I guess in theory one could think or go even steps further, namely if one wouldn't only have specific 2 DNAs (from both parents of offspring with such qualitative change), one could check for the set of possible gametes each parent can produce and the ways in which those can combine, so that (at least in theory, if one somehow via model simulation or otherwise had exhausted the combinatorial possibilities) if one had already done all the checks for variations of the offspring DNA (that lead to a qualitative change) to know which of them would still lead to the change and which wouldn't (and one could get a ratio between the cases as proxy for obtaining a probability of the occurrence), then for the set of gametes from the parent generation one could also check for how many of those combinations of male & female gametes would lead to a variation of (or the exact same) DNA that leads to the qualitative physiological change, and which not (and again one could compare frequency ratios for probabilities). And I suppose if one even had the DNA of all 4 individuals of the parent generation of both parents (of the "special" offspring), then one could continue these kinds of checks further, and so on.
And I guess on the topic of dependence just on the DNA for the expression of a new physiological feature, unless it were either after many empirical tests or for theoretical reasoning clear that the DNA were to determine the presence or absence of a "special" feature with 100% consistency, independent of e.g. what the female parent consumes during pregnancy, then for all the variations of parent-generation-DNA combination candidates, one could also test for them the statistical consistency (with high sample counts of tests) how consistent the link between DNA (of which one found out that it can lead to the feature) and the feature is, but the same also for those parent-generation DNAs where one at first didn't get the feature expressed for the offspring, as it might be able to do so, even if it wasn't observed at first. And after all that, one could obtain a whole set of DNAs that can create the feature at all, and each with associated probability, and one could compare them by their differences, as some DNA may be closer to a given DNA than another DNA, and one could see how and how much the probabilities can change up between the cases.
