Speaking as someone who is neither the OP nor Norbert Wiener, I think even the task of posing an adequate mathematical model should not be taken for granted. Thousands of physiologists looked at Drosophila segments and tiger stripes before Turing, thousands of ecologists looked at niche differentiation before Tilman, thousands of geneticists looked at the geological spread of genes before Fisher and Kolmogorov, etc. In all these cases, the solution doesn't require math beyond an undergraduate level.

Also, concern over an exact solution is somewhat misplaced given that the greater parts of the error are going to come from the mismatch between model and reality and from imperfect parameter estimates.