Monthly Archives: April 2016

Evolution is SLOW

26 Tuesday Apr 2016

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A long time ago I had a course by Prof Jim Sandeful of Georgetown U and Dr Monica Neagoy on teaching with “discrete math” — very useful and interesting stuff that often does not get discussed in the standard American curriculum. I enjoyed it a lot.

Among other topics, I decided to write a little computer program that would model exponential random decay of radioactive elements. (Iirc I did this in Pascal and in BASIC, on the C-64, IBM-PC, Apple II, and Commodore Amiga. That was fun.)

One subtopic that came up, but which I never figured out how to model, was how to describe the frequency of some trait (eg red hair, striped tail, or growing a third eye…) in a population. I had long thought about how to do that but not until today did I begin to make some progress, so please allow me to share.

I’m going to make up a very-much simplified example using a Punnett square, something like this:


If you have no idea what this means, let this non-biologist try to explain as best I can:

Upper-case B and lower-case b in this diagram stand for two different versions of a particular (but mostly imaginary) gene that controls whether a person has blue eyes or brown. In this hypothetica example, the upper-case B gene causes brown eyes and is dominant, where the lower-case “b” causes eyes to be blue and is recessive. Thanks to the magic of sexual reproduction, you get two copies of each gene, 1 from Mom and one from Dad, whether they stick around and raise you or not. (You have two similar-but-not-identical copies of each chromosome except for the X and Y chromosomes; your two versions of each gene are carries in corresponding locations on each of the two chromosomes. If I got this right.)

If you have brown eyes, then your genes might be BB or they might be Bb or bB (same thing). If you have blue eyes, then you have bb genes for sure — again, in this hypothetical scenario.

This Punnett square shows the probability of what will happe if two parents who carry Bb genes have sex and produce offspring. It reminds me very much of how we use an area model to show that (X + Y)*(X + Y) equals X^2 + 2*X*Y + Y^2.

In any case, each of those parents carries Bb genes, and when the eggs and the sperm cells are manufactured inside the parent’s ovaries and testes, one or the other version of the gene is put inside, but not both. And it’s random. So since each parent has a Bb gene, its probability of passing along upper case B (brown) is 1/2 or 50%, as is the probability of passing along lower case b (blue eyes).

You can now find the probability of all of the outcomes shown in the interior of the diagram. The upper left hand corner is BB, pure brown eyes, with probability 1/4 because 1/2*1/2=1/4 and also in this case all of the sections really do have equal areas.

The upper right hand and lower left hand corners represent the Bb cross; the child will have brown eyes. The probability of a Bb cross is 1/4 plus 1/4, or 1/2.

The lower right hand corner is the region representing the probability of pure bb offspring  which have (recessive) blue eyes. The probability of bb is 1/4.

Now let us add a couple of features.

1. This is not just a single mom-dad pairing: this is a representation of an entire reproducing population where genes B and b are present, each 50% of the time.

2. Let us also pretend that the bb combination is fatal: not a single one of them survive to adulthood and to leave offspring. (This is a very extreme hypothetical example of how evolution operates. Normally Deleterious genes aren’t so uniformly fatal!) or alternatively, a breeder of plants or animals might decide to not permit any of the blue-eyed bb offspring to reproduce. Eugenicists used to advocate sterilizing anyone who exhibited harmful, recessive genes,in order to improve the remainder of the human race.

At first glance, You would think that this sort of genetic selection, either by artificial or natural means, would work very quickly, and that after just a few generations, the proportion of the population that was blue-eyed would vanish.

Jim Sandefur said no, it would take a really long time. I forgot the details, and just worked them out today. I’ll work out the details for you later when I have a larger screen. But:

Bottom line: even with this 100% culling of recessive genes, the proportion of blue eyes goes down as the harmonic series (1/X), where X is 4, then 5, 6, 7, 8, etc

So if the first generation has 1/4 (25%) blue eyes, and if every single individual with blue eyes is somehow prevented from reproducing, then the next generation will still carry the lower-case b gene 1/5 (20%) of the time.

And if children with blue eyes (bb) are still prevented from reproducing, the third generation will still pass on  the lower-case b gene one-sixth, or 16.67% of the time, and the next generation will pass on the lower-case b gene one-seventh (14.29%) of the time. The next generation passes on b genes one-eighth (12.50%) of the time, then one-ninth of the time (11.11%), then one-tenth of the time (10.00%) and so on. At first the decrease is pretty rapid, but after that it slows to a craw, and the world would never be entirely free of the pure bb. After 100 generations, there still would be 1/103 (almost 1%) of the population carrying genes that can pass on blue eyes.

