CHAPTER 6

Providing that genes assort independently, the product and summation laws can be used to predict the phenotypic and genotypic ratios from crosses.

The phenotypic and genotypic ratios for F2 of a dihybrid cross where the genes are on different chromosomes are:

Genotypic- 1:2:1:2:4:2:1:2:1

Phenotypic- 9:3:3:1

The recombination frequency (RF) is 50%

If an individual that is a double heterozygote (AaBb) is test crossed the phenotypic ratios of the offspring are:

1:1:1:1

If genes are located on the same chromosome they are said to be linked. Linked alleles for different genes will segregate to the same gametes unless a crossing over occurs between them during prophase I of meiosis. If an individual is doubly heterozygous for two genes the alleles may be arranged in a cis configuration (wild types together and mutants together) or they may be in a trans configuration (wild type allele with a mutant allele).

The further apart two genetic loci are on a chromosome, the greater the probability of a crossing over occurring between these loci. Therefore, the recombination frequency can be used to establish an index of how far apart loci are located on the chromosome. Such a procedure establishes a linkage map. 1% RF represents 1 centiMorgan. When two genetic loci are studied the maximum RF is 50%. Therefore, if loci are widely separated on a chromosome they effectively assort independently of each other.

When three genetic loci are studied the arrangement of the genes can be established. This is called a three point cross. In a three point cross, a triple heterozygote individual is test crossed so that the relative frequency of offspring reflect the relative frequency of gametes produced by the tested individual. The two most common offspring types reflect the linkage groups (parental types). The two least frequent recombinants reflect the cases involving double crossing over events. Each parent will have two alleles in common with one or the other double crossover recombinant. The allele that differs is the centrally located locus. The distance between the central locus and an end locus is calculated by adding the relevant single cross over and double cross over recombinants and dividing this sum by the total number of offspring. The distance between the two outer loci must be determined by summing the two internal distances.

Often a crossing over influences the likelihood of a nearby crossing over. We can calculate the expected number of double crossing overs using the product rule on the probabilities of the two single crossing overs. Dividing the observed double crossing overs by the expected double crossing overs yields a quantity called the coefficient of coincidence (coc). Interference = 1 - coc.

Because of sampling problems, the observed phenotypic ratios will usually not be exactly what are expected based on theoretical considerations. We would like to assess whether any differences we observe are meaningfully different than what we expect. To do this we establish a null hypothesis based on our expectations and then use statistical techniques to see if the observed results are too inconsistent with our hypothesis for us to accept it as likely. To do this, we calculate an index that reflects the difference between our observations and expectations. This index is then compared to a critical value established by statisticians that will only be exceeded by chance with a certain probability P. Scientists often choose P=0.05. A common index used is the chi-squared statistic (Table 5-2). To use this technique you must obtain a critical value from the appropriate row in Table 5-2. The appropriate row is equal to the number of phenotypic categories minus one (e.g. for the F2 of a dihybrid 9:3:3:1; the row is 3).

Chi-squared statistic= ∑ (observed-expected)² /expected

This procedure disregards the possibility of differential viability of meiotic products. A technique that handles such a situation is a Contingency Table Analysis.