Figure 1. Johann Gregor Mendel is considered the father of genetics.

Johann Gregor Mendel (1822–1884) (Figure 1) was a lifelong learner, teacher, scientist, and man of faith. As a young adult, he joined the Augustinian Abbey of St. Thomas in Brno, in what is now the Czech Republic. Supported by the monastery, he taught physics, botany, and natural science courses at the secondary and university levels. In 1856, he began a decade-long research pursuit involving inheritance patterns in honeybees and plants.  He ultimately settled on pea plants for his primary research.  In 1865, Mendel presented his experimental results with nearly 30,000 pea plants to the local Natural History Society. He demonstrated that traits are transmitted faithfully from parents to offspring independently of other traits and in dominant and recessive patterns. In 1866, he published his work, Experiments in Plant Hybridization,^[1] in the proceedings of the Natural History Society of Brünn.

Mendel’s work went virtually unnoticed by the scientific community. They believed that the process of inheritance involved a blending of parental traits producing an intermediate physical appearance in offspring.  Offspring appear to be a “blend” of their parents’ traits.   The blending theory of inheritance asserted that the original parental traits were lost or absorbed by the blending in the offspring.  We now know that this is not the case. Mendel was the first researcher to see it. Instead of continuous characteristics, Mendel worked with traits that were inherited in distinct classes.  Mendel’s choice allowed him to see, experimentally, that the traits were not blended or absorbed in the offspring, but rather kept their distinctness and could be passed on. In 1868, Mendel became the abbot of the monastery and exchanged his scientific pursuits for his pastoral duties.  Mendel was never recognized for his extraordinary scientific contributions during his lifetime. It was not until 1900 that his work was rediscovered, reproduced, and revitalized by scientists on the brink of discovering the chromosomal basis of heredity.

Mendel’s Model System

Mendel’s work was accomplished using the garden pea, Pisum sativum, to study inheritance. This species naturally self-fertilizes and the flower petals remain sealed tightly until after pollination, preventing pollination from other plants. The result is highly inbred, or “true-breeding,” pea plants. True-breeding plants always produce offspring identical to the parent. Mendel chose well with the garden pea  Not only was it true-breeding, but it also reached maturity in one season. This allowed several generations to be evaluated over short time periods. Finally, large quantities of garden peas could be cultivated simultaneously, allowing Mendel to conclude that his results did not come about simply by chance.

Mendelian Crosses

Mendel performed hybridizations, mating two true-breeding individuals with different traits. In the pea, which is naturally self-pollinating, this is done by manually transferring pollen from the anther of a mature pea plant of one variety to the stigma of a separate mature pea plant of the second variety.  To prevent self-fertilizing and confounding his results, Mendel painstakingly removed all of the anthers from the plant’s flowers before they had a chance to mature.

Plants used in first crosses were called P₀, or parental generation, plants (Figure 2). Mendel collected the seeds belonging to the P₀ plants that resulted from each cross and grew them the following season. These offspring were called the F₁, or the first filial (filial = offspring), generation.  Mendel examined the characteristics in the F₁ generation of plants, then allowed them to self-fertilize naturally. He then collected and grew the seeds from the F₁ plants to produce the F₂, or second filial, generation. Mendel’s experiments extended beyond the F₂ generation to the F₃ and F₄ generations, and so on. But the results from the first two generationswere the most intriguing and became the basis for his research.

Figure 2. In one of his experiments on inheritance patterns, Mendel crossed plants that were true-breeding for violet flower color with plants true-breeding for white flower color (the P generation). The resulting hybrids in the F₁ generation all had violet flowers. In the F₂ generation, approximately three quarters of the plants had violet flowers, and one quarter had white flowers.

