Relating food web structure to resilience, keystone status and uncertainty in ecological responses

Abstract

Food webs often include substructures that occur in much higher numbers than would be expected in random networks. These are referred to in the literature as network motifs. Here we explore how feedbacks within the most common food web motifs influence their responses to external factors such as environmental change or harvesting of species. We have used qualitative modelling approaches to demonstrate that simple three‐ and four‐member motifs that include a closed feedback loop can exhibit a diverse range of qualitative responses, some of which are non‐intuitive. The same outcomes are demonstrated to be emergent behaviors of larger food webs represented in complex ecosystem models. The sensitivity of ecological responses to small differences in food web motifs underlines the broader importance of structural uncertainty in ecological models. It is also argued that the resilience of species and their keystone status may be strongly influenced by their ecological role within particular motifs. Examples are provided from fisheries off southeastern Australian, where the slow recovery rates of some species have not previously been explained.

Introduction

Many food webs are highly interconnected, implying that wide ranges of population responses are possible. This makes predicting an ecosystem's response to change particularly challenging. While we can respond to this challenge with models of increasingly complexity, our ability to understand their full range of responses and explore the associated model structural uncertainties is limited (Grimm 1994, Metcalf et al. 2011). This issue is compounded when we consider that the structure of food webs can evolve through time in response to environmental or other external influences (e.g., O'Connor et al. 2009). An important step in addressing these issues is to better understand the role of key substructures within the broader trophic network.

Previous studies have identified substructures that occur at much higher numbers than would be expected in random networks. These are referred to in the literature as network motifs (Milo et al. 2002). Because the number of substructure types increases exponentially with the number of species (or functional groups), interest has focused on motifs limited to three or four members. The simplest three‐member motifs are commonly referred to in the literature as the simple food chain (SFC; Fig. 1a–c), exploitative competition (EC; Fig. 1d–e) and apparent competition (AC; Fig. 1f–g). From seven published terrestrial and aquatic food webs (Williams and Martinez 2000), Milo et al. (2002) found that the most over‐represented three‐member motif (compared to a random network) was SFC.

Common three‐member motifs that do not include closed feedback loops: simple food chain (SFC, top row); exploitative competition (EC, middle row); and apparent competition (AC, bottom row). The columns correspond to perturbations applied at different trophic levels (lower, mid or upper). Qualitative responses to these perturbations determined from loop analysis are indicated by shading. All responses reverse if the sign of the perturbation is changed from negative to positive. Note that in addition to the predator‐prey interactions shown between groups, each group also had a negative self‐effect (i.e., density dependence) that is not explicitly shown but was important for the system's stability.

The most over‐represented four‐member motif identified by Milo et al. (2002) involved two mid‐trophic species with a common predator and a common prey (Fig. 2a–c). This structure combines EC (mid and lower trophic groups) and AC (mid and upper trophic groups), and we refer to it here as exploitative/apparent competition (EAC). It differs fundamentally from the previous motifs in that the structure includes a closed feedback loop, which can have important implications for the dynamical response of the system. Closed feedback loops can also form within three‐member motifs, which in an ecological context correspond to omnivory (Fig. 2d–f). While omnivory has been studied quite extensively (e.g., Tanabe and Namba 2005, Stouffer et al. 2007, Bascompte 2009), when considered in isolation it is only those systems in which the mid‐trophic group outcompetes the omnivorous intra‐trophic group that are stable (e.g., Holt and Huxel 2007, Kondoh 2008).

As in Fig. 1 for common three‐ and four‐member motifs that include closed feedback loops: combined exploitative/apparent competition (EAC, top row); omnivory (middle row); and intraguild predation (IGP, bottom row). The columns correspond to perturbations applied at different trophic levels (lower, mid, intra or upper).

