In this lecture, we will continue our investigation
of classical genetics by looking a little
bit beyond Mendel. We will be looking at Mendelian
inheritance patterns that don't quite exhibit
the expected ratios. This isn’t that Mendel
is wrong; they are just extensions of his
concepts. By the end of this lecture, you
will be able to predict the outcomes of mono
and dihybrid crosses using probability methods
as well as interpret test cross data to determine
unknown phenotypes and finally you will be
able to explain why not all crosses exhibit
Mendel's predicted phenotypic outcomes.
First let us begin by looking at probabilities.
We can predict the outcome of test crosses
using a much simpler method really than Punnett
squares. Some of us get hooked on Punnett
square, but realistically probability methods
are a much more simple way to go about it.
I don't know how much experience you've had with
probability, but we will take a quick look
at two rules. One is the rule of addition
and one is the rule of multiplication. And
these are rules that really allow us to turn
sentences into mathematical equations.
The rule of addition states that two mutually
exclusive events, the probability of either
event occuring is the sum of their two probabilities.
Now that seems like a lot of words. Let us
look at an example so that you can see what
we mean exactly. Let us say you have one six
sided dice and you want to roll that dice
and get either a 1 or 2 or 3 or 5 or 6. Well you
probably already have a pretty good idea that
no matter what six sided dice you roll with
six numbers on them, you are very likely to
get one of those numbers as in 100 percent
of the time unless it balances on a corner
something strange. You will get either one
of these six numbers. Let us take a look at
that mathematically. There is a probability
of one sixth that we could get a number of
1 or there is a probability that we could
get a number 2, 1/6 or we could get a 3 or
a 4 or a 5 or a 6.
When we sum these probabilities indeed,
we do find that the math verifies that we have a 100
percent probability of rolling 1 of the 6
sides of the dice. The addition rule means
OR. Any time you see OR or can stuff an OR
into a sentence it means you are getting to
add the probabilities of the independent events.
Now let us look at the rule of multiplication.
This is an AND rule. Anytime you can stuff
an AND in, we will multiply. It states that
the probability of two independent events
both occurring is the product of their individual
probabilities. Let us take a look at that
on a dice so that we can put some meaning
behind all those crazy words. Let us say we
have two dice this time and you want to roll
a 1 and a 6. There is a one-sixth probability
of rolling 1 and on the second dice and you
want to roll the 6. We have 1/6 x 1/6 and
that gives us 1/36 chance of doing it exactly
this way. We can have a 1 and then a 6. AND
really means to multiply. Anytime you can
jam AND into a sentence for more thinking
about probability, you are going to multiply
the two probabilities. Any time you can put
a OR in and you will add them. You don’t really
need to know the specific language of the
probability law just the AND and OR part.