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There are actually two laws related to heredity that are associated with Mendel.
The first law, the Law of Segregation, forms the cornerstone of most genetic study. At their core, Mendelian genetics state that each parent holds two or more genetic factors which they will then pass down to their children. How the genetic factors (two or more per parent) combine will determine whether or not the child has the particular trait in question.
For example, Albinism -- whether or not the child has Albino qualities -- functions under a simple Mendelian genetic model. Let's look at a model below.
Let's say there are two types of factors that each parent may possess. They may either possess a dominant gene, which would lead to no Albinism, or a recessive gene, which could potentially lead to Albinism. Thus, the possibilities for the parent are to have a dominant gene (A) or a recessive gene (a). As each parent has two factors, they each hold the following potential combinations:
AA - Two dominants -- No Albinism
Aa - Heterozygous -- Carrier for Albinism (50/50)
aa - Homozygous recessive - Albino
When procreating, this parent will also mix with another parent with the same three potential types. Like the first parent, the second parent's potential combinations are AA, Aa, or aa.
When the parents mix, they each contribute one of their factors to a new child's genetic pair. Depending on what the parents have, the children may have Albinism, depending on the mix.
For example, if both parents are heterozygous dominant (AA), there is no chance of Albinism. As a reminder, aa = Albino and there are no small "a"s in a AA-AA pairing. Likewise, if both parents are Albinos (aa-aa) with homogeneous pairings, the children will most certainly be Albino.
The hazy gray area is when oneboth of the parents are heterozygous. For example, let's say that both parents are non-Albino, but both are carriers (Aa-Aa). Since both parents only contribute one factor (i.e. one letter), the following combinations are possible: AA, Aa, and aa. Thus, it would be possible for the parents to have an Albino child if they both contributed their small "a" factor to the child's pairing (making an "aa" child).
All of the above relates to Mendel's first law. Mendel's second law, the Law of Independent Assortment, essentially states that factors for each gene or trait function independently of each other.
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