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Using Mendel to Predict non-Mendelian

Mendel is sometimes called ‘the father of genetics’. Genetics was not unknown prior to Mendel’s time. Knowledge of genetics has probably been used my humans since the earliest transition to agriculture. Farmers knew that they could select the biggest and best seed to plant the next year’s crops, and that they could get the best characteristics of both parents in breeding of livestock. The ability to make predictions is a major element of the scientific process, and the major contribution made by Mendel was giving the science of genetics a method to make predictions. Before Mendel, it was known that the offspring characteristics were a blend of the parents. One example I have used to illustrate this is the breeding of a cocker spaniel and a poodle resulting in a cockapoo. Mendel, by looking at only one characteristic at a time, found that the offspring were either like one parent, or they were like the other.

Was he lucky, or did he discard evidence which did not support his theory? We will never know since his books and papers were all burned after his death, and his papers were not really widely read until almost 50 years after his death. The beauty of Mendel’s methods of prediction, is that we can use his algorithms even when the inheritance is non-Mendelian. We have the benefit of knowledge gained in the more than 100 years since Mendel. There is a confluence of ideas including Mendelian genetics, meiosis and the biochemistry of protein synthesis.

Mendel picked a characteristic such as plant height which had either tall plants or short plants. We now know that the plant is tall if the hormone, gibberellin, is produced and the plant is short if the hormone is not produced. The prediction works if the hormone is coded for two times (homozygous dominant) or only one time (heterozygous). Unlike peas, human height is the product of many genes interacting with environmental factors. Thus Mendel’s methods do not appear to work for predicting the height of humans. You may wish to have more mathematically inclined students play with numbers as follows.

If you were to graph the probable offspring when there is one gene, two alleles with incomplete dominance and thus three phenotypes, the outcome is in a 1:2:1 ratio as follows:

Incomplete Dominance with 1 gene

If two genes are considered, then the probable outcome is:

Incomplete Dominance 2 Genes

This results in a 1:4:6:4:1 ratio.

Now, if three genes are considered, the mathematics gets a little tougher, the predicted outcome has a ratio of 1:6:15:20:15:6:1.

The take-home lesson here is that as the number of genes influencing a characteristic increases, there is an increasing tendency towards a bell curve distribution.

I believe the reason this information is important in a genetics discussion is that it reinforces the concept that the model is correct, and just the mathematics gets more complicated. What we learn in Biology class is not just a connection of unrelated factoids, but ultimately all pieces of the puzzle discussed in an earlier blog (see also Genomics and the Curriculum).

Using Mendel to Predict non-Mendelian

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