Probability and Punnett Squares
In his discoveries about recessive and dominant alleles, and segregation, Mendel concluded that he could use probability to predict his results. Probability is a mathematical principle concerning the likelihood of certain things happening.
The way alleles segregate when the gamete is formed uses this principle. If the two F1 plants had both one dominant and one recessive allele, you would think that half of the offspring would show one allele and one half the other. But since one allele is recessive, the dominant allele will still always show if it is combined with a recessive. Using the principle of probability, we can estimate that only one fourth will show the recessive allele. Mendel found that this was the case for all the seven genes he tested. Since there are three combinations of alleles, XX, Xx and xx (other letters than x can be used), we have divided them into groups. There are two groups: homozygous and heterozygous. Homozygous means that both alleles are the same (XX and xx), while heterozygous means that both alleles are there (Xx).
Since probability is only a guess of likelihood, it is often wrong. However, the more trials (in Mendel’s case, cross-pollinations) you do, the more accurate probability will be.
Something else that Mendel discovered was that each organism had a genetic makeup (the combination of genes such as XX, Xx and xx) and physical traits. These two can vary from organism to organism. The genetic makeup is called the genotype, and the physical traits are called the phenotype. In many cases, the genotype of organisms will be different, but the phenotype will be the same.
A very good way to determine the probability of genetic crosses is something called a Punnett Square; a very simple diagram. Basically, you start with a square, and then line up the segregated alleles of the parents on perpendicular sides (usually the left and top) of the square. You then fill in all the combinations of possible genotypes, by adding one allele from each parent in the place where the two segregated alleles meet. When all the combinations have been found, you can divide the results into groups depending on the phenotype (XX and Xx in one group, xx in another group). You can then look at the ratio between the groups to find the probability of each phenotype.
Figure 11-2a, Punnet Square
Mendel did not just investigate the genes one at a time. He also tried to find how two different genes affect each other. The mixing of two genes is called a two-factor or dihybrid cross. Mendel did two-factor experiments on both true-breeding (F1) and hybrid (F2) plants.
When he tried pure-breeding plants in the experiment the two parents’ genotypes were XXYY and xxyy. For this reason, all the offspring got one dominant and one recessive allele (they were all heterozygous), so they all had the dominant phenotype.
After he tried the experiment with true-breeding plants, he used their offspring to try the experiment with hybrids. The genotypes of both parents were XxYy. Because the parents were heterozygous this time, the offsprings’ genotypes were very varied. Mendel got XXYY, XXYy, XXyy, XxYY, XxYy, Xxyy, xxYY, xxYy and xxyy (in different ratios), meaning that some of the offsprings’ phenotypes were from neither the parents nor the “grandparents”. This proved that alleles could segregate on their own, and were not really affected by the alleles of the other gene. Mendel’s results created the principle of independent assortment, which says that different genes can segregate independently in the creation of gametes. This is the cause behind the wide range of different genotypes and phenotypes in nature.
Figure 11-2b, Two-factor Punnett Square
A Summary of Mendel’s Principles
Mendel discovered many principles of heredity and genetics. They are:
- The passing on of biological traits depends on genes from the parents.
- If there is more than one allele of a gene, some alleles will be dominant and some will be recessive.
- In most sexually reproducing species, the offspring will have two sets of each gene (one from each parent). The genes will then segregate when the gametes of the offspring are made.
- Alleles of different genes often segregate without any effect from the other gene(s).
Mendel’s discoveries apply more to organisms than plants. Thomas Hunt Morgan (USA) did similar experiments to Mendel’s in the 1900s. He used fruit flies instead, and found that the same principles apply to the flies as well. It is confirmed that Mendel’s principles also apply to humans and other organisms.
11-2a Punnett Square. Digital image. Johnson Life Science Henry World School. 09 Feb. 2011. Web. 08 Dec. 2012. <http://johnsonhenryworldschool.blogspot.se/2011/02/activity-61-gene-squares.html>.
11-2b Two-factor Punnett Square. Digital image. Scioly.org. 13 Nov. 2012. Web. 08 Dec. 2012. <http://scioly.org/wiki/index.php/Designer_Genes>.