What a good question. Most species of nonaquatic plants are able to modify root structures to varying degrees in order that they might cope with cultural conditions. I'm pretty sure you're asking after pneumataphoric roots. These are root modifications stimulated by oxygen deficit due to soggy soils, and help the roots get the O2 needed to carry on their normal work. I'll go look for something I wrote that gives a better idea of what happens.
From something I wrote for a GW Container Gardening thread:
The roots that form on cuttings rooted under soggy conditions or in water are quite different from those produced in highly aerated media (perlite - screened Turface - the gritty mix ....). Physiologically, you will find these roots to be much more brittle than normal roots due to a much higher percentage of aerenchyma (a tissue with a greater percentage of intercellular air spaces than normal parenchyma).
Aerenchyma tissue is spongy and filled with airy compartments. The compartments form as a result of highly selective cell death and dissolution in the root cortex in response to hypoxic (airless) conditions in the rhizosphere (root zone). There are 2 types of aerenchymous tissue. One type is formed by cell differentiation and subsequent collapse, and the other type is formed by cell separation without collapse ( as in water-rooted plants). In both cases, the long continuous air spaces allow diffusion of oxygen (and probably ethylene) from shoots to roots that would normally be unavailable to plants with roots growing in hypoxic media. In the case of fresh cuttings placed in water, aerenchymous tissue forms due to the same hypoxic conditions w/o cell death & dissolution.
Note too, that under hypoxic (airless - low O2 levels) conditions, ethylene is necessary for aerenchyma to form. This parallels the fact that low oxygen concentrations, as found in water rooting, generally stimulate trees and other plants to produce ethylene. For a long while it was believed that high levels of ethylene stimulate adventitious root formation, but lots of recent research proves the reverse to be true. Under hypoxic conditions, like submergence in water, ethylene actually slows down adventitious root formation and elongation.
Your plants need better aeration in the root zone.
Al