Table 1.
Results on population differences in chlorophyll a concentration, adult Daphnia abundance, and juvenile Daphnia abundance for the pre‐fish, high‐fish, and reduced‐fish populations in the (A) Control treatment and (B) Predation treatment using linear mixed‐effect models structured with repeated measures and supplemented by Tukey post hoc tests and using simplex projections
| Linear mixed‐effect model | Tukey post hoc test | Simplex projections | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| df | F | p | ||||||||
| (A) Control treatment | ||||||||||
| Chlorophyll a concentration | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 126.24 | <.01 | Pre‐fish | X | ✓.001 | Pre‐fish | X | ✓ (4) | |
| Daphnia population | 2 | 6.42 | <.01 | High‐fish | X | High‐fish | X | ✓ (1) | ||
| Day | 54 | 4.60 | <.01 | Reduced‐fish | X | X | ||||
| Adult Daphnia abundance | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 364.63 | <.01 | Pre‐fish | X | X | Pre‐fish | X | X | |
| Daphnia population | 2 | 0.27 | .76 | High‐fish | X | High‐fish | X | X | ||
| Day | 18 | 9.53 | <.01 | Reduced‐fish | X | X | ||||
| Juvenile Daphnia abundance | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 284.05 | <.01 | Pre‐fish | ✓.023 | ✓.023 | Pre‐fish | X | ✓ (4) | |
| Daphnia population | 2 | 4.54 | .01 | High‐fish | X | High‐fish | X | ✓ (5) | ||
| Day | 18 | 11.75 | <.01 | Reduced‐fish | X | X | ||||
| (B) Predation treatment | ||||||||||
| Chlorophyll a concentration | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 263.37 | <.01 | Pre‐fish | X | X | Pre‐fish | X | ✓ (2) | |
| Daphnia population | 2 | 1.10 | .33 | High‐fish | X | High‐fish | X | ✓ (5) | ||
| Day | 54 | 10.47 | <.01 | Reduced‐fish | X | X | ||||
| Adult Daphnia abundance | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 152.79 | <.01 | Pre‐fish | X | X | Pre‐fish | ✓ (3) | X | |
| Daphnia population | 2 | 1.14 | .32 | High‐fish | X | High‐fish | X | X | ||
| Day | 18 | 20.27 | <.01 | Reduced‐fish | X | X | ||||
| Juvenile Daphnia abundance | High‐fish | Reduced‐fish | Pre‐fish | High‐fish | Reduced‐fish | |||||
| Intercept | 1 | 307.16 | <.01 | Pre‐fish | X | X | Pre‐fish | ✓ (4) | ✓ (4) | |
| Daphnia population | 2 | 0.05 | .95 | High‐fish | X | High‐fish | ✓ (1) | X | ||
| Day | 18 | 12.21 | <.01 | Reduced‐fish | ✓ (1) | X | ||||
Symbol “✓” indicates significance, and symbol “X” indicates nonsignificance. The number between brackets for the report on the simplex projections indicates the number of forecast time step lengths, of the 5 tested, in which the row population could significantly better predict itself than the column population could (see Supporting Information SI2 for more details on the results). Significant p‐values are shown in bold.