What is the probability that a couple will have three consecutive offspring that are all male?

Dominant Inheritance

When a trait is dominant, only one allele is required for the trait to be observed. A dominant allele will mask a recessive allele, if present. A dominant allele is denoted by a capital letter (A versus a). Since each parent provides one allele, the possible combinations are: AA, Aa, and aa. Offspring whose genotype is either AA or Aa will have the dominant trait expressed phenotypically, while aa individuals express the recessive trait.

One example of a dominantly inherited trait is the presence of a widow’s peak (a V-shape) at the hairline.

Let (W) represent the dominant allele, and (w) represent the recessive allele. An individual with a (WW) or (Ww) genotype will have a V-shaped peak at the hairline. Only ww individuals will have a straight hairline. To determine the probability of inheritance of a widow’s peak (or any other dominant trait), the genotypes of the parents must be considered. For

example, if one parent is homozygous dominant (WW) and the other is homozygous recessive (ww), then all their offspring will be heterozygous (Ww) and possess a widow’s peak. If both parents are heterozygous (Ww), there is a 75% chance that any one of their offspring will have a widow’s peak (see figure). A Punnett square can be used to determine all possible genotypic combinations in the parents.

Pedigree

A pedigree that depicts a dominantly inherited trait has a few key distinctions. Every affected individual must have an affected parent. Dominantly inherited traits do not skip generations. Lastly, males and females are equally likely to receive a dominant allele and express the trait. In this pedigree both heterozygous and homozygous individuals are affected since the trait is dominant.

Image courtesy of Michael A. Kahn, DDS

CLICK HERE to learn more about patterns of inheritance
CLICK HERE to learn more about recessive inheritance
CLICK HERE to learn more about X-linked 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. We will explore some of these exceptions in the next section of the tutorial.