Mendel's Laws of Inheritance
In the nineteenth century, there were several theories that attempted to explain the heredity of characteristics. Lamark proposed the inheritance of acquired characteristics, where traits are modified by use or disuse during individual’s lifetime and inherited by offspring. On the other hand, Darwin theorized the blending inheritance, where hereditary material of parents “mixes” in offspring, giving intermediate phenotypes and predicting erosion of variation over generations.
Mendel proposed that traits are determined by discrete
hereditary factors (that we now call alleles), transmitted intact across
generations (particulate inheritance). This explains two observations:
- Why recessive phenotypes can disappear in one generation
and reappear in later ones (alleles persist in heterozygotes);
- Why offspring phenotypes can be either identical or
different from parents.
Neither inheritance
of acquired characteristics nor blending inheritance explain these
observations.
Nowadays three laws
have been derived from Mendel’s original two - Law of Segregation, Law of
Independent Assortment, and Law of Dominance. In this article, we will focus on
the original two – Segregation (First Law) and Independent Assortment (Second
Law).
In “Population Genetics
language”, individuals are diploid – they have two copies of alleles (what
Mendel called factors). During meiosis and gamete formation, those copies
separate (First Law, Aa → ½ A, ½ a), and if loci have no ligation, they are
independent (Second Law, AaBb → ¼ AB, ¼ Ab, ¼ aB, ¼ ab).
First Mendel’s Law – Segregation
Formulation:
Explanation:
Consider a locus with two alleles: A and a. The possible
genotypes are AA, Aa and aa. In gamete formation:
aa → produces a gametes only;
Aa → produces ½ A gametes and ½ a gametes (assuming total segregation).
For example, a classical monohybrid crossing:
Crossing Aa × Aa, each progenitor has ½ A, ½ a gametes. The descendance genotypes are:
¼ AAConditions:
- Diploid organisms (or two copies per locus in study)
- Normal meiosis – nondisjunction and no distortion on
segregation (segregation distortion / drive)
Second Mendel’s Law – Independent Assortment
Formulation:
For loci that segregate independently
(normally in different chromosomes or very far apart), the way one allele of
one locus enters in each gamete is independent of the way of the other allele
of the other locus.
Explanation:
Having the AaBb genotype (two A and B loci):
B: alleles B / b.
The First Law states:
In B locus ½ B, ½ b.
The Second Law states:
The combinations in the same gamete are the product:
P(Ab) = ½ × ½ = ¼
P(aB) = ½ × ½ = ¼
P(ab) = ½ × ½ = ¼
The resulting phenotypes of the two dihybrid cross (AaBb × AaBb) is has the “famous” 9:3:3:1 relative frequency.
Conditions:
Independence assumes:
- Loci in different chromosomes or very far apart to
segregate independently during meiosis (recombination rate ≈ 50%). If A and B
are physically close in the chromosome, alleles tend to be inherited together
(linkage) and P(AB) is not ¼; (depends on recombination rate r).
What violates and does not violate Mendel’s Laws
Does not violate the laws:
- Incomplete dominance – heterozygous with intermediate
phenotype;
- Codominance – heterozygous expresses both alleles;
- Pleiotropy – one gene affects multiple characters;
- Epistasis – one locus can affect the effect of another.
Note that in all these cases the alleles segregate ½-½ (First
Law) and distant loci continue to assort independently (Second Law). The only
thing that changes is the genotype → phenotype mapping, and consequently, the
phenotypic proportions (3:1, 9:3:3:1, …).
Violates the laws:
- Meiotic drive / segregation distortion – heterozygous A/a
produces gametes diferente than ½ A and ½ a (e.g. 0.7 A e 0.3 a), violating the
First Law;
- Non-disjunction / aneuploidies – if meiosis fails (e.g.
gametes with the wrong number of chromosomes, the logic “1 allele per loci” is
broken;
- Linkage / Low recombination – some phenotypes become more frequent than the product of the marginal frequences (no independence), violating the Second Law.