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).