The empirical cases presented above indicate the necessity to merge ‘food web metacommunity’ and ‘landscape ecosystem’ ecology into a single framework for the study of spatially structured ecosystems. Such a framework does exist: the metaecosystem concept (Loreau et al. 2003) consider all ecosystem compartments in simple patch-based models. Here we illustrate this framework using two theoretical studies that show how novel insights can arise when we simultaneously consider the movements of traits and materials. These two examples are only meant to illustrate that insights can be gained by such efforts. Future work can and should be performed in more realistic and comprehensive ways (e.g. with a more realistic perspective on trophic interaction, spatially explicit formulation, etc.).
Metaecosystems as extended interaction matrices
In the first example, we take a general, simplistic approach in which we combine spatial movements of traits or materials with classical approaches based on ‘interaction matrix models’ previously used to evaluate the stability of large complex systems (May 1972; Kokkoris et al. 2002). This model links the expected dynamical properties of an ecosystem with the distribution of interaction coefficients among species pairs (values of the interaction matrix components) and the number of species involved (size of the interaction matrix). We show that the dynamical properties of a metaecosystem, described as an interaction matrix involving trophic interactions and dispersal, depend on total system materials.
Consider a large closed system consisting of populations of different agents (species or abiotic material stocks) which interact either through consumption (interspecific interactions) or movement (intraspecific interactions). Let ni be the biomass of population i. Under the Lotka-Volterra formulation of predator–prey interactions, the rate at which population j biomass is converted into population i biomass through predation is proportional to ni, and noted niaij, where aij is the rate at which an individual predator from population i preys on preys from population j (this rate summarizes attack rate and energy conversion efficiency). Similarly, the rate at which population j biomass is converted into population i biomass through movements is noted dij (this only applies between populations of the same agent). Following this simple model and neglecting processes other than predation and migration, the dynamics of agent i biomass are governed by:
where Ai denotes the set of populations interacting with population i (either preys, aij > 0, or predators, aij < 0) and Mi is the set of populations exchanging migrants with population i, including population i itself as a donor of migrants to other populations (dij > 0 for i ≠ j, and dii < 0).
When the system is assumed closed, the sum of its components’ biomass n = ∑ ni is constant, and it is more useful to consider the dynamics of pi = ni/n which is the proportion of total system’s materials contained in population i. If the metacommunity consists of a single patch (i.e. all dij coefficients are zero), eqn 1 can be time-scaled by T = nt, so that the dynamics of pi are given as:
Apart from the typical time of the dynamics (which is scaled to n), nothing in eqn 2 is bound to depend on total system’s biomass. In other words, dynamical properties of the system governed by eqn 2 will only depend on the interaction coefficients among species, i.e. on traits only.
By contrast, if we consider a system in which some populations harbour the same species and exchange migrants, applying the same time-rescaling to eqn 1 leads to the following dynamics:
In eqn 3, total metacommunity biomass n plays an explicit role: the bulkier the system, the more important predation traits are over migration traits to determine the dynamical properties of the system. Thus, when total biomass is very low, individuals from all species are scarce, and predatory interactions (which occur with a rate proportional to the product of predator and prey abundances) are rare compared with the constant flow of migrants among populations of the same species. By contrast, when total system’s biomass is high, predatory interactions occur more often and tend to act on the system more quickly than migration. This phenomenon is similar to the impact of constant prey immigration on the stability of the Rosenzweig–MacArthur model of predator–prey interactions (Murdoch et al. 2003). The contribution of constant prey immigration to system dynamics is more important at low prey density (i.e. low biomass) than at high density, thus causing an indirect density-dependence of the prey and stabilizing system dynamics.
This simplistic model highlights one simple fact emerging in spatial food webs: when interactions between populations have different degrees of dependence (here, predation rate scales with predator abundance while migration rate is constant), total biomass influences system dynamics. More precisely, interactions that have a higher degree of dependence on populations’ biomass are more important when total biomass is high, whereas simpler interactions are more important when system’s biomass is low. It is worth mentioning that, besides favouring migration over predation (a deterministic result), low system biomass will also tend to make all species rarer, and thus to make stochasticity more conspicuous in population dynamics (e.g. Gurney & Nisbet 1978). Because our model is overly simplistic on some aspects (e.g. no mortality terms, functions for interactions were assumed linear), the generality of our conclusions may be questioned, and we hope future models will do. However, the methodology behind our model – considering separate populations for the different agent types and sites, rescaling equations, and comparing trophic interactions with movement interactions – highlights the potential for new insights coming from considering metaecosystems.
