 Description of Quantitative Traits

Quantitative Traits Statistics

## Statistics of Quantitative Traits

Because quantitative traits exhibit a continuous distribution of phenotypes, they cannot be analyzed in the same manner as traits controlled by a few genes. Rather, these traits are described in terms of statistical parameters. The two primary statistic s used are the mean and the variance.  An associated statistic that is also relevant is the standard deviation because it is in the same units as the mean. The mean is the average value of the distribution. Two distribution can have the same mean, but widely different shapes. A wide distribution suggests a large range of values, whereas a narrow distribution occurs when the range of observed values is small. The variance is a measure of the variability of the distribution. The following graph demonstrates two distributions with the same mean but different variances. A simple way to describe a distribution is in terms of its mean and its standard deviation. The mean ± one standard deviation encompasses *66% of the distribution. Thus a larger standard deviation suggests that the distribution is wider than one with a smaller standard deviation. Furthermore, *95% of the distribution is found within ± two standard deviations of the mean and *99% of the distribution is found within ± three standard deviations.

Example: Quantitative genetics of ear length in corn

Generation Mean (cm) Standard deviation (cm)
Tom Thumb (P1)

16.80

0.816

BMS (P2)

6.63

1.887

F1

12.12

1.519

F2

12.89

2.252

Several observations can be made from the above data.

1. Even though the mean ear length of the BMS is smaller, the standard deviation is larger. This suggests that it is more variable than the long ear line.

2. Because the F1 population is derived from two pure lines, it should be entirely homogeneous (all are heterozygotes). Thus all the variance associated with that population is environmental variance.

3. The mean of a quantitative trait in a F1 population is intermediate to the two parents, and the mean of the F2 is approximately equal to that of the F1.

4. The F2 population is more variable than the F1.

5. The extreme values of the distribution should be equivalent to the two parents used in the cross because this small portion of the population will have the same genotypes as the parents. If two genes control the trait 1/16 of the F2 populations will equal either of the two parents. If five genes control the trait then 1/243 of the F2 populations will equal either parent.

Copyright © 1997. Phillip McClean