Garden Pea Characteristics Revealed the Basics of Heredity

In his 1865 publication, Mendel reported the results of his crosses involving seven different characteristics. The characteristics included plant height, seed texture, seed color, flower color, pea pod size, pea pod color, and flower position. For the characteristic of flower color, the two contrasting traits were white versus violet. To fully examine each characteristic, Mendel generated large numbers of F₁ and F₂ plants, reporting 19,959 F₂ plants alone. His findings were consistent.

What results did Mendel find for flower color? First, he confirmed that he had true-breeding plants for white and violet flower color. Regardless of how many generations Mendel examined, all self-crossed offspring of parents with white flowers had white flowers, and all self-crossed offspring of parents with violet flowers had violet flowers. Other than flower color, Mendel confirmed that the pea plants were physically identical.

Once these validations were complete, Mendel applied the pollen from a plant with violet flowers to the stigma of a plant with white flowers. After gathering and sowing the seeds that resulted from this cross, Mendel found that 100 percent of the F₁ hybrid generation had violet flowers. Most scientists would have predicted the hybrid flowers to be pale violet or to have equal numbers of violet and white flowers. In other words, the contrasting parental traits were expected to blend in the offspring. Instead, Mendel’s results demonstrated that the white flower trait in the F₁ generation had completely disappeared.

But, Mendel did not stop there.  He allowed the F₁ plants to self-fertilize.  Of F₂-generation plants, 705 had violet flowers and 224 had white flowers. This was a ratio of 3.15 violet flowers per one white flower, or approximately 3:1. When Mendel transferred pollen from a plant with violet flowers to the stigma of a plant with white flowers and vice versa, he obtained about the same ratio regardless of which parent, male or female, contributed which trait.  For the other six characteristics Mendel examined, the F₁ and F₂ generations behaved in the same way as flower color. One of the two traits would disappear completely from the F₁ generation only to reappear in the F₂ generation at a ratio of approximately 3:1 (Table 1).

Upon compiling his results, Mendel concluded that the characteristics could be divided into expressed(dominant) and latent(recessive) traits. Dominant traits are observable traits inherited unchanged in a hybrid cross.  Recessive traits become latent, or disappear, in the offspring of a hybrid cross. The recessive trait does reappear in the progeny of the hybrid offspring. In Mendel’s flower color cross, the dominant trait is the violet color, while white-colored flowers carry the recessive trait. Since the recessive trait reappears in the F₂ generation, the traits remained separate, not blended, in the plants of the F₁ generation. Mendel proposed that plants possessed two copies of the trait for the flower-color characteristic, with each parent giving one of its two copies to the offspring.  Upon observing a violet flower, the dominant trait could include two dominant versions of the characteristics or one dominant and one recessive.  If the white flower were observed, then no dominant trait would have been passed on.

So why did Mendel repeatedly obtain 3:1 ratios in his crosses? To understand how Mendel deduced the basic mechanisms of inheritance that lead to such ratios, we must first review the laws of probability.

Probability Basics

Probabilities are mathematical measures of likelihood. The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of opportunities for the event to occur. It is possible to calculate theoretical probabilities by dividing the number of times that an event is expected to occur by the number of times that it could occur. Empirical probabilities come from observations. Theoretical probabilities come from knowing how the events are produced and assuming that the probabilities of individual outcomes are equal. A probability of one for some event indicates that it is guaranteed to occur, whereas a probability of zero indicates that it is guaranteed not to occur. An example for a genetic event is a round seed produced by a pea plant. In his experiment, Mendel demonstrated that the probability of the event “round seed” occurring was one in the F₁ offspring of true-breeding parents, one of which has round seeds and one of which has wrinkled seeds. When the F₁ plants were subsequently self-crossed, the probability of any given F₂ offspring having round seeds was now three out of four. In other words, in a large population of F₂ offspring chosen at random, 75 percent were expected to have round seeds, whereas 25 percent were expected to have wrinkled seeds. Using large numbers of crosses, Mendel was able to calculate probabilities and use these to predict the outcomes of other crosses.

