Metapopulation persistence despite local extinction: predator-prey patch models of the Lotka-Volterra type

Abstract

Many arthropod predator-prey systems on plants typically have a patchy structure in space and at least two essentially different phases at each of the trophic levels: a phase of within-patch population growth and a phase of between-patch dispersal. Coupling of the trophic levels takes place in the growth phase, but it is absent in the dispersal phase. By representing the growth phase as a simple presencelabsence state of a patch, metapopulation dynamics can be described by a system of ordinary differential equations with the classic Lotka-Volterra model as a limiting case (e.g. when the dispersal phases are of infinitely short duration).When timescale arguments justify ignoring plant dynamics, it is shown that the otherwise unsrdbk! Lotka-Volterra model becomes stable by any of the following extensions: ( I ) a dispersal phase of the prey, (2) variability in prey patches with respect to the risk of detection by predators,(3) (sufficiently high) interception of dispersing predators in predator-invaded prey patches, and (4) prey dispersal from predator-invaded prey patches. The parameter domain of stability shrinks when the duration of within-patch predator-prey interaction is fixed rather than variable, and when predators do not disperse from a patch until after prey extermination. A dispersal phase of the predator has a destabilizing effect in contrast to a dispersal phase of the prey. When the timescale of plant dynamics is not very different from predator-prey patch dynamics, the Lotka-Volterra predator-prey patch model should be extended to a predator-prey-plant patch model, but this greatly modified the list of potential stabilizing mechanisms. Several of the mechanisms that have a stabilizing effect on a ditrophic model lose this effect in a tritrophic model and may even become destabilizing; for example, the dispersal phase of the prey confers stability to the predatory-prey model, but destabilizes the steady state in the predator-prey-plant model in much the same way as the dispersal phase of the predator destabilizes the steady state in the predator-prey model. Other mechanisms retain their stabilizing effect in a tritrophic context; for example, dispersal of prey from predator-invaded prey patches has a stabilizing effect on both predator-prey and predator-prey-plant models.

Dispersal delays, predator–prey stability, and the paradox of enrichment

“…Another approach uses so called "patch occupancy models," which keep track of the number of habitat patches that are in various states, e. g., empty, or occupied by prey, or occupied by predators. In contrast to our results, Sabelis et al (1991) showed that while the addition of a pool of dispersing prey was stabilizing in a simple patch occupancy model, dispersing predators could be destabilizing. When it comes to the effects of dispersal on predator-prey dynamics, the details of how dispersal is incorporated appear to be important.…”

Metapopulation dynamics of a persisting predator–prey system in the laboratory: time series analysis

“…Sabelis et al (1991) studied the effect of prey and predator dispersal on the dynamics of a simple Lotka-Volterra metapopulation model inspired by acarine predator-prey systems like the one studied here. They found that the dispersal of prey had a stabilizing effect on the dynamics, whereas the dispersal of predators had a destabilizing effect.…”

Can plants betray the presence of multiple herbivore species to predators and parasitoids? The role of learning in phytochemical information networks

“…This may have been the case for diamondback moths, as they prefer to oviposit on plants infested by cabbage white larvae (Shiojiri et al 2002). Such temporary or partial refuges may have an important impact on population dynamics, as they are shown to increase prey density, yet promote the persistence of otherwise unstable one predator-one prey systems of the Lotka-Volterra or Nicholson-Bailey type (Hassell 1978;Sabelis et al 1991Sabelis et al , 2005a, as well as more complex and diverse systems (e.g. Vos et al 2001).…”