eyes and little teeth.

00:23:22.010 --> 00:23:31.810
And if I were to say blue eyes,
blue and big teeth, what

00:23:31.810 --> 00:23:32.900
are the combinations there?

00:23:32.900 --> 00:23:35.750
Well, this is blue eyes and big
teeth, blue eyes and big

00:23:35.750 --> 00:23:39.650
teeth, blue eyes and big
teeth, so there's three

00:23:39.650 --> 00:23:41.110
combinations there.

00:23:41.110 --> 00:23:45.210
And if I want to be recessive on
both traits, so if I want--

00:23:45.210 --> 00:23:46.480
let me do this.

00:23:46.480 --> 00:23:51.490
I want blue eyes, blue
and little teeth.

00:23:54.900 --> 00:23:57.090
There's only one.

00:23:57.090 --> 00:24:00.250
Out of the 16, there's only one
situation where I inherit

00:24:00.250 --> 00:24:05.490
the recessive trait from both
parents for both traits.

00:24:05.490 --> 00:24:07.310
So if you look at this, and
you say, hey, what's the

00:24:07.310 --> 00:24:09.920
probability-- there's only
one of that-- what's the

00:24:09.920 --> 00:24:12.590
probability of having a big
teeth, brown-eyed child?

00:24:12.590 --> 00:24:14.240
And these are all
the phenotypes.

00:24:14.240 --> 00:24:17.240
There were 16 different
possibilities here, right?

00:24:17.240 --> 00:24:20.640
There are 16 squares here, and
9 of them describe the

00:24:20.640 --> 00:24:22.860
phenotype of big teeth
and brown eyes, so

00:24:22.860 --> 00:24:25.420
there's a 9/16 chance.

00:24:25.420 --> 00:24:28.090
So it's 9 out of 16 chance
of having a big

00:24:28.090 --> 00:24:29.830
teeth, brown-eyed child.

00:24:29.830 --> 00:24:32.090
What's the probability
of a blue-eyed

00:24:32.090 --> 00:24:33.700
child with little teeth?

00:24:33.700 --> 00:24:37.080
1 in 16.

00:24:37.080 --> 00:24:41.010
So hopefully, in this video,
you've appreciated the power

00:24:41.010 --> 00:24:43.530
of the Punnett square, that it's
a useful way to explore

00:24:43.530 --> 00:24:46.340
every different combination of
all the genes, and it doesn't

00:24:46.340 --> 00:24:47.560
have to be only one trait.

00:24:47.560 --> 00:24:51.440
It can be in this case where
you're doing two traits that

00:24:51.440 --> 00:24:54.300
show dominance, but they assort
independently because

00:24:54.300 --> 00:24:55.840
they're on different
chromosomes.

00:24:55.840 --> 00:24:58.560
You could use it-- where'd
I do it over here?

00:24:58.560 --> 00:25:02.260
You could use it to explore
incomplete dominance when

00:25:02.260 --> 00:25:04.870
there's blending, where red and
white made pink genes, or

00:25:04.870 --> 00:25:07.820
you can even use it when there's
codominance and when

00:25:07.820 --> 00:25:10.110
you have multiple alleles,
where it's not just two

00:25:10.110 --> 00:25:12.640
different versions of the genes,
there's actually three

00:25:12.640 --> 00:25:13.730
different versions.

00:25:13.730 --> 00:25:16.120
So hopefully, you've
enjoyed that.


Introduction to Heredity

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:04.790
Well, before we even knew what
DNA was, much less how it was

00:00:04.790 --> 00:00:07.160
structured or it was replicated
or even before we

00:00:07.160 --> 00:00:11.020
could look in and see meiosis
happening in cells, we had the

00:00:11.020 --> 00:00:14.700
general sense that offspring
were the products of some

00:00:14.700 --> 00:00:16.480
traits that their parents had.

