Global Persistence Despite Local Extinction in Acarine Predator-Prey Systems: Lessons From Experimental and Mathematical Exercises

Empirical studies show that local populations of predator and prey mites on plants frequently become extinct, because of both intrinsic local dynamics and traveling waves of predators that overwhelm local prey populations. Despite frequent local extinctions, the predator-prey metapopulation persists and exhibits either large-amplitude cycles or small-amplitude aperiodic fluctuations. This chapter reviews how our understanding of predator and prey metapopulation dynamics in mites has been advanced by comparing laboratory experiments with both a "baseline" model and simulation models that break down the assumptions of the "baseline" model. The most critical assumptions are that: 1) habitat structure matters, but spatial configuration does not; and 2) local dynamics of prey and predator are deterministic, fully determined by the first colonization and always end in prey extinction after a single oscillation, followed by predator dispersal. The "baseline" model predicts multiple stable states, either with or without predators, when there are many patches that harbor only few prey. Stable predator-prey cycles surface, however, when the number of patches is low and can harbor many prey. Virtually all acarine predator-prey metapopulation experiments published to date have been done under the latter conditions and show metapopulation-level cycles that are either periodic with large amplitudes or aperiodic with small amplitudes. Simulations suggest the large amplitude cycles arise when survival in the dispersal phase is low, whereas the small amplitude cycles surface when survival in the dispersal phase is relatively higher, yet low enough to allow persistence of predators and prey at the metapopulation level. The "baseline" model is further analyzed to detect which factors cause persistence or extinction at the metapopulation level. Persistence was promoted by prey dispersal from predator-occupied patches, time spent by prey in the dispersal phase, interception of predators in predator-occupied patches, and heterogeneous colonization risks among patches. Extinction is promoted by predator dispersal after extermination of prey in a patch and time spent by predators in the dispersal phase. The relative importance of all of these factors is yet to be determined. Moreover, the relevance of spatial patterning of predator-prey interactions is much debated. Model-based simulations to analyze an experimentally established time series suggest that what matters to persistence is reduced discovery of prey patches, not the spatial configuration per se. However, the last word has not been said about this, since spatial predator-prey models suggest configuration to play an important role. The "baseline" model is not evolutionary robust, in that its structure arises from individual traits that are not favored by natural selection. It is based on the assumption that first colonization is the single determinant of local predator or prey dynamics and that predator dispersal is delayed until after prey extermination. Delayed predator dispersal cannot evolve, however, when only the initial colonization of prey-only patches by a predator is taken into account. It also does not evolve in simulations with a model, parameterized for the acarine predator-prey system, in which not only the first colonization but also subsequent invasions are taken into account. However, observations on the behavior of field-collected predators show that delayed dispersal is the rule rather than the exception. We argue that delayed predator dispersal prevails in the field because local populations are subject to catastrophes which give predators little control over the exploitation of their local prey population. Hence, natural selection in the field will favor predators that exploit the local prey population as fast as possible and delay dispersal until after prey extermination. The important lesson to be drawn from this review is that the insights came from comparing a suite of models that all differed in key assumptions from a comprehensive yet formal "baseline" model and from testing these models against laboratory experiments. Understanding the complex dynamics observed in acarine predator-prey metapopulations requires more than spotting an arbitrary caricatural model with a dynamic behavior that corresponds qualitatively to that of the biological system.