3.9: Genotype-phenotype relationships- discrete and continuous traits

When we think about genetic polymorphisms and alleles (different versions of the same gene), it is tempting to assume simple relationships. In some ways, this is an unfortunate residue from the way many are introduced to genetics. Perhaps you remember Gregor Mendel (1822-1884) and his peas. He identified distinct versions (alleles) of particular "factors", now called genes, that he linked to distinct phenotypes - yellow versus green peas, wrinkled versus smooth peas, tall versus short plants, etc. In the real, wild type world peas, for example display a range of colors, ranging from green to yellow and including intermediate shades. How allelic variations in genes influence traits (phenotypes) is more complex and involves both internal and external environmental factors, stochastic events, and the individual's genetic background (more in chapter 15).

For now we will consider one "simple" example of a gene-trait connection, namely the determination of blood type. Which alleles of the ABO gene you inherit determines whether you have an O, A, B or AB blood type. While we will consider how genes work in greater detail later on, for now it is enough to know that the ABO gene encodes the sequence of a polypeptide that acts as a glycotransferase, a catalyst (an enzyme) that facilitates the addition of a specific chemical group, a carbohydrate, to a protein. Differences in the DNA sequences of the A, B, and O alleles result in differences in the encoded polypeptides. The polypeptides encoded by the A and B alleles differ in the reactions that they catalyze – different sugar groups are added by the A and B versions of the glycotransferase. The polypeptide encoded for by the O allele is inactive, it does not function as a glycotransferase. Remember your cells are diploid; each cell has two copies of each gene (with the exception of the sex chromosomes - in humans, known as X and Y). Each cell involved in synthesizing blood has two copies of the ABO gene, one inherited from your mom and one from your dad. The two ABO alleles you inherited may be the same or different.^[119] If they are A and B, the proteins on your red blood cells will have both the A and B modifications, resulting in an AB blood type. If they are A and O or A and A, your red blood cells have only the A modification, if they are B and O or B and B, your red blood cells have only the B modification, and if you have O and O, no modifications (of this type) occur and you have an O blood type (→). These are examples of what are known as discrete traits; you have either an A, B, AB, or O blood type – there are no intermediates. You cannot be 90% A and 10% B.^[120] The situation when the presence of a particular allele uniquely determines a trait, as in the case of the ABO gene, is rare – most traits are more complex, they are known as polygenic (many genes) and influenced by non-genetic factors.

Most traits are continuous rather than discrete, they involve hundreds to thousands of genes and their alleles. For example, people come in a continuous range of heights, rather than in discrete sizes. If we look at the values of a trait within a population, that is, if we can associate a discrete number to a trait (which is not always possible), we find that each population can be characterized graphically by a distribution. For example, consider the weights in a group of 8440 adults in the USA (←). The top panel (A) presents a graph of the weights, along the horizontal or X-axis, versus the number of people with that weight along the vertical or Y-axis. We can define the “mean” or average of the population (x̅) as the sum of the individual values of a trait (in this case each person’s weight) divided by the number of individuals measured, as defined by the equation: \[\bar{x}=\frac{x_1+x_2+\cdots+x_n}{n}\nonumber\]

In this particular data set, the mean weight of the population is ~180 pounds. It is common to recognize another characteristic of the population, the median. The median value is the point at which half of the individuals have a smaller value of the trait and half have a larger value. In this case, the median is ~176. Because the mean does not equal the median, we say that the distribution is asymmetric, that is there are more people who are lighter than the mean value compared to those who are heavier. Another way to characterize the shape of the distribution is by what is known as its standard deviation, indicated by the Greek letter sigma (σ). There are different ways to calculate the standard deviation that reflect the shape of the population distribution; we will use a simple one, the so-called uncorrected sample standard deviation (→).^[121] To calculate this value subtract the mean value for the population (x̅) from the value for each individual (x_i); since x_i can be larger or smaller than the mean, this difference can be a positive or a negative number. We take the square of the difference, which makes all values positive (hopefully this makes sense). We add together these squared differences, divide that sum by the number of individuals in the population (N), and take the square root, which reverses the effects of our squaring x_i, to arrive at the standard deviation of the population. The smaller the standard deviation, the narrower the distribution - the more organisms in the population have a value near to the mean. The larger σ is, the greater is the extent of the variation in the trait in the population. \[\boldsymbol{\sigma}=\sqrt{ \frac{1}{N} \sum_{i=1}^N\left(x_i-\bar{x}\right)^2}\nonumber\]

How do we determine whether a complex trait, like height or weight, is genetically determined or influenced? A standard approach is to ask whether there is a correlation between the phenotype in the parents (e.g. their heights) and the phenotypes of their offspring (their heights). Such a correlation between parents and offspring exists for height is suggested by this graph (→), but notice we are seeing a trend, parental height is not a perfect predictor of offspring height - other factors must be involved.

One thing that we cannot determine from such data, however, is how many genes and how allelic interactions influence the "strength" of the trait or how these effects are effected by intrinsic noise (stochasticity), environment and the offspring’s specific history. As an example, “human height has been increasing during the 19^th century when comprehensive records began to be kept. The mean height of Dutchmen, for example, increased from 165cm in 1860 to a current average height of 184cm, a spectacular increase that reflects improvements in health care and diet, rather than changes in genes."^[122] Geneticists currently estimate that allelic differences at more than ~50 genetic loci (positions in the genome) make significant contributions to the determination of height, while allelic differences at hundreds of other genes have smaller effects.^[123] At the same time, specific alleles of certain genes can lead to extreme shortness or tallness. For example, mutations that inactivate or over-activate genes encoding factors required for growth can lead to dwarfism or gigantism.

On a didaskalogenic note you may have learned that alleles are often described as either dominant or recessive (a topic to which we will return). But the extent to which an allele is dominant or recessive often depends upon how well we define a particular trait and the extent to which it is influenced by other genetic, developmental, and environmental factors. These effects reveal themselves through the fact that people carrying the same alleles of a particular gene can display (or not) the associated trait, which is known as penetrance, and they can vary in the "strength" of the trait, which is known as expressivity.^[124] Both the penetrance and expressivity of a trait can be influenced by genetic background, the presence or absence of particular alleles of other genes. Environmental factors can also have significant effects on the phenotypes associated with a particular allele or genotype. In his studies, Mendel used extensive inbreeding and controlled environments to minimize these effects. In normal (wild type) populations of peas, pea color ranges from green to yellow rather than being green or yellow. Through controlled breeding, he removed the genetic variation that lead to intermediate colors. Another British scientist Walter F.R. Weldon (1860 – 1906) pointed out these complicating factors, but died before he published a complete account of his observations.^[125]

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