Focusing on the five largest food webs compiled at the time, Bascompte and Melian (2005) identified a second over‐represented four‐member motif, obtained by adding an upper trophic group to omnivory (Fig. 2g–j). Following Bascompte and Melian (2005) we refer to this motif as intraguild predation (IGP), while acknowledging that this terminology is sometimes used synonymously with omnivory (e.g., Holt and Huxel 2007, Kondoh 2008). Because IGP encompasses all of the other common substructures represented in Figs. 1 and 2, its dynamical response may be influenced by a larger number of feedback loops. It is also of particular interest in the marine realm, where some of the Earth's most productive ecosystems revolve around pelagic interactions involving krill (lower trophic), small pelagic fish (mid‐trophic), squid (intra‐trophic) and larger predators such seabirds or mammals (upper trophic) (e.g., Ainley et al. 1991).

Previous studies have demonstrated that particular trophic motifs form the building blocks of many larger trophic networks, and are persistent structural features of these networks (Stouffer and Bascompte 2010). However, questions remain as to whether the dynamical responses of individual motifs are retained when they are part of a larger food web (Brose et al. 2005), and whether these responses can dominate the broader food web response. For example, particular motif structures may support species in keystone roles (i.e., relatively low biomass species that strongly influence the structure and dynamics of the broader ecosystem; Paine 1995, Power et al. 1996). This would provide a conceptual link between motifs and topological keystone species traditionally identified through network indices (Jordan et al. 2006, Vasa and Jordan 2006).

Here we use qualitative network models to explore the range of potential trophic motif responses. We then use a fully quantitative model of a large marine ecosystem to demonstrate that these motif responses can persist within a larger food web that varies in space and time. The potential for relating these responses to population and community characteristics such as resilience and keystoneness is then explored.

Methods

Network motifs and qualitative modelling

As in previous studies, our focus here is on motifs with four or less members. Apart from the practical need to limit the total number of motif structure types, small motifs have the advantage that their potential responses can be determined qualitatively (i.e., whether groups increase or decrease) from the trophic structure itself without detailed knowledge of interaction strengths. This can be achieved using qualitative network modelling approaches (Levins 1974, Dambacher et al. 2003, Ramsey and Veltman 2005). Loop analysis begins by defining the system structure in terms of its key dynamical components and interactions between them, which can be represented in the form of signed digraphs (Figs. 1 and 2). Interactions are expressed qualitatively in the form of positive or negative influences on other components. Its structure can then be mathematically analyzed (loop analysis) to determine its linear stability, its predictability, and its qualitative response (increase, decrease, or neutral) to a sustained perturbation to any of the system components (Levins 1974). As well as being restricted to purely qualitative predictions, the analysis assumes that the system remains near equilibrium and therefore does not capture temporal propagation of responses through the system or potential transitions to new states with differing components or interactions.

The signed digraph defines a matrix of interactions (i.e., the community matrix) that can be used to predict the sign of the response of each system component to a sustained change (by calculating the adjoint of the community matrix; Levins 1974). In many instances, the sign of the predicted responses is the sum of both positive and negative feedback loops. The response sign is then ambiguous and further analysis is required to resolve it. Ambiguities can be identified by calculating an index called the weighted predictions, which is essentially the net feedback loops (positive and negative) divided by the absolute number of feedback loops for each prediction (Dambacher et al. 2002). If this quantity equals one, then all the feedbacks are driving the response in the same direction and the result will be the same irrespective of the relative strengths of the feedbacks (i.e., no ambiguity). Dambacher et al. (2003) further showed that we can have a relatively high level of confidence in the sign of the response if the weighted prediction is >0.5. However, if the weighted prediction is <0.5 then the prediction is likely to be unreliable. Clearly the latter condition becomes increasingly likely as the system is made more complex and the absolute number of feedback loops increases. Indeed, we will demonstrate that this condition is common even for relatively simple motifs that include closed feedback loops.

Whole of ecosystem modelling

Because many ecosystems are highly interconnected, the most challenging task in developing useful qualitative models is identifying the few interactions that dominate the response of the larger system. Here we have used the responses of a calibrated and extensively published ecosystem model to test if the theoretical motif responses persist in the more realistic context of a complex (model) ecosystem and, if so, whether these responses are quantitatively significant at the broader ecosystem level.

