Whether environmental conditions –in particular energy and water availability– are sufficient to account for species richness gradients (e.g. Currie 1991), or the effects of other biotic and historical or regional factors need to be considered as well (e.g. Ricklefs 1987), was the subject of debate during the 1990s and 2000s (e.g. Francis & Currie 2003; Hawkins et al. 2003, 2006; Currie et al. 2004; Ricklefs 2004). The metabolic theory of ecology (Brown et al. 2004) provided a solid and well-rooted theoretical support for the preponderance of energy as the main driver for richness variations. As any good piece of theory, it provided testable predictions about the sign and shape (i.e. slope) of the relationship between temperature –a key aspect of ambient energy– and species richness. However, these predictions were not supported by empirical evaluations (e.g. Kreft & Jetz 2007; Algar et al. 2007; Hawkins et al. 2007a), as the effects of a myriad of other environmental gradients, regional factors and evolutionary processes result in a wide variety of richness–temperature responses across different groups and regions (Hawkins et al. 2007b; Hortal et al. 2008). So, in a textbook example of how good theoretical work helps advancing science even if proves to be (partially) wrong, the evaluation of this aspect of the metabolic theory of ecology led to current understanding that, while species richness does respond to current climatic conditions, many other ecological, evolutionary and historical factors do modify such response across scales (see, e.g., Ricklefs 2008; Hawkins 2008; D’Amen et al. 2017). And the kinetic model linking mean annual temperature and species richness (Allen et al. 2002; Brown et al. 2004) was put aside as being, perhaps, another piece of the puzzle of the origin of current diversity gradients.

Segovia (2021) puts together an elegant way of reinvigorating this part of the metabolic theory of ecology. He uses quantile regressions to model just the upper parts of the relationship between species richness and mean annual temperature, rather than modelling its central tendency through the classical linear regression family of methods –as was done in the past. This assumes that the baseline effect of ambient energy does produce the negative linear relationship between richness and temperature predicted by the kinetic model (Allen et al. 2002), but also that this effect only poses an upper limit for species richness, and the effects of other factors may result in lower levels of species co-occurrence, thus producing a triangular rather than linear relationship. The results of Segovia’s simple and elegant analytical design show unequivocally that the predictions of the kinetic model become progressively more explanatory towards the upper quartiles of the relationship between species richness and temperature along over 10,000 tree local inventories throughout the Americas, reaching over 70% of explanatory power for the upper 5% of the relationship (i.e. the 95% quantile). This confirms to a large extent his reformulation of the predictions of the kinetic model. 

Further, the neat study from Segovia (2021) also provides evidence confirming that the well-known spatial non-stationarity in the richness–temperature relationship (see Cassemiro et al. 2007) also applies to its upper-bound segment. Both the explanatory power and the slope of the relationship in the 95% upper quantile vary widely between biomes, reaching values similar to the predictions of the kinetic model only in cold temperate environments ­–precisely where temperature becomes more important than water availability as a constrain to plant life (O’Brien 1998; Hawkins et al. 2003). Part of these variations are indeed related with changes in water deficit and number of frost days along the XXth Century, as shown by the residuals of this paper (Segovia 2021) and a more detailed separate study (Segovia et al. 2020). This pinpoints the importance of the relative balance between water and energy as two of the main climatic factors constraining species diversity gradients, confirming the value of hypotheses that date back to Humboldt’s work (see Hawkins 2001, 2008). There is however a significant amount of unexplained variation in Segovia’s analyses, in particular in the progressive departure of the predictions of the kinetic model as we move towards the tropics, or downwards along the lower quantiles of the richness–temperature relationship. This calls for a deeper exploration of the factors that modify the baseline relationship between richness and energy, opening a new avenue for the macroecological investigation of how different forces and processes shape up geographical diversity gradients beyond the mere energetic constrains imposed by the basal limitations of multicellular life on Earth.

References

Algar, A.C., Kerr, J.T. and Currie, D.J. (2007) A test of Metabolic Theory as the mechanism underlying broad-scale species-richness gradients. Global Ecology and Biogeography, 16, 170-178. doi: https://doi.org/10.1111/j.1466-8238.2006.00275.x

Allen, A.P., Brown, J.H. and Gillooly, J.F. (2002) Global biodiversity, biochemical kinetics, and the energetic-equivalence rule. Science, 297, 1545-1548. doi: https://doi.org/10.1126/science.1072380

Brown, J.H., Gillooly, J.F., Allen, A.P., Savage, V.M. and West, G.B. (2004) Toward a metabolic theory of ecology. Ecology, 85, 1771-1789. doi: https://doi.org/10.1890/03-9000

Cassemiro, F.A.d.S., Barreto, B.d.S., Rangel, T.F.L.V.B. and Diniz-Filho, J.A.F. (2007) Non-stationarity, diversity gradients and the metabolic theory of ecology. Global Ecology and Biogeography, 16, 820-822. doi: https://doi.org/10.1111/j.1466-8238.2007.00332.x

