TOPIC TWO: Models for Mendelian Genetics

The real reading for the topic on Mendelian Genetics is the one of that title on the page whose link is this.
All that needs to be done first is to give a brief introduction to basic probability.

Some common misconceptions about probability:AN00020A.gif (1492 bytes)  [That's supposed to be a cichlid!]

I.  Let's say that there is this lake, perhaps Lake Victoria, in which 30% of the fish in this lake are have a brown spot on their tail.  This DOES mean that the if a fish is picked at random from this lake that its probability of having a brown spot on it is 0.3.  This DOES NOT mean that that if you pick 10 fish at random from this lake that 3 of the 10 WILL have a brown spot on them.

In fact, if you think about it, perhaps none of the fish in this sample of 10 have brown spots. That certainly COULD happen and therefore it need not be that 3 of the 10 WILL have brown spots.

II. Now, you might guess that it is more likely for 3 of those 10 to have spots on them than for any other possibility.   That is, you might guess that the probability that 3 of the 10 have spots is larger than, say, the probability of 4 of the 10 having spots, and you'd be CORRECT.   Why do I say you are correct?  How do I KNOW that.   After all, there could be a law a nature that says that even though 30% of the fish have brown spots, nonetheless, every time you pick 10 of them randomly it is always the case that 4 of the 10 have these brown spots.  The ONLY way to make a statement about how the world works is to do an experiment.  Well, we'll do just sort of an experiment during one of the presentations you'll see next week.

III. One more sort of confusing thing.   Take this same lake with 30% of the fish having a brown spot, and this time scoop out 10,000 fish!  Well, 30% of 10,000 is 3,000.  So although you might now have realized that it is not a sure thing that you'd get 3000 brown spotted fish, you may believe that getting a sample having exactly 3,000 of the 10,000 is rather likely, happening perhaps, say, half the time you scoop out 10,000 fish, or maybe even more often.  Well, you'd be WRONG!   In fact getting exactly 3.000 hardly ever happens.  One can compute the chance of that happening (we won't be saying how in this course) and if you did, the chance of getting exactly 3,000 brown spotted fish from a sample of 10,000 when the lake itself has 30% of its fish with brown spots is equal to: 0.000103. That is, the chance of the scoop of 10,000 fish containing exactly 3,000 ones with a brown spot on their tail about 1/10,000.  So, on average, this event happens once every 10,000 times you take a scoop of 10,000 fish.

Now, we need only one more idea before you should start the reading the article on Mendelian Genetics.  This idea is called the Multiplication Rule for Independent Events:

The Multiplication Rule for Independent Events:

Assume there are these two events that could happen and the probability that the first one happens is the number p and the probability that the second event happens is the number q.

Then, if these two events happen independently (that is, if whether or not one of them happens has no effect on whether or not the other happens), then the Probability that they BOTH happen is the product pq.

What does this have to do with genetics?   This is hard to explain without your having read at least part of that article, but.....

Let's consider the situation of sexual reproduction. Assume there is a certain gene occurring in one of two forms.  Perhaps we are talking about cichlids and the characteristic we are considering is whether the fish is a left-handed or right-handed scale biter.  [See page 79 of Darwin's Dream Pond.]  The gene for right-handedness is dominate over the one for left-handedness.  Let A stand for the dominant gene and a for the recessive gene.

Consider, say, a male whose body cells are of type Aa and a female whose body cells are also of type Aa.

QUESTION:  If these two fish mate, what is the probability that the offspring is a left-handed scale biter?

ANSWER: [We'll apply the RULE above.]  The only way to be a left-handed scale biter is to be of type aa, since the gene A is dominant.  For this to happen, the male's sperm must be of type a [This is the FIRST event.] and the female's egg must be of type a [This is the SECOND event.]  The probability of this first event is 1/2 since sperm formed from a cell of type Aa is of type a with probability 1/2.   Similarly, the probability of the egg being of type a is also 1/2.  

THEREFORE, by the The Multiplication Rule for Independent Events, the probability of BOTH sperm and egg being of type a is (1/2)(1/2).  Thus the ANSWER to the question above is 1/4.

OK, go look at that article on Mendelian Genetics.