00:00:16.480 --> 00:00:22.170
That if I had a guy with blue
eyes-- let me say this is the

00:00:22.170 --> 00:00:27.430
blue-eyed guy right here --and
then if he were to marry a

00:00:27.430 --> 00:00:32.800
brown-eyed girl-- Let's say this
is the brown-eyed girl.

00:00:32.800 --> 00:00:36.410
Maybe make it a little
bit more like a girl.

00:00:36.410 --> 00:00:39.450
If he were to marry the
brown-eyed girl there, that

00:00:39.450 --> 00:00:42.230
most of the time, or maybe in
all cases where we're dealing

00:00:42.230 --> 00:00:45.030
with the brown-eyed girl,
maybe their kids are

00:00:45.030 --> 00:00:46.870
brown-eyed.

00:00:46.870 --> 00:00:50.210
Let me do this so they have a
little brown-eyed baby here.

00:00:53.000 --> 00:00:54.980
And this is just something--
I mean, there's obviously

00:00:54.980 --> 00:00:57.420
thousands of generations of
human beings, and we've

00:00:57.420 --> 00:00:58.180
observed this.

00:00:58.180 --> 00:01:00.590
We've observed that kids look
like their parents, that they

00:01:00.590 --> 00:01:05.280
inherit some traits, and that
some traits seem to dominate

00:01:05.280 --> 00:01:06.140
other traits.

00:01:06.140 --> 00:01:09.960
One example of that tends to
be a darker pigmentation in

00:01:09.960 --> 00:01:11.570
maybe the hair or the eyes.

00:01:11.570 --> 00:01:15.710
Even if the other parent has
light pigmentation, the darker

00:01:15.710 --> 00:01:17.900
one seems to dominate, or
sometimes, it actually ends up

00:01:17.900 --> 00:01:20.420
being a mix, and we've seen
that all around us.

00:01:20.420 --> 00:01:23.410
Now, this study of what gets
passed on and how it gets

00:01:23.410 --> 00:01:26.590
passed on, it's much older than
the study of DNA, which

00:01:26.590 --> 00:01:29.840
was really kind of discovered
or became a big deal in the

00:01:29.840 --> 00:01:31.110
middle of the 20th century.

00:01:31.110 --> 00:01:32.820
This was studied a long time.

00:01:32.820 --> 00:01:36.750
And kind of the father of
classical genetics and

00:01:36.750 --> 00:01:38.455
heredity is Gregor Mendel.

00:01:41.720 --> 00:01:45.650
He was actually a monk, and he
would mess around with plants

00:01:45.650 --> 00:01:48.795
and cross them and see which
traits got passed and which

00:01:48.795 --> 00:01:51.230
traits didn't get passed and
tried to get an understanding

00:01:51.230 --> 00:01:55.650
of how traits are passed from
one generation to another.

00:01:55.650 --> 00:02:02.090
So when we do this, when we
study this classical genetics,

00:02:02.090 --> 00:02:05.230
I'm going to make a bunch of
simplifying assumptions

00:02:05.230 --> 00:02:08.080
because we know that most of
these don't hold for most of

00:02:08.080 --> 00:02:11.140
our genes, but it'll give us a
little bit of sense of how to

00:02:11.140 --> 00:02:16.340
predict what might happen
in future generations.

00:02:16.340 --> 00:02:21.270
So the first simplifying
assumption I'll make is that

00:02:21.270 --> 00:02:24.840
some traits have kind of this
all or nothing property.

00:02:24.840 --> 00:02:26.690
And we know that a lot
of traits don't.

00:02:26.690 --> 00:02:28.690
Let's say that there are in
the world-- and this is a

00:02:28.690 --> 00:02:35.220
gross oversimplification --let's
say for eye color,

00:02:35.220 --> 00:02:38.520
let's say that there
are two alleles.

00:02:38.520 --> 00:02:40.390
Now remember what
an allele was.

00:02:40.390 --> 00:02:44.030
An allele is a specific
version of a gene.

