Comment on general fugacity‐based model for multiple chemical species

In a recent paper published in Environmental Toxicology and Chemistry (ET&C) Cahill et al. [1] present a general fugacity-based four-compartment model that allows for simulating the fate of several chemical species originating from one or several parent compounds. The model is applied to three chemical case studies that illustrate convincingly the importance of assessing not only the parent compound, but also the stable or toxic products of transformation or chemical speciation. Mathematically, the model is based on a set of first-order linear differential equations that are solved numerically by using Euler’s method to give time-dependent concentrations for four chemical species (e.g., one parent compound and three degradation products). Specifically, the model allows any of the four species to transform into another species, thus allowing for branching and chemical cycling in the degradation pathway. In the introduction, the authors review the literature on existing multispecies models to motivate their research. However, this literature review does not include a study conducted in our group that is highly relevant to the topic [2]. Furthermore, it seems to contain some misinterpretation of our work on multispecies models [2,3]. Therefore, we feel that we need to clarify some of the points raised. According to Cahill et al. [1], our earlier work on transformation products [3] has three limitations: It applies only to a parent chemical and a single transformation product; no environmental concentrations were predicted even though such a model can be applied to predict environmental concentrations; and the model assumes all product yields to be unity, which would thus limit its applicability to more complex reaction pathways. Two of our more recent publications [2, 4], however, do address these issues. In these two publications, our model is applied to three chemical case studies, nonylphenol polyethoxylates (NPnEO), perchloroethylene, and atrazine, with up to 12 chemical species and complex transformation schemes in each environmental compartment. While the article in Risk Analysis [4] focuses on the calculation of the joint persistence, the second paper [2] calculated realistic environmental concentrations of NPnEO and its transformation products for Swiss freshwaters and used them to assess the risk stemming from the simultaneous presence of a parent chemical and its transformation products by means of a mixture risk quotient. Even without the illustrations of the later papers, one can find that the general mathematical formulation of the modeling framework introduced earlier ([3], pp. 3810–3811) enables it to satisfy all the points raised by Cahill et al. [1]. Although the exemplary case studies in that publication embrace only one parent compound and a single transformation product, Figure 2 [3] in combination with Equation 3 [3] shows how the mathematical setup is applicable to any transformation scheme and number of chemical species. Specifically, the formation term y dc (t) i xy x xy x x 5 1 k c (t) 5 1 u k c (t) O O i i i i i dt x x