The quantitative model is based on Atlantis: a spatially resolved end‐to‐end marine ecosystem model encapsulating extensive physical, biogeochemical and dietary data within a single nutrient‐conserving framework (Fulton et al. 2004). Solutions can be computed over time on any grid of polygonal cells with multiple vertical layers. The most widely tested and utilised implementation of this model is Atlantis South‐East (Atlantis‐SE). It covers 3.7 million square kilometers of continental shelf, slope and open ocean waters surrounding southeastern Australia (Appendix: Fig. A1) and has been comprehensively described by Fulton et al. (2007). Atlantis‐SE was originally developed to explore alternative integrated management solutions for southeast Australian fisheries and has had ongoing testing, refinement and calibration through a diverse range of applications related to fisheries, conservation and climate change (Fulton et al. 2004, 2005, Worm et al. 2009, Branch et al. 2010, Fulton 2010, Smith et al. 2011).

Physical exchanges between model cells in Atlantis‐SE were estimated using outputs from a high‐resolution global ocean model (Schiller et al. 2008) while initial and boundary conditions for nutrients (nitrogen and silica) were taken from seasonal climatology (Condie and Dunn 2006). The model included 59 biological groups, which were either composite functional groups, or single species groups for the dominant fisheries target species (Appendix: Table A1). The conditions used to aggregate species into composite functional groups were that they had comparable physiological rate constants and similar predators and prey (Gardner et al. 1982, Fulton et al. 2003). Most of the invertebrate groups were represented using biomass pools, while cephalopods, prawns and vertebrate groups were presented as age‐structured stocks. In addition to these living biological groups, pools of ammonia, nitrate, silica, carrion, and labile and refractory detritus were also represented dynamically.

While some previous applications of Atlantis‐SE have included fully dynamic fisheries, a simple fishing mortality term was sufficient for the current study. The fishing mortality of fish, cephalopods and crustaceans from commercial fisheries was incorporated using average daily catch values from annual catch statistics from 1990–2004 by both federal and state fisheries (e.g., Lyle et al. 2004, Smith and Wayte 2005). For fish and cephalopods, these catches were distributed across cohorts above a specified age‐class so as to account for the size selectivity of various fishing gears.

Within a broad set of possible trophic links (Appendix: Fig. A2), diets in Atlantis‐SE were free to vary dynamically in space and time, allowing for both ontogeny and dietary switching. The full set of possible links was analyzed using an algorithm (see Supplement) that checked the links of every species and functional group in the model and identified those that matched any of the motif substructures in Figs. 1 and 2. The algorithm also computed simple network statistics such as the total number of links. The size and complexity of the diet matrix (including explicit representation of many juvenile groups) resulted in a very large number of substructures or motifs. We focused mainly on the most complex of the motifs (IGP), which contained all the other common motifs as substructures. The IGP motifs were first ranked according to the strength of their weakest interaction (based on proportion of diet). The top 100 were then filtered to exclude interactions that were never realised in the dynamical model runs.

There were three constraints on predation applied during runtime that restricted the number of trophic interactions realised in the model to a small subset of the potential interactions represented in the dietary matrix: (1) predator and prey needed to spatially coexist (geographically and by depth); (2) any habitat requirements for successful predation needed to be satisfied; and (3) the relative sizes needed to allow predation (i.e., gape limitations applied). As is generally the case for empirical food webs (Stouffer et al. 2007), these prey selection mechanisms determined the emergent structural properties of the food web.

Analysis of outputs from a status quo model run (defined below) indicated only 26 of the previously identified top 100 potential interactions were realised. The previous ranking (in order of the minimum proportion of their diets corresponding to any of the motif links) was then applied to these 26 motifs. This ensured that the study focused only on trophic interactions that were important for the species or groups involved.

We began the Atlantis‐SE model simulations at 2005 biomasses and fishing levels and projected the model forward for 30 years. The 2005 biomasses and age structures were taken from longer runs that had been tuned to produce observed historic catches without extirpation of any group (Fulton et al. 2007). A ‘burn‐in' period of 10 years was run with the 2005 fishing mortalities, which was sufficient for transient fluctuations generated in the lower trophic levels to decay.

