Commentary: Rare earth elements affect the growth and fitness of free-floating plant Lemna minor L

The study by Gjata et al. (2025) addressed a timely and important question in ecotoxicology:revealed the toxicological impact of rare earth elements (REEs) on aquatic plants. Using the modelfree-floating species Lemna minor, where they measured the authors assessed effects of REEs on growth, rate, photosynthetic pigment contentconcentrations, and oxidative stress markers of the plants. A cornerstonekey point of such toxicity studies is the accurateprecise measurement of plant growth, expressed as the relative growth rate (RGR).RGR quantifies exponential growth per unit time and) of the plants which is the primary metric for determining inhibitory thresholds (Naumann et al., 2007). In their methods, Gjata et al.The authors correctly defineddescribed RGR usingby the standard formula: RGR=(ln(Nt)-ln(N0))/t, where N0 and Nt are the initial and final frond numbers, and t is time in days. However, critical examination of the RGR values in their Table 1 reveals profoundgreat mathematical and biological inconsistencies.contradiction. This commentary identifiesreveals the likely error source, recalculates plausible growth rates, and discusses implicationssuggestions for the study's conclusions on REE toxicity.Under optimal conditions, typical RGRs for duckweed range from 0.15 to 0.5 day⁻¹ (Ziegler et al., 2015). Hence, the RGR values reported in Table 1 (Gjata et al., 2025) exceed the biologically reasonable rates for L. minor by one order of magnitude. As an example, the mean control RGR for day 7 was indicated as 9.52 day -1 . With an initial frond number of N0=10, this rate would result in a final frond number (Nt) over 7 days (t=7) as follows: Nt=N0⋅e (RGR×t) = 10⋅e (9.52×7) ≈ 8.774×10 29 fronds-an astronomical and impossible figure.The pattern of reported values suggests that the authors calculated the absolute increase in frond number per day, that is (Nt-N0)/t instead of RGR.Using the reported day 7 control RGR (9.52), and an initial N0=40 fronds (Section 2.1),