abstract
Keystones are defined as relatively low biomass species with a structuring role in their food
webs. Thus, identifying keystone species in a given ecosystem may be formulated as: (1) estimating the impact on the different elements of an ecosystem resulting from a small change to the biomass of the species to be evaluated for its ‘keystoneness’; and (2) deciding on the keystoneness of a given species as a function of both the impact estimated in (1) and its own biomass. Experimental quantification of interaction strength necessarily focus on few
species, and require a priori assumptions on the importance of the interactions, which can
bias the identification of keystone species. Moreover, empirical measurements, although
very important, are expensive and time consuming and, owing to the spatio-temporal heterogeneity of habitats, physical conditions, and densities of organisms, published results tend to be case-specific and context-dependent.
Although models can only represent but a caricature of the complexity of the real world,
the modelling approach can be helpful since it allows overcoming some of the difficulties
mentioned. Here we present an approach for estimating the keystoneness of the functional groups (species or group of species) of food web models. Network mixed trophic impact analysis, based on Leontief’s economic input–output analysis, allows to express the relative change of biomasses in the food web that would result from an infinitesimal increase of the biomass of the observed group, thus identifying its total impact.
The analysis of the mixed trophic impacts presented here was applied to a suite of massbalance models, and the results allow us to rank functional groups by their keystoneness. Overall, we concluded that the straightforward methodology proposed here and the broad use of Ecopath with Ecosim (where mixed trophic impact analysis is implemented) together give a solid empirical basis for identification of keystone functional groups.
Introduction
Keystones are defined as species with a structuring role within ecosystems and the food webs that interconnect in spite of a relatively low biomass and hence food intake (Power et al., 1996). It may be noted that the
low biomass requirement eliminates species that structure ecosystems by virtue of their high biomass, such as
Corresponding author at: Dept. Oceanography, Istituto Nazionale di Oceanografia e di Geofisica Sperimentale—OGS, Borgo Grotta Gigante
42/. 34010 Sgonico (TS), Italy. Tel.: +39 040 2140376; fax: +39 040 2140266.
E-mail addresses: [email protected], [email protected] (S. Libralato).0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2005.11.029
trees in terrestrial forests, or seagrass and kelp in coastal ecosystems.Keystone species affect the communities of which they are part in a manner disproportionate to their abundance (Power et al., 1996). Keystone species strongly influence the abundances of other species and the ecosystem dynamic (Piraino et al., 2002). Therefore, it is important to identify keystone species, notably to maintain ecosystem integrity, and biological diversity in the face of exploitation and other stresses (Naeem and Li, 1997; Tilman, 2000). However, it is expected that all species of a given ecosystem rank in a continuum of levels of ‘keystoneness’, with only some designated to be keystone species.Identifying keystone species in a given ecosystem may be thus formulated as
1. Estimating the interaction strength as the impact on the
different elements of an ecosystem resulting from a small
change to the biomass of the species to be evaluated for its
keystoneness.
2. Deciding on the keystoneness value of a given species as a
function of the impact estimated in (1) and its biomass.
Several studies report on field-based, experimental quantification of interactions strength, as evaluated through the
impacts induced by changes in abundance of one species on the other species in a community (Paine, 1992; Wootton, 1994; Wootton et al., 1996; Berlow, 1999). However, these experiments necessarily focused on few species; thus, they required a priori assumptions on the importance of the interactions, in order to exclude the uninteresting species from the experiment, which can bias the identification of keystone species (Wootton, 1994; Bustamante et al., 1995).
Although the importance of indirect interactions is recognized (Wootton, 1993, 1994; Yodzis, 2001), their explicit consideration within a purely experimental approach is difficult. Most indirect interactions are weak, which seemingly justifies their being neglected. However, indirect interactions can also be magnified by cascading effects (Brett and Goldman, 1996; Pace et al., 1999), and thus need to be taken into account.
