Ordering the Yukawa couplings from bigger to smaller, they follow a clear exponential relationship. Is there a reason for it?
There's no reason they should. The Yukawa couplings are independent of one another, at the level of the classical action.
The way to check any such relationship is known: Just calculate how the couplings change under the renormalization group flow. This is now a standard exercise.
Manuel Urueña Palomo As mentioned the Yukawa couplings are independent variables, at the classical level. Quantum fluctuations lead to a dependence on the scale. This paper might be useful: https://arxiv.org/abs/1403.3058.pdf
This dependence is expressed by differential equations. Now it's possible to impose a particular relation between the couplings at some scale-for instance exponential, in the example at hand-and then use the equations to check whether this relation holds as the scale varies. Such relations can be, in turn, deduced by studying the symmetries of the system of differential equations.
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