Eli Bendersky's website - Science

Genetical relatedness

2009-02-20T12:53:59-08:00

I often want to recall how this stuff works, but I keep forgetting. Here's a short summary of computing the degree of genetic relatedness of two relatives.

Preliminaries

Human cells are diploid, meaning that each cell has two chromosomes, each containing the same genes at the same loci but possibly different genetic information, called alleles, at those genes. One chromosome comes from the father, another from the mother.

Sex (sperm/egg) cells are produced in the process of meiosis. Since each sex cell contains only one chromosome, the information from both chromosomes (father's and mother's) is mixed by the process of recomobination to create it. For further discussion we can assume that about 50% of the father's and 50% of the mother's genes make their way into it.

When during conception a male's sperm cell fuses with a female's egg cell, the relevant chromosomes pair and we once again have normal diploid cells that construct the embryo.

Basics of relatedness

So what is genetic relatedness? Roughly defined, it's the percentage of similar genes shared by two persons.

Let's consider the happy family of Mom, Dad, Sonny and Junior (parents + 2 children, who aren't identical twins).

By the process described in the previous section, it should be clear that when Dad's sperm fuses with Mom's eggs, the newly created embryo will have half of Dad's genes and half of Mom's genes. Therefore the relatedness of a child to either of his parents is 50%.

What about the Sonny and Junior. How are they related? Sonny's genes are half Mom's and half Dad's, so are Junior's. But they're not the same halves!

Think of it this way: Dad has some gene G. The chance that it made it to Sonny is 50%. So is the chance that it made it to Junior. So on average, about 25% of Sonny's and Junior's genes are shared from their father [1]. But that's not all, there's also Mom. By the same reasoning, 25% of Sonny's and Junior's genes are shared from their mother. In total, 50% of Sonny's and Junior's genes are shared. Therefore, the relatedness of two full siblings is 50%.

Some more calculations

From here let's leave the detailed analysis alone and just focus on the resulting maths, which is quite simple. What about half siblings? Say Sonny's and Junior's fathers are different persons. They still share 25% of Mom's genes, but no genes from the fathers, so they're only 25% related.

Uncles: Sonny's children will be 25% related to Junior. This is because Sonny and Junior are 50% related, and Sonny's genes are further 50% "diluted" by his wife's genes in his children, so it's 25% total.

Cousins: Since we saw that Junior is 25% related to his nephews, his children are 12.5% related to their cousins, because Junior's genes are mixed with his wife's genes 50-50 in them.

A method

Here's a computation method suggested by Richard Dawkins in "The Selfish Gene" (pp. 91-92):

First identify all the common ancestors of A and B. For instance, the common ancestors of a pair of first cousins are their shared grandfather and grandmother. Once you have found a common ancestor, it is of course logically true that all his ancestors are common to A and B as well. However, we ignore all but the most recent common ancestors. In this sense, first cousins have only two common ancestors. If B is a lineal descendant of A, for instance his great grandson, then A himself is the 'common ancestor' we are looking for.

Having located the common ancestor(s) of A and B, count the generation distance as follows. Starting at A, climb up the family tree until you hit a common ancestor, and then climb down again to B. The total number of steps up the tree and then down again is the generation distance. For instance, if A is B's uncle, the generation distance is 3. The common ancestor is A's father (say) and B's grandfather. Starting at A you have to climb up one generation in order to hit the common ancestor. Then to get down to B you have to descend two generations on the other side. Therefore the generation distance is 1 + 2 = 3.

Having found the generation distance between A and B via a particular common ancestor, calculate that part of their relatedness for which that ancestor is responsible. To do this, multiply 1/2 by itself once for each step of the generation distance. If the generation distance is 3, this means calculate 1/2 x 1/2 x 1/2 or (1/2)^3. If the generation distance via a particular ancestor is equal to g steps, the portion of relatedness due to that ancestor is (1/2)^g.

But this is only part of the relatedness between A and B. If they have more than one common ancestor we have to add on the equivalent figure for each ancestor. It is usually the case that the generation distance is the same for all common ancestors of a pair of individuals. Therefore, having worked out the relatedness between A and B due to any one of the ancestors, all you have to do in practice is to multiply by the number of ancestors. First cousins, for instance, have two common ancestors, and the generation distance via each one is 4. Therefore their relatedness is 2 x (1/2)^4 = 1/8. If A is B's great-grandchild, the generation distance is 3 and the number of common 'ancestors' is 1 (B himself), so the relatedness is 1 x (1/2)^3 = 1/8.

Uncommon relations

Consider the following case: A and B are married, and A's brother C is married to B's sister D. How related are their children?

The generation distance between the children of A and B, and the children of B and D is 4 (like normal first-cousins). But instead of having just 2 common ancestors, they have 4 (the parents of A and C, and the parents of B and D). So, according to Dawkins' method the relatedness is 4 x (1/2)^4 = 1/4.

[1]	There are 4 options for gene G. Either it made it into both Sonny and Junior, or it made it into Junior only, or into Sonny only, or into neither. Assuming uniform random distribution, the chance of each occurrence is 25%.