Moreover, empirical measurements of interaction strengths are usually limited to easily accessible, sessile
or errant macrobenthic species (Paine, 1992, 2002; Wootton, 1994; Wootton et al., 1996; Berlow, 1999), or microscopic
species (Naeem and Li, 1997), because these are easier to manipulate and control than nektonic species (especially
large fish, or marine mammals), for which only indirect evidence is available (Power et al., 1996).
Finally, empirical measurements, although very important,are expensive and time consuming (Ernest and Brown, 2001).Consequently, and owing to the spatio-temporal heterogeneity of habitats, physical conditions, and densities of organisms(Paine, 1994, 2002; Piraino et al., 2002), published results tend to be case-specific and context-dependent (Power et al., 1996).
The modelling approach allows overcoming some of the difficulties of the experimental quantification of keystoneness. Through a model it is possible to estimate the strength of the interactions between model functional groups (here referred to as ‘species’, although often composed of groups of species with similar sizes and feeding habits). Therefore, the modelling approach provides at least a pre-screening analysis and allows for improved planning of subsequent field experiments.
This suggestion is not new. Previous estimates of keystone species from mathematical models exists, based on successive elimination of functional groups from a trophic web and evaluating impacts on the other functional groups using a graph theoretical method (Jordan et al., 1999; Jordan, 2001; Sole and Montoya, 2001), or evaluating changes in the biomass of ecosystem with dynamic models (Okey et al., 2004a).
However, estimating the trophic impact on the functional groups of an ecosystem resulting from a change (increase) of
the biomass of a single group can be achieved more directly and rigorously through the mixed trophic impact matrix, M, as adopted for food webs by Hannon (1973) from input–output analysis of Leontief (1951). Each element of the matrix represents the relative change of biomass that would result from an infinitesimal increase of the biomass of the functional groups in the rows (Ulanowicz and Puccia, 1990). Thus, M can be used to estimate the total effect of one functional group on all the others in a given model.
The analysis of the mixed trophic impacts presented here was applied to a suite of mass-balance models built with the software package Ecopath with Ecosim (http://www.ecopath.org; Christensen and Walters, 2004), allowing the estimation of keystoneness for the functional groups of models representing marine ecosystems spread over
the world. The results allow us to rank groups by their keystoneness, which then can be compared with ranking from
previous studies, and with the ecological experience resulting from previous experimental research.
Also, the use of models constructed using the same approach, i.e., using Ecopath with Ecosim, allows standardizing the evaluation of species’ roles and the quantification of the interaction strengths in various environments, thus providing at least some of the pre-screening alluded to above, and required for the design of experimental studies.
The present paper aims to answer the following questions:
(1) How can we use the matrix M obtained for mass-balance
models to quantify the total impact of one functional
group on the others in the ecosystem?
(2) Do the resulting estimates obtained in this manner make
ecological sense?
(3) How do we ensure that our measure of keystoneness
correctly balances the strength of interactions measured
through the total effects (by and on species) and the effect
that species exert due to their biomass?
(4) What are, in general, the major features of keystone
species identified in a comparative analysis of models representing different ecosystems?
Methods
Ecopath approach
Ecopath is the core routine of the Ecopath with Ecosim (EwE), a software package based on an approach proposed by Polovina (1984) and subsequently upgraded with a variety of ecologi-cal and theoretical approaches (Christensen and Pauly, 1992; Walters et al., 1997, 2000; Pauly et al., 2000; Christensen and Walters, 2004). Ecopath allows construction of a massbalance model of a given trophic network by representing the ecosystem functional groups as interacting by means of feeding relationships and, when necessary, subjected to fishing (Christensen and Walters, 2004). The balance of mass (energy, or nutrients) for any functional group (i) of the network is obtained by setting its production equal to the sum of the consumption components, expressed as
where production, on the left side of the equation, is expressed as the product between the production–biomass ratio (P/Bi) and the biomass (Bi), and the right-hand side terms are the sum of the predation terms, each expressed as the product of the consumption–biomass ratio (Q/Bj), the biomass of the predators (Bj) and the proportion of the prey i in the diet of the predator j (DCij); the net flow trough the boundaries of the system, i.e., dispersal (Ei); the fishing exploitation, represented through the catches (Yi); the accumulation or depletion of biomass (BAi); and non-predation natural mortality, expressed by means of the ecotrophic efficiency (EEi). The resulting system of equations, when solved, provides a snapshot of the flows within a trophic web (numerous examples are reported in Christensen and Pauly, 1993; see also http://www.ecopath.org).
