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Monday, 18 November 2019


Note: there may be some flaw in the logic of this argument.  Or, alternatively, it may be an established result in genetics that my (brief...) researches have failed to find.  If either, tell me in the comments and I will amend as necessary. But if neither, I present it as a possible explanation of an important phenomenon.

There is a meta-analysis in Nature Genetics on 14,558,903 (!) partly dependent twin pairs that shows that the heritibility of a wide range of traits is 49%.  That is to say those phenotypical traits are 49% determined by a person's genes, and 51% by their environment.

This seemed rather close to 50% to me, and set me wondering if there is an evolutionarily stable strategy (ESS) at play that is forcing the figure to 50%.  The first such ESS that was discovered (by R.A. Fisher) is the one that gives a 50/50 sex ratio in a wide range of species.  An ESS doesn't have to settle at 50%; for example the ESS between hawks and doves in the human population (and many others) is heavily weighted towards the doves.

So.  The question to ask is, if you are a gene, in order to maximise your fitness how much of the phenotype you develop should you control, and how much influence should you hand over to the environment?  (Note importantly that "the environment" here includes all the other genes in the organism and any influence that they might have over that phenotype; and that those genes will be subject to the forces I am about to describe as well.)

Let's look at a simple specific made-up example.

Suppose you are a gene that controls everything about a fur-colour phenotype and you are a gene for green fur.  There is another, rival, genetic allele for brown fur.  In a verdant forest you, green-gene, will leave more offspring, and brown-gene will diminish in the population.  In contrast, in a brown-coloured savanah your brown-gene competitor will come to dominate.

Now suppose a mutation arises that causes neither green nor brown, but that turns the phenotype fur the colour of its surroundings when the organism of which it is a part is developing.  Clearly individuals posessing that new mutation will be able to colonise both the forest and the savanah, and the new gene will come to dominate (assuming the cost of its working is not greater than that of the other two).  This new gene has handed over some of the determination of its phenotype to the environment, and has thereby gained an advantage over its more dictatorial predecessors.

But a gene that has no influence at all over any phenotype, and which leaves the determination of the phenotypes to the environment (which includes the other genes, remember), has no fitness because it cannot influence its reproductive success.  It may get carried along for the reproductive ride as non-coding DNA, or it may just be eliminated altogether.

In our example, suppose the developing organism adopts the colour of the nearest object during its development, as opposed to switching between just green and brown.  And suppose it grows up in a nest surrounded by bright orange flowers.  Clearly, in this case, the gene will have given up too much control to the environment.

So in general we can see that it makes sense for a gene to allow some environmental influence over its phenotype to allow a versatile response to different conditions.  But it must not allow too much environmental influence lest it loses control and hence loses fitness.  We can show this graphically:

The X axis and the blue line are the proportion of the influence of the gene on the phenotype, which allows the gene to control things. The red line is one minus this - the proportion of the influence of the environment on the phenotype, which allows the phenotype to adapt to its surroundings in some way.  If we multiply those together, we get the yellow curve, which is the benefit the gene gets for a given proportion.  That is, the gene "wants" control, and it "wants" adaptability, but these are in opposition, so it can't have all of both; when one increases that increase necessarily drives the other one down. Unsurprisingly, given the symmetry of this example, the maximum - the most beneficial point for the gene - is at 50%, which is the figure we set out to explain.  But the symmetry seems a bit of a cheat.

So suppose we change the form of the blue line (and consequently the red one) so it is merely some (in general non-symmetrical) function, f, of the genetic proportion (call that g) along the horizontal axis.  As in the graph above for the simple case f(g) = g, the new general f(g) generates values in the interval [0, 1].  The yellow curve, the benefit the gene sees, B, is now:

B = f(g) . [1 - f(g)] = f(g) - f(g)2

(all other things being equal, the gene's fitness, ω, will be proportional to B) The maximum value of will be where dB/dg = 0:

dB/dg = f'(g) - 2f'(g)f(g) = 0

which gives:

f(g) = 1/2 .

So the watershed value of 50% for the maximum benefit to the gene doesn't change, regardless of the form of f(g).

There must, of course, be exceptions to this simple analysis.  But it does show how, for phenotypes that must adapt to their environment, the genes that control them would be expected to hand exactly 50% of their influence over the phenotype to that environment.

