What is the probability of two parents who are both carriers of one copy of the recessive allele producing children affected by CF?

Traits (such as eye color or risk for disease) are passed to your children by genes. Each person has two genes for each trait. One gene is from the mother and one gene is from the father.

Índice Show

Penetrance and probability
Novel variants
Supporting the family

Autosomal recessive inheritance refers to conditions caused by changes (“mutations”) in genes located on one of the 22 pairs of autosomes. Autosomes are the numbered chromosomes that are the same in all males and females. Autosomal conditions occur in both men and women and are not related to whether a person is male or female.

In an autosomal recessive disorder, two changed copies of a gene are inherited—one from each of the parents—which causes the child to have the disorder. The child is called “affected” because she or he has the disorder.

A carrier has only one changed copy of the gene. They are called “carriers” of the trait because they do not show any signs of the disorder. Although they have one copy of a gene that is changed, the partner copy of the gene is working correctly, so they do not develop the disorder.

When both parents are carriers for a recessive disorder, each child has a 1 in 4 (25 percent) chance of inheriting the two changed gene copies. A child who inherits two changed gene copies will be “affected,” meaning the child has the disorder.

There is a 1 in 2 (50 percent) chance that the child will inherit one changed copy and one normal copy of the gene, and therefore be an unaffected carrier (just like the parent).

There is a 1 in 4 (25 percent) chance that the child will inherit both normal copies of a gene, and be unaffected and not a carrier.

If only one parent is a carrier and the other is not, none of the children will have the condition. But each child will have a 50 percent chance of being a carrier.

For example, cystic fibrosis (CF) is an autosomal recessive disease caused by mutations in a gene called CFTR. If both parents are carriers, each parent can pass on the changed copy or the normal copy to their children. Children who inherit two changed copies of the CFTR gene are “affected” and have the disease cystic fibrosis.

Genetic heredity is inherently probabilistic – sexual reproduction ensures that even when we know everything about the parents’ genomes, we don’t know what assortment of their genes will end up in each of their offspring. It can be fun to wonder if a new baby will look more like their mum or dad, but when a genetic condition runs in the family, the unpredictability can be worrying.

We can, however, predict the possible outcomes based on chance. For example, for a couple who are both carriers of the gene variant for a recessive condition, the chance that their child will be affected is 25%. But it does not follow that if they have three healthy children, then the fourth will have the condition. They could have four healthy children, or four who are all affected. The 1-in-4 chance is the same each time, for each child.

Penetrance and probability

Often, the fact that a person carries a gene variant associated with a particular disease does not guarantee that they will be affected.

For example, there is a wealth of evidence linking the BRCA genes to breast and ovarian cancers, but not every woman who carries a pathogenic variant on one of these genes will get cancer in her lifetime. Such genes are said to have incomplete penetrance.

Around 12% of women in the general population will develop breast cancer at some point during their lives, and this goes up to 72% of women with a pathogenic variant in BRCA1 and about 69% of women with a pathogenic BRCA2 variant. So, while the risk is much greater for women with these gene variants, it is by no means certain.

Conversely, many women develop breast cancers every year who do not carry these BRCA variants. In fact, because BRCA and other gene variants associated with breast cancer are comparatively rare, they only account for 5%-10% of all breast cancer diagnoses.

Researchers have identified more than 100 other genes linked to increased risk of breast cancer, but none have effects as significant as the BRCA genes. We also know that environmental and lifestyle factors may affect the risk of developing breast cancer. But even if we had all this information, we still cannot predict whether an individual will develop cancer or not. There will always be rare individuals at high risk who remain unaffected, and individuals at low risk who develop the condition against the odds.

Novel variants

Sometimes a genetic condition can arise with absolutely no warning, when a de novo variant occurs in a gene.

Achondroplasia is the most common form of dwarfism, affecting around one in 25,000 people. It is a genetic condition, resulting from a variant in a gene called FGFR3, and is inherited in an autosomal dominant pattern. It is 100% penetrant, so everyone who has the variant has achondroplasia.

However, around 80% of people with achondroplasia do not inherit the condition from their parents; it is the result of a new variant that arises when the egg or sperm (or their precursor cells) were made. Because this is a random event, there is no way to predict when this will happen.

Supporting the family

Where a genetic condition appears to run in a family, a useful first step is to take a genetic family history (you can learn more about this in our short online course). A referral to clinical genetics may be appropriate, along with access to genetic counselling.

For families who know they carry the gene variant for a genetic disease, options are available when it comes to family planning. Some couples opt for pre-implantation genetic testing (PGD) to select an unaffected embryo. Another option is prenatal testing during pregnancy to find out if their child will be affected, such as amniocentesis or CVS (chorionic villus sampling). Non-invasive tests are also being developed for some single-gene disorders.

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Please note: This article is for informational or educational purposes, and does not substitute professional medical advice.

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.