# 3.10: A short aside on the genotype-phenotype relationship

- Page ID
- 3928

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)When we think about polymorphisms and alleles, it is tempting to assume simple relationships. In some ways, this is a residue from the way you may have been introduced to genetics in the past.^{79} Perhaps you already know about Mendel and his peas. He identified distinct alleles of particular genes that were responsible for distinct phenotypes - yellow versus green peas, wrinkled versus smooth peas, tall versus short plants, etc. Other common examples might be the alleles associated with sickle cell anemia (and increased resistance to malarial infection), cystic fibrosis, and the major blood types. Which alleles of the ABO gene you inherited determines whether you have O, A, B or AB blood type. Remember you are diploid, so you have two copies of each gene, including the ABO gene, in your genome, one inherited from your mom and one from your dad. There are a number of common alleles of the ABO gene present in the human population, the most common (by far) are the A, B, and O alleles. The two ABO alleles you inherited from your parents may be the same or different. If they are A and B, you have the AB blood type; if A and O or A and A, you have the A blood type, if B and O or B and B, you have the B blood type, or if you have O and O, you have the O blood type. These are examples of discrete traits; you are either A, B, AB, or O blood type – there are no intermediates. You cannot be 90% A and 10% B.^{80} As we will see, this situation occurs when a particular gene determines the trait; in the case of the ABO gene, the nature of the gene product determines the modification of surface proteins on red blood cells. The O allele leads to no modification, the A allele leads to an A-type modification, while the B allele leads to a B-type modification. When A and B alleles are present, both types of modifications occur. However, most traits do not behave in such a simple way.

The vast majority of traits are continuous rather than discrete. For example, people come in a continuous range of heights, rather than in discrete sizes. If we look at the values of the trait within a population, that is, if we can associate a discrete number to the trait (which is not always possible), we find that each population can be characterized graphically by a distribution. For example, let us consider the distributions of weights in a group of 8440 adults in the USA (see →). 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:

In this case, the mean weight of the population is 180 pounds. It is common to recognize another characteristic of the population, the median. The median 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 heavier than the mean value compared to those who are lighter. For the moment we will ignore this asymmetry, particularly since it is not dramatic. Another way to characterize the shape of the distribution is by what is known as its standard deviation (σ). There are different versions of the standard deviation that reflect the shape of the population distribution, but for our purposes we will take a simple one, the so-called uncorrected sample standard deviation.^{81} To calculate this value, you 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 then take the square of the difference, which makes all values positive (hopefully this makes sense to you). We sum these squared differences together, 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 similar to the mean. The larger is σ, the greater is the extent of the variation in the trait.

So how do we determine whether a particularly complex trait like weight (or any other non-discrete, continuously varying trait) is genetically determined? We could imagine, for example, that an organism’s weight is simply a matter of how easy it was for it to get food. The standard approach is to ask whether there is a correlation between the phenotypes of the parents and the phenotypes of the offspring. That such a correlation between parents and offspring exists for height is suggested by this graph. Such a correlation serves as evidence that height (or any other quantifiable trait) is at least to some extent genetically determined. What we cannot determine from such a relationship, however, is how many genes are involved in the genetic determination of height or how their effects are influenced by the environment and the environmental history that the offspring experience. For 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 184cm, a spectacular increase that probably reﬂects improvements in health care and diet”, rather than changes in genes.^{82} Geneticists currently estimate that allelic differences at more than ~50 genes make significant contributions to the determination of height, while allelic differences at hundreds other genes have smaller effects that contribute to differences in height.^{83} 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 related didaskalogenic note, you may remember learning that alleles are often described as dominant or recessive. But the extent to which an allele is dominant or recessive is not necessarily absolute, it depends upon how well we define a particular trait and whether it can be influenced by other factors and other genes. These effects reveal themselves through the fact that people carrying the same alleles of a particular gene can display (or not display) the associated trait, which is known as penetrance, and they can vary in the strength of the trait, which is known as its expressivity. Both the penetrance and expressivity of a trait can be influenced by the rest of the genome (i.e., the presence or absence of particular alleles of other genes). Environmental factors can also have significant effects on the phenotype associated with a particular allele or genotype.

## Contributors and Attributions

Michael W. Klymkowsky (University of Colorado Boulder) and Melanie M. Cooper (Michigan State University) with significant contributions by Emina Begovic & some editorial assistance of Rebecca Klymkowsky.