00:02:44.030 --> 00:02:48.400
So let's say that you could
have blue eye color or you

00:02:48.400 --> 00:02:52.460
could have brown eye color.

00:02:52.460 --> 00:02:55.220
That we live in a universe where
someone could only have

00:02:55.220 --> 00:02:58.320
one of these two versions
of the eye color gene.

00:02:58.320 --> 00:03:01.230
We know that eye color is far
more complex than that, so

00:03:01.230 --> 00:03:02.970
this is just a simplification.

00:03:02.970 --> 00:03:04.340
And let me just make
up another one.

00:03:04.340 --> 00:03:14.110
Let me say that, I don't know,
maybe for tooth size, that's a

00:03:14.110 --> 00:03:17.590
trait you won't see in any
traditional biology textbook,

00:03:17.590 --> 00:03:23.470
and let's say that there's one
trait for big teeth and

00:03:23.470 --> 00:03:28.330
there's another allele
for small teeth.

00:03:28.330 --> 00:03:30.850
And I want to make very clear
this distinction between a

00:03:30.850 --> 00:03:32.100
gene and an allele.

00:03:35.230 --> 00:03:37.740
I talked about Gregor Mendel,
and he was doing this in the

00:03:37.740 --> 00:03:41.890
1850s well before we knew what
DNA was or what even

00:03:41.890 --> 00:03:48.590
chromosomes were and how DNA was
passed on, et cetera, but

00:03:48.590 --> 00:03:53.060
let's go into the microbiology
of it to understand the

00:03:53.060 --> 00:03:53.840
difference.

00:03:53.840 --> 00:03:56.170
So I have a chromosome.

00:03:56.170 --> 00:03:59.710
Let's say on some chromosome--
let me pick

00:03:59.710 --> 00:04:00.900
some chromosome here.

00:04:00.900 --> 00:04:02.930
Let's say this is
some chromosome.

00:04:02.930 --> 00:04:04.590
Let's say I got that
from my dad.

00:04:04.590 --> 00:04:09.130
And on this chromosome, there's
some location here--

00:04:09.130 --> 00:04:11.550
we could call that the locus on
this chromosome where the

00:04:11.550 --> 00:04:15.330
eye color gene is --that's
the location of

00:04:15.330 --> 00:04:16.579
the eye color gene.

00:04:16.579 --> 00:04:19.279
Now, I have two chromosomes,
one from my father and one

00:04:19.279 --> 00:04:22.010
from my mother, so let's say
that this is the chromosome

00:04:22.010 --> 00:04:23.260
from my mother.

00:04:26.020 --> 00:04:27.800
We know that when they're
normally in the cell, they

00:04:27.800 --> 00:04:30.180
aren't nice and neatly organized
like this in the

00:04:30.180 --> 00:04:32.860
chromosome, but this is just to
kind of show you the idea.

00:04:32.860 --> 00:04:35.690
Let's say these are homologous
chromosomes so they code for

00:04:35.690 --> 00:04:36.970
the same genes.

00:04:36.970 --> 00:04:41.460
So on this gene from my mother
on that same location or

00:04:41.460 --> 00:04:45.710
locus, there's also the
eye color gene.

00:04:45.710 --> 00:04:51.020
Now, I might have the same
version of the gene and I'm

00:04:51.020 --> 00:04:52.760
saying that there's only
two versions of

00:04:52.760 --> 00:04:54.220
this gene in the world.

00:04:54.220 --> 00:04:56.690
Now, if I have the same version
of the gene-- I'm

00:04:56.690 --> 00:04:58.510
going to make a little
shorthand notation.

00:04:58.510 --> 00:05:01.101
I'm going to write big B--
Actually, let me do

00:05:01.101 --> 00:05:02.010
it the other way.

00:05:02.010 --> 00:05:04.040
I'm going to write little b
for blue and I'm going to

00:05:04.040 --> 00:05:07.420
write big B for brown.

