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Interpretation and predictions of the Emergent neutrality model: a reply to Barabás et al.

Remi Vergnon, Egbert H. van Nes and Marten Scheffer

R. Vergnon (remi.vergnon@wur.nl), E. H. van Nes and M. Scheffer, Dept of Aquatic Ecology and Water Quality Management, Wageningen Univ., PO Box 47, NL-6700 AA Wageningen, the Netherlands. RV also at: Dept of Animal and Plant Sciences, Univ. of Sheffield, Western Bank, S10 2TN, Sheffield, UK.

Formulated in 2006, Scheffer and van Nes’ Emergent neutrality model predicts that competing species might self-organize into groups of species similar in their traits. Recently, Vergnon et al. showed that the model consistently generates multi-modal species abundance distributions, in accordance with empirical data. Barabás et al. argue that Emergent neutrality model relies on unmodeled, ‘hidden’ species differences. They also suggest that an Emergent neutrality model explicitly integrating such differences may fail to generate multimodal species abundance distributions, while other models can robustly produce those patterns. Here we demonstrate that density dependence the process deemed problematic by Barabás et al. may permanently maintain groups of similar species without need for additional species differences. More broadly, we make it clear that density dependence is not the only likely mechanism that could allow the permanent coexis-tence of similar species in the Emergent neutrality framework. We welcome the finding that models other than Emergent neutrality can generate multimodal abundance distributions and we briefly discuss their novelty and relevance.

The theory of self-organized similarity (SOS) predicts the self-organized, competition-driven emergence of regu-larly distributed groups of similar species in niche space (Scheffer and van Nes 2006). The model suggests that in order to coexist competing species must be either similar in their traits (i.e. belong to the same emerging group) or radically different (i.e. belong to distinct groups). Species occupying intermediate niche space positions in between groups are rapidly driven to extinction by competitive exclusion. In line with the simpler two-species Lotka– Volterra models SOS expands on, competitive exclusion within emerging groups of similar species is extremely slow and becomes increasingly so with increasing species simi-larity (Scheffer and van Nes 2006). When implemented in an evolutionary context, SOS predicts that communi-ties of randomly distributed species in niche space should converge towards increasing similarity within distinct self-organized species groups (see Scheffer and van Nes 2006 Fig. 3). Although neutrality per se (perfect equivalence of two or more species) is a limit case in the SOS model, the predicted emergence of long-lasting groups of many com-petitively similar species led Holt (2006) to suggest the alter-native name of Emergent neutrality (EN hereafter) model.

The EN model has now received robust empirical support in a number of different natural communities (Vergnon et al. 2009, Segura et al. 2011, 2013, Muschick et al. 2012). Even though this was not intended as a formal test of the model, Vergnon et al. (2012) recently explored

EN predictions of multimodal species abundance distribu-tions (SADs) that also matched with observations.

Barabás et al. (2013) criticize both the interpretation of the EN model and our recent discussion of the model predictions in terms of species abundance distributions. Although we appreciate their constructive contribution, we do not agree with their conclusions and present our argu-ments here.

A case of ‘hidden differences’?

The novel insight delivered by the EN model the emer-gence of groups of similar species in niche space is the result of resource competition alone (Scheffer and van Nes 2006). Indeed species self-organize and coexist extensively in those regularly-distributed areas of niche space where weaker community-wide competitive forces allow species persistence (Scheffer and van Nes 2006). Although self- organized groups are eventually reduced to single species by competitive exclusion, the lack of a marked fitness advantage between similar competitors slows down this species loss process considerably. As a consequence tran-sient groups of similar species can exist for extremely long periods of time in the model, potentially spanning thou-sands of generations (Scheffer and van Nes 2006). The result is one of very slow-changing guilds of competitively similar species that appear constant at shorter time scales. Slowly transient communities could be common in nature,

Oikos 000: 001–003, 2013 doi: 10.1111/j.1600-0706.2013.00790.x

© 2013 The Authors. Oikos © 2013 Nordic Society Oikos Subject Editor: Dustin Marshall. Accepted 5 July 2013

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where biological systems are often not in a state of equilib-rium (Hastings 2004, Hastings and Higgings 1994).

Scheffer and van Nes (2006) elaborated on the basic, purely competition-driven EN model to explore mecha-nisms by which the long-term coexistence of self-organized similar species could be made truly permanent. They sug-gested top–down density-dependence as one such mecha-nism and implicitly modelled it in a further version of the model (Scheffer and van Nes 2006 Eq. 2).

The main criticism formulated by Barabás et al. (2013) concerns the realism of a density-dependent control of simi-lar species in this specific version of the EN model. We sum-marize their reasoning here. In the basic (without additional density dependence) EN model functionally similar species occupy nearby positions in niche space symbolized by their positions on a single niche axis. Barabás et al. (2013) state that the addition of density dependence in the model contra-dicts the assumption that closeness on the niche axis equates to functional similarity. This is because stabilizing density-dependent agents must be able to distinguish between com-peting species to regulate them: in the limit case where two species are infinitely close on the niche axis, no regulating density-dependent agents can tell them apart and efficient control breaks down. The authors conclude that in order for density dependence to play its stabilizing role, the model must imply hidden, unmodeled differences allowing density- dependent regulators to distinguish between seemingly simi-lar species on the niche axis. The consequence would be that species packed in the self-organized groups emerging in the EN model are not genuinely similar. We agree that the origi-nal formulation of the density-dependence term in Scheffer and van Nes (2006) implies an unrealistic ability of regulat-ing agents to tell apart extremely similar species. However we argue that a more realistic density-dependent term would not imply the presence of additional differences between species nor change the interpretation of the model.

