So much of science depends on how well you can communicate. I’m now on the least favorite part of any research project from my perspective: The communication part.
Here’s the question that motivated this particular bit: Natural selection acts on the phenotype, i.e. on the adaptability and competence of a particular individual. The search for improvement works by mutating the genotype, and unfortunately(?), even if there is a beneficial mutation in the germline, the individual whose progeny will carry that mutation does not benefit at all in its lifetime. Now: If mutations alter the phenotype to be inherited, then the genotype that leads to the selected parent phenotype will not really play much of a role since mutations will provide the progeny with a phenotype that may not be as good. So there has to be some sort of interplay between mutation resistance and adaptability, but in principle a dynamical system that is adaptable may not be stable to parameter perturbations (due to mutations) and vice versa.
So I suggested a little thought experiment to my postdoc (Zeina Shreif): Imagine two parts of a network, one which receives some environmental input and another that gets some signal from this part and produces some output. If the system is adaptable, we expect that it should be able to maintain the same output for a change in input. However, how exactly can the output part of the network distinguish between a change in the input or a change in some parameter in the input part of the network? So I conjectured that in fact these two properties must be correlated, that statistically homeostatic networks will be robust with respect to parameter fluctuations.
It turns out that this is true. Heroic work by Zeina has demonstrated this all the way up to 50 node random networks! So this is an exciting (to me) result, and so it is worth it to try to write this in a way that people will understand it. The problem is that there are so many exciting ramifications that I am very reluctant to do the careful writing. Must be done 😦