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  Principles of independent assortment, Biology tutorial

Mendel's Second Law of Inheritance:

Though Mendel's first law is very significant basic law, it deals with pattern of inheritance of alleles at only one locus. Though, it is very hardly ever the case that two individuals vary at only one locus. Mendel identified this fact and so carried out experiments in which he studied immediate inheritance of more than one phenotype. Simplest example of such a case is one in which there are 2 phenotypes, each handled by one locus. The term wild type is utilized to explain any phenotype that is most common in flies in wild; such a phenotype may be either dominant or recessive. Wild type fly has red eyes and long bristles on different parts of body. A mutant gene, purple, changes eye color to purple. This gene is symbolized by symbol, pr, and its wild type allele for red eyes is symbolized as pr + superscript "+" signifying that it is a wild type allele. Another gene, spineless (ss), considerably reduces length of bristles. Its wild type allele is symbolized as SS+. Dihybrid cross i.e. cross in which parents differ with regard to two characters.

In this F1 is explained as a dihybrid as it is product of parent who varies with regard to two characters. In future crosses, wild type eye color and bristles will be referred to as red and normal respectively. Wild type phenotype of F1 indicates that both purple and spineless are recessive, as they are not expressed when present in combination with respective wild type alleles.

At this stage of experiment, result of cross is not different from that of monohybrid cross; all F1 contain same phenotype. Four phenotypic classes of F2 are attained. Numbers immediately below classes illustrate number of each class of progeny. These numbers work out to ratio of 9 : 3 : 3 : 1. Using sum of the ratios as denominator, 9/16 of F2 are red, normal, 3/16 are red, spineless etc. This result looks extremely different from F2 of monohybrid cross in which there were only two phenotypic classes in ratio of 3:1.

The F2 ratio change is only apparent one as the 9 : 3 : 3 : 1 ratio is same as expression (3 red: 1 purple) (3 normal: 1 spineless). When that expression is extended that is multiplied, it provides 9 red, normal : 3 red, spineless : 3 purple, normal : 1 purple, spineless.

This conclusion is confirmed by analyzing testcross. One of the parents in testcross is homozygous recessive; in this case two lock are involved, as one parent is purple, spineless in phenotype. This testcross is also backbone as homozygous recessive parent is identical with one of parents in F generation of our cross.

Genotypes are listed under corresponding phenotypes. When combined, genotypes of pure breeding parents are pr+/pr+, ss+/ss+, and pr/pr, ss/ss. Red, normal F1 are pr+/pr, ss+/ss . At this phase it is relevant to recall some of appropriate principles:

1. According to Chromosomes Theory, every kind of chromosome should be represented in gamete. As genes are on chromosome, it follows that every gene/locus (two loci in that case) should be represented in gamete.

2. According to Mendel's first law, there is segregation of alleles, so only one member of pair enters gamete. Thus there should be segregation at every locus present.

In each P - parent, alleles at each locus are the same, so each parent produces only one kind of gamete. Red, normal parent will generate pr+, ss+ gamete and purple, spineless will generate pr, ss gametes. Fertilization will generate doubly hererozygous F1 genotype derived above. Genotype conforms with red, normal F1 phenotype. On the basis of proceeding, genotype of F1 testcross parent is pr+/pr, ss+/s and that of purple, spineless parent is pr/pr, ss/ss.

The next step is to find out genotype of each of four classes of testcross progeny. It is easy to find out one half of genotype of each class of progeny as the purple, spineless testcross parent is (it has to be) homozygous for each of two recessive genes. This parent will hence generate only one kind of gamete, having genotype of pr. As these two alleles that are contributed to all testcross progeny are both recessive, they won't obscure effects of alleles contributed by F1 parent.

In the case of red, spineless class, to have red phenotype F1 parent should contribute dominant alleles, pr+ and for spineless, there should be homozygosit for recessive alleles. Hence in this case the gamete from the F1 parent is pr+. You can go through the steps of determining the gametic contributions of the F1 parent in the last two classes.

F1 parent generated four kinds of gametes. Four kinds are possible because, F1 are heteroxygous at both loci. We can also see that with respect to each locus two of four kinds of gametes have one allele, e.g. pr+ while other two have other allele, pr, using same example. As phenotypes (and genotypes) that we attained among testcross progeny were in final analysis determined by gametic contributions of F1 parent. All different kinds of gametes from F1 parent are evenly likely to fuse with gamete from other parent.

As there are four kinds of gametes from each parent, there would be 16 possible fusions (boxes). Additionally since gametes are present in equal proportions each box represents 1/16 of F2. Hence by counting number of boxes corresponding to each phenotype we can find out frequency of that class of progeny. Fourth phenotype classes are recognized by different kinds of shading. To have dominant phenotype for each locus, there should be at least one dominant allele at each locus. This class of progeny is represented by unshaded boxes that are nine in number. Thus 9/16 of F2 are red, normal.

Genotypic ratio in F2 is different from phenotypic ratio. Different genotypes among progeny have been numbered in Punnett squares. There are nine different genotypes in the ratio of 1: 2 :2 :4 :1 : 2 : 1 : 2 : 1. Make sure you understand how the genotypes correspond to the phenotypes. The fractions are in sixteenths like the phenotypic fractions and they add up to one.

Mendel derived second law of inheritance governing simultaneous inheritance of genes at two or more loci. The law may be expressed as: in formation of gametes, two alleles of the given gene assort independently of pairs of alleles of other genes on nonhomologous chromosomes.

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