Ejecta rays point to the problem with ‘ideal’ models

2 minute read

The PNAS Journal Club points to an interesting research study on craters: “Journal Club: Researchers may’ve finally solved mystery of crater ray formation”.

The problem is that craters on celestial objects like the Moon are surrounded by distinct rays of ejecta, but those didn’t form in experiments at high velocity.

Full moon showing ejecta rays around craters
Photo: Renden Yoder

Why did the model fail to generate the real-world phenomenon of ejecta rays? Because the model conditions were too ideal:

The team tried to vary every parameter they could imagine—changing the grains’ diameters, mixing grains of different sizes, increasing the speed of the balls—but the eventual solution came about by accident. One day, Chakraborty’s fatigued postdoc, Tapan Sabuwala, failed to follow normal protocols and smooth down the surface of their sandbox before dropping in their impactor. After the drop, voilà—a beautiful crater and its rays appeared.
The jagged landscape, which schoolroom students naturally produced when they haphazardly dumped out their bags of flour, seemed to be the key to creating crater rays. The team followed-up with 135 more experiments in which they pressed a repeating hexagonal honeycomb pattern into their granular surface and found that they could consistently make rays. Moreover, the number of crater rays depended on only two factors—the size of the impactor and the spacing of the hexagonal bumps.

There is a strong rationale to use simple models in physics. You want the conditions to be easily described with mathematics, and easily replicable by other scientists, so you specify exactly the ideal conditions for the model.

But the kids were using an even simpler model, in the sense that anybody can make a pile of flour and throw stuff at it. What is ideal is not necessarily simple. In this case, the real-world physics of planets and asteroids is more similar to the real-world physics of particles than the ideal physics of surfaces and ballistics.

As I read this story, I thought about genetics. We use a lot of “simple” ideal models in human genetics. The hypothetical reconstructions of populations like the “Basal Eurasians” are based upon ideal panmictic populations with mathematically ideal genetic exchanges. The quantification of Neanderthal genetic contributions to humans has likewise been based upon ideal population models and discrete mixture events.

These ideal populations may be easy to model with math, but they bear little resemblance to the spatial heterogeneity of living human populations or the irregular temporal distribution of mixture and contact.

What would a more realistic model look like? For human populations, it would have heterogeneity—not populations as single points, but populations with a spatial extent, varying degrees of mixture as they came into contact, and biased growth.

Would the outputs of such a model look more like the real world? It’s not easy to say. Possibly there is no real difference, and the more complex models come with a greater danger of overfitting because they add so many parameters.

But not all parameters are created equal. My biggest concern about simplistic population models is that they fit data better when new point populations and sources of mixture are added. What if some of those “ghost populations” are really not necessary, if we examine a more complex, more realistic model?

Today’s most surprising findings about human prehistory are pretty strongly model-dependent, and few population geneticists are examining the effect of model selection on these conclusions.