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Inheritance

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Back in the day, Mendel crossed different varieties of pea plants to establish rules of inheritance. He didn't know what we know today about genes and DNA. So what do we know, and what did he find out?

The entirety of genetic material in an organism is called a genotype. It can also refer to specific things, like a genotype for a certain trait in a given organism.

The genotype refers to the physical constitution of a little part of DNA. Its expression, however (that is what protein a gene encodes, and what that protein ends up doing in the organism) is a separate entity which is subject to environmental influence. This is called the phenotype.

Humans have 2 sets of chromosomes, so for each distinct chromosome e.g. chromosome 1, there are two copies. How do the same genes on both homologous chromosomes interact if they result in different phenotypes? Which has priority?

If you crossed a green pea plant with a yellow pea plant, what colour would the offspring be? What about their offspring's offspring?

This is precisely what you'll be able to answer by thee end of this topic.


Basics

Versions of the same gene that give rise to different phenotypes are called alleles. For example, the gene responsible for ear shape in a cat may have 2 alleles: pointy shape and oval shape.

One of these alleles may be expressed at the expense of another, where both are present together in a cat. Say that the oval shape allele is dominant while the pointy shape is recessive.

Because cats also have 2 copies of each chromosome (and therefore gene), these alleles are written as 2 letters. 

If the gene for ear shape is abbreviated as E or e for ear, then the alleles would be:

E (dominant) for oval shape and 
e (recessive) for pointy shape

These upper case - dominant, lower case - recessive notation rules are used universally. So what combinations may be present in a cat?

EE, ee or Ee

The first two examples are called homozygous because the same allele (E or e) is present twice, while the last example is heterozygous because different alleles (E and e) are present.

So what happens in crossing?

EE x ee gives rise to 4 combinations: Ee, Ee, Ee and Ee! 100% heterozygous where the cats will appear oval-ear shaped, yet also carry the recessive allele for pointy ears. Let's do a second cross.

Ee x Ee gives rise to 4 combinations: EE, Ee, eE and ee. That's 50% homozygous and 50% heterozygous. 3/4 will have oval ears while 1/4 will have pointy ears.





Now see what happened in Mendel's pea plant experiments?

It's also possible to have multiple (more than 2) alleles for a given gene. Say there is also a round ear allele. It could be that this allele is codominant with the pointy ear allele, so that both traits are simultaneously expressed.


Other interactions

Sex linkage refers to a trait that is carried on a sex chromosome like the X chromosome. Because someone might have a different number or combination of sex chromosomes such as a single X chromosome or two X chromosomes, the expression of various traits can differ.




If for example the allele on the affected X chromosome means that an essential protein isn't being made, the carrier XX child has another unaffected X chromosome to fall back on and be able to produce the essential protein. The carrier XY child only has the affected X chromosome and cannot make the protein. This results in an illness for example.

Autosomal linkage is the other option. An autosome is a chromosome that isn't a sex chromosome. In humans this could be chromosome 1, chromosome 2, etc.




Since autosomes are inherited evenly, the outcome for the children follows the same pattern as for dominant/recessive interactions. If a child inherits two recessive alleles of a key protein that cannot be produced or is faulty, a disease may be expressed.

Multiple alleles involve three or more variations (alleles) of a gene. A common example is blood type: A, B, AB or 0 given by three alelles, i, IA and IB.

Relative to type 0 (i-i), both A (i-IA or IA-IA) and B (i-IB or IB-IB) are dominant, while A and B are codominant enabling option AB (IA-IB).



Epistasis refers to the interdependence of separate genes and their effects. These interactions can be vast and subtle, and create many unexpected outcomes. It also enables a huge diversity of phenotype and potential for evolution. In this silly example, a gene inducing baldness creates an outcome that interjects the outcome of genes for hair colour, as the hair would not get to show itself anyway.





Through this interaction, the different alleles for the colour gene are suddenly and non-linearly disabled.


Chi-squared test

The chi-squared (c2) test is a measure of expected frequency versus observed frequency to determine how closely aligned they are; whether what is observed would be expected or whether it is different to what would be expected.

The default expectation is the null hypothesis which states that no difference exists between the things we are experimenting with, observing or comparing and their default, or control state.

The chi-squared value we obtain from the chi-squared test is put against a probability scale. The probability refers to the probability that for a given chi-squared value (which is defined by how different our observation is from what we would expect), what we observe really is different to what we expect to a significant extent that enables us to reject the null hypothesis.

For example, our expected values for a 154-pupil school would be:

Gender: 77 girls and 77 boys

The expected values cannot be below 1 for the chi-squared test.

Say our survey reveals that in fact there are:

Gender: 98 girls and 56 boys

The way to carry out a chi-squared test is to take the difference between the observed (O) and expected (E) values, square it, and then divide by the expected number (E). This is done for both categories and then added together for the final chi-squared value. The extra 0.5 taken away is know as the Yates correction and is used if our comparison only has two groups.

(O-E-0.5)2 / E for girls = (98-77-0.5)2 / 77

= 5.46

(O-E-0.5)2 / E for boys = (56-77-0.5)2 / 77

= 6.00

We then add the two, 0.03 + 1 and get 11.46. The reference table for the chi-squared values looks something like this:




The most often used threshold for the significant probability value is 0.05, or 5%. This means as long as the probability of mistaking whether there is a difference between observed and expected is less than 5%, we will assume the difference is indeed real.

The degree of freedom refers to the number of groups being compared - 1. So in our girls-boys example we get 2 - 1 = 1. Our degree of freedom is 1.

The p value for 1 degree of freedom at 0.05 is 3.84. Our chi-squared value for gender is above this, so we can reject the null hypothesis and say that there is a significant difference between the observed and expected numbers of girls and boys.

Ok byeeeeeeeeeeeeee

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