Currie, D.J. (1991) Energy and large-scale patterns of animal- and plant-species richness. The American Naturalist, 137, 27-49. doi: https://doi.org/10.1086/285144

Currie, D.J., Mittelbach, G.G., Cornell, H.V., Field, R., Guegan, J.-F., Hawkins, B.A., Kaufman, D.M., Kerr, J.T., Oberdorff, T., O'Brien, E. and Turner, J.R.G. (2004) Predictions and tests of climate-based hypotheses of broad-scale variation in taxonomic richness. Ecology Letters, 7, 1121-1134. doi: https://doi.org/10.1111/j.1461-0248.2004.00671.x

D'Amen, M., Rahbek, C., Zimmermann, N.E. and Guisan, A. (2017) Spatial predictions at the community level: from current approaches to future frameworks. Biological Reviews, 92, 169-187. doi: https://doi.org/10.1111/brv.12222

Francis, A.P. and Currie, D.J. (2003) A globally consistent richness-climate relationship for Angiosperms. American Naturalist, 161, 523-536. doi: https://doi.org/10.1086/368223

Hawkins, B.A. (2001) Ecology's oldest pattern? Trends in Ecology & Evolution, 16, 470. doi: https://doi.org/10.1016/S0169-5347(01)02197-8 

Hawkins, B.A. (2008) Recent progress toward understanding the global diversity gradient. IBS Newsletter, 6.1, 5-8. https://escholarship.org/uc/item/8sr2k1dd

Hawkins, B.A., Field, R., Cornell, H.V., Currie, D.J., Guégan, J.-F., Kaufman, D.M., Kerr, J.T., Mittelbach, G.G., Oberdorff, T., O'Brien, E., Porter, E.E. and Turner, J.R.G. (2003) Energy, water, and broad-scale geographic patterns of species richness. Ecology, 84, 3105-3117. doi: https://doi.org/10.1890/03-8006

Hawkins, B.A., Diniz-Filho, J.A.F., Jaramillo, C.A. and Soeller, S.A. (2006) Post-Eocene climate change, niche conservatism, and the latitudinal diversity gradient of New World birds. Journal of Biogeography, 33, 770-780. doi: https://doi.org/10.1111/j.1365-2699.2006.01452.x

Hawkins, B.A., Albuquerque, F.S., Araújo, M.B., Beck, J., Bini, L.M., Cabrero-Sañudo, F.J., Castro Parga, I., Diniz-Filho, J.A.F., Ferrer-Castán, D., Field, R., Gómez, J.F., Hortal, J., Kerr, J.T., Kitching, I.J., León-Cortés, J.L., et al. (2007a) A global evaluation of metabolic theory as an explanation for terrestrial species richness gradients. Ecology, 88, 1877-1888. doi:10.1890/06-1444.1. doi: https://doi.org/10.1890/06-1444.1

Hawkins, B.A., Diniz-Filho, J.A.F., Bini, L.M., Araújo, M.B., Field, R., Hortal, J., Kerr, J.T., Rahbek, C., Rodríguez, M.Á. and Sanders, N.J. (2007b) Metabolic theory and diversity gradients: Where do we go from here? Ecology, 88, 1898–1902. doi: https://doi.org/10.1890/06-2141.1

Hortal, J., Rodríguez, J., Nieto-Díaz, M. and Lobo, J.M. (2008) Regional and environmental effects on the species richness of mammal assemblages. Journal of Biogeography, 35, 1202–1214. doi: https://doi.org/10.1111/j.1365-2699.2007.01850.x

Kreft, H. and Jetz, W. (2007) Global patterns and determinants of vascular plant diversity. Proceedings of the National Academy of Sciences USA, 104, 5925-5930. doi: https://doi.org/10.1073/pnas.0608361104

O'Brien, E. (1998) Water-energy dynamics, climate, and prediction of woody plant species richness: an interim general model. Journal of Biogeography, 25, 379-398. doi: https://doi.org/10.1046/j.1365-2699.1998.252166.x

Ricklefs, R.E. (1987) Community diversity: Relative roles of local and regional processes. Science, 235, 167-171. doi: https://doi.org/10.1126/science.235.4785.167

Ricklefs, R.E. (2004) A comprehensive framework for global patterns in biodiversity. Ecology Letters, 7, 1-15. doi: https://doi.org/10.1046/j.1461-0248.2003.00554.x

Ricklefs, R.E. (2008) Disintegration of the ecological community. American Naturalist, 172, 741-750. doi: https://doi.org/10.1086/593002

Segovia, R.A. (2021) Temperature predicts the maximum tree-species richness and water and frost shape the residual variation. bioRxiv, 836338, ver. 4 peer-reviewed and recommended by Peer community in Ecology. doi: https://doi.org/10.1101/836338

