Essay \" Gregor Mendel \'s work on Mono Hybrid and Dihybrid Crosses \" PDF

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Gregor Mendel’s Work on Monohybrid and Dihybrid Crosses Gregor Mendel [1822-1884] was a researcher of genetics and a teacher of maths and physics. During his life, his work on genetics did not gain much attention, but did after his death. He is known as the “father of modern genetics”. [1] Mendel’s Laws of Inheritance form the foundation for predicting the phenotypes [and their ratios] of organisms when bred. His first law [Law of Segregation] states that each individual has a pair of alleles for any particular trait that segregate during the formation of gametes and end up in different gametes. The second law [Law of Independent Assortment] states that separate genes for separate traits are passed from parent to offspring without interfering with each other. The last law [Law of Dominance] is that dominant alleles will always mask recessive alleles. Mendel’s Law of Independent Assortment can be shown by selectively crossbreeding pea plants [breeding plants that produced and seeds with plants that produced and seeds] [2], he was able to discover the probability that a plant from the F2 generation [two generations after the parent plants [2] would have a certain combination of these characteristics. Given that R and Y represent round and yellow seeds [the plants that produce these are homozygous dominant] and r and y represent plants that produce green, wrinkled seeds [homozygous recessive], this is how Mendel found the probabilities. For the F1 generation [crossing RRYY against rryy]:

Note that this is a dyhybrid cross – we are considering two characteristics [the shape of the seeds and their colour]. All the offspring produced have the genotype RrYy. This means that the gametes for this generation are RY, Ry, rY and ry. Crossing for the F2 generation:

The font colour represents the phenotype [expressed genotype] of the plants from the F2 generation. The expected probability of a round and yellow phenotype [for the seeds produced] is 3/4, 3/16 for round and green, 3/16 for wrinkled and yellow and 1/16 for wrinkled and green [discrete distribution]. This gives Mendel’s ratio of 9:3:3:1. Since all combinations were assessed with the test cross and since Mendel’s observed probabilities agreed [a hypothesis test can be used to confirm this], Mendel’s Law of Independent Assortment has been shown to be true – the assortment for the alleles for shape do not interfere with the assortment of alleles for colour because the possible phenotype ratios predicted are correct.

This ratio is important because if an observed F2 generation has a known ratio [which may be different to the expected probabilities], the hypothesis test can be used to find whether the parent generation have both a homozygous recessive and homozygous dominant genotype or otherwise. This is done by using the expected probabilities Mendel found to find the expected [mean] values of each phenotype for a know number of individuals [2]. For example, 160 pea plants [F2 generation] are observed to have a ratio [yellow round: green round: yellow wrinkled: green wrinkled] of 94:28:31:7. A researcher claims that the parent generation has homozygous dominant and homozygous recessive genotypes. To test his claim, a chi-squared test must be carried out [α=5%] to test whether a discrete random distribution is suitable to predict phenotypes. [I feel like I should explain hypothesis testing if I’m going to talk about it. A hypothesis test is based around the idea that with a given distribution, some values are unlikely to occur under a certain test statistic that we are testing. If these unlikely values come up often enough, they are said to be significant which means the test statistic for the distribution differs to what we thought it was. The significance level tells us where the critical regions are for the distribution. If the probability of a value coming up is less than the significance level [α] , these values are in the critical region(s) [depending on whether the test is one-tailed or two-tailed] – the set of values that would lead us to rejecting the null hypothesis. Anyway…]

H0 – There is no difference between the expected probabilities and the observed probabilities. H1-There is a difference between the expected and observed probabilities. O²/E

The value of = ∑ [(O-E) ²/E], where O is the observed number for that phenotype and E is the expected number. Notice how ∑O=∑E=N, where N is the total number of individuals in the sample. After expanding the RHS of the equation above, it can be shown that an easier method of finding is [∑O²/E] – N. In this example, =56/45, which is roughly 1.24 [2dp]. The number of degrees of freedom for this test = number of cells – number of constraints [4]. Each parameter calculated is a constraint and we have only calculated the expected values therefore we have 4-1=3 degrees of freedom. At a significance level of 0.05 and 3 degrees of freedom, the critical value is 7.82 [2]. If...