Results from the ranking of IGP motifs (presented below) indicated that a small number of groups were involved in many of the top motifs. While some of these groups corresponded to individual species with limited distributions, the broader squid and small pelagic fish groups were both highly ranked and of relevance to systems globally. Model scenarios were therefore designed to understand the trophic responses of these two functional groups. These scenarios used fishing as a convenient driver to explore system responses. However, there is no suggestion that the scenarios were related to any current or planned fisheries strategies.

The three scenarios were defined as follows:

1. Status‐quo scenario: 2005 fishing levels continued through to the end of the 30‐year projection period on all groups except small pelagic fish, which were not fished.

2. Small pelagic fishing scenario: as in scenario 1 with annual fishing mortality on small pelagic fish increased from 0% to 15% (nominally corresponding to the estimated maximum sustainable yield or MSY).

3. Squid extirpation scenario: as in scenario 2 with fishing mortality on squid increased from 25% to 75%.

The most significant impacts of scenarios 2 and 3 on biological groups were identified by dividing the average biomass of each group over the final five years (to account for inter‐annual variations) by the same quantity from the status‐quo scenario.

Results

Qualitative responses

Responses of all the previously identified motifs to perturbations applied on lower, mid‐ and upper trophic levels have been estimated using loop analysis. Both the sign of the response (increasing, decreasing or potentially either) and the level of certainty (certain if weighted prediction is equal to 1.0; likely if weighted prediction is >0.5; or uncertain if weighted prediction is <0.5) are provided for each case (Table 1, Figs. 1 and 2).

The adjoint of the community matrix for exploitative/apparent competition (EAC), omnivory and intraguild predation (IGP) shown in Fig. 2.

In the absence of any closed feedback loops, the qualitative responses of SFC, EC and AC were all certain (weighted prediction = 1.0) and easily interpreted. In the case of SFC, the adverse effect of a negative perturbation cascaded up through the mid and upper trophic levels as typified by bottom‐up control (Fig. 1a). Application at the mid‐trophic level produced a middle‐out (wasp‐waist) response with the lower trophic group increasing and the upper trophic group decreasing (Fig. 1b). Negative perturbation of the upper trophic level produced a top‐down response with the mid‐trophic group increasing under reduced predation and the lower trophic level decreasing under increased predation (Fig. 1c). EC also exhibited a simple bottom‐up control (Fig. 1d), while AC exhibited top‐down control (Fig. 1g). However, when the perturbation was applied at a trophic level with two parallel groups, the second group showed a counter response to the first with top‐down and bottom‐up control operating on opposite sides of the two motifs (Fig. 1e, g).

The existence of closed feedback loops within the trophic structure introduced a diversity of potential responses (Fig. 2). A negative perturbation applied to the lower trophic group of EAC generated a bottom‐up response (Fig. 2a) with substructure responses consistent with those of SFC (Fig. 1a) and EC (Fig. 1d). However, additional feedback pathways introduced uncertainty into the responses of both mid‐trophic groups (Fig. 2a), reflecting the potential for a top‐down response to dominate one side of the motif. When the perturbation was applied to one of the mid‐trophic levels of EAC, the second mid‐trophic group always showed a counter response (Fig. 2b) as found for EC (Fig. 1e) and AC (Fig. 1f). Under these conditions the responses of both the lower and upper trophic levels of EAC were uncertain. When the upper trophic level was perturbed there was a top‐down response consistent with SFC (Fig. 1c) and AC (Fig. 1g) and the mid‐trophic responses were again uncertain.

Omnivory exhibited an even more complex range of responses (Fig. 2d–f). While the qualitative responses of two of the groups were certain, the response of the third group was always uncertain with equal numbers of positive and negative feedbacks. The response of this third group is therefore entirely dependent on the relative strengths of its links to the other two groups. If one of these links is assumed to dominate (so the other is removed) then one of the other three‐member motifs is recovered (Fig. 1) and the response becomes unambiguous. More importantly, omnivory can result in less intuitive responses. For example, a decline in the lower trophic group can potentially result in an increase at the mid‐trophic level due to the influence of an intra‐trophic group (Fig. 2d).