Mixed trophic impact
Given the mass-balance model of a trophic network, the mixed trophic impact is estimated for each pair of functional groups (i, j, interacting directly or not) of the trophic web, by means of the net impact matrix. According to Ulanowicz and Puccia (1990), the net impact of i on j (qij) is given by the difference between positive effects, quantified by the fraction of the prey I in the diet of the predator j (dji), and negative effects, evaluated through the fraction of total consumption of I used by predator j (fij). Therefore the resulting matrix of the net impacts, Q, has elements:
The mixed trophic impact mij is then estimated by the product of all the net impacts qij for all the possible pathways
in the trophic web that link the functional groups i and j. Ulanowicz and Puccia (1990) demonstrated that the matrix of
the mixed trophic impacts, M, can be obtained by the inverse of the matrix Q, as it is calculated in EwE (Christensen et al.2004). Table 1 shows the elements of such matrix M derived from a food web representing the ecosystem off the coast of Newfoundland (Bundy, 2001).
The elements mij of the matrix M quantify the direct and indirect impacts that each (impacting) group i has on
any (impacted) group j of the food web (Ulanowicz and Puccia, 1990). Positive/negative values of mij indicate the increase/decrease of biomass of the group j due to a slight increase of biomass of the impacting group i. Thus, the
mixed trophic impacts represent the first order partial derivatives, in term of biomass, of the Ecopath master equation
(1). This can be illustrated by Ecosim simulations, as shown below.
Moreover, from Eq. (2) one can tell that negative elements of matrix M indicate a prevailing of negative effects, i.e. the
effects of the predator on the prey; analogously, positive elements of M indicate prevailing effects of the prey on the predator. Therefore, negative elements of M can be associated to prevailing top-down effects and positive ones to bottom-up effects.
Ecosim
The dynamic routine of the EwE package, Ecosim, is based on a set of differential equations, derived from the Ecopath’s master equation (1), allowing dynamic representation of the system variables, i.e. biomasses, predation, andproduction (Christensen and Walters, 2004). In order to describe dynamically the predator–prey interaction, Ecosim uses Lotka–Volterra relationships modified to account for foraging arena theory (Walters et al., 1997, 2000), which allow to avoid the unrealistic Lotka–Volterra assumption of uniform and random distribution of interactions, typically assumed with the mass-action functions (Walters and Martell, 2004). In foraging arena theory, rather, the biomass of the prey available to predators is only a vulnerable fraction of total biomass, with exchanges rates between the vulnerable and the invulnerable states calculated using vulnerability coefficients set by the user (Christensen and Walters, 2004).
