## 10.1 Essential ideas

### 10.1.2 Non-Mendelian inheritance

If all traits were determined by a single gene locus, and if all alleles were inherited independently of each other, we would always observe Mendelian ratios in genetic crosses. Figure 10.1.2a – Mendelian genotypic ratio (9:3:3:1) resulting from a dihybrid cross

### Polygenic traits

• Only a small number of observable traits are determined by a single gene locus. Most traits are polygenic, meaning that the trait involves a number of different genes at different loci. Figure 10.1.2b – Discrete vs Continuous variation

• The phenotypes of polygenic traits tend to display continuous variation, as opposed to discrete variation. The more genes involved in the development of a specific phenotype, the greater the variation observed.
• Polygenic traits are often influenced by environmental factors, such as diet and exercise in humans, and various abiotic factors – pH, temperature, salinity, etc. Figure 10.1.2c – Linked and unlinked genes

• A linkage group is a group of genes that tends to be inherited together because of their proximity on a chromosome. When two loci are close together on a chromosome, there is less likely to be a crossing-over event between them during meiosis.

### Chi-square tests

• We can determine if genes are linked using a chi-square (x2) test. Figure 10.1.2d – The chi-square value is equal to the sum of all the squared standard normal deviations, where O is the observed frequency, and E is the expected frequency

• When genes are unlinked, they assort independently and the F2 ratio from a dihybrid cross will be 9:3:3:1. In a chi-square test, the null hypothesis (Ho) is that the alleles assort independently, so we expect these ratios.
• If the x2 value is greater than the critical value listed on the distribution table, for the correct degrees of freedom, then the difference we observe is statistically significant.
• In biology, we accept values at 95% confidence. This means that we always look at the value on the table where p = 0.95. Figure 10.1.2e – Table of critical x2 values

• If the calculated x2 value is less than the one listed, then we accept the null hypothesis. We conclude that the variation we have observed will be due to chance 95% of the time – the genes are probably unlinked.
• If the calculated x2 value is greater than the one listed, then we reject the null hypothesis. It means that the variation we have observed is not due to chance 95% of the time – the genes are probably linked.

### Worked example – Chi-square test for genelinkage

When true breeding pea plants with purple flowers and long pollen were crossed with pea plants having red flowers and round pollen, all of the F1 generation had purple flowers with long pollen.

• Ho: Purple flowers (P) are dominant to red flowers (p); long pollen (L) is dominant to round pollen (l). The genes are unlinked and will produce a Mendelian ratio of 9:3:3:1 in the F2.
• In the F2 generation the following pea plants were observed:

Purple flowers, long pollen: 296

Purple flowers, round pollen: 85

Red flowers, long pollen: 28

Red flowers, round pollen: 18

Total: 427

Let’s compare the observed and expected frequencies for the F2:

 Category Expected ratio Observed frequency (o) Expected frequency (e)* (o–e) (o–e)2 e Purple, long 9 296 240 56 13.07 Purple, round 3 85 80 5 0.312 Red, long 3 28 80 –52 33.80 Red, round 1 18 27 –9 3.00 Total 16 427 427 – X2 = 50.18

*Calculation of e: [(Expected ratio/16) x total number of F2 plants]

• The value for x2 is 50.18.  This is much greater than the critical value of 7.814 (see Figure 10.1.2e). The alleles have not assorted independently. The genes are linked. Figure 10.1.2f – Human height
NBA basketball player Jeremy Lin with his mom and dad: polygenic traits such as human height may also be influenced by environmental factors. Figure 10.1.2g – Pea flowers
Pea flowers show discrete variation.

### TOK

The law of independent assortment turns out to have many exceptions. What is the difference between a law and a theory in science?

### Concept help

• There is a distinction between sex-linkage and autosomal gene linkage. Sex-linked genes are genes found on the X-chromosome. Examples of traits that are linked to sex can be found in 3.1.4.
• The degree of freedom refers to the number of comparisons being made. It is always one less than the total number of categories (df = n–1). For a dihybrid cross, there are four (n = 4) possible combinations of alleles, and there are three comparisons being made, and so there are 3 degrees of freedom. Figure 10.1.2h – Rajan and Sajan
Polygenic traits are more likely to show continuous variation, even in identical twins. Can you name at least five traits that are likely to be polygenic in humans?