At 25-30 years for a human population to reproduce, you are talking about 2,500 to 3,000 years!

However, the fraction of the population that actually is born with blue eyes apparent to everybody will fall much faster.  The proportions would be 1/4 in the initial generation, followed by 1/9, then 1/16, then 1/25, then 1/36, then 1/49, then 1/64, and so on, with the ratio being 1/X^2 (one over x-squared) rather than 1/x.

So, by 10 generations, under this hypothetical, 100%-effective sterilization or extermination regime, the proportion of the population with visible blue eyes would have fallen to 1/169, about six-tenths of a percent. However, the fraction of the population that still carries the genes for blue eyes would remain at 1/13 of the population, about 7.7% of the total.

However, perhaps conditions might flip-flop. In my hypothetical problem here, perhaps the conditions making blue eyes fatal would disappear after a number of generations. (Even if Hitler’s nasty 1000-year Reich would not have been enough to eradicate whatever enemy genes!) In fact, perhaps the reverse would be true: having brown eyes would be a fatal handicap under some conditions. Then the prevalence of blue eyes would rise to the fore in their place, but there would be an enormous die-off of all those who had brown eyes, which would mean the vast majority of the population. So all that would be left would be those formerly recessive genes, and the formerly dominant genes would be wiped out completely.

More realistically: recessive genes that make people susceptible to die from some particular disease or parasite or environmental factor do definitely get reduced in frequency over time, as I hope I have shown. However, they do not disappear completely for a very long, long time (if ever!) unless the entire population is reduced to just a handful of individuals, none of whom carry that gene, just by chance.

Evolution does work on those time scales. Human societies and any proposed eugenics program do not. Evolution has no direction, and is essentially blind, like a mathematical algorithm.

People often say that everything happens for a reason. Often, that reason is simply the laws of probability, which are extremely hard for most people to handle. Myself included.

 

2016 Hopewell Observatory Fall Open House and Star Party October 29/30

23 Saturday Apr 2016

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2016 Hopewell Observatory

Spring Open House and Star Party

October 29/30

 
Anybody interested in the night sky, including members of local astro clubs like NCA and NOVAC, are invited to the Fall 2016 astronomical open house and star party at Hopewell Observatory on the night of October 29/30 (Saturday evening and on into Sunday morning), 2016. Feel free to pass this invitation to friends, neighbors, and family and anybody else you care to notify.

 

We are located about 30 miles west of the Beltway on Bull Run Mountain – a ridge that overlooks Haymarket VA from an elevation of 1100 feet, near the intersection of I-66 and US-15. Detailed directions are below.

 

Assuming good weather, you’ll get to see planets, star clusters and nebulae and the Milky Way itself, as well as many other galaxies. If you like, you can bring a picnic dinner and a blanket or folding chairs, and/or your own telescope, if you own one and feel like carrying it. We have outside 120VAC power, if you need it for your telescope drive, but you will need your own extension cord and plug strip. If you want to camp out or otherwise stay until dawn, feel free!

 

Warning: While we do have bottled drinking water (and will have hot water and the makings for tea, cocoa & coffee) and we do have hand sanitizer, we do not have running water; and, our “toilet” is of the composting variety. Plus, you may want to consider bug spray, since we are completely surrounded and protected by woods. Do check carefully for ticks when you get home. If you do apply insect repellent while visiting, please keep the spray downwind from anybody’s telescopes!!

 

The road up here is partly paved, and partly gravel or dirt. It’s suitable for any car except those with really low clearance, so leave your fancy sports car (if any) at home. Consider car-pooling, because we don’t have huge parking lots. We will have signs up at various places along the way to help guide you, and will try to have parking spaces denoted.

 

Two of our telescope mounts are permanently installed in the observatory under a roll-off roof. We have others that we roll out onto the grass in our roughly one-seventh-acre field. We have two 14-inch scopes (one hand-made Dob and one Celestron SCT), a 30-cm Wright-Newtonian entirely built by our oldest member, and a 10” f/9 reflecting scope also made by hand. The entire observatory was hand-built, and is maintained, by the labor of its founders and current members.

 

The drive is about an hour from DC. After parking at a cell-phone tower installation, you will need to hike about 100 yards to our observatory. Physically handicapped people, and any telescopes, can be dropped off at the observatory itself, and then the vehicle will need to go back to park near that tower. To look through some of the various telescopes you will need to climb some stairs or ladders, so keep that in mind when making your plans.

