Data analysis
Four populations were excluded from all analyses because they declined rapidly and went extinct despite growing in the medium without the addition of ZnSO4. The excluded populations had high leverage on the results but were qualitatively very different from all other populations. The four populations were each a replicate of the pairing LgLm at 0 mg/L Zn (both species), of L. turionifera in the pairing LtLm at 0 mg/L Zn, and of L. minor in the isolated setting at 0 mg /L Zn. Subsequently, population growth rates for each individual population (n=104) were calculated as ln(N2/N1)/(t1-t2). We used the initial population abundance at the start of the experiment (t1, 20.07.2021) and the final time point after 17 days (t2, 6.8.2021) to calculate total growth rates. Because most other studies examining the influence of Zn on duckweed growth were conducted over less than 10 days, we additionally calculated initial growth rate comparing the first day of the experiment (t1) with day 8 (t2, 28.7.2021). Initial growth rates represent growth rates for when we can be confident that nutrients were not limiting. In the mixed setting, we calculated growth rates for each species separately. Total and initial growth rate were then used as response variable in the linear models. The treatment variables were species identity (L. gibba (Lg), L. minor(Lm) or L. turionifera (Lt)), Zn concentration (0 mg/L, 0.45 mg/L, 1.82 mg/L, and 11.35 mg/L Zn), the setting (isolated vs. mixed) and composition (isolated, pairing with species 1, pairing with species 2). lmerTest (Bates et al., 2015; Kuznetsova et al., 2017) was used for the mixed models. Composition and position were included as random factors where appropriate. All analyses were done in R (R version 4.1.0, R Development Core Team, 2021).