The qualitative responses of IGP were similar to those of omnivory (cf. 2d–f with 2g–i). However, with the inclusion of an upper predator, the number of IGP feedbacks was much higher (Table 1), so that there were very few qualitative responses that were certain and a number that were uncertain with equal numbers of positive and negative feedbacks (Fig. 2g–j). A negative perturbation applied to the mid‐trophic level of IGP (Fig. 2h) corresponds to the example mentioned previously involving krill (lower trophic), small pelagic fish (mid‐trophic), squid (intra‐trophic) and larger predators such seabirds or mammals (upper trophic). While the qualitative response of the corresponding SFC (without squid) is certain for all groups (Fig. 1c), the only certain response of IGP is the decline of small pelagic fish (Fig. 2h).

Quantitative ecosystem responses

We begin the analysis of the Atlantis model results by deriving some of the network properties of the Atlantis‐SE diet matrix. However, it should be recognised that these statistics relate to the structure of the theoretical diet matrix and additional analysis was required to determine if these potential interactions were realised in the dynamical simulations. The number of directed trophic links in the diet matrix was L = 723, so that the average number of potential prey or predator links for each group in the model was L/N = 14.2, where N = 51 is the number of groups represented in the model. The connectance or density of the dietary matrix was D = L/[N(N − 1)] = 0.284. Given that many of the potential links were never realised in the simulations, these values are upper limits and unsurprisingly fall at the high end of those reported for most other aquatic systems (e.g., Dunne et al. 2002) with other large marine food webs yielding comparable values (e.g., Link 2002). What is clear is that the Atlantis‐SE system can be categorised as sparse (D < < 1). This suggests that relatively isolated substructures (i.e., motifs) are common and that the functioning of the system may be heavily dependent on a relatively small number of groups.

All of the motifs represented in Figs. 1 and 2 were common within the structure of the SE‐Atlantis diet matrix. Even IGP, which encompasses all of the other motifs as substructures, occurred in over 17 thousand distinct combinations. However, only a small subset of these potential interactions were realised within model runs (having satisfied the three criteria identified previously). The strongest sets of IGP interactions from the status‐quo scenario involved many of the large fish, sharks and mammals and a significant number of lower trophic level prey groups (Table 2). However, the mid‐trophic and intra‐trophic roles were represented by a remarkably small number of groups or species (five in total, with seabirds only involved in this role through the weakest of the interactions). In the mid‐trophic role small pelagic fish and morwong both interacted with multiple intra‐trophic groups, while in the intra‐trophic role squid interacted with both small pelagic fish and juvenile gemfish in the mid‐trophic role.

Top intraguild predation (IGP) motifs selected on the strength of their weakest interaction (between all four groups) and ordered by the relative strength (in terms of proportion of diet) of the predator‐prey interaction between intra‐trophic and mid‐trophic groups.

Results from scenarios 2 and 3 illustrate how interactions within IGP can influence the system response (Fig. 3). When fishing on small pelagic fish was increased, the largest trophic responses (relative to the status‐quo scenario 1) were in the populations of seabirds, seals, baleen whales, and skates and rays (squid themselves had only a very weak response). With the exception of seabirds, the direction of these responses was the same irrespective of whether squid were present or not. Seals showed a small decline as a direct response to the decline in abundance of their small pelagic prey, consistent with a middle‐out (wasp‐waist) response in SFC (Fig. 1c). Baleen whales increased slightly due to reduced competition with small pelagic fish for zooplankton (krill and copepods), their major prey. This is consistent with the EC response (Fig. 1e). Skates and rays increased significantly by feeding on the additional discards from the small pelagic fishery. The magnitude of this last response was sensitive to the presence or absence of squid (compare scenarios 2 and 3 in Fig. 3), reflecting significant competition between these groups for discards (another EC type response).

