Probability of Traits

Inheriting Traits

Every person has a set of characteristics, or physical traits, that allows you to identify that person. Height and hair color are two of these traits. Specific examples of these physical traits, such as blond hair or short height, are called the phenotype of the person.

Alleles and Traits

The genetic makeup of an organism is called its genotype. This genetic makeup involves combinations of alleles, or different forms of a gene, that influence an organism’s phenotype. Pairs of alleles make up the genotype that controls the expression of a trait. For example, a pea plant that has a tall phenotype could have the genotype TT. However, because the allele for tallness is dominant, the tall pea plant could also have one allele that codes for tallness (T) and another masked, or recessive, allele that codes for shortness (t) . In this case, the genotype of the pea plant would be Tt. A pea plant that has a short phenotype must have two recessive alleles, so it would have the genotype tt. An organism with the same two alleles for a trait (for example, TT or tt) is homozygous for that trait. An organism with two different alleles for a trait (for example, Tt) is heterozygous for that trait. Some human traits, such as the type of earwax a person has, are determined by just two alleles, one dominant and one recessive. However, most human traits are controlled by multiple alleles or by multiple genes. The color of hair you have, for example, is such a trait. Traits are also influenced by environmental conditions.

Think about Science

Directions: Answer the following questions.

Dark purple flowers (P) are dominant in pea plants, and white flowers (p) are recessive.

  1. What is the flower phenotype for a pea plant with the genotype Pp?
    A. All white flowers B. All dark purple flowers C. Flowers of both colors D. All light purple flowers
  2. If a pea plant has dark purple flowers, what could be its genotype? A. PP only B. Pp only C. pp only D. PP or Pp

Punnett Squares

A Punnett square shows how the alleles for one or more traits could combine during a cross, or mating, of two parents to produce specific genotypes and phenotypes in the offspring, the individuals of the next generation. Punnett squares are useful for predicting the probabilities of genotypes for traits that have dominant-recessive inheritance.

Using Punnett Squares

To use a Punnett square for a mono-hybrid cross, a mating between two parents that differ in only one trait, draw a box with four squares in it. Place the genotype for one parent across the top. Place the genotype for the other parent down the side. Then fill in the boxes, placing the corresponding allele from each column and row in each box. The combinations of alleles in the boxes represent the possible genotypes of the offspring. The Punnett square here shows all possible genotypes for the offspring of a cross between two tall parent pea plants, each with the genotype Tt. The following symbols represent this cross: Tt x Tt. According to the Punnett square, the offspring from this cross could have the TT, Tt, or tt genotype. Those with the TT or Tt genotype would have the dominant phenotype, which is tall height. Those with the tt genotype would have the recessive phenotype, which is short height.

Percents

Once a Punnett square is completed, you know the possible genotypes of the offspring. You can then describe these genotypes using percents. A percent describes a part of 100. For example, 50 percent means 50 out of 100. In the Punnett square shown here, one out of four boxes has the TT genotype. Other ways to write “one out of four” are one-fourth and 1/4. A fraction can be written as a percent. The fraction 1/4 is equal to 25 percent, so you can predict that there is a 25 percent chance that an offspring will have the TT genotype.

The same is true for the tt genotype. Half of the boxes, or two out of four, have the Tt genotype. The fraction f is the same as the fraction 1/2 and this fraction is equal to 50 percent.

Now think about the phenotypes of the offspring. A plant will be tall if it inherits one dominant allele. Three of the four boxes, written as a fraction as 3/4 or 75 percent, include a dominant allele. Therefore, there is a 75 percent probability that an offspring will be tall and a 25 percent probability that an offspring will be short.

Think about Science

Directions: Answer the following questions.

  1. Construct a Punnett square for a cross between a pea plant with purple flowers (Pp) and a pea plant with white flowers (pp). How many boxes in the Punnett square show the genotype pp?
    A. 1 box B. 2 boxes C. 3 boxes D. 4 boxes
  2. A pea plant with yellow seeds (YY) is crossed with a pea plant with green seeds (yy). What is the percent chance that an offspring would have green seeds?
    A. 0 percent B. 25 percent C. 50 percent D. 100 percent

Predicting Traits

Do the percents you found mean that if two plants produce 100 offspring, exactly 25 will be short? No, they do not. Punnett squares help you predict the probability, which means the likelihood, that particular combinations of alleles will be produced. The actual outcome may be higher or lower than the predicted number. As an example, think about flipping a coin. When you flip a coin, it might land heads-up or tails-up. The probability that the coin will land heads-up is one out of two, which is 50 percent. You can predict that if you flip a coin 10 times, it will land heads-up 50 percent of the time, which is five times. If you then go ahead and flip a coin 10 times, it may land heads-up one time, four times, eight times, or even 10 times. The result is a matter of chance. It is the same way with living organisms. The Punnett square helps you make predictions about the offspring of a cross. Only careful observations tell the actual results of the cross.

Using Probability to Infer Genotype

When examining traits in a real population, you can infer the genotype of parents by examining the phenotypes of offspring and determining which cross would yield the percentages you see. For example, let’s say you crossed two purple-flowered pea plants, and you got 462 offspring: 120 with white flowers and 342 with purple flowers. When you determine the percentage of each type of flower, you have 26 percent with white flowers and 7 4 percent with purple flowers. This is close to the 75 percent and 25 percent you predict when you cross two plants that are heterozygous for the trait. Therefore the genotypes of the parents are most likely Pp and Pp.

Multiple Traits and Other Patterns of Heredity

You can sometimes use a Punnett square to find the probability of multiple traits. In a dihybrid cross, two traits are crossed at the same time. You must use a larger Punnett square of 16 squares to accommodate all the possible combinations of the two traits. The Punnett square shown here predicts allele combinations in offspring for the human traits of freckles and earwax. Wet earwax (W) is associated with a dominant allele, as are freckles (F).

Sometimes traits are determined by genes on sex chromosomes, or the X and Y chromosomes that determine gender. Genetic females carry two X chromosomes. Genetic males carry one X and one Y chromosome. Traits that are determined by sex chromosomes are known as sex-linked traits.

One sex-linked trait is color blindness. People who are color blind cannot see the difference between certain colors such as red and green. Red-green color blindness is caused by a recessive allele carried on the X chromosome. Because it is a recessive trait, a female will be color-blind only if she receives the allele for color blindness from both parents. A female who carries an allele for a disorder but does not exhibit the disorder is considered to be a carrier of that disorder. Because males have only one X chromosome, if a male inherits the allele for color blindness on the X chromosome he receives from his mother, he will be color-blind.

Punnett squares can be used to predict the genotypes of offspring for traits that have multiple alleles. For example, the ABO blood group gene has three alleles - IA, IB, and i - that combine in pairs to form the different blood types A, AB, B, and 0. Instead of three possible genotypes (as in dominant recessive inheritance), the ABO blood-group inheritance has six possible genotypes: IAIA, IAIB, IBIB, IAi, IBi, and ii.

Think about Science

Directions: Answer the following question.

  1. If two people with no freckles and dry earwax have a child, what is the probability that the child would have the same phenotype as the parents?
    A. 0 percent B. 25 percent C. 56 percent D. 100 percent