TY  - JOUR
A1  - Fussmann, Gregor F.
A1  - Ellner, Stephen P.
A1  - Shertzer, Kyle W.
A1  - Hairston, Nelson G.
T1  - Crossing the Hopf bifurcation in a live predator-prey system
N2  - Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and Laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of interacting populations. We studied the dynamical behavior of a two- species aquatic Laboratory community encompassing the interactions between a demographically structured herbivore population, a primary producer, and a mineral resource, yet still amenable to description and parameterization using a mathematical model. The qualitative dynamical behavior of our experimental system, that is, cycles, equilibria, and extinction, is highly predictable by a simple nonlinear model.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Shertzer, Kyle W.
A1  - Ellner, Stephen P.
A1  - Fussmann, Gregor F.
A1  - Hairston, Nelson G.
T1  - Predator-prey cycles in an aquatic microcosm : testing hypotheses of mechanism
N2  - 1. Fussmann et al. (2000) presented a simple mechanistic model to explore predator-prey dynamics of a rotifer species feeding on green algae. Predictions were tested against experimental data from a chemostat system housing the planktonic rotifer Brachionus calyciflorus and the green alga Chlorella vulgaris. 2. The model accurately predicted qualitative behaviour of the system (extinction, equilibria and limit cycles), but poorly described features of population cycles such as the period and predator-prey phase relationship. These discrepancies indicate that the model lacked some biological mechanism(s) crucial to population cycles. 3. Here candidate hypotheses for the 'missing biology' are quantified as modifications to the existing model and are evaluated for consistency with the chemostat data. The hypotheses are: (1) viability of eggs produced by rotifers increases with food concentration, (2) nutritional value of algae increases with nitrogen availability, (3) algal physiological state varies with the accumulation of toxins in the chemostat and (4) algae evolve in response to predation. 4. Only Hypothesis 4 is compatible with empirical observations and thus may provide important insight into how prey evolution affects predator- prey dynamics.
Y1  - 2002
UR  - http://www.blackwell-synergy.com/Journals/issuelist.asp?journal=jae
ER  -