00:05:07.420 --> 00:05:11.210
There's a situation where this
could be a little b and this

00:05:11.210 --> 00:05:12.800
could be a big B.

00:05:12.800 --> 00:05:17.010
And then I could write that my
genotype-- I have the allele,

00:05:17.010 --> 00:05:20.320
I have one big B from my
mom and I have one

00:05:20.320 --> 00:05:24.440
small b from my dad.

00:05:24.440 --> 00:05:29.120
Each of these instances, or
ways that this gene is

00:05:29.120 --> 00:05:30.660
expressed, is an allele.

00:05:30.660 --> 00:05:40.360
So these are two different
alleles-- let me write that

00:05:40.360 --> 00:05:42.880
--or versions of
the same gene.

00:05:42.880 --> 00:05:46.340
And when I have two different
versions like this, one

00:05:46.340 --> 00:05:50.140
version from my mom, one version
from my dad, I'm

00:05:50.140 --> 00:05:53.480
called a heterozygote, or
sometimes it's called a

00:05:53.480 --> 00:05:54.730
heterozygous genotype.

00:06:00.410 --> 00:06:05.000
And the genotype is the exact
version of the alleles I have.

00:06:05.000 --> 00:06:08.170
Let's say I had the
lowercase b.

00:06:08.170 --> 00:06:11.690
I had the blue-eyed gene
from both parents.

00:06:11.690 --> 00:06:16.040
So let's say that I was
lowercase b, lowercase b, then

00:06:16.040 --> 00:06:18.600
I would have two identical
alleles.

00:06:18.600 --> 00:06:21.840
Both of my parents gave me the
same version of the gene.

00:06:21.840 --> 00:06:29.930
And this case, this genotype
is homozygous, or this is a

00:06:29.930 --> 00:06:33.900
homozygous genotype, or I'm a
homozygote for this trait.

00:06:36.400 --> 00:06:38.510
Now, you might say,
Sal, this is fine.

00:06:38.510 --> 00:06:43.400
These are the traits that you
have. I have a brown from

00:06:43.400 --> 00:06:47.550
maybe my mom and a
blue from my dad.

00:06:47.550 --> 00:06:50.850
In this case, I have a blue
from both my mom and dad.

00:06:50.850 --> 00:06:54.590
How do we know whether my eyes
are going to be brown or blue?

00:06:54.590 --> 00:06:56.900
And the reality is it's
very complex.

00:06:56.900 --> 00:06:58.410
It's a whole mixture
of things.

00:06:58.410 --> 00:07:02.830
But Mendel, he studied
things that showed

00:07:02.830 --> 00:07:04.080
what we'll call dominance.

00:07:09.260 --> 00:07:12.930
And this is the idea that
one of these traits

00:07:12.930 --> 00:07:14.090
dominates the other.

00:07:14.090 --> 00:07:17.160
So a lot of people originally
thought that eye color,

00:07:17.160 --> 00:07:20.490
especially blue eyes,
was always dominated

00:07:20.490 --> 00:07:21.500
by the other traits.

00:07:21.500 --> 00:07:23.140
We'll assume that here,
but that's a gross

00:07:23.140 --> 00:07:24.510
oversimplification.

00:07:24.510 --> 00:07:34.200
So let's say that brown
eyes are dominant

00:07:34.200 --> 00:07:36.130
and blue are recessive.

00:07:39.320 --> 00:07:42.960
I wanted to do that in blue.

00:07:42.960 --> 00:07:49.560
Blue eyes are recessive.

00:07:49.560 --> 00:07:52.330
If this is the case, and this
is a-- As I've said

00:07:52.330 --> 00:07:55.730
repeatedly, this is a gross
oversimplification.