Sunday, 12 May 2019


I prompted a bit of a discussion on Twitter the other day by asking, "How deep a hole would you have to dig on Mars for the atmospheric pressure at the bottom to be 1 bar?"

1 bar is 1 Earth atmosphere, for non-metric people.  It turns out that the answer is 55 Km deep, which is rather inconvenient if you want to use this as a way to produce comfortable human living space...

But, as SCUBA divers know, every 10m deep you dive in water increases the pressure by 1 bar.  So how can we live on Mars under water?  We'll need a copious supply of water anyway that we would recycle, and the diagram above gives a rough idea how we could use that both to pressurise the living space and to create a radiation shield.

On Mars the 1 bar water depth would be at about 28m, because of the lower gravity.  But, if we were prepared to have a lower air pressure, that depth could be reduced to 20m.  (That would give the same pressure as the inside of a cruising airliner cabin - about 0.7 bar.)

So we dig a circular hole about 35m deep and about 40m in diameter.  We line and seal the walls to make them air and water tight.  Then we put in a transparent skin that forms the bottom of a water tank about 15m from the floor, and another skin at ground level.  We fill between the skins with water, while raising the air pressure under the bottom skin to balance the load.

When the structure is complete the water would be supported by the higher air pressure underneath.

The water would freeze at the top because of the Martian surface temperature.  The top skin is needed to keep the water/ice dust-free and to prevent loss by sublimation.  For safety, the bottom skin under the water would probably have to be made strong enough to survive both a loss of atmospheric pressure underneath it, and a loss of the water above it.  Alternatively, almost all the water could be allowed to freeze.  Then it would become a strong part of the structure, especially if it were mixed with transparent fibres with the same refractive index as ice.

As anyone who has dived in clear tropical waters knows, plenty of sunlight would be available in the living area at the bottom.  And water is an excellent radiation shield, so, together with the surrounding ground, the problem of Martian surface radiation would be eliminated.  If care was taken to control the freezing of the top layer of water to eliminate bubbles, it may even be possible to make the water roof optically clear, so the Martian settlers could see the sky.

Digging a cylindrical hole using a descending circular shield and lining the walls above the shield with a resin/rock-dust composite is a job eminently suitable for a robot.  It could work away for years before people arrived, preparing a hexagonal grid of living cylinders interconnected by short corridors at the bottom.  Another robot would be ferrying ice from the Martian poles to the site.  When people landed they could do the more fiddly job of fitting the skins and airlocks, gradually expanding to occupy more cylinders as needed.

In order to get all this working, we'd obviously have to try it out on Earth first.  Maybe we should do so at Coober Pedy in the Australian outback.  People there already live in artificial underground caves because of the heat.

And the whole project might run at a profit because of the Coober Pedy opals the robot dug up...

Monday, 18 March 2019


This is a post about heartburn and the origins of religious belief.  Run with me here...

You can give pigeons religion.  You observe them and, whenever one sticks its left wing out, say, you give it some food.  Soon the pigeons have a conditioned reflex that sticking out their left wing produces food. It becomes their "Give us this day ours daily bread" prayer.  Random coincidences can give the same effect without the intention of an experimenter: breaking mirrors and bad luck, and so on.

I have suffered from heartburn for a few years.  This year, I decided to do something about it.  So

  1. I changed the foods I eat.
  2. I changed the time of day of my main meal.
  3. I stopped drinking regular coffee.
  4. I started taking betaine hydrochloride (to increase stomach acid) and pepsin before every meal.
  5. I started eating a small amount of ginger (of which I am anyway fond...) after every meal.
Now.  I'm not a complete moron.  I know that the scientific way to do this would be to change just one thing at a time and to record the results.  But I wanted a cure NOW, so I just threw everything that might work at the problem at once.

And that everything did work.

But now I don't know which of those five changes made the difference.  I could just cut one out at a time and see when the problem returns.  But I really don't want the problem to return.  So I'll just carry on with my cure in ignorance of which bits of it actually worked and which are just snake oil.

And, of course, the snake oil bits are my religion.  They do nothing.  I half have faith that they work.  And I'm not prepared to subject them to empirical verification.

They are my pigeon's prayer.