In an allelopathic experiment, I have observed that sometime more inhibition of specific weed species occur at low rate of application of desired allelochemical, however, application of similar allelochmical, at higher rate of application did not produce much inhibitory effect. However, in totality, the differential rate of allelochemical (from lower to higher rates) produces inibitiory effect as compared to the weed check (no application of allelochemical). This is bit different from the hormesis phenomenon where the lower rate of application of allelochemical produces stimulatory response, whereas higher rates of application produces the inhibitory response. Moreover, in most of the published literature, increasing the rate of allelochemical produces the higher rate of inhibition.
Therefore, in light of above-said fact, I would like to know whether is there any phenonomon/ dose-response mathematical model describes the higher inhibition response of species at lower rate of allelochemical application rather than applied at higher rates??
I think you are referring to the low concentration of allelochemical (when you say low rate..)
If so, yes, relatively the lower concentration of allelochemicals, like any other toxic chemical gives better inhibition. Supra-optimal dose leads to death. It is like homoeopathy principle or in simple terms as a little of common salt is effective; more of it will become lethal.
The allelochemicals you are trying most likely are the mix of phenolic acids and other biomolecules and not the pure ones.
To my mind, there is no mathematical model to determine it as such or the way you are perhaps looking for. However, you may consult the paper, "A Mathematical Model to predict the tissue response to Parthenin - an allelochemic" Biologia Plantarum 35(4) : 567-576 ISSN: 0006-3134
The impact is governed by the C x T relationship, where "C" is concentration and "T" the time period.
Best wishes
Allelo chemicals, by and large, exhibit toxic effects at certain cardinal doses beyond which there may be marginal effect. This follows the law of diminishing returns like any input response .
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