Ecological Archives E096-279-A6
Wojciech Uszko, Sebastian Diehl, Nadine Pitsch, Kathrin Lengfellner, and Thomas Müller. 2015. When is a type III functional response stabilizing? Theory and practice of predicting plankton dynamics under enrichment. Ecology 96:3243–3256. http://dx.doi.org/10.1890/15-0055.1
Appendix F. Application of the stability condition to Murdoch et al.‘s (1998) parameter values.
Table F1. redicted equilibrium algal densities (R*) and stability properties of Daphnia-algae dynamics under modified parameter assumptions. Daphnia’s loss rate (maintenance plus mortality) m=0.12, Daphnia’s conversion efficiency e=0.5 and the dilution rate D=0 are as in Murdoch et al. (1998) (mortality was not temperature adjusted because Murdoch et al. did not specify a temperature). Functional response parameters, estimated from ingestion (IR) or clearance rate (CR) data, are from this study and identical to the values in Table 2. The stability condition compares parameter b with to the left and right of the inequality, respectively.
Species pair |
IR / CR data |
R* |
Stability condition |
Asymptotical stability |
D. hyalina + |
IR |
0.053 |
1.63 > 1.21 |
Yes |
CR |
0.050 |
1.44 > 1.19 |
Yes |
|
D. hyalina + |
IR |
0.104 |
2.46 > 1.20 |
Yes |
CR |
0.090 |
1.67 > 1.15 |
Yes |
|
D. hyalina + C. meneghiniana, 16°C |
IR |
0.059 |
2.17 > 1.60 |
Yes |
CR |
0.060 |
1.46 > 1.39 |
Yes |
|
D. magna + |
IR |
0.084 |
2.26 > 1.78 |
Yes |
CR |
0.133 |
1.19 < 1.46 |
No |
Literature cited
Murdoch, W. W., R. M. Nisbet, E. McCauley, A. M. deRoos, and W. S. C. Gurney. 1998. Plankton abundance and dynamics across nutrient levels: tests of hypotheses. Ecology 79:1339‒1356.