12.1 Mendel's Experiments and the Laws of Probability

He is considered the father of genetics.

He was a man of faith and a lifelong learner.

He joined the Augustinian Abbey of St. Thomas in the Czech Republic as a young adult.

He taught physics, botany, and natural science at the secondary and university levels.

In 1865, the results of his experiments were presented to the local Natural History Society.
He showed that trait transmission from parents to offspring is independent of other trait and pattern.
Experiments in Plant hybridization was published in the proceedings of the Natural History Society of Brunn.

The scientific community believed that the process of inheritance involved a blend of parental traits that produced an intermediate physical appearance in offspring.

The process appeared to be correct because of what we know now.
Offspring seem to be a blend of their parents' characteristics.

It was possible for him to see that the traits were not blended in the offspring.

In 1868, Mendel became abbot of the monastery and traded his scientific interests for his pastoral duties.

He wasn't recognized for his contributions to science.
His work was rediscovered, reproduced, and rejuvenated by scientists on the verge of discovering the chromosomal basis of heredity in 1900.

The garden pea, Pisum sativum, was used to study inheritance.

This species selffertilizes by pollen in individual flowers.
The flower petals are sealed until pollination takes place.
Highly inbred pea plants are the result.
These plants produce offspring that look like their parent.
Experiments with true-breeding pea plants avoided the appearance of unexpected traits in offspring that might occur if the plants were not true breeding.
Several generations could be evaluated over a short time due to the fact that the garden pea grows to maturity within one season.
Mendel was able to conclude that his results did not come about by chance because large quantities of garden peas could be cultivated simultaneously.

The stigma of a mature pea plant is transferred from the anther of the first variety to the stigma of the second variety by manual pollination.

The male gametes are carried to the stigma, a sticky organ that traps pollen and allows the sperm to move down the pistil to the female gametes.
To prevent the pea plant from self-fertilizing, he removed all of the anthers from the flowers before they had a chance to mature.

The seeds from the P0 plants were collected by Mendel and he grew them the following season.

After examining the characteristics of the F1 generation of plants, he allowed them to self-fertilize naturally.
The ratio of characteristics in the P0-F1-F2 generations were the most intriguing and became the basis for Mendel's postulates.

In one of his experiments, he crossed plants that were true-breeding for violet flower color with plants that were true-breeding for white flower color.

The F1 generation had a hybrid that had violet flowers.
Three quarters of the plants had violet flowers, and one quarter had white flowers in the F2 generation.

The results of his crosses were reported in his 1865 publication.

The characteristics included plant height, seed texture, seed color, flower color, pea Pod size, and flower position.
The characteristic of flower color was white versus violet.
The results of 19,959 F2 plants alone were the result of large numbers of F1 and F2 plants.
His findings were consistent.

He confirmed that he had plants that bred for white or violet flowers.

All offspring of parents with white flowers had white flowers, and all offspring of parents with violet flowers had violet flowers.

The stigma of a plant with white flowers was applied to the pollen from a plant with violet flowers.

After sowing the seeds that resulted from this cross, he found that 100 percent of the F1 hybrid generation had violet flowers.
The blend theory predicted that the hybrid flowers would be pale violet or that they would have equal numbers of white and violet flowers.
The offspring were expected to have contrasting parental qualities.
The white flower trait in the F1 generation had disappeared according to the results of the study.

Mendel did not stop his experimentation there.

He allowed the F1 plants to self-fertilize and found that 705 had violet flowers and 224 had white flowers.
The ratio was 3:1 for violet flowers and 3:1 for white flowers.
When he transferred pollen from a plant with violet flowers to the stigma of a plant with white flowers, he obtained the same ratio regardless of which parent contributed which trait.

The male and female in one cross have the same characteristics, but the male and female in the other cross have different characteristics.

The F1 and F2 generations behaved the same way when it came to flower color.
One of the two traits would disappear completely from the F1 generation only to reappear in the F2 generation at a 3:1 ratio.

When he compiled his results for thousands of plants, he found that the characteristics could be divided into expressed and latent ones.

He called them dominant and recessive.
The offspring of the hybrid offspring have the recessive trait.
The violet-flower trait is a dominant trait.
White-colored flowers are a trait.
Plants have two copies of the flower-color characteristic and each parent can transmit one of them to their offspring.
The physical observation of a dominant trait could mean that the genetic composition of the organisms included two dominant versions of the characteristic.
The organisms lacked any dominant versions of the trait that was observed.

We need to review the laws of probability to understand how the basic mechanisms of inheritance are deduced.

The mathematical measures of likelihood are called probabilities.

The total number of opportunities for the event to occur is divided by the number of times the event occurs to calculate the empirical probability.
By dividing the number of times that an event is expected to occur by the number of times that it could occur, it is possible to calculate theoretical probabilities.
Empirical probabilities are derived from observations.
Knowing how the events are produced and assuming that the probabilities of individual outcomes are the same is what theoretical probabilities are.
There is a difference between a probability of one and a probability of zero.
A round seed produced by a pea plant is an example of a genetic event.

One experiment showed that the probability of a round seed occurring was one in the F1 offspring of a true-breeding parent.

The probability of any given F2 offspring having round seeds was three out of four when the F1 plants were self-crossed.
75 percent of F2 offspring were expected to have round seeds, whereas 25 percent were expected to have wrinkled seeds.
Mendel was able to predict the outcomes of other crosses using large numbers of crosses.

The pea plants transmit their characteristics from parent to offspring.

Different seed colors and seed texture could be considered in separate probability analyses after being determined that they were transmitted independently of one another.
The offspring of a cross between a plant with green, wrinkled seeds and a plant with yellow, round seeds had a 3:1 ratio of yellow:green seeds and a 3:1 ratio of wrinkled:round seeds.
The texture and color did not have an effect on each other.

The product rule states that the probability of two independent events occurring together can be calculated using the individual probabilities of each event.

Imagine rolling a six-sided die and flipping a penny at the same time.
The die can roll any number from 1-6, whereas the penny can turn up heads or tails.
The outcome of rolling the die has no effect on flipping the penny.
Each event is expected to occur with equal probability, and there are 12 possible outcomes of this action.

The die has a 1/6 chance of rolling a two, and the penny has a 1/6 chance of coming up heads.

The probability that you will get the combined outcome 2 and heads is based on the product rule.
The product rule can be applied with the "and" signal.

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 sum rule should be applied.
Imagine you are flipping a penny and a quarter.
The outcome can be achieved if the penny is heads or tails, or if the quarter is heads or tails.
The outcome was fulfilled in either case.
The probability of getting one head and one tail is calculated using the sum rule.
Before we summed them, we used the product rule to calculate the probability of PH and QT.