Probability and Statistics part 6

Probability and Statistics, Part 6

By Madison Nef

Probability plays a large role in biology- especially in determining the genetic makeup of a child. One of the most-asked questions in biology is what a child will look or act like in comparison to the parents. Probability lies at the very center of biological and genetic makeup. The basic idea of genetics is that each parent donates some genetic makeup to their child, and how the child looks and acts is based off of what genes it inherited from its parents. To keep things simple, let’s use blue and brown eye colors to demonstrate how probability would work in deciding what eye color the child would have. While in reality, many genes decides a child’s eye color, to keep is simple we’ll pretend only one gene decides.

Alleles, or genes, can be either brown (B) or blue(b). People can have any combination of these: BB, Bb, or bb alleles, and parents can only contribute one allele each. If one parent donates a dominant allele (B), then that is the allele that the child will receive. In any other case, the child will inherit the recessive allele (b). This makes the probability for getting the recessive gene 25%, given that both parents carry one (b) allele.

Even so, by random chance, percentage of getting certain alleles is altered in each generation. The percentage of getting a certain allele always changes, no matter what allele you may have. This change is called genetic drift; and it is quite similar to a random walk, only using genetics rather than flipping a coin. Genetic drift works quickly in small populations, but takes much longer to happen in larger ones. All of this tells us that no natural selection is happening that affects the percentage of alleles… in other words, no trait has an advantage in the number of children that a person WITH THAT CERTAIN TRAIT can produce.

Genetic makeup can also change through mutation. A mutation is a healthy and stable change to DNA that is often not seen and passed on to children, and affects nonessential DNA for many reasons. These mutations are very useful when measuring time, and can help calculate how far back a person’s ancestry goes. It is through this that we actually now know that the woman who most humans share DNA with can be traced back to having lived 150,000 years ago. Amazing, huh?

Let’s take another example of probability. HIV tests are given out to about 300,000,000 people living in the US each year. OF those 300 million, only 500,000 of them will test out positive. This means that 299,500,000 people do not have the disease. The test for HIV, while accurately showing if a person has HIV 95% of the time, also shows a false-positive 1% of the time. So, 95% of people with HIV will get a positive result on their test. Since the test shows a false positive 1% of the time, 2,950,000 people will get a false positive on their test and 95% of the 500,000 people who actually have the disease (475,000) will be shown as having HIV, when in fact only the initial 475,000 have it.

This leaves us with the statistic that if you test positive on a HIV test, your chances of ACTUALLY having the disease are 475,000/3,470,000… which is less than 15%. This an example of probability, but also of probabilistic anomaly that shows that testing for rare diseases are more likely to show a false positive than to ACTUALLY diagnose the disease in those who have it.

Maddie