Claudio Gutierrez

We call Mendelian inheritance the transmission of heredity traits that occurs in essential accord with the laws stated by the Austrian monk Gregor Mendel (1822-1884) on the basis of his crossbreeding of several varieties of pea plants. It is to be noted that Mendel, besides having an outstanding scientific curiosity and being extremely patient and hardworking, was lucky enough to have chosen for his experiments plants and characteristics which, by mere chance, happened to obey especially well the laws conceived by him. In fact, few cases exist where transmission of specific hereditary traits occurs without being interdependent with the transmission of other traits, that is, where a gene determines its trait without the collaboration of other genes, as stated by Mendel's fourth law.

Mendel was able to establish with his research several surprising correlations. For instance, when crossing a tall plant with a short plant, the hybrids obtained would be similar to the tall or to the short parent, instead of being average-height plants. Furthermore, in a certain number of cases, a trait disappeared in the immediate generation but reappeared in a subsequent one. Strictly speaking, Mendel did not work with plant heights but rather with a more accurate magnitude: stem length. In order to explain such interesting phenomena, Mendel did not restrict himself to writing relational tables connecting facts observed, as a less gifted mind would have done. He undertook, in addition, a superb theoretical exploit on whose foundation, half a century later, the new science of genetics began to be built. Let us examine this feat in some detail.

A Theoretical Concept

In the solitude of his garden or cell, Mendel tackled rationally with the problem posed by his findings. Through an act of great abstraction and deprived of the means for observation and manipulation which biologists of our age take for granted, he concluded by mere reasoning that there had to be some elements in organisms functioning as the discreet units of heredity. Such elements, what we today call 'genes,' would not be discovered as material entities until one century later, when their identity with segments of the molecular structure of a DNA strand got established. It was on virtue of this daring theoretical concept that the brilliant monk was able to formulate his four lucid laws of heredity.³⁴⁷

The Laws of Heredity

Based upon his theoretical concept and having as background the data of his experiments, clamoring for explanation, Mendel formulated his impressive four laws of heredity:³⁴⁸

1. Law of parity: Inheritance is based on pairs of units, each one determinant of a specific trait. Mendel called them “elements” or "factors"; we call them “genes.” Of each pair, offspring receives one from each parent.

2. Law of antagonism: Of each pair of factors received by the offspring, one is dominant and the other recessive. Mendel called them “antagonistic factors”; we call them “alleles.” When both parents contribute a dominant element or when both parents contribute a recessive one (AA or aa), the individual will be called pure for such a trait. If the parents contribute one dominant and one recessive elements (Aa or aA), the individual will be a hybrid, but have the same appearance as the dominant.

3. Law of conservation: Heredity elements remain uncontaminated and equal to themselves throughout generations. Existing in pairs in the organism, they are separated when seminal female and male substances are formed, mixing back into new pairs at the conjoining of sperm and ovum by fertilization. The mechanisms of meiosis and the concepts of diploidy and haploidy were here anticipated.

4. Law of independent segregation: If two or more pairs are hybrids in the same organism, they are assorted independently to form eggs or sperm, the segregation of one of the hybrid pairs not being influenced by the segregation of the other. The implication is that the laws of heredity apply to each trait separately.

These laws, which anticipated in broad strokes the essentials of the contemporary scientific heredity doctrine, were presented by Mendel to the Society for the Study of Natural Science, in Brünn (today's Czech Republic), on February 8 and March 8, 1865. The members of the scientific society heard him politely but did not accept his ideas, which were totally at odds with the official doctrine of the time. The new doctrine, published in the Proceedings of the Society, fell into oblivion. It was rediscovered, concurrently, in the year 1900, by Carl Correns, Erich von Tschermak, and Hugo de Vries. It became immediately the cornerstone of a new revolutionary science.

A Mathematical Illustration

A note from the Beadles' book for the benefit of students:

If you want to check on Mendel’s math and at the same time show yourself how many different individuals can result from just three paired traits, draw a checkerboard with 64 squares and place the following symbols for egg or sperm cells: ABC, ABc, AbC, Abc, aBC, aBc, abC, abc. One begins to see, with this exercise, why no human being –whose cells contain not three but thousands of traits– is ever like another human being (unless he is an identical twin). What the authors expect the students to do is building for three traits what the accompanying table presents for two of them.