2.1 What types of dynamics can be distinguished?

2.2 Dynamics of food web modules

Insights from specific ‘few-species-interaction-configurations’ or modules (Menge 1995; Holt 1997; Bascompte and Melian 2005) of consumer–resource interactions have much increased over the last few decades. For example, we know much more now about resource competition (Schoener 1974; Tilman 1982), mutualism (Oksanen 1988), apparent competition (Holt 1977), indirect mutualism (Vandermeer 1980; Ulanowicz 1997), intra-guild predation (Polis et al. 1989), positive interactions such as facilitation (Callaway 2007), positive (p. 27 ) feedbacks (DeAngelis et al. 1986), regulatory feedbacks (Bagdassarian et al. 2007), trophic cascades (Carpenter et al. 2008) and multiple stable state dynamics (Scheffer and Carpenter 2003). These may all be considered organizational forces that structure food webs, but they may not all be of equal importance. For example, Ulanowicz (1997) makes a strong case for the special importance of indirect mutualism as an organizational force in food webs, as the resulting feedback loops ‘attract’ resources towards them. Other authors, such as Tilman (1982), have emphasized the importance of competition as a key organizational force in ecological communities. Again others, such as Krebs et al. (1999) emphasize the importance of predator–prey interactions in structuring communities. Despite the insights gained into such specific processes, the question remains how such modules together organize into complex interaction webs, and how to address their relative importance.

Food web modules are characterized by the fact that they are small systems (two or three trophic levels) that possess explicit dynamics (Fig. 2.1a–e). With these simple ‘building blocks’, more realistic food webs can be ‘built’ (Fig. 2.1f), which in turn are subsets of the true complexity in trophic interactions found in real ecosystems. For example, Fig. 2.2 shows the network of trophic interactions as found on intertidal sand flats in the Wadden Sea, a soft-bottom intertidal ecosystem with complex trophic structure. This example shows how exploitative competition, food chains, apparent competition and intra-guild predation can operate simultaneously within the same ecosystem. In this, it should be realized that food web descriptions in terms of interaction topology and flows (as in Fig. 2.2) generally capture the long-term averages of organism densities and fluxes. The actual abundances may vary due to external drivers (such as varying weather conditions) and internal dynamics (e.g. limit cycles). To illustrate this point, Fig. 2.3 shows observations of the long-term population dynamics of some of the bivalve species shown in the food web of Fig. 2.2. In this case, winter

(p. 28 ) temperatures are thought to control abundances through their effect on recruitment (Beukema et al. 2001).

Not all modules will be equally important in every ecosystem. For example, ecosystems that are dominated by many species within the same trophic level, such as diverse grasslands, may be strongly structured by exploitative competition. On the other hand, ecosystems such as the marine pelagic zone seem dominated by trophic chains. Bascompte and Melian (2005) recently compared the frequency of different types of modules across natural food webs. They found that apparent competition and intra-guild predation (Fig. 2.1) were generally overrepresented with respect to a suite of null models, while the level of omnivory varied highly across ecosystems.

The relative importance of external forcing versus internal dynamics as causes of dynamics in food webs under natural conditions is still hard to assess, despite a long history of research on the subject (Pimm 1982, 1991; Loreau and de Mazancourt 2008). Various research lines can be distinguished here, depending on their theoretical versus experimental nature, the complexity of the system under study and the level of control of variation in external conditions (exclusion or inclusion of forcing factors). Some theoretical studies have investigated the dynamics of species organized in simple modules (DeAngelis 1992). Several studies have been performed under experimentally controlled conditions, in which the influence of external variation on populations has been mostly eliminated, e.g. as in the study by Beninca (p. 29 )

et al. (2008). Such studies are expected to mostly show dynamics that arise from the internal structure of food webs, and have been performed with both small modules and more complex webs. Other studies have explored the dynamics of interacting species populations under field conditions, which allows the assessment of the importance of external forcing factors. However, there is a necessary trade-off here.

2.3 Internal dynamics in food web modules or simple webs

In theory, consumer–resource interactions consist of two trophic levels that can fluctuate for a long time, but can also lead to unstable dynamics, with the precise type of dynamics depending on model formulation (Fig. 2.4). A good example of a study of a simple consumer–resource interaction is that of the limnetic crustacean zooplankton species Daphnia and its edible algal prey. McCauley et al. (1999) found large- and small-amplitude cycles in the same global environment, i.e. consumer–resource (predator–prey) and cohort (stage-structured) cycles (Fig. 2.5). In cohort cycles, demographic stages (usually thought to be the juvenile stage in Daphnia) are capable of strongly suppressing the other stages (adults) by competing for food. As the suppressing stage matures or dies, a pulse of reproduction or growth follows in the other stage, causing a cycling strongly out of phase (McCauley et al. 1999).

