Fundamentals of InheritanceIn the 1860s, Gregor Mendel studied seven clearly defined traits in pea plants, each of which occurred in one of two characteristic forms. After eight years of rather painstaking study on how traits were passed from one generation to another, Mendel presented his findings to an audience unable to understand it or its significance. Mendel lived in the 1800s. His contemporaries thought parent's "hereditary fluids" mixed together in some unknown manner during the formation of progeny and "blended" to produce offspring with a mixture of their parent's characteristics. It was not until 1900, years after his death, that three other scientists, working independently, rediscovered his work and recognized its significance. The study of the pattern of inheritance that follows the laws formulated by Mendel is often referred to as Mendelian Genetics. We will take a look at Mendel's laws in a moment, but first lets look at some terminology. You have probably used the term, gene. A gene is a piece of DNA consisting of many nucleotides that codes for some gene product. When passed on to progeny, genes represent hereditary information. Mendel thought of them as "particles" or beads on chromosomes. His concept is not so inaccurate because genes are located on specific portions of a chromosome; however, they are not like beads on a string. Remember that sexually reproducing organisms are diploid. Diploid cells have two sets of chromosomes, one set inherited from each parent. Therefore, they have two chromosomes of each kind and two genes for each characteristic. When gametes are produced by meiosis, reduction division occurs to reduce the chromosome number to haploid and to produce cells (eggs, sperm) that have one chromosome of each of the pairs that was in the diploid cell that underwent meiosis. Sexual reproduction implies the fertilization of a haploid egg cell by a haploid sperm cell. Therefore, the resulting zygote has inherited one gene of each type from both parents. The following diagram explains these relationships. Once again, each diploid organism has two genes for each characteristic. These two genes for the same trait or characteristic are referred to as alleles. The following diagram explains this idea of alleles. There may be several alternative forms of each gene in a population. Alleles are always located on a pair of chromosomes where one allele is opposite the other at some same specific location or locus. The genome is a set of all the genes necessary to specify an organism's characteristics. The genotype of an organism is a listing of the genes present in that organism. Since it consists of the cell's DNA code, you cannot really see a genotype. It is probably not possible to know the complete genotype of most organisms although we are working on it for humans. It is certainly possible, however, to know the genes present that determine a particular characteristic. Look around at several of your classmate's earlobes. Some will have the lobe attached to their head; others will have the lobe free. This trait is inherited. Let's call the allele for free earlobes a capital E. And, let's call the allele for attached earlobes a lowercase e. Now consider the genotypic combinations of the two alleles possible for an individual:
The expression of one's genotype, such as EE, Ee or ee, is called one's phenotype. For various reasons, certain genes may not express themselves. Sometimes, the physical environment determines whether or not certain genes function. An human example for this sort of thing would be freckles. While the gene for freckles may be present, it will not be expressed unless the individual is exposed to sunlight. The expression of some genes is directly influenced by the presence of other alleles in the organism. For any particular pair of alleles in an individual, the two alleles from the two parents are either identical or not identical. The individual is homozygous for the trait when it has two identical alleles. In the example above about earlobes, both the EE and ee individuals are homozygous for the trait. The person with the Ee genotype is heterozygous for the trait, in this case, free earlobes. An individual is heterozygous for a trait when it has two different allelic forms of a particular gene. The heterozygous individual received one form of the gene from one parent and a different allele from the other parent. Often one gene expresses itself and the other does not. A dominant allele expresses itself and masks the effect of the other trait. The allele for free earlobes is dominant. A recessive allele is one that, when present with another allele, does not express itself; it is masked by the effect of the other allele. If you have attached earlobes, you have two alleles for the trait. Recessive genes are not less likely to be inherited. They must, however, be present in a homozygous condition to be expressed. Mendelian genetics involves the study of the transfer of genes from one generation to another and the ways in which the genes received from the parents influence the traits of offspring. Let's return now to Mendel. Mendel concluded which of the traits that he studied were dominant and which were recessive. What made his work unique was that he studied only one trait at a time. What he found is shown in the following table.
Previous investigators had tried to follow numerous traits at the same time and became hopelessly muddled because a large set of characteristics is cumbersome to work with. Mendel also used traits with clear-cut alternatives such as purple or white flower color. He was also lucky to have chosen pea plants because they self-pollinate. When self-pollination occurs, it is possible to develop a population of plants that is homozygous for a number of characteristics. Such a population is known as a pure line. Mendel took a pure line of pea plants having purple flowers, removed the male parts (anthers) and discarded them so that they could not self-pollinate. He then took anthers from a homozygous white flower pea plant and pollinated the antherless purple flowers. When the pollinated flowers produced seeds, Mendel collected them and planted them. They eventually produced flowers and all of the flowers were purple. This result collided with the prevailing notion of the day that would have predicted the resulting flower color to have be a "blend" of white and purple--a lighter purple. Another favored notion of the day was that the resulting flowers should have been a mixture of white and purple flowers. But all the flowers were purple. Mendel repeated his experiments with homozygous strains for the other traits in the table above. The results were the same: the offspring showed the characteristic of one parent and not the other. Next, Mendel crossed the offspring of the purple-white flower cross (all of which had purple flowers) with each other to see what he would get in a third generation of plants. Had the characteristic of the white flowered parent been lost? When the seeds produced by this cross were planted and the plants allowed to flower, Mendel noted that three-fourths of them produced purple flowers; one-fourth produced white flowers. After Mendel analyzed his data, he came up with several findings which have since become known as "laws."
Keep in mind that biologists knew nothing of chromosomes or DNA or the processes of mitosis and meiosis during Mendel's time. Mendel just assumed that each gene was separate from other genes. It was indeed fortunate for him that the characteristics he chose to study in pea plants are found on separate chromosomes. In order to study hereditary problems, you need to have a simple understanding of probability. Probability is the chance that an event will happen, and is often expressed as a percent or a fraction. It is not the same as a possibility. When you flip a coin, the probability of your getting a "heads" is 0.5 or 50% because there are only two sides to the coin. Probability can be expressed as a fraction as follows: 
So, the probability of cutting a deck of playing cards and getting the ace of spades is 1/52. You can also determine the probability of two independent events that occur together. This probability is the product of their individual probabilities. For instance, if you throw a pair of dice, it is possible that both will be fours. What is the probability? The probability of one die being a four is 1/6. Therefore, the probability of throwing two fours is: 
The first kind of heredity problem I will work out for you is the easiest type; a single-factor cross. I will use the earlobes alleles as an example. In humans, remember, the allele for free earlobes is dominant and the allele for attached earlobes is recessive. If both parents are heterozygous (have one allele for free earlobes and one allele for attached earlobes), what is the probability that they can have a child with free earlobes? with attached earlobes? Here is how to solve this query.
Since the male has both the free earlobe allele and the attached-earlobe allele, half of his gametes will contain the free-earlobe allele and the other half will contain the attached-earlobe allele. The same is true for the female since she has the same genotype. Now put this information into a Punnett square, a box that allows you to determine genotypes and phenotypes of offspring from a particular cross. 
Looking at the allelic combinations, determine the phenotype of these possible combinations. In the above box, three of the offspring EE, Ee, and Ee have free earlobes. One offspring, ee, has attached earlobes. The probability of having offspring with free earlobes then is 3/4; for attached earlobes, it is 1/4. Below is an interactive Punnett square generator. You may duplicate one of Mendel's crosses by selecting the various parental types.
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