00:07:55.730 --> 00:08:00.670
But if that is the case, then
if I were to inherit this

00:08:00.670 --> 00:08:05.540
genotype, because brown eyes
are dominant-- remember, I

00:08:05.540 --> 00:08:12.400
said the big B here represents
brown eye and the lowercase b

00:08:12.400 --> 00:08:16.670
is recessive --all you're going
to see for the person

00:08:16.670 --> 00:08:19.450
with this genotype
is brown eyes.

00:08:19.450 --> 00:08:20.880
So let me do this here.

00:08:20.880 --> 00:08:21.710
Let me write this here.

00:08:21.710 --> 00:08:27.680
So genotype, and then I'll
write phenotype.

00:08:27.680 --> 00:08:31.030
Genotype is the actual versions
of the gene you have

00:08:31.030 --> 00:08:33.780
and then the phenotypes
are what's expressed

00:08:33.780 --> 00:08:35.030
or what do you see.

00:08:39.690 --> 00:08:43.860
So if I get a brown-eyed gene
from my dad-- And I want to do

00:08:43.860 --> 00:08:46.310
it in a big-- I want
to do it in brown.

00:08:46.310 --> 00:08:49.670
Let me do it in brown so
you don't get confused.

00:08:49.670 --> 00:08:54.490
So if I've have a brown-eyed
gene from my dad and a

00:08:54.490 --> 00:09:05.130
blue-eyed gene from my mom,
because the brown eye is

00:09:05.130 --> 00:09:08.580
recessive, the brown-eyed allele
is recessive-- And I

00:09:08.580 --> 00:09:11.370
just said a brown-eyed gene, but
what I should say is the

00:09:11.370 --> 00:09:13.870
brown-eyed version of the
gene, which is the brown

00:09:13.870 --> 00:09:16.820
allele, or the blue-eyed version
of the gene from my

00:09:16.820 --> 00:09:18.890
mom, which is the blue allele.

00:09:18.890 --> 00:09:22.290
Since the brown allele is
dominant-- I wrote that up

00:09:22.290 --> 00:09:25.410
here --what's going to be
expressed are brown eyes.

00:09:30.830 --> 00:09:34.450
Now, let's say I had
it the other way.

00:09:34.450 --> 00:09:39.850
Let's say I got a blue-eyed
allele from my dad and I get a

00:09:39.850 --> 00:09:41.750
brown-eyed allele for my mom.

00:09:41.750 --> 00:09:42.490
Same thing.

00:09:42.490 --> 00:09:46.940
The phenotype is going
to be brown eyes.

00:09:46.940 --> 00:09:49.730
Now, what if I get a brown-eyed
allele from both my

00:09:49.730 --> 00:09:52.470
mom and my dad?

00:09:52.470 --> 00:09:54.930
Let me see, I keep changing
the shade of brown, but

00:09:54.930 --> 00:09:55.960
they're all supposed
to be the same.

00:09:55.960 --> 00:09:59.130
So let's say I get two dominant
brown-eyed alleles

00:09:59.130 --> 00:10:00.820
from my mom and my dad.

00:10:00.820 --> 00:10:01.770
Then what are you
going to see?

00:10:01.770 --> 00:10:02.640
Well, you could guess that.

00:10:02.640 --> 00:10:08.280
I'm still going to
see brown eyes.

00:10:08.280 --> 00:10:10.570
So there's only one last
combination because these are

00:10:10.570 --> 00:10:12.800
the only two types of alleles
we might see in our

00:10:12.800 --> 00:10:15.510
population, although for
most genes, there's

00:10:15.510 --> 00:10:16.710
more than two types.

00:10:16.710 --> 00:10:18.400
For example, there's
blood types.

00:10:18.400 --> 00:10:21.490
There's four types of blood.

00:10:21.490 --> 00:10:25.540
But let's say that I get two
blue, one blue allele from

00:10:25.540 --> 00:10:30.400
each of my parents, one from
my dad, one from my mom.

00:10:30.400 --> 00:10:33.080
Then all of a sudden, this is a
recessive trait, but there's

00:10:33.080 --> 00:10:34.550
nothing to dominate it.

