The metapopulation processes of immigration, emigration and extinction have a prominent role in understanding the population dynamics of single-species (Hanski 1999), pairwise (Ellner et al. 2001) and multispecies interactions (Holt 1997; Bonsall & Hassell 2000). The premise that the persistence of extinction-prone interactions could be enhanced through the inclusion of some spatial processes was acknowledged originally in a number of early studies (e.g. Nicholson & Bailey 1935; Andrewartha & Birch 1954). Generically, increased persistence occurs as habitat subdivisioning and heterogeneity acting at the regional scale effectively reduces the probability of global extinction by allowing rescue of locally extinct patches. However, not until relatively recently has the extent to which space can affect species interactions been more thoroughly explored (Gilpin & Hanski 1991; Hanski & Gilpin 1997; Tilman & Karieva 1997).
For instance, simple predator–prey interactions are known to be locally unstable (Lotka 1925; Volterra 1926; Nicholson & Bailey 1935) and, in certain cases, non-persistent (Nicholson & Bailey 1935). The inclusion of spatial processes was hypothesized initially to increase the persistence of the system (Nicholson & Bailey 1935; Skellam 1951) and demonstrated in a unique series of laboratory microcosm experiments by Huffaker (1968; see also Huffaker, Shea & Herman 1963). The persistence of simple predator–prey interactions was shown to depend on the inclusion of architecturally complex habitats (Huffaker et al. 1963; Pimentel, Nagel & Madden 1963). In fact, Pimentel et al. (1963) argued that laboratory predator–prey microcosms may not be simplistic and the inclusion of habitat complexity (e.g. baffles for restricting dispersal) could clearly affect the persistence of the system. Empirical observations of metapopulation processes in predator–prey interactions have established that dispersal and shifting dynamic patterns are key drivers in predator–prey interactions. Nachman (1991), for example, illustrated that mite predator–prey metapopulations were unstable and non-persistent at the individual plant scale but at the regional, greenhouse-scale systems were maintained through a shifting mosaic of interactions between predator and prey.
More recently, the effects of spatial structure on predator–prey interactions have been extended to assess whether metapopulation processes (local breeding populations, risk of extinction, probability of recolonization, asynchronous dynamics) can influence the persistence of these resource–consumer interactions (Ellner et al. 2001; Bonsall, French & Hassell 2002). For instance, Ellner et al. (2001) have shown that persistence in a mite predator–prey system is influenced more by modification of the predator's search behaviour than the subdivisioning of the habitat into local patches that are accessed only by dispersal. In a host–parasitoid metapopulation, Bonsall et al. (2002) demonstrated that the conditions for metapopulation persistence can be evaluated and showed that the dynamics of this predator–prey interaction were influenced by local demographic processes and habitat structure.
It is well known that populations are influenced by uncertainty or random perturbations. Stochasticity can affect the persistence and dynamics of populations (May 1973; Roughgarden 1975; Lande 1993; Ludwig 1996). In particular, stochastic perturbations acting within a population or across a metapopulation can affect the likelihood of local or global extinction, and understanding how such stochastic processes influences the deterministic population dynamics (Casdagli et al. 1991; Rand & Wilson 1991) remains a focus of contemporary ecological research (Dennis et al. 2001; Grenfell, Bjørnstad & Finkenstadt 2002). Such random perturbations can be manifest into two ways: as demographic or environmental stochasticity.
Demographic stochastic effects depend on the intrinsic uncertainty associated with an individual's reproduction, survival and dispersal, and is most influential in small populations. Essentially, these sampling effects are averaged out as population size increases and Bartlett (1960) showed for a variety of different ecological scenarios how demographic stochasticity can influence the dynamics of single-species, competitive and predator–prey interactions. In a series of developments, these ideas were extended to illustrate how demographic stochasticity (associated with births and deaths only) can affect colonization in island–mainland models of species diversity (MacArthur & Wilson 1967), is likely to be negligible as population size increases (May 1973), has important implications for conservation and species risk assessment (Kokko & Ebenhard 1996) and can lead to Allee effects (Lande 1998). More recently, the role of demographic noise on the dynamics of single-species populations has been thoroughly explored. For example, the dynamics of Tribolium castaneum have been shown to display a range of population dynamic behaviours from stable dynamics through to seemingly chaotic dynamics (Costantino et al. 1995, 1997). Using an age-structured model skeleton, Dennis et al. (2001) illustrated that the dynamics of T. castaneum showed significant departures from the predicted dynamics. These departures could, however, be adequately described by coupling demographic noise and the deterministic age-structured model. Similarly, the effects of demographic noise coupled with non-linear density dependence has been shown to influence the observed dynamics in childhood diseases (e.g. Grenfell et al. 2002). In particular, the predictability of measles dynamics has been shown to depend on the interaction between population size, noise and the underlying deterministic process. Grenfell et al. (2002) suggest that demographic noise can have a major effect on the dynamics of measles even when population sizes remain relatively large.
In contrast, environmental stochasticity refers to randomness imposed on a population or metapopulation by the environment. Principally, these density-independent processes are manifest through fluctuations in the birth rate or in the carrying capacity (Roughgarden 1975; Leirs et al. 1997; Grenfell et al. 1998; Heino 1998). For instance, Grenfell et al. (1998) illustrated how the dynamics of Soay sheep across the St Kilda archipelago are correlated by climatic variabilities and Coulson et al. (2001) extended this analysis to show how age-structure and environmental noise can act concomitantly to lead to variable dynamics in this single-species interaction. More recently, it has been predicted that in relatively simple single-species interactions environmental noise acting on births can lead to sustained oscillations whereas fluctuations in the deterministic system would decay away (Greenman & Benton 2003). Understanding how populations filter this environmental noise (Lundberg et al. 2002; Greenman & Benton 2003) has important implication for realistically interpreting not only single-species but also multispecies interactions. Moreover, the form or degree of correlation in the environmental noise can affect the dynamics of single-species (Dennis et al. 1995), pairwise (Ripa & Ives 2003) and multispecies (Petchey et al. 1999) interactions in counter-intuitive ways by modifying individual species interaction strengths (May 1973).
Stochasticity has, however, many largely unexplored consequences for metapopulation dynamics. It is entirely plausible that the population processes of birth, death, immigration and emigration are all influenced by local and regional stochastic fluctuations, and the effects of stochasticity at the regional scale on resource–consumer interactions could operate in non-intuitive ways. Here, using empirical data from a predator–prey metapopulation, we compare and contrast different forms of noise (demographic, environmental) acting on the dynamics and persistence of a pairwise host–parasitoid interaction. We begin by introducing the empirical system and the statistical methods of model fitting. Here, we emphasize that rather than selecting the most appropriate population model (although this is a important aspect of model fitting) our aim is to evaluate the different forms of stochasticity in a predator–prey metapopulation. In particular, our hypothesis is that demographic noise should be influential within local patches and scale to affect the persistence and dynamics of the regional, predator–prey metapopulation systems. We show that the interaction is influenced heavily by demographic stochasticity; however, this noise is masked at the regional metapopulation scale. The study concludes with a discussion of the effects of environmental and demographic stochasticity on population and metapopulation persistence, dynamics and scaling.