Gregor Mendel was one of the first biologists to use mathematical analysis to prove hypotheses. He used elementary probability theory in his work. He was also inspired by the atomic theory of matter (an appropriate example of cross-fertilization in science). He wondered whether hereditary traits were also passed as particles to future generations. Previously, it was thought that traits from parents blended to form a new mix in offspring. Mendel proved his hypothesis and published his results starting in 1865. However, his contribution was not recognized until the principles were rediscovered independently by others some 35 years later.

Mendel deduced several of the basic principles of heredity. Here we summarize all of the principles as known today. Then several of Mendel's and others' results will be described as examples. The principles of heredity can be summarized as eleven rules:

Environmental Biology for Engineers and Scientists, by David A. Vaccari, Peter F. Strom, and James E. Alleman Copyright © 2006 John Wiley & Sons, Inc.

1. A gene is a sequence of nucleotides that codes for a specific polypeptide. [Recall that a protein can consist of several polypeptides, and possibly other factors such as metal atoms (e.g., hemoglobin, which has four polypeptides and iron atoms).] Not all genes in a particular cell actually produce their polypeptide. Cells that do produce the polypeptide associated with a gene are said to express the gene.

2. The genes are contained in the chromosomes.

3. A gene may come in a variety of mutated forms, called alleles. For example, the gene for eye color may have an allele for blue eyes and another allele for brown eyes. Although all the organisms of a single species will have the same genes, each individual can have a unique combination of alleles.

4. The particular combination of alleles that an individual has is called its genotype. The particular set of genetically controlled traits possessed by an individual is called its phenotype. That is, the phenotype is the result of expression of the genotype.

5. Most higher organisms, in particular most plants and animals, are diploid, having chromosomes in pairs. Thus, they have two copies of each gene.

6. The two copies can have the same or different alleles. If both chromosomes have the same allele, the organism is said to be homozygous for that gene. If the alleles are different, the organism is heterozygous. For example, a human can have a blue-eyed allele on one chromosome and a brown-eyed allele on the other. That individual would be heterozygous for eye color. Alternatively, both alleles could be for blue eyes, and the person would be homozygous for eye color.

7. When the two alleles for a gene are different, several situations can occur:

a. Complete dominance: one allele is expressed; the other is not. An allele that is expressed at the expense of another is said to be dominant. The allele that is not expressed in a heterozygous genotype is said to be recessive. For example, brown eye color is dominant and blue eye color is recessive. Blue eye color is expressed only if both alleles are for blue eyes. When a gene is homozygous for a recessive allele, it is said to be double recessive, and the recessive allele can be expressed.

b. Incomplete, or partial, dominance: In this case, a mixed phenotype results in a heterozygous individual. For example, if snapdragons with red flowers (homo-zygous for red) are crossed with those with white flowers (homozygous for white), all the offspring will be heterozygous and will have pink flowers. However, if these are then crossbred with each other, about one-fourth of the next generation will be red, one-fourth white, and one-half pink.

c. Codominance is when both traits are fully expressed in the heterozygous organism. This is usually seen only in biochemical traits. An example is human blood type. If a heterozygous individual has allele A and allele B, their blood cells will have both type A and type B antigens.

8. Meiosis separates the two alleles of a diploid organism. Thus, gametes have only one allele. This is called segregation.

9. Random assortment in meiosis distributes the chromosomes to the gametes independently. That is, the chromosomes of an individual's gametes can have any combination of its maternal and paternal chromosomes. In genetics, this is called independent assortment. For example, the fruit fly Drosophila has four pairs of chromosomes, one of each pair coming from each parent. However, its egg cells, which are haploid, may contain chromosome 2 from the father and chromosomes 1,3, and 4 from the mother, or any other combination.

10. All of the genes on a chromosome tend to segregate together. Therefore, genes on the same chromosome are not assorted independently. Their traits tend to be passed on to the next generation together. The tendency for genes on the same chromosome to be inherited together is called gene linkage.

11. Recombination caused by crossing-over in meiosis acts to weaken linkage between genes on the same chromosome. Because of crossing-over, a maternal chromosome in a gamete may include pieces of the paternal chromosome. The closer together two genes are located, the less likely that crossing-over will separate them and the stronger will be their linkage. Two genes that are at extreme ends of the same chromosome will exhibit weak linkage and in fact may show independent assortment, behaving as if they were on different chromosomes.

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