Comparison between simulation outputs and matrix M
In order to test if the elements of M represent the relative change of biomass that would result from an infinitesimal
increase of the biomass of the functional groups in the rows, a set of Ecosim simulations (covering a period of 100 years) were done. Since biomass and production are multiplicative terms in EwE formulations, changing proportionally one or the other has identical resulting effects. Therefore, since changes in production are easier to implement in Ecosim than biomass changes, simulations were done perturbing production. In each simulation, the initial (Ecopath) production was kept constant for the first 10 years and then perturbed. From year 10 to year 20 of each simulation, indeed, the initial production of the functional group being observed (corresponding to the
group in the row of the M matrix) was decreased linearly to 90% of its initial value, then maintained constant until the end of the simulation and the resulting ecosystem changes observed. Following Christensen and Walters (2004), a forcing function was used, in Ecosim, to represent this production decrease. The perturbation on the observed group produced dynamic changes on the biomass of other groups in the web. The resulting relative changes in the biomass (excluding detritus and the observed group), were compared with the corresponding elements of the row of the matrix M. Therefore, each mij was
Estimating total impact
Given that there is agreement between the mij and Sij (see below), it is appropriate to estimate the total impact of one
functional group on the ecosystem through the mixed trophic impact. Since each impact can be either negative or positive, we define our proposed measure of the overall effect of each group as
in which the effect of the change in biomass on the group itself (i.e., mii) is not included.The normalized flows in Eq. (2) bound the sum of the elements of the rows and columns of matrix Q between the interval −1 to +1 (Ulanowicz and Puccia, 1990), which guarantees that the overall effect, estimated as the sum of the elements of M as in Eq. (4), does not need to be weighted by the numbers of groups used to describe the trophic network.
Accounting for the positive and negative contributions to the overall effect estimated as in Eq. (4), allows evidencing for a given group, respectively, bottom-up and top-down effects contributing to its overall effect.
Identifying an index of keystoneness
Several alternatives for combining overall effect and biomass in our keystoneness index were explored. The biomass component was adequately represented by the contribution of the functional group to the total biomass of the food web (Power et al., 1996), that is:
was strongly influenced by the biomass proportions, attributing high keystoneness to functional groups with low biomass (as required) and low overall effect (which should not be the case; see Fig. 1A).Therefore, in order to balance the two components (overall effect and biomass), we define our index of keystoneness as follows:
groups such as macrophytes. Moreover, the negative and positive contributions to the overall effect, as outlined above, allow calculating the bottom-up and top-down effects contributing to the keystoneness index of Eq. (7).
The estimation of the total impacts and of the ‘keystoneness’ proposed here (Eq. (7)) was applied to each living functional group (thus excluding detritus groups) of a suite of 33 Ecopath models considered well described and
detailed, i.e., with a minimum of 24 functional groups used for describing the ecosystem. These models represent the
trophic web of marine ecosystems that differ for location, period and type of habitat represented. The proposed analysis was applied also to 9 models representing different upwelling ecosystems in different periods, for a total of 42 models analysed.
Results
The comparison between the observed changes resulting from the Ecosim simulations, Sij, and the changes predicted by means the mixed trophic impact, mij, are given in Figs. 2–4, respectively, for the Prince William Sound, the Gulf of Thailand and the North Pacific model. The comparisons showed, with few exceptions, a high Spearman’s (rank) correlation (Zar,1999) between changes observed by means of the dynamic simulation (abscissa) and the correspondent row of the matrix M (ordinate of each plot of the figures). The bisecting line is also shown, together with the rank correlation coefficient between observed and predicted values. The Prince William Sound functional groups (Fig. 2), showed low rank correlations only for the herbivorous zooplankton and adult salmon (both with R2 = 0.02), while the analysis on the Gulf of Thailand model (Fig. 3) resulted in low correlations for rays (R2 = 0.03), phytoplankton (R2 = 0.05), ‘trashfish’ (R2 = 0.09), Priacanthus spp. (R2 = 0.12) and juveniles Nemipterus spp. (R2 = 0.13). The lowest rank correlation for the North Pacific model (Fig. 4) was R2 = 0.17 for the large blue shark group. However, most of the functional groups show high agreement between simulated biomass change and mixed trophic impacts. Thus the overall rank correlations were 54.8%, 51.5% and 54.5%, respectively, for the Prince William Sound, the Gulf of Thailand and the North Pacific. Results of non-parametric test of correlation significance (Zar, 1999) evidenced that the above reported overall rank correlations are all significant at p < 0.001.
The high agreement between the mij and Sij, show that it is legitimate to use Eq. (4) to draw inferences on total
impacts from the M matrix, and subsequently applying Eq. (7) to calculate the ‘keystoneness’ of its various functional
groups. Fig. 5 represents the estimated keystoneness index for the functional groups of four selected models, representing the ecosystems of Newfoundland (after Bundy, 2001), Eastern Tropical Pacific (Watters et al., 2003), Chesapeake Bay (Baird and Ulanowicz, 1989) and Bolinao reef (Alin˜ o et al., 1993).
