Before we start focusing on a single locus, a review of Mendelian Genetics will help lay the groundwork. Mendel defined or coined a lot of the basic terminology that we use in genetics. He recognized that genes come in different forms which are referred to as alleles and each (diploid) organism has two alleles for each inherited characteristic; one allele from the father and one from the mother. Each spermatozoa and oocyte carry one allele for each characteristic since allelic pairs segregate during the production of gametes (meisosis). He also figured out that when two alleles are different, one is expressed and the other is masked. Loosely paraphrased, his Law of Segregation says “Allelic pairs segregate during gametic formation and the paired condition is restored by random fusion of gametes at fertilization.”

We know now that this was an over simplified view of the situation. For example, his characterization of alleles being expressed or masked doesn’t allow for incomplete dominance where both alleles are expressed to some extent. However, even though Mendel’s presentation was simplistic compared to what we know now, he had the basics figured out and as a result laid the groundwork on which our current understanding of genetics is based.

Taking Mendel’s Law of Segregation, we often represent the possible inheritance of alleles using a Punnet Square. This representation is used to figure out what alleles the progeny might inherit from their parents. You can use actual parents or you can use population allele frequencies to determine progeny inheritance and how frequent each genotype would be. For example:

In Table 1, a basic version of a Punnet Square is shown. In this version, the parental alleles are shown in the top row and leftmost column. The possible progeny genotypes are shown in the four cells below and to the right of the parental alleles. In this version of the Punnet Square, the alleles are assumed to be of equal frequency so the parental genotypes are both Aa and the progeny genotypes are therefore AA, Aa and aa. We don’t normally follow alleles specifically by parent of origin, so most of the time Aa would be equivalent to aA and lumped together as all being Aa. In this specific example, the genotypes would occur in the ratio of one AA to two Aa to one aa or a classic 1:2:1. As we go further in this e-book, note that the classic 1:2:1 will rarely be considered as we will more generally consider the situation where the allele frequencies may be different which gives us the second version of the Punnet Square, one with allele frequencies included.

In Table 2, we have a more general version of the Punnet Square in which the allele frequencies of the parents are shown along with the genotypic frequencies of the resulting progeny. Again, we usually combine the Aa and aA genotypes as a single Aa genotype and add the frequencies together so f(Aa) = 0.20 + 0.30 = 0.50 in this example. Calculating a Punnet Square assumes that the population is randomly mating so parental alleles occur randomly in proportion to their frequency.

Notice that Table 2 is not 1:2:1 because the parental alleles were not at equal frequencies. It is important to note that the frequency of the progeny genotypes is always determined by the frequency of the parental gametes which in turn is determined by the frequency of the parental genotypes. How these genotypes are expressed as phenotypes and hence what we observe about what we think the genotypes might be is determined by other factors.

What can mess up the classic 1:2:1?

With a single locus and parents that are both heterozygous (i.e. Bb), we (almost) always get the classic 1:2:1 ratio of genotypes but we don’t always see the same ratio of phenotypes. The ratio of phenotypes depends on the way the alleles are expressed. If the B allele is dominant over the b allele, then the ratio appears as 3:1 since the BB and Bb genotypes both produce the same phenotype. If the B allele is co-dominant or incompletely dominant then the Bb individuals have a distinct phenotype and we can count them to observe the 1:2:1.

A lethal genotype is the one situation that messes up both the genotypic and phenotypic ratios. An example in horses is the lethal white overo allele in the Paint/Pinto colour pattern. In this case, the recessive w allele is lethal when homozygous and ww individuals die soon after being born since they don’t have a complete digestive tract. In the newborn foal population, a 1:2:1 ratio can be observed in both genotypes and phenotypes but in the adult population, we only observe WW and Ww  (colour pattern) phenotypes and genotypes in a 1:2 ratio if we mate two Ww  parents.

Independent Segregation

Although it is jumping ahead to multiple loci a little bit, it is worth looking at the simple case of two loci in the context of Mendel’s work while we are on that subject. Mendel also came up with a Law of Independent Segregation to describe what happens with two (or more) loci that are independent of one another. Basically, it is just an extension of the single locus case of the Law of Segregation; namely that two independent loci will behave independently and both follow the Law of Segregation. So, if we have two parents that are heterozygous at two independent loci (Aa and Bb), each parent will produce gametes with equal frequency of the possible combinations of alleles; AB, Ab, aB and ab with ¼ of each. The resulting offspring genotypes will be ¼ AA, ½ Aa, ¼ aa and independently ¼ BB, ½ Bb, ¼ bb. Since the loci are independent, the frequency of any combination of the genotypes of the two loci can be worked out from there (i.e. f(AABB) = ¼ x ¼ = 1/16 and f(AaBb) = ½ x ½ = ¼ ). This calculation also demonstrates two more of Mendel’s results – the Rule of Multiplication and the Rule of Addition. These rules are actually based on probability principles. The Rule of Multiplication is used to calculate the probability or frequency of a specific genotype. In the example above, the probability of the AABB genotype is the product of probabilities of the individual AA and BB genotypes occurring together. The keyword here is and – when calculating the probability of the two genotypes, AA and BB we multiply the frequencies of the individual genotypes together.  To calculate the probability or frequency of multiple different genotypes, we use the Rule of Addition. For example, with a mating between two heterozygous parents, the probability or frequency of the heterozygous genotype in the offspring is the probability or frequency of getting Bb or bB. As soon as we use the word or we need to add the probabilities or frequencies together: f(Bb) = ¼ , f(bB) = ¼ so f(heterozygote offspring) = ¼ + ¼ = ½ .