00:10:34.550 --> 00:10:39.130
So, all of a sudden, the
phenotype will be blue eyes.

00:10:39.130 --> 00:10:42.380
And I want to repeat again, this
isn't necessarily how the

00:10:42.380 --> 00:10:45.130
alleles for eye color work, but
it's a nice simplification

00:10:45.130 --> 00:10:48.370
to maybe understand how
heredity works.

00:10:48.370 --> 00:10:52.040
There are some traits that can
be studied in this simple way.

00:10:52.040 --> 00:10:54.920
But what I wanted to do here
is to show you that many

00:10:54.920 --> 00:10:58.970
different genotypes-- so these
are all different genotypes

00:10:58.970 --> 00:11:02.090
--they all coded for
the same phenotype.

00:11:02.090 --> 00:11:05.000
So just by looking at someone's
eye color, you

00:11:05.000 --> 00:11:09.000
didn't know exactly whether
they were homozygous

00:11:09.000 --> 00:11:16.740
dominant-- this would be
homozygous dominant --or

00:11:16.740 --> 00:11:19.080
whether they were
heterozygotes.

00:11:19.080 --> 00:11:21.350
This is heterozygous
right here.

00:11:21.350 --> 00:11:23.650
These two right here
are heterozygotes.

00:11:27.990 --> 00:11:31.680
These are also sometimes called
hybrids, but the word

00:11:31.680 --> 00:11:33.600
hybrid is kind of overloaded.

00:11:33.600 --> 00:11:36.800
It's used a lot, but in this
context, it means that you got

00:11:36.800 --> 00:11:40.940
different versions of the
allele for that gene.

00:11:40.940 --> 00:11:43.740
So let's think a little bit
about what's actually

00:11:43.740 --> 00:11:48.155
happening when my mom and
my dad reproduced.

00:11:50.970 --> 00:11:53.100
Well, let's think of a couple
of different scenarios.

00:11:55.950 --> 00:11:57.630
Let's say that they're
both hybrids.

00:11:57.630 --> 00:12:03.470
My dad has the brown-eyed
dominant allele and he also

00:12:03.470 --> 00:12:08.020
has the blue-eyed recessive
allele.

00:12:08.020 --> 00:12:11.560
Let's say my mom has the same
thing, so brown-eyed dominant,

00:12:11.560 --> 00:12:14.780
and she also has the blue-eyed
recessive allele.

00:12:14.780 --> 00:12:17.880
Now let's think about if these
two people, before you see

00:12:17.880 --> 00:12:20.630
what my eye color is, if you
said, look, I'm giving you

00:12:20.630 --> 00:12:22.760
what these two people's
genotypes are.

00:12:22.760 --> 00:12:24.010
Let me label them.

00:12:26.200 --> 00:12:27.790
Let me make this the mom.

00:12:27.790 --> 00:12:30.090
I think this is the standard
convention.

00:12:30.090 --> 00:12:34.730
And let's make this right
here, this is the dad.

00:12:34.730 --> 00:12:37.910
What are the different genotypes
that their children

00:12:37.910 --> 00:12:38.490
could have?

00:12:38.490 --> 00:12:40.630
So let's say they reproduce.

00:12:40.630 --> 00:12:44.090
I'm going to draw a
little grid here.

00:12:44.090 --> 00:12:45.660
So let me draw a grid.

00:12:50.390 --> 00:12:55.990
So we know from our study of
meiosis that, look, my mom has

00:12:55.990 --> 00:12:59.870
this gene on-- Let me draw
the genes again.

00:12:59.870 --> 00:13:02.240
So there's a homologous
pair, right?

00:13:02.240 --> 00:13:04.880
This is one chromosome
right here.

00:13:04.880 --> 00:13:07.070
That's another chromosome
right there.

00:13:07.070 --> 00:13:10.130
On this chromosome in the
homologous pair, there might

00:13:10.130 --> 00:13:16.760
be-- at the eye color locus
--there's the brown-eyed gene.

