Lesson 5
Probability is something we all come across every day. Have you ever heard someone say, "Oh, it'll probably snow today." Well there you go. When a forecaster of any event is attempting to predict, he or she will always give a probability: "There's a forty-two percent chance of hail today." That statement means that in conditions similair to those that the forecaster is commenting on, forty-two times out of one-hundred, hail fell from the heavens.
Probability is very related to heredity and genetics. The probability that offspring will be a boy or a girl is fifty percent. So if two parents had one child, there is an equal chance that it is a boy or girl. If the same parent's have a second child, that individual child has a 50% chance of being boy or girl, but if you take the two children together then the chance that they will both be girls is 25% and there is a 25% chance them being boys. The reason for this is that the probability that an event will happen is given by the number of that particular event over the total number of outcomes. So in the preceeding case you wanted to see the probability of a [girl,girl] combination. Well, all the possible outcomes are [girl,girl], [boy,girl], [boy,boy], and [girl,boy]. In this case [girl,girl] is only one of four outcomes, the same with [boy,boy], so ultimately the probability of having [girl,girl] is 1/4, .25, or 25% Q.E.D.
The reason for this is that these events are independent of each other, in other words they do not affect each other. This allows us to use a method for finding the probability for groups of events that are independent to happen. If the event has a 50% chance of happening, then lets say you want to find out the chance of it happening three times, well 50% * 50% * 50% = 12.5%. There you go.
Statistics is involved in trying to predict events by using large groups of things and recording the data. Using the data, the future probabilities can be predicted. But why use a large group? Why is one not enough? The fact is, the smaller the group, the more randomness there will be in the data collected. We all know by means of our unique reasoning capabilities that a fair coin has only two equally possible sides it can land on. Heads or tails. By equally possible I mean that there is a 50% chance of it landing on either side. Now I toss the coin once and observe the outcome. It is heads. If I only go by this article of data then I would say that every time you toss that coin it has a 100% chance of landing on heads. We all know this is wrong. So I toss it again. It lands on heads again. Again, I cannot accept this small ammount of data that I have collected (the information that it gives me also contradicts the laws of probability). I'll flip it a hundred more times. Over this time I'll be landing on heads and tails, and when I finally come to observe my data, it will be very close to 51 times heads and 51 times tails, 50% heads, 50% tails. Try it yourself. If the data is not exactly what was predicted this is called deviation. The deviation is calculated as follows:
|events expected - events occured|/number of tries. Where the vertical bars stand for absolute value of.
If you do this experiment and calculate the deviation after every ten times you do the experiment, you'll see that the deviation well become smaller and smaller.
We already know that the gene is the unit of heredity. It is what passes traits on from parents to offspring. We even know how it goes about doing this. But we don't know everything we need to know.
Remember that genes can have different forms. The gene that makes a pea plant seed green in one plant, makes it yellow in a different plant. These two different forms of that gene are called alleles. The allele for the dominant form of the trait (in this case yellow) will be represented by a letter chosen based on the following rules:
The letter should be capital.
It should be a letter that is somehow related to the trait.
The letter should not look the same uppercase as it does lowercase (although on a computer you can choose almost any letter).
So, abiding by this set of rules we'll choose the letter 'Y' to represent the dominant allele, and 'y' will represent the lowercase allele.
Now that we've learned about alleles we can look at Mendels results in terms of them. Let 'R' stand for the round seed allele and 'r' stands for the wrinkled seed allele.
Mendel started with the P1 generation. These were pure-breed for the trait that he was looking at. This means that they were what is called homozygous which means that the duplicate alleles are the same. So the 'wrinkled allele' would be represented by r/r (since wrinkled is the recessive trait), and the round pure-breed plants would be represented by R/R.
P1 R/R r/r
The plants had their gametes which each receive one allele, in the case of pure-breeds there is no probability involved. The R/R plants would make R gametes and the r/r plants would make r gametes.
gametes R[100%] r[100%]
He then cross-pollinated, so the new plants received one allele from one plant and the other allele from the other.
gametes R[100%] r[100%]
| x |
F1 R/r R/r
The new generation generated their gametesm which now had a 50% chance of carrying a R allele or a r allele.
gametes R[50%] r[50%] R[50%] r[50%]
These gametes were then crossed.
gametes R[50%] x R[50%]
|
F2 R/R[25%]
gametes R[50%] x r[50%]
|
F2 R/r[25%]
gametes r[50%] x R[50%]
|
F2 R/r[25%]
gametes r[50%] x r[50%]
|
F2 r/r[25%]
All of the preceding is of course the same generation. As you can see, there will be a 75% chance of the plant having round seeds and only a 25% chance of wrinkled seeds. There is only a 25% chance for the plant to be homozygous recessive or homozygous dominant, and a 50% chance that the plant will be hybrid (having mixed forms i.e. R/r) or heterozygous.
As you can see, the look of an organism is influenced by its genes. What this "look" is called scientifically is the phenotype. The alleles are what form the genetic makeup, which is refered to as the genotype.
Mendel was working with traits that showed clear dominance and recessiveness. But some species have what is called codominance. This expresses itself in the following way. Lets say we have an animal with the following genotype for its hair color, B/B (B standing for the dominant black form and b standing for the recessive white form). Our pet mates with another pet, b/b. We have:
F1 R/R x r/r
This must lead to an offspring with the genotype: R/r.
Alright, funny thing is, our new, baby pet has grey fur color. In other words, its fur color is neither that of its mother or father.
This leads to many more interesting things. The fact is, most of our traits aren't simply controlled by two alleles. This would be to constricting. Some genes may have many alleles (which is another form of codominance). One famous example of this is our blood type. It is determined by three alleles, Ia, Ib, and i. Ia forms blood type A, Ib forms blood type B, and i forms none of the other two. These can be combined in the following way:
Ia/Ia, or Ia/i-----A Blood type
Ib/Ib, or Ib/i-----B Blood type
Ib/Ia--------------AB Blood type
i/i----------------O Blood type
These multiple allele genes definetely add flavor to our lives. They control, what are termed, continuous traits. Continuous traits are traits such as tallness, that vary in such a way that you could draw a continuous graph, a graph with no gaps in it. The other type of gene, the eithor/or one is naturally called discontinuous (discrete).
The reason continuous variability comes about is because the trait usually depends on many genes as well as alleles, but external factors can affect it as well. This allows a species to adapt and change to its environment. The technical name for this is multifactorial inheritance.
On to Lesson 6 -- X-Linked Traits, Sex Determination, and Pedigrees