[Coral-List] Geometry, coral bands, and tree rings
John Ware
jware at erols.com
Fri Mar 25 12:40:58 EDT 2011
Dear List,
I suppose that what I am going to provide has been done to death in many
places, but here goes some simple geometric considerations. There will
be a bunch of simplifying assumptions, but I doubt that making the
problem more complex will change the conclusions much.
Suppose we have a hemispherical coral colony with each polyp able to
deposit a fixed amount of CaCO3 each year. This increases the volume of
the coral head and thus its area. Increasing the area allows for more
polyps to occupy the space. And so on. The process is, of course,
non-linear. So I wrote a little computer program that simulates the
process.
I picked some numbers that I thought were reasonable and that resulted
in a 10 cm coral growing to a diameter of 3.2 m in 500 yrs and 6.2 m in
1000 yrs. What is interesting about this little experiment is that the
coral diameter increase is NOT linear with time. The rate of change of
diameter (and hence the spacing between bands) actually increases each
year. HOWEVER, the rate of change is very small. The increase in
diameter at 100 yrs is 0.610 cm/yr and at 1000 yrs is 0.615 cm/yr.
I find similar results across a range of assumed growth rates.
The rate of change is probably much too small to be detected leading to
the conclusion that bands are about of equal width throughout the life
of the coral.
Now trees are a little different. There are lots of things that can act
to evolve various growth strategies (competition, bending stress in
winds, and so on). However, it is not unreasonable to assume that the
amount of energy that can be devoted to growth is proportional to crown
area and that trunk area is proportional to crown area. If some
fraction of the energy absorbed each year from radiation goes into
increasing the cross-sectional area of the trunk, then this area will
increase linearly. This will result in the radius increasing as the
square root of the area with the result that growth rings will get
closer and closer together.
Well, I don't suppose I did anything particularly new or clever, but I
thought I would throw it out there anyway.
John
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