(p. 30 )

(p. 31 )

(p. 32 ) This interaction between this grazer species and its prey can be thought of as an ‘elemental oscillator’, the basic building block for ecological communities (Vandermeer 1994). Leibold et al. (2005) working with a more complex food web, consisting of three grazer species (Daphnia, Ceriodaphnia and Chydorus) and edible algae, hypothesized that the dynamics in such complex food webs can be understood in terms of the simple subsets used by McCauley et al. (1999). The behaviour of these more complex food webs might be understood by thinking of coupled oscillators consisting of many such oscillators with interacting damping and amplifying harmonics (Hastings and Powell 1991). They also found both consumer–resource and cohort cycles. This indicates that interactions of zooplankton and algae in complex systems still consist of the same basic elements – in this case consumer–resource cycles and cohort cycles – and their dynamics can be understood from the dynamics of their component parts. In the study with a more complex marine web consisting of phytoplankton and zooplankton, Beninca et al. (2008) found strong chaotic fluctuations (Fig. 2.6). Species interactions in this food web are indicated as the driving forces. The persistence of this food web despite the great density fluctuations and unpredictability of the abundances is a rarely demonstrated phenomenon. It may also be more common than we think. The constant external conditions used in this study may be an artefact in itself, causing high productivity, leading to a situation that has been called the paradox of enrichment (Rosenzweig 1971). Many other important aspects of this study that distinguish it from real food webs under natural conditions are the absence of higher trophic levels and the exclusion of interactions between organisms and their abiotic environment, e.g. through local nutrient depletion or organism–sediment feedback. Even though isolated modules of species may exhibit chaotic dynamics, this may be highly dampened or even excluded by these effects in natural systems.

2.4 Dynamics enforced by external conditions

In addition to dynamics that arise internally within communities, species populations are also often subject to strong external forcing, e.g. where regional climatic conditions affect local air, water or soil temperature. Ecophysiological differences among species in ability to cope with these changes may result in species-specific responses (Karasov and Martinez del Rio 2007), thus leading to community dynamics under varying external conditions. This external forcing is the key ‘point of entry’ in studying effects of climate change on food webs, but also how toxic pollutants will affect trophic structure and ecosystem functioning. For example, ectotherms (at lower trophic levels) and endotherms (at higher trophic levels) are expected to respond very differently to short- or long-term temperature changes. Surprisingly, although there are good reasons to suspect its importance in natural populations, e.g. in the level of synchrony between species in long-term ecological monitoring (Bakker et al. 1996), environmental forcing has hardly received any attention in the study of consumer–resource interactions, food webs or other interaction webs. There is, however, some relevant theoretical work: a mechanistic-neutral model describing the dynamics of a community of equivalent species influenced by density dependence, environmental forcing and demographic stochasticity. The model shows that demographic stochasticity alone cannot oppose the synchronizing effect of density dependence and environmental forces (Loreau and de Mazancourt 2008). Vasseur and Fox (2007) have shown in their model food web study that the synchronization of dynamics is the result of environmental fluctuations. This synchrony promotes stability, because the maximum abundance of top predators is reduced by the synchronous decline in the density of consumers and synchronous increase in consumer density is changed by resource competition into synchronous decline. These authors conclude that future studies on food web dynamics should take into account the joint action of internal feedbacks and external forcing.

Another example concerns recovery after perturbation. The reaction of a system to a perturbation depends on the size of the ‘basin of attraction’. The basin of attraction is a theoretical measure of the maximal perturbation that the system can absorb without shifting to another state and is often referred to as ‘ecological resilience’ (Peterson et al. 1998; (p. 33 ) Folke et al. 2004). Systems with a high ecological resilience can be seen as particularly stable systems, whereas systems with a low ecological resilience can be seen as unstable systems close to the tipping point into an alternate state. Recent studies have explored whether there are early warning signals for this shift into another state. The slow recovery from perturbations may be a possible indicator of an impending state shift (van Nes and Scheffer 2007).

2.5 Equilibrium biomass at different productivities

Important lessons can be learned from comparing the configuration of food webs (abundances of different species on different trophic levels) under different external conditions. A simple approach that has been used is to compare systems subject to different boundary conditions that impose constraints on their level of primary production. Such differences can be caused by variation in temperature or nutrient input into the system.

This approach can be used to study simple food chains consisting of a predator, a consumer and a resource species. This approach can also be used for simple systems with three levels, or for systems where all species at one trophic level are lumped into ‘trophic species’, under the assumption that the ‘food chain module’ in the system (see Fig. 2.1) strongly overrules the dynamics of the system with respect to other modules (whether this is true is, however, an open question). This approach to simplify systems leads to the concept of trophic cascades. Hairston et al. (1960) and Fretwell (1977) mention this trophic cascade phenomenon in their writings about population regulation, although they did not call the process by this particular name (Morin 1999). Paine (1980) used the term trophic cascade to describe how the top-down effects of predators could influence the abundances of species in lower trophic levels, a concept that was developed further by Oksanen et al. (1981) (Fig. 2.7a). If we increase the length of this trophic food chain by adding one additional trophic level (top carnivores) (Fig. 2.7b), indirect mutualism between non-adjacent trophic levels and a decrease or constancy in the abundance of ‘odd’ levels with increasing productivity appear.