 

It’s not the inky-scary dark of the Chilean Atacama or the Rockies, but Hopewell Observatory is mostly surrounded by nature preserves maintained by the Bull Run Mountain Conservancy and other such agencies. Also, our Prince William and Fauquier neighbors and officials have done a pretty good job of insisting on smart lighting in the new developments around Haymarket and Gainesville, which benefits everybody. So, while there is a pretty bright eastern horizon because of DC and its VA suburbs, we can still see the Milky Way whenever it’s clear and moonless.

 

This will be the official night of New Moon for October 2016. Venus and Saturn will be setting soon after the Sun, which will set at 6:12 pm with real darkness (and the end of all twilight) holding off for about another hour. The sun will rise at about 7:36 the next morning. Mars will be low in the south-west at sunset, and Jupiter will rise shortly before dawn.

 

We should also be able to track down and examine many, many deep-sky objects, including the famous Andromeda galaxy and the Orion nebula.

You can find detailed directions and a map to the observatory below:

 

DIRECTIONS TO HOPEWELL OBSERVATORY:

[Note: if you have a GPS navigation app, then you can simply ask it to take you to 3804 Bull Run Mountain Road, The Plains, VA. That will get you to step 6, below.]

(1) From the Beltway, take I-66 west about 25 miles to US 15 (Exit 40) at Haymarket. At the light at the end of the ramp, turn left/south onto US 15. (Exit is at approximately latitude 38°49’00″N, longitude 77°38’15″W.)

(2) Go 0.25 mi; at the second light turn right/west onto VA Rt. 55. There is a Sheetz gas station & convenience store at this intersection, along with a CVS, a McDonald’s, and a Walmart-anchored shopping center on the NW corner. This is a good place to stop for restrooms or supplies.

(3) After 0.7 mi on Va 55, turn right (north) onto Antioch Rd., Rt. 681. You will pass entrances for Boy Scouts’ Camp Snyder and the Winery at La Grange. (38°49’12″N, 77°39’29″W)

(4) Follow Antioch Rd. to its end (3.2 mi), then turn left (west) onto Waterfall Rd. (Rt. 601), which will become Hopewell Rd. (38°51’32″N, 77°41’10″W)

(5) After 1.0 mi, bear right onto Bull Run Mountain Rd., Rt. 629 (this is beyond Mountain Rd.). This will be the third road on the right, after Mountain Rd. and Donna Marie Ct. (38°52’00″N, 77°42’08″W) Please note that Google Earth and Google Maps show a non-existent road, actually a power line, in between Donna Marie Ct. and Bull Run Mtn. Rd.

(6) In 0.9 mi, enter the driveway on the right, with the orange pipe gate. There is a locked stone and metal gate on the left, opposite our entrance, labeled 3804 Bull Run Mountain Road. Don’t take that road – it goes to an FAA radar dome. Instead, go to the right (east). We’ll have some signs up. This is a very sharp right hand turn. (38°52’36″N, 77°41’55″W)

(7) Follow the narrow paved road up the ridge to the cell phone tower station. You should park around the tower (any side is fine) or in the grassy area before the wooden sawhorse barrier. Then you should walk the remaining hundred meters to the observatory on foot. Be sure NOT to block the right-of-way for automobiles.

(8) If you are dropping off a scope or a handicapped person, move the wooden barrier out of the way temporarily, and drive along the grassy track to the right of the station, into the woods, continuing south, through (or around) a white metal bar gate. The few parking places among the trees near our operations cabin, the small house-like structure in the woods, are reserved for Observatory members. If you are dropping off a handicapped person or a telescope, please do so and then drive your car back and park near the cell phone tower.

Please watch out for pedestrians, especially children! The observatory itself is in the clearing a short distance ahead. We do not have streetlights, and there will not be any Moon to light your way, so a flashlight is a good idea. In the operations cabin we have a supply of red translucent plastic film and tape and rubber bands so that you can filter out everything but red wavelengths on your flashlight. This will help preserve everybody’s night vision. In the cabin we also have a visitor sign-in book; a supply of hot water; the makings of hot cocoa, tea, and instant coffee; hand sanitizer; as well as paper towels, plastic cups and spoons.

The location of the observatory is approximately latitude 38°52’12″N, longitude 77°41’54″W. The drive takes about 45 minutes from the Beltway. A map to the site follows. If you get lost, you can call me on my cell phone at 202 dash 262 dash 4274.

map to hopewell june 2016