Sexual reproduction involves the combining of a sperm cell and an egg cell from two individuals. The offspring of this "cross" will have characteristics from both "parents". Organisms that are produced by crossing individuals with different traits are known as hybrids. In most cases, hybrid organisms are more successful than those that are produced from a very limited gene pool. This is sometimes called hybrid vigor. While gene sharing is well understood today, before Gregor Mendel the process was a mystery. 

Gregor Mendel is known as the father of modern genetics. Mendel's genius was that he noticed differences in peas being grown in his garden and applied the scientific method to determine the cause of these differences. See Mendel's Experimental Approach. He published a paper in 1865 with these three conclusions to his research:

• Principle of Dominance - One factor in a pair may mask the effect of the other.
• Principle of Segregation - The two factors for a characteristic separate during the formation of eggs and sperm.
• Principle of Independent Assortment - The factors for different characteristics are distributed to reproductive cells independently.

At the time, chromosomes and the process of meiosis were unknown. Mendel's work was considered obscure and unimportant until 1900, when Walter Sutton proposed the Chromosome Theory.

Important genetic terms:

Genotype - the genetic makeup of an organism.
Phenotype - the external appearance of an organism.
Homozygous trait - the genes for that trait are the same.
Heterozygous trait - the genes for that trait are not the same.
Monohybrid cross - a cross between individuals with one pair of contrasting genes.
Dihybrid cross - a cross between individuals with two pairs of contrasting genes.
Parents - the two organisms whose genes produce offspring.
F₁ generation - the offspring from parents.
F₂ generation - the offspring produced by crossing two F₁ individuals.

To understand genetics, one must understand probabilities.

The traits that are passed from parents to offspring are determined by the combination of genes that are in the gametes. This is a random event in nature. The probability of a particular event occuring is the fraction of outcomes in which that event occurs.

What is the probability of the number 5 coming up when a dice is rolled?

• A single roll of a dice has the possible outcomes 1, 2, 3, 4, 5, 6.
• There are a total of 6 possible outcomes, one of those being the number 5.
• The probability of the number 5 coming up is 1/6.

What is the probability of rolling an even number with a dice?

• The even numbers are 2, 4, 6.
• Each of these has a 1/6 chance of occuring.
• This gives us three chances in six of rolling an even number. 3/6 = 1/2

What is the probability of cutting an ace from a deck of shuffled cards?

Introduction to Punnett Squares:

A Punnett Square is a chart drawn to determine the probable results of a genetic cross. To be able to draw a Punnett Square, you must know the genotype of both parents.

Sample Problem 1.   In roses, red flowers are dominant over white flowers. What are the possible offspring when a homozygous red rose is crossed with a homozygous white rose.

Nine steps are needed to solve problem 1: Write genotype for each parent. Use a capital case letter of the dominant trait to represent a dominant gene. R - for the dominant trait red. Use a small case letter of the dominant trait to represent a recessive gene. r - for the recessive white. If no dominant trait is present, use a small letter of each trait. Both parents are homozygous in the sample problem. The genotypes for the cross are -  RR X rr Write the possible gametes of one parent across the top. Write the possible gametes of the other parent down the side. Draw the lines of your Punnett Square. This is the first time you know how many squares are inside the Punnett Square. Combine the gametes from each parent in the squares. Always write capital letters first. Count the number of each possible combination present in your Punnett Square. These are the offspring genotypes. 1   R r The phenotypes are the way the offspring appear. 1   red Since the genes are not the same, this trait is heterozygous. Divide the number of each combination type by the total combinations. You now have the probability ratio for the offspring of the parents. 1 / 1 One out of one, or all, of the offspring will be heterozygous red, R r

Sample Problem 2.   Draw a Punnett Square showing the possiblities when two of the Rr offspring above are crossed.  What genotypes are predicted by this square?  What phenotypes are predicted by this square?

Sample Problem 3.   In carnations, neither red nor white is dominant. What are the possible results when two pink carnations are crossed? Since neither trait is dominant, no capital letters are used in the Punnett Square. Use the first letter of each trait to indicate that gene in the square.

Genetics Practice Problems