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Wednesday, April 16, 2008

Can Host-Parasitoid Metapopulations Explain Successful Biological Control? - Statistical Data Included

Ecology, August, 2000 by John M. Kean, Nigel D. Barlow


Abstract. Host--parasitoid models with host density dependence were used to investigate the features that maximize biological control success. Relationships were derived in nonspatial models between parasitism level and host suppression at equilibrium. Spatially explicit metapopulation models could produce higher host suppression, and over a larger range of parameters, than nonspatial models. However, persistence of the metapopulation interaction depended critically on the starting conditions; for a realistic biological control starting point, a maximum mean suppression of 84% was compatible with persistence, although much greater host suppression could be achieved from less realistic initial conditions. This result was unchanged by spatial stochasticity. Overall metapopulation dynamics, as well as those of individual subpopulations, were best modeled by random parasitoid attack, even when the true attack behavior was otherwise. Fitting such models suggested that an independent estimate of host carrying capa city may be required when estimating host rate of increase from subpopulation data within a host--parasitoid metapopulation.

Key words: biological control; coupled map lattice; dispersal; metapopulation dynamics; persistence; stability; suppression.


Parasitoids introduced for classical biological control may often cause a permanent reduction of 90% or more in field populations of their hosts (Beddington et al. 1978). This has been interpreted to mean that a successful biocontrol agent drives its host to a low stable equilibrium. However, conventional simple models, lacking either implicit or explicit spatial heterogeneity of risk, cannot reproduce stable host reductions of [greater than]60% (Beddington et al. 1978).

As a mechanism for stability in host--parasitoid models, implicit spatial heterogeneity was an early suggestion (Varley 1947, Bailey et al. 1962, Hassell and Varley 1969). Beddington et al. (1978) showed that it also provided the most likely mechanism for high host suppression. Later, explicitly spatial metapopulation models (Levins 1969, Hanski and Gilpin 1991, Hanski and Simberloff 1997) showed that dispersal between subpopulations may allow long-term persistence of an otherwise non-persistent interaction, though the stability per se of the equilibria was unaffected (Reeve 1988, 1990, Rohani et al. 1996). Even as few as two subpopulations linked by dispersal may allow persistence of unstable host-parasitoid models (Adler 1993). This result relies on asynchrony in subpopulation dynamics (Crowley 1981), so that local population extremes may be buffered by dispersal to and from surrounding localities. It also demonstrates that stability is not a necessary condition for a persistent host--parasitoid interactio n, so long as the system is divided into discrete, semi-independent subpopulations (Murdoch et al. 1985).

Long-term persistence of a locally unstable host--parasitoid metapopulation was demonstrated by Allen (1975) and Hassell et al. (1991), the latter emphasizing the remarkable range of dynamic behavior emerging from the simplest host--parasitoid metapopulation models with local dispersal. Their demonstration of self-organizing spatial patterns in such systems led to considerable subsequent research and debate (e.g., Comins et al. 1992, Sole et al. 1992, Hassell et al. 1993, 1994, Rohani and Miramontes 1995, Comins and Hassell 1996, Ruxton and Rohani 1996, Rohani et al. 1997, Sherratt et al. 1997, Wilson and Hassell 1997).

Here, we consider how realistic these spatial patterns are, and whether such behavior can occur in more realistic models which include local host density dependence. In terms of biological control, we investigate whether persistence is possible with high overall host suppression in a metapopulation context, and what form the overall model for such a metapopulation takes. More generally, we ask whether nonspatial models may be sufficient to capture the dynamics of a spatial world, and if so, how? Is it necessary to understand the behavior of a population in space in order to understand and predict its behavior in time?


Few host--parasitoid models have dealt in a general way with the effects of explicit host density dependence. We describe general local and metapopulation models, and look in particular at the effects of host density dependence, handling time, and aggregated attack.

Local dynamics

We consider three general models for the local dynamics of host and parasitoid populations, differing in the ordering of density dependence and parasitism in the life cycle of the host. In all cases it is assumed that host larvae (N) are the stage of interest; therefore, host reproduction is always the last step in the modeled life cycle. We assume that each adult host produces a constant number of offspring, [lambda], while a parasitized host gives rise to exactly one new parasitoid in the next generation, and that all host density dependence is in the mortality term. In model 1, density dependence acts after parasitism:

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