As might be seen, the keystoneness index estimated here show a common pattern in different ecosystems, and allows
ranking the groups of each model by decreasing keystoneness. The keystone functional groups are those that have value of the proposed index close to or greater than zero.
Different groups of marine mammals (cetaceans, harp and hooded seals) show high keystoneness in the Newfoundland ecosystem, where capelin, a forage species, ranks second. Toothed whales rank second in the Eastern Pacific, between large and small sharks, which rank first and third, respectively. For the Chesapeake and Bolinao ecosystems, zooplankton has the highest keystoneness.
Tables 2 and 3 lists, for the 42 Ecopath models analysed, the four functional groups that ranked highest in term of their keystoneness. The top-down effect as percentage contributions to the keystoneness for each species, evaluated through the proportion of the negative values contributing to the sum in Eq.(4), is also reported in Tables 2 and 3.
Table 2 contains the results of the analysis applied to 33 models considered well described and detailed on the basis
of the number of groups used to describe the ecosystems (minimum 24 groups, maximum 59 groups). Marine mammals often have high keystoneness, and rank first (Alaska gyre, Azores, Newfoundland, Norwegian Barents Sea models) or second (Easter tropic Pacific models, Floreana, Georgia Strait, Newfoundland 1985–1987) in many models. Sea birds rank third in Lancaster model and fourth in the Prince William Sound model. Sharks and rays have high keystoneness in many ecosystems, ranking first (Biscaya, Easter tropic Pacific, Floreana, Hong Kong, Morocco models) or second (Gulf of Thailand and Western Gulf of Mexico) in many models. All these
functional groups have effects on the other components of the ecosystem mainly via top-down impacts.A few ecosystems (North Coast Central Java, Prince Williams Sound) show high keystoneness for phytoplankton, while in coastal and semi-enclosed marine environments(Bolinao reef, Chesapeake Bay, Georgia Strait, Gulf of Thailand), the zooplankton group has high keystoneness.
Table 3 presents analogous results for the nine models of upwelling ecosystems. The seabirds are important
in the California (both models) and Peru (1960) upwelling ecosystems, while marine mammals rank second and third
in the California models. Mackerel has high keystoneness in California (77–85), Peru and Northwest Africa. The zooplankton and phytoplankton groups rank for keystoneness among the first four in all the upwelling ecosystems analysed. Moreover, models of the same upwelling system in different periods seem to show an increase of keystoneness of intermediate trophic levels concomitant with a decrease of keytoneness of top predators over time: marine mammals are ranking second in California model for 1965–1972.while they rank third in the model for the later period (1977–1985); in Peru 1960 cormorants are ranking first while later periods show high keystoneness for lower TL functional groups (large scombrids in 1964–1971 and horse mackerel in 1973–1981).
Discussion
The high general agreement between the mixed trophic impacts estimated by the mass-balance routine, Ecopath,
and the observed relative changes in the biomasses obtained with long-term Ecosim simulations, allowed use of the mixed trophic impact matrix M as a straightforward basis to quantify the effect one functional group has on all the other groups in the ecosystem. Thus, the method proposed allows estimating the keystoneness of the species or group of species in a model without having to perform the time-dynamic simulations, as performed, e.g. by Okey et al. (2004a), thus avoiding differences induced by different simulation protocols.
The wide use of EwE and the easy implementation of the method proposed here allow standardizing the procedure to
estimate the keystoneness of functional groups in models of different marine ecosystems and of the same ecosystem at different periods or scales. Although the methodology has the potential for ranking groups across models we examined here rankings of keystoneness within models.