Our argument stems from classic resource competition theory. In order to coexist permanently, two competing spe-cies that differ in their traits (and therefore in their fitness) require a stabilizing density-dependent process to offset those differences (Chesson 2000 Eq. 4). In the absence of such stabilizing mechanism, the worst competitor goes extinct. However as differences between competitors become smaller, competitive exclusion occurs after increasingly long periods of time. This is evident in the basic EN model: in the absence of stabilizing density dependence, exclusion time in self-organized species groups tends toward infinity for increas-ingly similar competitors (Loreau 2004, Scheffer and van Nes 2006). Hence the smaller the difference between similar competitors i.e. the more likely they are to be undistin-guishable the less density-dependent regulation matters to their long-term coexistence. Even though realistic density-dependent agents may fail to regulate them, infinitely similar species would coexist for infinitely long periods of time (i.e. permanently) in emerging groups. When moving away from the limit case of infinite similarity, species can realistically be regulated by density dependence and coexist stably. It is difficult to estimate what is the minimum ‘amount of spe-cies difference’ regulators can effectively perceive in nature. Empirical evidence suggests that even small differences can be detected. For instance, single pathogen species causing

density-dependent losses (Schnitzer et al. 2011) can special-ize to become truly host-specific in local tropical forest com-munities (Konno et al. 2011) where coexisting species are understood to differ little (Hubbell 2001). We conclude that realistic regulating agents may permanently maintain groups of similar species in the EN model without need for addi-tional differences to come into play. They do not imply a contradiction with the emergence of self-organized groups of similar species generated by competition forces in the EN model.

In a broader context, it is important to stress that mecha-nisms other than density dependence could allow the tran-sient coexistence of self-organized similar species to become permanent in the EN model. Notably, migration is another ubiquitous process that can play this role. Loreau and Mouquet (1999) show that within a network of connected local communities, dispersal can lead to durably high local diversity when combined with different environmental con-ditions in each local patch. We evoke the effect of dispersal in the EN framework in a recent study (Vergnon et al. 2013) and Barabás et al. (2013) themselves demonstrate its influ-ence (see their Fig. 3).

Multimodality in SADS

We now move to the second critique mentioned by Barabás et al. (2013) and aimed specifically at a recent study by Vergnon et al. (2012) discussing the EN prediction of multimodal species abundance distributions. Their claim was two-fold: 1) that a model explicitly representing so-called hidden differences may not be able to produce multimodal SADs and 2) that models other than EN could generate those multiple modes. We have discussed the ‘hidden differences’ issue above and stand by the claim that the EN model pro-duces genuine multiple modes in abundance distributions in a robust way. We therefore only consider here Barabás et al.’s (2013) demonstration that resource partitioning models and neutral models can produce multimodal SADs when integrating stochastic migration.

As mentioned in Vergnon et al. (2012) and acknowl-edged by Barabás et al. (2013), we reiterate that both neutral and resource partitioning models are widely used to gener-ate unimodal abundance distributions. Barabás et al. (2013) underline that empirical observations influenced by stochas-tic processes may differ from such mean unimodal patterns (Etienne 2005). The fact that individual realizations of a sto-chastic migration process produce multimodal SADs in those models further broadens the field of possible mechanisms for this pattern. This is in line with Vergnon et al.’s (2012) statement that there exist multiple possible explanations for multimodal SADs, with alternatives to EN also including environmental heterogeneity and species asymmetries. As Barabás et al. (2013) explain themselves, the resource parti-tioning model they present is essentially the EN model, with a process other than density dependence (stochastic migra-tion) allowing for permanent coexistence within groups of similar species. Since density dependence is not an obliga-tory process in the EN theory and can indeed be substituted by migration (Vergnon et al. 2013), the new and original incarnations of the model do not appear to differ funda-mentally. As for the neutral model, the well-documented

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failures of purely neutral predictions against empirical tests (Turnbull et al. 2005, Wootton 2005) perhaps make it a less credible contender than EN as an explanation for multi-modal SADs. Barabás et al.’s (2013) conclusion that it is not currently possible to associate outright a single mechanism to multimodal SADs is in accordance with what Vergnon et al. (2012) previously stated.

Conclusion

While much remains to be explored, we believe Emergent neutrality to be sound in its principles and so far empirical tests have given credit to this claim. Emergent neutrality is a solid base on which further improvement can and should be made, such as the explicit modelling of the mechanisms allowing the permanent coexistence of similar species.

Acknowledgements – We thank György Barabás, Rafael D’Andrea, Rosalyn Rael, Géza Meszéna and Annette Ostling for providing the opportunity for a constructive debate. We also thank Robert Freck-leton from the Dept of Animal and Plant Sciences at the Univ. of Sheffield for commenting on the manuscript.

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