The Product Rule and Sum Rule

Mendel demonstrated that the pea-plant characteristics were transmitted as discrete units from parent to offspring.  Mendel also determined that different characteristics, like seed color and seed texture, were transmitted independently of one another and could be considered in separate probability analyses.  Performing a cross between a plant with green, wrinkled seeds and a plant with yellow, round seeds still produced offspring that had a 3:1 ratio of green:yellow seeds (ignoring seed texture) and a 3:1 ratio of round:wrinkled seeds (ignoring seed color). The characteristics of color and texture did not influence each other.

The product rule of probability can be applied to this phenomenon of the independent transmission of characteristics. The product rule states that the probability of two independent events occurring together can be calculated by multiplying the individual probabilities of each event occurring alone. To demonstrate the product rule, imagine that you are rolling a six-sided die (D) and flipping a penny (P) at the same time. The die may roll any number from 1–6 (D_#), whereas the penny may turn up heads (P_H) or tails (P_T). The outcome of rolling the die has no effect on the outcome of flipping the penny and vice versa. There are 12 possible outcomes of this action (Table 2), and each event is expected to occur with equal probability.

Of the 12 possible outcomes, the die has a 2/12 (or 1/6) probability of rolling a two, and the penny has a 6/12 (or 1/2) probability of coming up heads. By the product rule, the probability that you will obtain the combined outcome 2 and heads is: (D₂) × (P_H) = (1/6) × (1/2) or 1/12 (Table 2).  The “and” is a signal to apply the product rule. Consider how the product rule is applied to the dihybrid cross: the probability of having both dominant traits in the F₂ progeny is the product of the probabilities of having the dominant trait for each characteristic, as shown : 3/4  X  3/4  =  9/16

The sum rule of probability is applied when considering two mutually exclusive outcomes that can come about by more than one pathway. The sum rule states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities. The “or” indicates that you should apply the sum rule. Imagine you are flipping a penny (P) and a quarter (Q). What is the probability of one coin coming up heads and one coin coming up tails? This outcome can be achieved by two cases: the penny may be heads (P_H) and the quarter may be tails (Q_T), or the quarter may be heads (Q_H) and the penny may be tails (P_T). Either case fulfills the outcome. By the sum rule, we calculate the probability of obtaining one head and one tail as [(P_H) × (Q_T)] + [(Q_H) × (P_T)] = [(1/2) × (1/2)] + [(1/2) × (1/2)] = 1/2 (Table 3). Notice that we used the product rule to calculate the probability of P_H and Q_T, and the probability of P_T and Q_H, before we summed them. Again, the sum rule can be applied to show the probability of having just one dominant trait in the F₂ generation of a dihybrid cross:  3/16  +  3/4  =  15/16

Using probability laws in practice, it is necessary to work with large sample sizes.  Small sample sizes are prone to deviations caused by chance. The large quantities of pea plants that Mendel examined allowed him calculate the probabilities of the traits appearing in his F₂ generation. This discovery meant that when parental traits were known, the offspring’s traits could be predicted accurately even before fertilization.

Section Summary

Working with garden pea plants, Mendel found that crosses between parents differing by one trait produced F₁ offspring that all expressed the traits of one parent. Observable traits are referred to as dominant, while non-expressed traits are described as recessive. When the offspring in Mendel’s experiment were self-crossed, the F₂ offspring exhibited a 3:1 ratio, confirming that the recessive trait had been transmitted faithfully from the original P₀ parent.  Further crosses generated identical F₁ and F₂ offspring ratios. By examining sample sizes, Mendel showed that his crosses behaved according to the laws of probability, and that the traits were inherited as independent events.

Two rules in probability can be used to find the expected proportions of offspring of different traits from different crosses. To find the probability of two or more independent events occurring together, apply the product rule and multiply the probabilities of the individual events. To find the probability of two or more events occurring in combination, apply the sum rule and add their individual probabilities together.