Responses of the Atlantis‐SE model to increased fishing of small pelagic fish for the case where squid were included in the model (scenario 2) and the case where squid were removed from the model (scenario 3). Biomasses were averaged over the last 5 years of the 30‐year model run and divided by the same quantity from scenario 1 with no fishing on small pelagic fish and status quo fishing on all other groups. The annual fishing mortality applied to small pelagic fish was 15% corresponding approximately to maximum sustainable yield.

The seabird response to an increase in fishing of small pelagic fish was very sensitive to the presence or absence of squid (Fig. 3). In the absence of squid, they declined in direct response to the reduced availability of their small pelagic prey, again consistent with the SFC response (Fig. 1c). However, when squid were part of the food web, the seabird response reversed with a significant increase in their population (Fig. 3). To explain this we need to consider the interactions of seabirds, small pelagic fish, zooplankton and squid that together form an IGP within the broader food web (Table 2, number 2). The addition of an intra‐trophic group (i.e., squid) makes the response of the upper trophic group (i.e., seabirds) less certain (Fig. 2h). Increasing seabird populations are expected when bottom‐up feedback via zooplankton and squid dominates over the combined feedbacks from small pelagic fish to seabirds and small pelagic fish to seabirds via squid. Ignoring the link between small pelagic fish and squid entirely, we see that the same response can also be generated by EAC (Fig. 2b).

Discussion

The responses of the Atlantis model to the various fishing scenarios confirms that the less intuitive responses implied by loop analysis can also occur within the context of more complicated model food webs. We might equally expect that other scenarios can lead to surprises. For example, if climatic or other changes reduced zooplankton stocks then, in the presence of a significant squid population, small pelagic fish could theoretically increase (Fig. 2d, g). Similarly, new fisheries targeting squid could allow squid predators to increase (Fig. 2i), while those targeting upper predators could reduce small pelagic fish (Fig. 2j). We also see that recovery of large predators such as seals and whales will not necessarily lead to declines in small pelagic fish (Figs. 2c, j). The sharp contrasts between these less intuitive responses and those generated by SFC (cf. 1b and 2h) underline the importance of identifying both structural uncertainties and parameter uncertainties that may change relative interaction strengths in ecosystem models. Such uncertainties can change not only the magnitude of predicted trends but also their direction.

Population resilience

Concepts such as population resilience are often ill‐defined and typically described indirectly through a range of loosely related indicators. While certainly not encapsulating all circumstances in which this concept might apply, our results may help identify tangible connections with food web structure and contribute to the development of more rigorous theoretical frameworks. For example, the model results suggest that the presence of intra‐trophic groups impose persistent predation and competition pressures on mid‐trophic groups, potentially impeding their recovery from any drop in population and possibly making them susceptible to depensation (i.e., the tendency for population growth to decrease with shrinking population). In other words, food web structure may reduce the resilience of some mid‐trophic species.

While the high fecundity and short lifecycles of small pelagic fish may help offset pressures from intra‐trophic groups, longer‐lived species such as gemfish and morwong (Table 2) may be more susceptible. The Atlantis model results showed a relatively strong interaction between juvenile gemfish (mid‐trophic) and squid (intra‐trophic) consistent with the association of both arrow squid (Nototodarus gouldi) and spawning of eastern gemfish (Rexea solandri) with mesoscale oceanographic features along the southeast Australian shelf‐break (Prince and Griffin 2001, Stark 2008). Since closure of the targeted fishery in 1993, gemfish recruitment has been lower than expected (Punt and Smith 1999). This is not related to recent fishery catches, which are at historically low levels (Little and Rowling 2010). These circumstances appear to confirm the low resilience of the gemfish population and, while factors such as depensation have been proposed (Little and Rowling 2010), the underlying ecological processes have not previously been identified. The hypothesis that emerges from this study is that depensation may be at least partially attributable to interactions with squid.