Generally, marine mammals ranked high in most ecosystems, but in some, they had low rank; thus, spotted dolphin
and baleen whales rank 24 and 33 in Eastern Pacific model. Similarly, skates and sharks ranked high in the Newfoundland model, but very low in the Eastern tropical Pacific model (dogfish was only 30th). Seabirds appear to have high keystoneness in shallow and very productive environments (upwelling systems), but low keystoneness in open seas, ranking e.g., last in Newfoundland and the Easter Tropic Pacific. In shallow coastal ecosystems, phyto- and zooplankton can have high keystoneness. Indeed, the lower part of the trophic web appears to be very important in these ecosystems, where other benthic groups also tend to have high keystoneness index.
Thus, we concur with Power et al. (1996) and Piraino et al. (2002), that keystones are not straightforwardly predicable.
Certainly, and perhaps surprisingly, there is no general correlation between trophic level and keystoneness.
The index proposed assign low keystoneness to functional groups with high abundance, whether they have high impacts or not, thus allowing us to distinguish between keystone species, and dominant and structuring species—with which keystones must not be confounded (Power et al., 1996). Macrobenthic producers generally have low keystoneness, e.g., in the Bolinao reef model, where seagrasses and seaweeds have low keystoneness index.
Another important result is that keystone species do not always exert their high impact by means of top-down effects,
a feature initially suggested to be a defining characteristic of keystone species (Paine, 1969), and thus proposed for identifying keystones (Davic, 2003). In fact, although results highlight that keystone functional groups exert their effect via topdown in many ecosystems (e.g., Newfoundland and Eastern tropical Pacific), keystoneness via bottom-up effects appears also very important in others (e.g., North Sea, Prince Williams Sound). These results are not contradicting previous works highlighting the high importance of top-down effects in keystoneness (Paine, 1966; Menge et al., 1994; Estes et al., 1998) and confirm that bottom-up influences can also be important
(Bustamante et al., 1995; Menge, 1995). Moreover, upwelling systems show a prevalence of keystone functional groups with intermediate positions in trophic webs. This indicates that these intermediate functional groups contribute to the mixture of top-down and bottom-up control typical of wasp-waist ecosystems (Cury et al., 2000). Moreover, changes over time of keystone functional groups in upwelling systems seem to evidence the increase of keystoneness of intermediate functional groups and the concomitant decrease of keystoneness of high trophic level groups thus suggesting an increase of wasp-waist control over time.
Conclusion
Since the first definition of keystone species by Paine (1969), their importance for conservation purposes has been widely recognized. However, difficulties in experimental approaches and the different roles assumed by species in time and space (Paine, 1994; Menge et al., 1994; Estes et al., 1998) lead to increasing scepticism about the original definition of the keystone species concept and the flourishing of different definitions (Mills et al., 1993; Bond, 2001; Davic, 2003). Therefore, although the importance of the concept is well recognized, a widely accepted approach for quantifying keystoneness is still lacking (Bond, 2001).
The straightforward methodology proposed here may contribute to filling this gap. The mixed trophic matrix upon
which it relies allows including direct and indirect effects of trophic interactions. Moreover, the broad use of EwE will facilitate application of the methodology to the large number of ecosystems for which models exist, thus providing a broad empirical basis for the new approach. In view of the key role experiments must continue to play (Paine, 1966, 1994; Menge et al., 1994; Power et al., 1996) the methodology proposed can also be used for a priori identification of keystone species, thus focusing empirical studies.
Acknowledgements
Simone Libralato gratefully acknowledges the Istituto Centrale per la Ricerca Applicata al Mare-ICRAM (Chioggia) for supporting his visiting period at Fisheries Centre—UBC, during which this work was deeply improved. S. Libralato also acknowledges Fabio Pranovi (Universita Ca’ Foscari, Venezia) for advice and support. Villy Christensen and Daniel Pauly gratefully acknowledge support from the Sea Around Us Project, initiated and funded by the Pew Charitable Trusts, Philadelphia. D. Pauly also acknowledges support from Canada’s Natural Science and Engineering Research Council.
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