Simple Genetic Analysis

Gregor Mendel is a great person to start off with when considering the analysis of genetic traits. This is becuase not only was he the first person to systematically do this, but also because he used surprisingly 'modern' seeming methods. He was extremely thorough in choosing his paths of investigation, and also extremely detailed and systematic in recording his results.
His investigations were so successful because he used an excellent organism to study, the Pea plant. It has a short generation time, which is vital when studying the distribution of characteristics over generations. They're also easy to control in terms of breeding, he could use a small brush or tweezers to control their breeding by physically manipulating their pollen bearing and receiving structures. They also produce a large number of offspring in each generation, this means that there are large datasets on which statistical analyses can be performed. Mendel used whats called "pure breeding lines" to begin his experiments, these are lines that are the result of a long series of breedings and that 'breed true' for a characteristic or trait, such as pod shape or pea colour. He'd then mate different pure breeding lines to create hybrids. The specific traits he picked to study were clearly identifiable. In systematic-phylogenetic terms he used 'bivariate' traits, ie traits that were either one of two extremes (green coloured or yellow coloured), rather than multivariate traits where there are a number of states that can be occupied or even a smeared out spectrum (ie, red, blue, yellow, or a continuum from blue to green to yellow).
Mendel performed reciprocral crosses for his study, mating, for example, purple flowering female to white flowering male, and then white flowering female to purple flowering male.

Some of the traits Mendel studied












Monohybrid Cross

The simplest type of cross Mendel would do is called a monohybrid cross, this means that the result is a generation hybridized for a single trait, rather than multiple traits. An individual from a pure breeding line for one trait is mated with an individual from a pure breeding line with the opposite trait.

Now the whole of the new generation, called the F1 generation, is only showing one of these clear traits, such as green colour or smooth pea shape, and the other traits, yellow colour or wrinkled shape, are lost. Next, the F2 generation is obtained by self-fertilization of F1 plants. Mysteriously (at the time), the lost trait reappeared, in proportion with the other trait also. The two types show up in a 3:1 portion, the lost trait reappears as a third of the whole population. Mendel concluded that there is latent information that is not expressed in the plant. That the lost trait was preserved somehow.

The trait that appears in all of the F1 generation is called 'dominant', the trait that is lost but will reappear is called 'recessive'. Mendel reasoned that each plant contains two discrete units of inheritance. Today we call the unit a gene and the discrete and different forms alleles.

Individuals in this case are diploid, they have a 2N genotype, iow they have two alleles for each trait. In gametes however, there is only a 1N genotype, the haploid condition. During gametogenesis only one allele is packaged into the gamete. This packaging process is called Segregation. From these genotypes result phenotypes, the actual displaying of characteristics and traits. Individuals with both alleles in the dominant form or both in the recessive form are said to be homozygous, whereas individuals with a mix of the dominant and recessive alleles are heterzygous.

In order to predict the percentages of different phenotypes and genotypes in a new generation, a Punnett Square can be used.

The outer edges of the square essentially represent individual and distinct gametes from the crossed individuals (the parental generation). The boxes within the square represent the genotypes of the individuals in the offspring generation, and from this the phenotype can also be determined. In a self-fertilization of the F1 generation, there are two phenotypes and three genotypes. Half of that generation are heterozygotes. A quarter are homozygous recessive and another quarter are homozygous dominant. This is a genotypic ratio of 1:2:1 , and a phenotypic ratio of 3:1

The Punnett Square follows two simple probability rules, the Sum and Products rules. The Product Rules states that the probability of two independant events both occuring is the probability of the first event times the probability of the second event. In a monohybrid cross (Yy X Yy), the probability of a gamete having a y allele is 1/2. The probability of a gamete having a Y allele is 1/2. So the probability of an individual having a genotype of YY or even yy is 1/4. The probability of getting the heterozygous condition is not independant. The Sum Rule states that the probability of two mutually exclusive events occuring is the sum of their individual probabilities. So the probability of one parent giving the y allele and then the other giving the Y allele is 1/2 x 1/2 = 1/4. The probability of the reverse, say the female parent giving y and the male giving Y, is also 1/4. The sum of these two events is the probability of an individual being heterozygous, Yy, which is 1/2.

Mendel then crossed his F2 generation. When he crossed F2 green peas he got all green offspring, and with F2 yellow peas he got all yellow offspring. Of this, 1/3 ended up being pure breeding. 2/3 gave rise to yellow and green peas in a ratio of 3:1 (iow they were hybrids).
To distinguish between pure breeding individual and a hybrid you perform a test cross, wherein the unknown is crossed with a known homozygous recessive. The ratios and types of offspring that result will allow one to work backwards to the parental genotypes.


<--phenotypes are all one type

phenotypes are half and half --->

For example, in cattle, the polled phenotype (which is hornless) is dominant over the horned condition. If a polled bull is crossed with

• Cow A, horned, and yields a horned calf
• Cow B, polled, and yields a horned calf
• Cow C, horned, and yeilds a polled calf

Then what are the genotypes of all those involved?

To determine, you'd consider a test cross with a homozygous recessive individual. A homozygous recessive individual is anyone who displays the recessive trait. A horned cow, such as Cow C, is therefore homozygous recessive. In order for a cross with Cow C to result in polled individuals, there must be at least a single polled allele in the bull. Thus we now know part of the polled Bull's genotype.

The cross with Cow A however results in a horned calf. Since that calf is horned, its also homozygous recessive, and that means that it has two recessive alleles, only one of which can have come from the Cow. So the other must have come from the bull, and therefore the bull has at least one recessive allele. These results taken together mean that the polled bull under consideration must be a heterozygote.

This means that in the cross with the polled Cow B, which results in a horned calf (which, again, must be homozygous recessive ), that Cow B must be heterozygous, in order for it to produce a gamete with the recessive allele.

The phenotypic ratios of offsprings from each crossing set can also be determined. Because crossing A and C is a homozygote and a heterozygote, this is the punnett square.

This results in half the offspring being polled and half being horned. A ratio of 1:1

The crossing with Cow B, which is another heterozygote, results in this Punnett Squar. Here the offspring phenotypes are in a 3:1 ratio.

Dihybrid Cross

Mendel also considered dihybrid crosses, wherein the individuals to be crossed have opposite characteristics for multiple traits. For example, in a cross of Pure breeding yellow-round peas with pure breeding green-wrinkled peas, (YYRR x yyrr), the F1 generation individuals were all yellow and round (all hybrids). In the F2 generation, he received the following:

• Yellow Round....315 (a parental type)
• Yellow Wrinkled....101 (recombinant type, new combination of characters)
• Green Round....108 (recombinant type, new combination of characters)
• Green Wrinkled...32 (the other parental type)

Notice that individual traits, such as Yellow, still appear in total in a 3:1 ratio.

In the dihybrid cross, the different pairs of alleles segregate independantly into the gametes. Thus in a YyRr individual, the possible gametes are YR, Yr, yR, yr.

The genotypes will become present in their specific ratios, as shown.

Given a mulitple cross of two heterzygous individuals for three traits (AbBbCc x AbBbCc) , what is the probability that offspring of aaBBcc genotype occuring?

1/4 x 1/4 x 1/4 = 1/64