00:13:16.760 --> 00:13:19.470
And at this one, at the eye
color locus, there's a

00:13:19.470 --> 00:13:20.890
blue-eyed gene.

00:13:20.890 --> 00:13:24.630
And similarly from my dad, when
you look at that same

00:13:24.630 --> 00:13:28.310
chromosome in his cells-- Let
me do them like this.

00:13:28.310 --> 00:13:30.740
So this is one chromosome there
and this is the other

00:13:30.740 --> 00:13:32.760
chromosome here.

00:13:32.760 --> 00:13:35.120
When you look at that locus
on this chromosome or that

00:13:35.120 --> 00:13:37.870
location, it has the brown-eyed
allele for that

00:13:37.870 --> 00:13:40.370
gene, and on this one,
it has the blue-eyed

00:13:40.370 --> 00:13:41.590
allele on this gene.

00:13:41.590 --> 00:13:44.680
And we learn from meiosis when
the chromosomes-- Well, they

00:13:44.680 --> 00:13:47.580
replicate first, and so you have
these two chromatids on a

00:13:47.580 --> 00:13:48.140
chromosome.

00:13:48.140 --> 00:13:51.520
But they line up in meiosis
I during the metaphase.

00:13:51.520 --> 00:13:53.220
And we don't know which
way they line up.

00:13:53.220 --> 00:13:56.510
For example, my dad might give
me this chromosome or might

00:13:56.510 --> 00:13:57.630
give me that chromosome.

00:13:57.630 --> 00:13:59.790
Or my mom might give me that
chromosome or might give me

00:13:59.790 --> 00:14:00.820
that chromosome.

00:14:00.820 --> 00:14:02.760
So I could have any of
these combinations.

00:14:02.760 --> 00:14:06.540
So, for example, if I get this
chromosome from my mom and

00:14:06.540 --> 00:14:09.760
this chromosome from my dad,
what is the genotype going to

00:14:09.760 --> 00:14:11.000
be for eye color?

00:14:11.000 --> 00:14:16.770
Well, it's going to be capital
B and capital B.

00:14:16.770 --> 00:14:21.510
If I get this chromosome from
my mom and this chromosome

00:14:21.510 --> 00:14:22.620
from my dad, what's
it going to be?

00:14:22.620 --> 00:14:28.330
Well, I'm going to get the big
B from my dad and then I'm

00:14:28.330 --> 00:14:30.790
going to get the lowercase
b from my mom.

00:14:30.790 --> 00:14:32.790
So this is another
possibility.

00:14:32.790 --> 00:14:35.510
Now, this is another possibility
here where I get

00:14:35.510 --> 00:14:42.490
the brown-eyed allele from my
mom and I get the blue eye

00:14:42.490 --> 00:14:44.380
allele from my dad.

00:14:44.380 --> 00:14:47.350
And then there's a possibility
that I get this chromosome

00:14:47.350 --> 00:14:51.260
from my dad and this chromosome
from my mom, so

00:14:51.260 --> 00:14:53.520
it's this situation.

00:14:53.520 --> 00:14:55.700
Now, what are the phenotypes
going to be?

00:14:55.700 --> 00:14:58.290
Well, we've already seen that
this one right here is going

00:14:58.290 --> 00:15:03.080
to be brown, that one's going to
be brown, this one's going

00:15:03.080 --> 00:15:06.250
to be brown, but this one
is going to be blue.

00:15:06.250 --> 00:15:07.860
I already showed you this.

00:15:07.860 --> 00:15:09.980
But if I were to tell you ahead
of time that, look, I

00:15:09.980 --> 00:15:11.090
have two people.

00:15:11.090 --> 00:15:13.980
They're both hybrids, or they're
both heterozygotes for

00:15:13.980 --> 00:15:16.610
eye color, and eye
color has this

00:15:16.610 --> 00:15:18.335
recessive dominant situation.