Subsequent research has shown that Mendel was extremely lucky in his work – he didn’t get tangled up with linkage or incomplete dominance and he picked a diploid organism for his research. He wrote about seven different phenotypes in peas that we now know are controlled by loci scattered across four chromosomes. So how is it that linkage did not mess up his work? He happened to work with and write about phenotypes that were controlled by loci that were either on different chromosomes or so very distantly located on the same chromosome that they behaved as if they were not linked. Did he look at any linked phenotypes and just discard his observations when he couldn’t explain what he saw? Or did he just happen to make crosses where linkage did not show up? Or would he have been able to explain linkage if he did encounter it? Would he have been so influential in our understanding of genetics if he had picked linked phenotypes to work with? We likely will never know – but it doesn’t matter, he presented clear evidence of inheritance that, when combined with the work of Darwin and others, formed the basis of humankind’s study of genetics.

The frequency or probability of phenotypes expressed by multiple loci isn’t quite as straightforward. Again, the underlying genotypes are always there because they are driven by the parental genotypes but how we observe the phenotypic expression corresponding to those genotypes is another story. There are three major factors affecting the expression of phenotypes from multiple genotypes; pleiotropy, epistasis and linkage. Of those three, we will be paying the most attention to linkage throughout this e-book.

Pleiotropy

Pleiotropy is a situation where one genotype affects multiple phenotypes. This can occur with a locus that is involved with a biochemical housekeeping pathway. For example, a locus involved with insulin regulation can result in hypoglycemia and from that condition many different phenotypes may be expressed; diabetes, problems with peripheral circulation and so on. Different phenotypes observed that all come from one underlying genotype. Another example of pleiotropy that is commonly used is deafness and white coat colour in cats. These two phenotypes appear to be different but they are actually caused by the same underlying mechanism; melanocytes. If a cat has a homozygous genotype for the defective melanocyte production allele, the lack of melanocytes will eliminate pigment in the hair and interrupt electrical transmission of signals in the inner ear. The result, white fur and no nerve impulses for sound which appear to us as separate phenotypes but in reality have a single, root cause. Once we know pleiotropy is involved, since there is a defined underlying genotype involved, we can treat each of the phenotypes independently or as a group at our convenience if we are studying them as there is a one-to-one match between genotype and phenotype that is happening multiple times.

Epistasis

Epistasis is a situation where one locus influences the expression of another locus. Colour patterns in dogs, cats and horses are examples of this type of locus interaction. The interacting loci can be on different chromosomes but the product produced from the transcription of one locus is involved in the regulation of the expression of the transcription product of the other locus. Coat colour in Labrador Retrievers is an oft used example of epistasis since it is controlled by two loci, one for expression (E) of coat colour and the other for the actual black or brown colour of the coat and skin (B). The expression (E) locus controls the expression of the colour (B) locus. If there is at least one copy of the dominant E allele, then the colour locus is expressed leading to the four possible genotypes for the black with the dominant B allele (EEBB, EEBb, EeBB and EeBb) and two possible genotypes for the chocolate lab with the recessive b allele (EEbb and Eebb). If the individual is ee then the colour locus is not expressed and the animal is yellow (which can range from almost platinum blond to reddish-yellow). The fun part is that since the B locus also controls the skin pigment which is not masked by the E locus, we can tell the yellow labs with black alleles (eeBB and eeBb) apart from the yellow labs with chocolate alleles (eebb) by the colour of the skin around their eyes and on their noses. Yellow-black labs have black skin pigment around their eyes and on their nose while yellow-chocolate labs have brown skin pigment around their eyes and on their noses.

As with pleiotropy, with epistasis, once we know what we are dealing with, we can explain the observed phenotypes and understand the underlying genotypes. It is then possible to study the phenotypes and genotypes by accounting for the control interactions between them. As we get further into the material and have epistatic interactions among loci involved in complex phenotypes, our ability to discern and study the epistatic interactions can be challenged and this e-book will not venture far into that area of discussion as it is typically considered a graduate-level topic.

Linkage

Linkage typically occurs when two (or more) loci are physically located on the same chromosome and alleles at the two (or more) loci are inherited together. However, the illusion of a physical linkage can also be created by selection for a phenotype that is controlled by loci located on more than one chromosome. With linkage, the two loci are not independent because the chromosomes tend to segregate relatively intact to the different gametes because recombination is generally a rare event, compared to the much more random process of assortment of chromosomes to gametes, becoming rarer as the loci are closer together. We’ll spend more time on linkage later.