Evidence for top-down trophic cascades is surprisingly scarce, and comes primarily from aquatic systems: stream communities (Power et al. 1985) and lakes (Carpenter and Kitchell 1993). There are few terrestrial examples: Emmons (1987), Terborgh

(p. 34 ) et al. (2006), Marquis and Whelan (1994) and Jefferies (1999). For example, Emmons and Terborgh et al. describe the disappearance of several common species of birds from Barro Colorado Island. The building of the Panama Canal created an island that was too small to sustain large predators, such as jaguars and pumas. Their extinction led to population increases of their prey species. These meso-predators fed on the eggs and young of ground-nesting birds and their increase in numbers was sufficient to wipe out many bird populations.

Another example concerns a terrestrial trophic cascade from a study by Marquis and Whelan (1994). They found strong effects of insectivorous birds foraging herbivorous insects on white oak trees. Birds significantly reduced the abundance of herbivorous insects on the oaks. Netting around some trees caused exclusion of birds from the insects, while other uncaged trees remained available to the birds. Oaks with birds and reduced herbivorous insects had less leaf damage from insects and subsequently had a higher biomass.

A slight modification of simple trophic cascades leads to intra-guild predation (IGP; Polis et al. 1989). This type of interaction can be seen as an extension of a simple predator–prey interaction: the predator also eats some of the consumers, but potentially competes with uneaten consumers as well for a common resource. Spiller and Schoener (1989) studied interactions between predatory Anolis lizards, predatory web-building spiders and their arthropod prey on small islands in the Bahamas. The interaction between lizards and spiders can be described as an IGP interaction, because lizards eat some spiders, but lizards also potentially compete with uneaten spiders for small arthropod prey. There is even an effect on the level of anti-herbivore defence of the dominant vegetation on the islands, Conocarpus erectus or buttonwood (Schoener 1988). On islands without lizards the leaves have trichomes to discourage insect attack; on islands with lizards, leaves are without them.

Summarizing we can state that in small food webs, oscillating consumer–resource interactions are not only predicted by models but also occur in natural systems. In chains of three or more levels trophic cascades are important, but experimental support is limited.

2.6 Dynamics of complex interactions

Food webs are conceptualized by their basic unit of interaction, consumption, and this basic process is oscillatory. When these basic units are connected, the conceptual framework becomes a system of coupled oscillators. This concept generated notable patterns in the theoretical literature as described by, for example, Vandermeer (2004). The conclusion that weak interactions can have strong effects on stabilizing ecosystems (McCann et al. 1998; Neutel et al. 2002) derives from this concept of coupled oscillators. According to May (1973), measures of interaction strength are the elements in a community matrix at equilibrium, which represent the direct effect of an individual of one species on the total population of another species at equilibrium. These results suggest that average interaction strength should be weak in species-rich, highly connected systems. The fundamental question is whether the configuration or distribution of interaction strengths within food webs is important for questions of community stability. de Ruiter et al. (1995) linked the differing approaches by deriving values of the matrices from empirical observations (Fig. 2.8). The data come from a terrestrial food web study, the Lovinkhoeve Experimental Farm (Integrated Management) in The Netherlands. This study indicates that the patterning of interaction strengths is essential for system stability. However, there is no direct correlation between interaction strength and stability. Weak interactions may be strong in terms of their stabilizing effects to the community. Further, it has been shown that long trophic loops contain relatively many weak links increasing food web stability because they reduce maximum loop weight, thus reducing the amount of intraspecific interaction needed for system stability (Neutel et al. 2002) (Fig. 2.9).

2.7 Conclusions

The types of dynamics leading to long-term co-occurrence of species in communities can be indicated as stable equilibria, alternate equilibria, stable limit cycles and chaotic dynamics. Although much of the attention to this subject is theoretical, empirical data are increasingly reported, although (p. 35 )

mostly still for experimental communities. For field studies, the life span of the organisms involved is often too long compared with the length of the study to unambiguously evaluate stability, but recent studies deal with that problem. Insights gained from the dynamics of specific food web modules have increased over the last few decades. But still the question remains how such modules are organized together into complex interaction webs, and how their interplay changes their dynamics as observed in isolated modules. The relative importance of external forcing versus internal dynamics for causing dynamics in food webs under natural conditions is still hard to assess. The study of the effects of climate change and toxic pollutants on food webs makes it necessary to concentrate in the future on the interplay of internal feedbacks and external forcing. Interesting lessons can be learned from the comparison of the configuration and dynamics of food webs under different external conditions, e.g. different temperatures that lead to different primary productivity. Where strong evidence for the existence of trophic cascades initially came from aquatic systems, terrestrial examples are now known. New studies on the dynamics of complex interaction webs have concentrated on the consequences of specific patterning of interaction strengths (p. 36 ) across the web for the stability of the overall system. Using classic stability analysis with Lotka–Volterra interaction terms, soil food webs with long trophic loops appear to contain relatively many weak links, which increases their stability. Future studies of more webs and with different modelling frameworks are required to show the generality of this phenomenon.

Acknowledgements

We thank Dick Visser for drawing Figure 2.2.