While the interactions of morwong with intra‐trophic groups tend to be much weaker than those of juvenile gemfish (Table 2), the multiplicity of these interactions may still have a significant net impact on the resilience of morwong populations. While there is little evidence of depensation in jackass morwong (Nemadactylus macropterus), recovery from overfishing in the 1970s and 1980s has been much slower than expected with lower than predicted recruitment in most years. There is evidence that changes in oceanographic conditions may have contributed to this situation (Wayte 2013) and interactions with intra‐trophic groups may well be a compounding factor.

Keystone species

Data from a large numbers of food webs suggests that the dynamical role of species (including keystone roles) may be directly related to their position within the trophic network (e.g., Stouffer et al. 2012) and these roles will not necessarily change with the complexity of the network (Brose et al. 2005). Of the many network indices that have been derived to identify keystone species (Jordan et al. 2006, Fedor and Vasas 2009, Ortiz et al. 2013), only a relatively small number take the direction of interactions into account (e.g., keystoneness index, mixed trophic impact) and even the value of some of these (e.g., number of dominated nodes) may be limited by their sensitivity to errors in food web structure (Fedor and Vasas 2009). In applying indices such as the (relatively robust) keystoneness index to the four‐member motifs in Fig. 2 (EAC and IGP) it is immediately apparent that the mid‐ and intra‐trophic groups in IGP have a higher index than the mid‐trophic groups in EAC due to the additional bottom‐up and top‐down paths provided by the intra‐trophic link. This is consistent with our quantitative model system responses that have been shown to be strongly dependent on interactions with intra‐trophic species such as squid. Squid have also been previously identified as keystone species with strong top‐down and bottom‐up influences in both the North Pacific (Libralato et al. 2005) and South Atlantic oceans (Gasalla et al. 2010). Our qualitative and quantitative model results seem to confirm that their removal can significantly alter the ecosystem dynamics. It seems plausible that their tendency to play an intra‐trophic role, with strong top‐down and bottom‐up influences (Table 2), is a significant factor in this keystone status.

Other species identified as intra‐trophic in SE‐Atlantis (gemfish, flathead and seabirds) may also play keystone roles around southeastern Australia. While the interactions were comparatively weak in the case of seabirds (Table 2), previous trophic modelling has identified seabirds as the primary keystone species in systems such as the Californian Upwelling (Libralato et al. 2005). The stronger interaction between gemfish and small pelagic fish suggests that gemfish may have played a keystone role in the past, although their ecological role has presumably been reduced by fishing pressure through the 1970s and 1980s, and may continue to be limited by the aforementioned predation of their juveniles by squid.

The postulated link between intra‐trophic and keystone species is consistent with the finding of Libralato et al. (2005) that keystone species can exert their influence through both top‐down and bottom‐up interactions at a range of trophic levels. If this link proves to be robust, then identification of intra‐trophic species using biological data may help reveal new keystone species a priori (i.e., without their experimental removal), particularly when used in concert with other a priori measures such as abundance distributions (e.g., Davic 2003).

Concluding remarks

Although network motifs have previously been identified across a diverse range of food webs, this is the first study to explore how these substructures relate to trophic responses that may contribute to key emergent ecosystem characteristics such as resilience and keystone functions. Making these links more tangible is valuable at a conceptual level and an important a step towards more rigorous testing of hypotheses relating to these important ecological concepts.

Acknowledgments

Our thanks to Rich Little, Neil Klaer, and an anonymous reviewer for their constructive comments on the manuscript.

Appendix

Table A1. List of trophic groups and their composition used in the Atlantis‐SE model.

Fig. A1. The domain and polygonal grid structure used for the Atlantis‐SE model. Each polygon was also divided into horizontal layers with interfaces at 50, 150, 250, 700, 1200, 1800 and 2000 m, plus one epibenthic layer and one sediment layer.

Fig. A2. Matrix of potential trophic connections used in the Atlantis‐SE model. For clarity, connections of the benthic invertebrates have been omitted. While this diagram is an aggregate of potential diets across age classes, the model included ontogenetic diet shifts.

Supplement

Supplement Octave (or Matlab) program for identifying intraguild predation (IGP) motifs within the Atlantis‐SE model food web (Ecological Archives C005‐008‐S1).