What are the Three Steps of the Monohybrid Cross?

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Charles Darwin, widely acclaimed for having discovered or co-discovered biological evolution in the 19th century, is often credited with catalyzing perhaps the single greatest jump in knowledge in the history of human scientific endeavors. Often lost in the awe and wonder of his discoveries and now convincingly validated theories is the fact that Darwin did not actually know the specific substrate, or organic material, on which natural selection acted at the cellular level. That is, Darwin knew that organisms inarguably passed along traits to their offspring in predictable ways, and that the passing of along of a given trait was usually not coupled to the passing along of a different trait (that is, a large brown cow might give birth to large brown calves, but also to large white calves or small brown calves). But Darwin did not know the exact manner in which this was done.

At around the same time Darwin was revealing his controversial findings to a world that still largely held to the notion of special biblical creation, a different scientist – in fact, an Augustinian monk – named Gregor Mendel (1822-1884) was busy using pea plants for simple yet ingenious experiments that revealed the basic mechanisms of inheritance in most living things. Mendel is considered the father of genetics, and his application of the scientific method to patterns of inheritance resonate with brilliance almost a century and a half after his death.

Background: Mendel, Pea Plants and Inheritance

In the 1860s, approaching middle age, Gregor Mendel started experimenting with a particular type of pea plant (Pisum sativum, the common pea plant) in a very patient attempt to clarify the exact mechanisms of inheritance in this species. Plants were a good choice, he reasoned, because he could limit and carefully control the number of external influences on the outcome of his plant matings.

Mendel, in breeding successive generations of plants, learned to create "families" that did not show variation from "parent" to "child" in their appearance with respect to given variables, each of which only showed two forms. For example, if he started with both tall pea plants and short pea plants, and if he manipulated the pollination process properly, he could develop a strain of plants that were "pure" for the height trait, so that the "children," "grandchildren" and so on of a given tall plant were also all tall. (At the same time, some might show smooth seeds while others showed wrinkled peas, some might have yellow peas while others had green peas and so on.)

Mendel, in fact, determined that his pea plants had seven different traits that varied in this binary manner (i.e., one or the other, nothing in between), independently of each other. The four he focused on most strongly were height (tall vs. short), pod shape (inflated vs. constricted), seed shape (smooth vs. winkled) and pea color (green vs. yellow).

Mendel's Hypotheses

Mendel's real stroke of genius was recognizing that when he had two sets of plants that "bred true" for two different variations of a given trait (for example, a set of only smooth-seed-producing pea plants and a set of only wrinkled-seed-producing pea plants), the results of breeding these plants were invariable: all of the peas in the first generation of offspring (termed F1) had only one of the traits (in this case, all had smooth seeds). There were no "in between" seeds. Also, when Mendel allowed these plants to self-pollinate, creating an F2 generation, the wrinkled trait re-emerged in exactly one in every four plants, given enough offspring to level out random variations.

This provided Mendel with a basis for formulating three distinct but related hypotheses about the way traits of living things, at least some traits, were inherited. These hypotheses introduce a lot of terminology, so don't be afraid to consult the References as you read and digest this new information.

Mendel's First Hypothesis: Genes (codes for development situated in substances in the body) for heritable traits occur in pairs. One gene is inherited from each parent. Alleles are different versions of the same gene. For example, for the pea-plant height gene, there is a tall version (allele) and a short version (allele).

Organisms are diploid, meaning that they have two copies of each gene, one from each parent. Homozygous means having two of the same allele (e.g., tall and tall) while heterozygous means having two different alleles (e.g., wrinkled and smooth).

Mendel's Second Hypothesis: If two alleles of a gene are different – that is, if the organism is heterozygous for a given gene – then one allele is dominant over the other. The dominant allele is the one that is expressed and shows up as a visible or otherwise detectable trait. Its masked counterpart is called the recessive allele. Recessive alleles are only expressed when two copies of the allele are present, a state called homozygous recessive.

A genotype is the total set of alleles an individual contains; the phenotype is the resulting physical appearance. The phenotype of a given organism for a set of traits can be predicted if its genotype for those traits is known, but the reverse is not always true, and more information about the organism's immediate ancestors is needed in these cases.