Emergent effects of material transports on patch dynamics and persistence
Of critical importance to the metapopulation and metacommunity frameworks is the patch dynamics perspective (Hanski & Gilpin 1997; Leibold et al. 2004). Central to this perspective is the idea that a species persists in a region despite local extinctions, given that the colonization rate from occupied patches is larger than the extinction rate. The dynamics of spatial occupancy (the proportion of occupied patches) were first formalized by Levins (1969) as follows:
where c is the colonization rate and m is the extinction rate. In this context, the metapopulation persists provided that c > m. This model captures the essential aspects of metapopulation dynamics, and it has also been extended to communities (Tilman 1994; Calcagno et al. 2006) and food webs (Holt 2002). Given a trade-off between competitive ability and colonization rate, such spatial dynamics allow many species to coexist on a uniform landscape (Tilman 1994; Calcagno et al. 2006). The patch dynamics perspective also provides an interesting explanation for the limitation of food chain length and the different slopes of species area relationships of prey and predators (Holt 1997a, 2002).
The patch dynamics perspective is solely based on exchanges of traits. There is no explicit accounting for the amount of material/individuals dispersing between patches. It does not matter how many seeds reach an empty patch as long as there is at least one of them. One feature of this model is that colonization rate (c) is independent of landscape properties. It does not consider for instance that the colonization rate into a small patch having a large perimeter/area ratio should differ from the one of a large patch (Hastings & Wolin 1989). It does not consider either that nutrients and energy could move between patches, having an effect on their local properties. In a disturbed forested landscape for instance, biomass such as leaves, twigs and branches fall from forested areas to canopy gaps, thereby increasing productivity of the newly disturbed locations. Animals may also move nutrients between empty and occupied patches as they forage, like large browsers transporting nutrients when they feed in recently disturbed forest areas and defecate in closed canopy forests (McNaughton et al. 1988; Seagle 2003).
In a disturbed landscape, the difference in productivity between empty and occupied patches influences spatial nutrient flows (Gravel et al. 2010a). On the one hand, nutrient consumption in occupied patches locally reduces the inorganic nutrient concentration relative to empty patches, making them sinks for the inorganic nutrient. On the other hand, biomass (either dead or alive) mostly flows from occupied to empty patches. Nutrients are thus flowing in both directions and the relative importance of inorganic vs. organic nutrient flows determines whether occupied patches act as sources or sinks (Gravel et al. 2010a). Even if the landscape consists of a single habitat type, nutrient dynamics create a strong spatial heterogeneity in resource distribution.
The balance between the different nutrient flows is influenced by spatial occupancy and affects biomass production. For instance, if only detritus are exchanged between patches (e.g. through leaf dispersal), then the amount received in empty patches should increase with spatial occupancy because there is higher regional production, impoverishing the occupied patches. The local biomass B should thus increase curvilinearly with spatial occupancy p when the net flow of nutrients goes from occupied to empty patches, or alternatively decreases when nutrients flow in the opposite direction. Consequently, if the reproductive output in a patch depends only on local biomass production, the effective colonization rate should depend on spatial occupancy and spatial nutrient flows. Gravel et al. (2010a) modified Levins’ model to introduce the effect of nutrient flows on patch dynamics. Patch dynamics were described by:
where the effective colonization rate c′ is proportional to the average local biomass, B, which is a function of spatial occupancy, i.e. c′ = cB(p). This modification creates a strong feedback between local and regional dynamics. The persistence and the equilibrium spatial occupancy are enhanced when nutrients flow from empty to occupied patches because higher biomass owing to the nutrient redistribution yields higher regional level propagule production. These essential descriptors of metapopulation properties become a complex function of spatial nutrient flows and local ecosystem properties such as nutrient uptake efficiency and recycling rate.
This slight modification of Levins’ model has several, often counter-intuitive, consequences on community assembly, illustrating the importance of accounting for both trait and material flows in spatial food web models. The local–regional coupling studied by Gravel et al. (2010a) showed that positive and negative indirect interactions arise between primary producer populations owing to spatial nutrient flows. Plants in this landscape are first limited at the very local scale, as they need enough nutrients to maintain a viable population (R* minimal resource requirement, see Tilman 1982 for details on resource limitation theory). When detritus have a higher diffusion rate than nutrients, the net flow of nutrients goes from occupied to empty patches, enriching them to the benefit of the good colonizers arriving first. This local enrichment could facilitate the establishment of a weak competitor with low resource uptake ability (it raises nutrient levels above the R*). Plants are also limited by their regional dynamics, and the enrichment to empty patches increases their propagule production (because of higher biomass). Interestingly, this nutrient redistribution may also facilitate the persistence of a strong competitor/poor colonizer when the weak competitor/good colonizer occupies the landscape first. The persistence of some species may thus rely on the presence of other ones, suggesting that habitat-driven extinctions can trigger cascading extinction events in landscapes characterized by nutrient flows linking local and regional dynamics. The difference between predictions from trait-based models of patch dynamics and this nutrient-explicit model illustrates how integrating ecosystem functioning and spatial population biology leads to novel insights.