In a diploid organism like a human, each individual receives one copy of a given gene from their parents. Often there are multiple variants of a gene present in a population; each different variant or version is called an allele. In a Punnett square, each of the possible combinations of alleles you could inherit from your mother is placed atop one column of a grid, while each of the possible combinations of alleles you could inherit from your father goes beside one of the rows. The grid makes it possible to quickly compute the ratio of one genotype or phenotype to another.
Determine how many rows and columns you need for your Punnett square grid. In general, you will have a row for each possible combination of alleles an individual can inherit from one parent, and a column for each possible combination they can inherit from the other. If you are working with only one gene that has two alleles, for example, your Punnett square should have two rows and two columns. If you are working with two genes, each of which has two alleles, your grid will have four rows and four columns. Punnett squares are not used in more complicated situations (for example, five genes with three alleles each would be an impossibly large grid).
Draw the grid. Above each column, write out one possible combination of alleles the organism could inherit from its mother. Next to each row, write one possible combination of alleles the organism could inherit from its father. Often alleles are represented with a letter, where a capital letter is a dominant allele and a lowercase letter is a recessive allele, and a different letter stands for each gene. If we have gene Y with two alleles, for example, we could have Y for the dominant allele and y for the recessive allele. Depending on what kind of problem you are working, however, you may find it more convenient to use other symbols instead.
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In each box of the grid, write the combination of alleles from father and mother together. If the column heading is Yh, for example, and the row heading is yh, the offspring would have Yyhh. This is its genotype -- a graphical representation of the combination of alleles it inherited for two specific genes.
Determine how many different kinds of genotypes are present by reading through your grid. Let's say you look at your grid and find genotypes YY, yY, Yy and yy, for example. yY and Yy are the same for our purposes, so these only count as one genotype: Yy.
Count the number of each kind of genotype present and convert it into a ratio. In our example, you would count the number of YYs, the number of Yys and the number of yys and represent this as a ratio. Let's say we find 1 YY, 2 Yys and 1 yy; the ratio would then be 1 : 2 : 1. This is the genotypic ratio, the relative proportion of each genotype we would expect to find among the offspring of the cross.
Determine what phenotype each genotype will manifest. A phenotype is the observable characteristic of an organism. Let's say we have a gene that affects hair color, for example. The genotype would be the allele of that gene that you inherited, while the phenotype would be your hair color. Typically, the phenotype associated with the recessive allele is ONLY manifested if the dominant allele is not present. If the dominant allele codes for red flowers in a plant, for example, and the recessive allele codes for white flowers, we would only expect to see white flowers in a plant that didn't inherit any of the red alleles, because the red alleles are dominant and win out over the recessive allele. In this case, if an organism inherits one dominant and one recessive, it has the same phenotype as an organism that has two dominants. Cystic fibrosis is a common example. If you inherit one "normal" allele or two "normal" alleles, you do not have cystic fibrorsis; it's only if you inherit two cystic fibrosis alleles that you have the disorder. Consequently, the cystic fibrosis allele is recessive.
In many cases, however, organisms can also exhibit incomplete dominance, in which case a combination of a recessive allele and a dominant allele creates an intermediate phenotype. In the flower example, for instance, incomplete dominance would occur if a combination of red and white allele made a pink flower. Organisms can also exhibit codominance, where dominant + recessive = a phenotype that includes both the recessive and the dominant phenotype. In either of these cases, an organism that inherits dominant + recessive has a different phenotype than recessive + recessive or dominant + dominant.
Count the number of each phenotype present in the Punnett square. Let's go back to our YY example. Your Punnett square contains one YY, two Yy and one yy, so your genotypic ratio is 1 : 2 : 1. If Y is dominant and y is recessive, there are only two phenotypes, because YY and Yy have the same phenotype, so your phenotypic ratio is 3 : 1 (the two Yys plus the one YY make 3 of that phenotype). If this trait exhibits codominance or incomplete dominance, however, you have three phenotypes, because YY, Yy and yy all have different phenotypes, so in this case your phenotypic and genotypic ratios are the same: 1 : 2 : 1.