Mendel's Third Hypothesis: Two alleles of a gene segregate (that is, they separate) and enter gametes, or sex cells (sperm cells or egg cells, in humans) singly. 50 percent of the gametes carry one of these alleles, and the other 50 percent carry the other allele. Gametes, unlike regular cells of the body, only carry one copy of each gene. If they did not, the number of genes in a species would double every generation. This reduces to the principle of segregation, which states that two gametes fuse to produce a zygote (a pre-embyro, destined to become offspring if unimpeded) that contains two alleles (and is therefore diploid).

The Monohybrid Cross

Mendel's work laid the foundation for a variety of previously unknown concepts that are now standard fare and indispensable to the discipline of genetics. Although Mendel passed away in 1884, his work did not become fully scrutinized and appreciated until some 20 years later. In the very early 1900s, a British geneticist named Reginald Punnett used Mendel's hypotheses to come up with grids, like mathematical tables, that could be used to predict the outcome of matings of parents with known genotypes. Thus was born the Punnett square, a simple tool for predicting the probability that the offspring of parents with a known combination of genes for a specific trait or traits will have that trait or a given combination of traits. For example, if you know that a female Martian, who will soon give birth to a litter of eight Martians, has green skin while the father Martian has blue skin, and you also know that all Martians are either all blue or all green and that green is "dominant" over blue, how many of the baby Martians would you expect to see of each color? A simple Punnett square and a basic computation is sufficient to provide the answer, and the underlying principles are refreshingly simple – or so they seem, with the benefit of hindsight and Mendel having cleared the way for the rest of humankind's understanding.

The simplest type of Punnett square is called a monohybrid cross. The "mono" means a single trait is under examination; the "hybrid" means that the parents are heterozygous for the trait in question, that is, each parent has a dominant allele and a recessive allele.

The following three steps can be applied to any Punnett square examining a single trait known to be inherited by the mechanisms described here, called, naturally, Mendelian inheritance. But a monohybrid cross is a specific kind of simple (2 × 2) Punnett square for which both parents are heterozygous.

Step One: Determine the Genotype of the Parents

For a monohybrid cross, this step is not necessary; both parents are known to have one dominant and one recessive allele. Assume you are dealing with Martian color again, and that green is dominant over blue. A convenient way to express this is to use G for the dominant skin-color allele and g for the recessive one. A monohybrid cross would thus include a mating between a Gg mother and a Gg father.

Step Two: Set up the Punnett Square

A Punnett square is a grid consisting of smaller squares, each of which holds one allele from each parent. A Punnett square with one trait under consideration would be a 2 × 2 grid. The genotype of one parent is written above the top row, and the genotype of the other is written beside the left-hand column. So, continuing with the Martian example, G and g would head the top columns, and because the parents in a monohybrid cross have the same genotype, G and g would also head the two rows.

From here, four different offspring genotypes would be created. The top left would be GG, the top right would be Gg, the bottom left would also be Gg and the bottom right would be gg. (It is conventional to write the dominant allele first in a dizygotic organism, i.e., you would not write gG even though this is not technically wrong.)

Step Three: Determine the Offspring Ratios

As you'll recall, genotype determines phenotype. Looking at the Martians, it is clear that any "G" in the genotype results in a green phenotype, whereas two recessive alleles (gg) spell a blue color. This means that three of the cells in the grid denote green offspring and one denotes a blue offspring. While the odds of any one Martian baby being blue in this type of monohybrid cross are 1 in 4, in smaller family units, it would not be unusual to see a higher or lower than expected number of green or blue Martians, just as flipping a coin 10 times would not assure exactly five heads and five tails. Across larger populations, however, these random quirks tend to fade from consideration, and in a population of 10,000 Martians resulting from a monohybrid cross, it would be unusual to see a number of green Martians vastly different from 7,500.

The take-home message here is that in any true monohybrid cross, the offspring ratio of dominant to recessive traits would be 3 to 1 (or 3:1, in the usual style of geneticists).

Other Punnett Squares

The same reasoning can be applied to mating crosses between organisms in which two traits are under examination. In this case, the Punnett square is a 4 × 4 grid. In addition, other 2 × 2 crosses not involving two heterozygous parents are clearly possible. For example, if you crossed a GG green Martian with a blue Martian known to have only blue Martians in her family tree (in other words, gg), what sort of offspring ratio would you predict? (The answer: All children would be green, because the father is homozygous dominant, in effect negating the mother's contribution to skin color altogether.)

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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