00:15:18.335 --> 00:15:22.530
And they're both heterozygotes
where they each have one brown

00:15:22.530 --> 00:15:24.980
allele and one blue allele, and
they're going to have a

00:15:24.980 --> 00:15:28.835
child, what's the probability
that the child has brown eyes?

00:15:35.670 --> 00:15:37.170
What's the probability?

00:15:37.170 --> 00:15:40.720
Well, each of these scenarios
are equally likely, right?

00:15:40.720 --> 00:15:42.400
There's four equal scenarios.

00:15:42.400 --> 00:15:44.130
So let's put that in
the denominator.

00:15:44.130 --> 00:15:45.950
Four equal scenarios.

00:15:45.950 --> 00:15:48.110
And how many of those
scenarios end

00:15:48.110 --> 00:15:49.780
up with brown eyes?

00:15:49.780 --> 00:15:52.110
Well, it's one, two, three.

00:15:52.110 --> 00:15:58.780
So the probability is 3/4, or
it's a 75% probability.

00:15:58.780 --> 00:16:01.830
Same logic, what's the
probability that these parents

00:16:01.830 --> 00:16:04.650
produce an offspring
with blue eyes?

00:16:04.650 --> 00:16:07.280
Well, that's only one of
the four equally likely

00:16:07.280 --> 00:16:15.840
possibilities, so blue
eyes is only 25%.

00:16:15.840 --> 00:16:19.400
Now, what is the probability
that they produce a

00:16:19.400 --> 00:16:20.390
heterozygote?

00:16:20.390 --> 00:16:23.130
So what is the probability
that they produce a

00:16:23.130 --> 00:16:24.425
heterozygous offspring?

00:16:27.360 --> 00:16:29.300
So now we're not looking at
the phenotype anymore.

00:16:29.300 --> 00:16:31.050
We're looking at the genotype.

00:16:31.050 --> 00:16:34.310
So of these combinations,
which are heterozygous?

00:16:34.310 --> 00:16:36.570
Well, this one is, because
it has a mix.

00:16:36.570 --> 00:16:37.360
It's a hybrid.

00:16:37.360 --> 00:16:39.380
It has a mix of the
two alleles.

00:16:39.380 --> 00:16:41.170
And so is this one.

00:16:41.170 --> 00:16:42.220
So what's the probability?

00:16:42.220 --> 00:16:45.050
Well, there's four different
combinations.

00:16:45.050 --> 00:16:48.020
All of those are equally likely,
and two of them result

00:16:48.020 --> 00:16:49.200
in a heterozygote.

00:16:49.200 --> 00:16:54.580
So it's 2/4 or 1/2 or 50%.

00:16:54.580 --> 00:16:56.570
So using this Punnett square,
and, of course, we had to make

00:16:56.570 --> 00:16:59.880
a lot of assumptions about the
genes and whether one's

00:16:59.880 --> 00:17:02.050
dominant or one's a recessive,
we can start to make

00:17:02.050 --> 00:17:03.880
predictions about the
probabilities

00:17:03.880 --> 00:17:05.530
of different outcomes.

00:17:05.530 --> 00:17:07.300
And as we'll see in future
videos, you can actually even

00:17:07.300 --> 00:17:07.970
go backwards.

00:17:07.970 --> 00:17:10.680
You can say, hey, given that
this couple had five kids with

00:17:10.680 --> 00:17:14.160
brown eyes, what's the
probability that they're both

00:17:14.160 --> 00:17:15.819
heterozygotes, or something
like that.

00:17:15.819 --> 00:17:19.000
So it's a really interesting
area, even though it is a bit

00:17:19.000 --> 00:17:20.490
of oversimplification.

00:17:20.490 --> 00:17:23.760
But many traits, especially some
of the things that Gregor

00:17:23.760 --> 00:17:27.190
Mendel studied, can be
studied in this way.