Interesting scientific facts

2006-04-16T18:32:54-07:00

Startribune posted a curious small article named Why is the sky blue? Facts you should know. I'll reproduce the questions and the answers:

What percentage of the earth is covered by water?
What sorts of signals does the brain use to communicate sensations, thoughts and actions?
Did dinosaurs and humans ever exist at the same time?
What is Darwin's theory of the origin of species?
Why does a year consist of 365 days, and a day of 24 hours?
Why is the sky blue?
What causes a rainbow?
What is it that makes diseases caused by viruses and bacteria hard to treat?
How old are the oldest fossils on earth?
Why do we put salt on sidewalks when it snows?
Extra credit: What makes the seasons change?

The answers are:

1. About 71 percent of the earth's surface is covered by water.

2. The single cells in the brain communicate through electrical and chemical signals.

3. No. Dinosaurs went extinct at the end of the Cretaceous period, 65 million years ago. Modern humans did not appear until around 200,000 years ago.

4. Darwin's theory of species origination says that natural selection chooses organisms that possess variable and heritable traits and that are best suited for their environments.

5. A year, 365 days, is the time it takes for the earth to travel around the sun. A day, 24 hours, is the time it takes for the earth to spin around once on its axis.

6. Solar radiation sunlight is scattered across the atmosphere by a process called diffused sky radiation. The sky is blue because much more short-wave radiation -- blue light -- is scattered across the sky than long-wave radiation -- red light.

7. Rainbows can be seen when there are water droplets in the air and the sun is shining. Sunlight, which contains all colors, is refracted, or bent, off the droplets at different angles, splitting into its different colors of red, yellow, blue, etc.

8. Influenza viruses and others continually change over time, usually by mutation. This change enables the virus to evade the immune system of its host so that people are susceptible to influenza virus infection throughout their lives. Bacteria mutate in the same way and can also become resistant if overtreated with antibiotics.

9. About 3.8 billion years; they're bacteria-like organisms.

10. Adding salt to snow or ice increases the number of molecules on the ground surface and makes it harder for the water to freeze. Salt can lower freezing temperatures on sidewalks to 15 degrees from 32 degrees.

Extra credit: Seasons occur because the earth is tilted at an angle of 23.5 degrees. At certain times of year the top half of the earth leans to the sun and therefore gets more sun and has summer. When that same half of the earth leans away from the sun it gets less light and has winter.

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Most of these are trivial. I wasn't sure about 6, 9, 8 and the Extra, had no idea about 10. In fact, the answer to 10 seems a bit strange to me - what does "increases the number of molecules on the ground surface" mean exactly. After some web research it appears that the answer is simple: salty water has a lower freezing temperature. That's about it...

first real fuel-cell application

2005-09-19T10:16:00-07:00

Toshiba unveils a fuel-cell based MP3 player.

It's only a prototype now, and the real product will get to the shelves in 2007, but I think it's an amazing move forward. The methanol-powered fuel cell will allow a flash-based device to play 35 hours on 3.5 ml of methanol.

3.5 ml is 3.5 cubic centimeters, or about the size of an AA battery. Methanol costs about $0.8 / liter, which means you can refill that MP3 player 300 times for about $1 (for a total playing time of 10000 hours - a year and a half of non-stop music).

Good stuff

china, pebble bed nuclear reactors and hydrogen

2005-07-03T21:09:00-07:00

A very interesting Wired article here about efforts of Chinise scientists and industries to open pebble-bed nuclear reactors for massive use.

Nuclear reactors have long been known to provide one of the most environmentally friendly power source, and surely the most powerful one. Their problem is safety (think three mile island, or Chernobyl).

The pebble-bed nuclear reactor design is different. It is inherently safe - its safety governed by physical laws. If you turn off all safety gear of such a reactor and send the operators home for supper, nothing will happen. The physical properties of the design impose a negative feedback that causes the reactor to cool off once it reaches a certain non-critical temperature. More about this on Wikipedia.

Moreover, such a reactor can be used to efficiently generate hydrogen - which will provide ample fuel for fuel-cell powered vehicles.

China plans on deploying 30 such plants by 2020 (the first will begin construction next year). I think it's great, perhaps from here will the freedom from oil come ?

Curious that such advances come from China. It is a huge country with a lot of bright people, and it has immense needs for power and other resources. Smart people + demand fuels scientific advance.

Book review: "The double helix" by James Watson

2005-05-15T20:35:00-07:00

Told by one of the researchers responsible for the discovery of the structure of the D.N.A. molecule, "The double helix" is mainly a mixture of auto-biography, obscure chemistry and a story of young researchers doing their work.

If you're not seriously into chemistry / biology this book's technical details, though not many, will be difficult for you (I barely understood it even with some editing comments that tried to clarify things). Make sure to read the Wikipedia entry on DNA first :)

Unfortunately, I expected it to be a pop-sci book, and got dissapointed. As a pop-sci book it's pretty bad - it's more of an autobiography.

Additionally, I didn't really enjoy Watson's style. It's quite dry and doesn't do a good job of "transmitting" the author's excitement to the reader. Someone like Simon Singh would do much better with this book.

The only really interesting thing I found in it is a curious exposition of the lives of researchers, from a different angle than is usually told. Other than this, though, the book has been a waste of time.

I only recommend it if you're a molecular-biology enthusiast eager to hear the details of Watson and Crick's discovery.