<< Chapter < Page | Chapter >> Page > |
The results of Mendel’s research can be explained in terms of probabilities, which are mathematical measures of likelihood. The probability of an event is calculated by the number of times the event occurs divided by the total number of opportunities for the event to occur. A probability of one (100 percent) for some event indicates that it is guaranteed to occur, whereas a probability of zero (0 percent) indicates that it is guaranteed to not occur, and a probability of 0.5 (50 percent) means it has an equal chance of occurring or not occurring.
To demonstrate this with a monohybrid cross, consider the case of true-breeding pea plants with yellow versus green seeds. The dominant seed color is yellow; therefore, the parental genotypes were YY for the plants with yellow seeds and yy for the plants with green seeds. A Punnett square , devised by the British geneticist Reginald Punnett, is useful for determining probabilities because it is drawn to predict all possible outcomes of all possible random fertilization events and their expected frequencies. [link] shows a Punnett square for a cross between a plant with yellow peas and one with green peas. To prepare a Punnett square, all possible combinations of the parental alleles (the genotypes of the gametes) are listed along the top (for one parent) and side (for the other parent) of a grid. The combinations of egg and sperm gametes are then made in the boxes in the table on the basis of which alleles are combining. Each box then represents the diploid genotype of a zygote, or fertilized egg. Because each possibility is equally likely, genotypic ratios can be determined from a Punnett square. If the pattern of inheritance (dominant and recessive) is known, the phenotypic ratios can be inferred as well. For a monohybrid cross of two true-breeding parents, each parent contributes one type of allele. In this case, only one genotype is possible in the F _{1} offspring. All offspring are Yy and have yellow seeds.
When the F _{1} offspring are crossed with each other, each has an equal probability of contributing either a Y or a y to the F _{2} offspring. The result is a 1 in 4 (25 percent) probability of both parents contributing a Y , resulting in an offspring with a yellow phenotype; a 25 percent probability of parent A contributing a Y and parent B a y , resulting in offspring with a yellow phenotype; a 25 percent probability of parent A contributing a y and parent B a Y , also resulting in a yellow phenotype; and a (25 percent) probability of both parents contributing a y , resulting in a green phenotype. When counting all four possible outcomes, there is a 3 in 4 probability of offspring having the yellow phenotype and a 1 in 4 probability of offspring having the green phenotype. This explains why the results of Mendel’s F _{2} generation occurred in a 3:1 phenotypic ratio. Using large numbers of crosses, Mendel was able to calculate probabilities, found that they fit the model of inheritance, and use these to predict the outcomes of other crosses.
Observing that true-breeding pea plants with contrasting traits gave rise to F _{1} generations that all expressed the dominant trait and F _{2} generations that expressed the dominant and recessive traits in a 3:1 ratio, Mendel proposed the law of segregation . This law states that paired unit factors (genes) must segregate equally into gametes such that offspring have an equal likelihood of inheriting either factor.
Notification Switch
Would you like to follow the 'Environmental biology' conversation and receive update notifications?