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Old 05-06-2011, 03:02 PM   #1 (permalink)
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Lightbulb Punnet Squares Explained: The Probability of Inheritance

Probability of Inheritance

The value of studying genetics is in understanding how we can predict the likelihood of inheriting particular traits. This can help plant and animal breeders in developing varieties that have more desirable qualities. It can also help people explain and predict patterns of inheritance in family lines.
One of the easiest ways to calculate the mathematical probability of inheriting a specific trait was invented by an early 20th century English geneticist named Reginald Punnett . His technique employs what we now call a Punnett square. This is a simple graphical way of discovering all of the potential combinations of genotypes that can occur in children, given the genotypes of their parents. It also shows us the odds of each of the offspring genotypes occurring.
Setting up and using a Punnett square is quite simple once you understand how it works. You begin by drawing a grid of perpendicular lines:
Next, you put the genotype of one parent across the top and that of the other parent down the left side. For example, if parent pea plant genotypes were YY and GG respectively, the setup would be:
Note that only one letter goes in each box for the parents. It does not matter which parent is on the side or the top of the Punnett square.
Next, all you have to do is fill in the boxes by copying the row and column-head letters across or down into the empty squares. This gives us the predicted frequency of all of the potential genotypes among the offspring each time reproduction occurs.
In this example, 100% of the offspring will likely be heterozygous (YG). Since the Y (yellow) allele is dominant over the G (green) allele for pea plants, 100% of the YG offspring will have a yellow phenotype, as Mendel observed in his breeding experiments.
In another example (shown below), if the parent plants both have heterozygous (YG) genotypes, there will be 25% YY, 50% YG, and 25% GG offspring on average. These percentages are determined based on the fact that each of the 4 offspring boxes in a Punnett square is 25% (1 out of 4). As to phenotypes, 75% will be Y and only 25% will be G. These will be the odds every time a new offspring is conceived by parents with YG genotypes.
An offspring's genotype is the result of the combination of genes in the sex cells or gametes (sperm and ova) that came together in its conception. One sex cell came from each parent. Sex cells normally only have one copy of the gene for each trait (e.g., one copy of the Y or G form of the gene in the example above). Each of the two Punnett square boxes in which the parent genes for a trait are placed (across the top or on the left side) actually represents one of the two possible genotypes for a parent sex cell. Which of the two parental copies of a gene is inherited depends on which sex cell is inherited--it is a matter of chance. By placing each of the two copies in its own box has the effect of giving it a 50% chance of being inherited.
If you are not yet clear about how to make a Punnett Square and interpret its result, take the time to try to figure it out before going on.

Are Punnett Squares Just Academic Games?
Why is it important for you to know about Punnett squares? The answer is that they can be used as predictive tools when considering having children. Let us assume, for instance, that both you and your mate are carriers for a particularly unpleasant genetically inherited disease such as cystic fibrosis . Of course, you are worried about whether your children will be healthy and normal. For this example, let us define "A" as being the dominant normal allele and "a" as the recessive abnormal one that is responsible for cystic fibrosis. As carriers, you and your mate are both heterozygous (Aa). This disease only afflicts those who are homozygous recessive (aa). The Punnett square below makes it clear that at each birth, there will be a 25% chance of you having a normal homozygous (AA) child, a 50% chance of a healthy heterozygous (Aa) carrier child like you and your mate, and a 25% chance of a homozygous recessive (aa) child who probably will eventually die from this condition.
If both parents are carriers of the recessive
allele for a disorder, all of their children will
face the following odds of inheriting it:
25% chance of having the recessive disorder
50% chance of being a healthy carrier
25% chance of being healthy and not have
the recessive allele at all
If a carrier (Aa) for such a recessive disease mates with someone who has it (aa), the likelihood of their children also inheriting the condition is far greater (as shown below). On average, half of the children will be heterozygous (Aa) and, therefore, carriers. The remaining half will inherit 2 recessive alleles (aa) and develop the disease.
If one parent is a carrier and the other has a
recessive disorder, their children will have the
following odds of inheriting it:
50% chance of being a healthy carrier
50% chance having the recessive disorder
It is likely that every one of us is a carrier for a large number of recessive alleles. Some of these alleles can cause life-threatening defects if they are inherited from both parents. In addition to cystic fibrosis, albinism, and beta-thalassemia are recessive disorders.
Some disorders are caused by dominant alleles for genes. Inheriting just one copy of such a dominant allele will cause the disorder. This is the case with Huntington disease, achondroplastic dwarfism, and polydactyly. People who are heterozygous (Aa) are not healthy carriers. They have the disorder just like homozygous dominant (AA) individuals.
If only one parent has a single copy of a
dominant allele for a dominant disorder,
their children will have a 50% chance of
inheriting the disorder and 50% chance
of being entirely normal.
Punnett squares are standard tools used by genetic counselors. Theoretically, the likelihood of inheriting many traits, including useful ones, can be predicted using them. It is also possible to construct squares for more than one trait at a time. However, some traits are not inherited with the simple mathematical probability suggested here.
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Old 07-23-2011, 10:50 AM   #2 (permalink)
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When dealing with a simple recessive trait, you base your expected results on an initial assumption (we assume that primary inherited epilepsy is a simple autosomal recessive gene). The "results" here would be the affected pups of the litter. In this case we also assume that both dog and bitch are carriers of the recessive trait, that is, they are ’Ne’ (N = dominant normal and e = recessive epileptic). Then by use of the Punnett square diagram we have:

where NN is a normal dog, Ne is a carrier, and ee is an affected dog. This analysis gives the following status of a litter of 4 puppies as: NN, Ne, Ne, ee, or 25% are normal, 50% are carriers and 25% are affected, that is, we have a ratio of 3:1, 3 "normal" and 1 affected. The word normal is placed in quotes to emphasize the fact that 3 of the 4 dogs are not affected but 2 of those 3 "not affected dogs" are carriers. After removing the affected dogs from a breeding program, the dogs that remain have a 66% chance of being carriers.
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Old 07-23-2011, 10:51 AM   #3 (permalink)
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It all depends on the mode of inheritance. Punnet squares get much more complicated. All right lets see if I can break it down for you.
You have a male who is a carrier for kink tail. K represents normal and k represents kink. Because he is a carrier his allele is Kk. The female is also a carrier meaning she is also Kk.
This is what your suares will look like

Now, what we have is Dad’s gametes (say) across the top and Mom’s (we assume) down the side. Notice that Dad himself has the genotype Kk – two alleles. So does Mom. What we have got across the top and down the side of the Punnett square are the types of gametes (sperm cells) that Dad could possibly make – he can give each sperm cell just one letter and either it will be a big K or a little k. Same for Mom with her egg cells.

Now, obviously, what we have in the square is one KK puppy, two Kk puppies, and one kk puppy. The KK and Kk puppies will be normal and the kk puppy will have a kink. You do not expect each litter to have exactly four puppies, three normal and one kink. You expect roughly a 3 normal : 1 kink ratio of puppies. Put another way: every puppy born to this kind of cross has a chance (25%) of having a kink, versus a chance (75%) of being normal.

Now say that the sire is not a carrierand the mother has a kink then all puppies will be carriers


If the sire is not a carrier and the mother is a carrier then 50% will be normal and 50% will be carriers
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Old 01-15-2012, 04:11 AM   #4 (permalink)
 

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That's weird. We studied that at biology class but I did not understand it before but when you showed it I now understand it.
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