Community Ecology Processes, Models, and Applications

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Figure 2.4The dynamics of two-species predator–prey interactions predicted by (a) the Lotka–Volterra model (Lotka,

1926; Volterra, 1926) and (b) the Nicholson–Bailey model (Nicholson and Bailey, 1935). In both models, the dynamics

are unstable. In the Lotka–Volterra model, the dynamics are neutral cycles with the period set determined by the model

parameters and amplitude set by the initial conditions. Predators lag prey by one-quarter of a cycle. In the Nicholson–

Bailey model, the dynamics show divergent oscillations with overexploitation by the predator, leading to the extinction

of both prey and predators. Dashed lines, prey; solid lines, predators. Reproduced with permission from May and

McLean (2007).

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Figure 2.5Large- and small-amplitude cycles in the same global environment. Population dynamics ofDaphnia
(triangles) and their edible algal prey (squares) in four nutrient-rich systems from one treatment. (a and b) Examples of
large-amplitude predator–prey cycles. (c and d) Examples of small-amplitude stage-structured cycles. The initial biomass
of the replicates is similar.Daphniabiomass is calculated from estimates of density and size structure, using length–
weight relationships measured for the clone used in the experiment. Algal biomass is measured as chlorophylla
concentration. Reproduced from McCauleyet al.(1999), with permission fromNature.
30 DYNAMICS