Segovia, R.A., Pennington, R.T., Baker, T.R., Coelho de Souza, F., Neves, D.M., Davis, C.C., Armesto, J.J., Olivera-Filho, A.T. and Dexter, K.G. (2020) Freezing and water availability structure the evolutionary diversity of trees across the Americas. Science Advances, 6, eaaz5373. doi: https://doi.org/10.1126/sciadv.aaz5373

In most vertebrate species, the period of life spanning from departure from the growing site until reaching a more advanced life stage (immature or adult) is critical. During this period, juveniles are often highly vulnerable because they have not reached the morphological, physiological and behavioural maturity levels of adults yet and are therefore at high risk of mortality, e.g. through starvation, depredation or competition (e.g. Marchetti & Price 1989, Wunderle 1991, Naef-Daenzer & Grüebler 2016). In line with this, juvenile survival is most often far lower than adult survival (e.g. Wooller et al. 1992). In species with parental care, juveniles have to acquire behavioural independence from their parents and possibly establish their own territory during this period of life. Very often, this is also the period that is least well-known in the life cycle (Cox et al. 2014, Naef-Daenzer & Grüebler 2016) because of reduced accessibility to individuals and/or adoption of low conspicuous behaviours. Therefore, our understanding of how juveniles acquire typical adult behaviours and how this progressively increases their survival prospects is still very limited (Naef-Daenzer & Grüebler 2016), and questions such as the length of this transition period or the cognitive (e.g. learning, memorization) mechanisms involved remain largely unresolved. This is particularly true regarding the acquisition of independent foraging behaviour (Marchetti & Price 1989).

Because direct observations of juvenile behaviours are usually very difficult except in specific situations or at the cost of an enormous effort, the use of remote tracking devices can be particularly appealing in this context (e.g. Ponchon et al. 2013, Kays et al. 2015). Over the past decades, technical advances have allowed the monitoring of not only individuals’ movements at both large and small spatial scales but also their activities and behaviours based on different parameters recording e.g. speed of movement or diving depth (Whitford & Klimley 2019). Device miniaturization has in particular allowed smaller species to be equipped and/or longer periods of time to be monitored (e.g. Naef-Daenzer et al. 2005). This has opened up whole fields of research, and has been particularly used on marine seabirds. In these species, individuals are most often inaccessible when at sea, representing most of the time outside (and even within) the breeding season, and the life cycle of these long-lived species can include an extended immature period (up to many years) during which most of them will remain unseen, until they come back as breeders or pre-breeders (e.g. Wooller et al. 1992, Oro & Martínez-Abraín 2009). Survival has been found to increase gradually with age in these species before reaching high values characteristic of the adult stage. However, the mechanisms underlying this increase are still to be deciphered.

The study by Delord et al. (2023) builds upon the hypothesis that juveniles gradually learn foraging techniques and movement strategies, improving their foraging efficiency, as previous data on flight parameters seemed to show in different long-lived bird species. Yet, these previous studies obtained data over a limited period of time, i.e. a few months at best. Whether these data could capture the whole dynamics of the progressive acquisition of foraging and movement skills can only be assessed by measuring behaviour over a longer time period and comparing it to similar data in adults, to account for seasonal variation in relation to both resource availability and energetic demands, e.g. due to molt.

The present study (Delord et al. 2023) addresses these questions by taking advantage of longer-lasting recordings of the location and activity of juvenile, immature and adult birds obtained simultaneously to investigate changes over time in juvenile behaviour and thereby provide hints about how young progressively acquire foraging skills. This study is performed on Amsterdam albatrosses, a highly endangered long-lived sea bird, with obvious conservation issues (Thiebot et al. 2015). The results show progressive changes in foraging effort over the first two months after departure from the birth colony, but large differences remain between life stages over a much longer time frame. They also reveal strong variations between sexes and over time in the year. Overall, this study, therefore, confirms the need for very long-term data to be collected in order to address the question of progressive behavioural maturation and associated survival consequences in such species with strongly deferred maturity. Ideally, the same individuals should be monitored over different life stages, from the juvenile period up to adulthood, but this would require further technical development to release the issue of powering duration limitation.

As reviewers emphasized in the first review round, one main challenge now remains to ascertain the outcome of the observed behavioural changes in foraging behaviour: we expect them to reflect improvement in foraging skills and thus performance of juveniles over time, but this would need to be tested. Collecting data on foraging efficiency is yet another challenge, that future technical developments may also help overcome. Importantly also, data were available only for individuals that could be caught again because the tracking device had to be retrieved from the bird. Here, a substantial fraction of the loggers (one-fifth) could not be found again (Delord et al. 2023). To what extent the birds for which no data could be obtained are a random sample of the equipped birds would also need to be assessed. The further development of remote tracking techniques allowing data to be downloaded from a long distance should help further exploration of behavioural ontogeny of juveniles while maturing and its survival consequences. Because the maturation process explored here is likely to show very different characteristics (e.g. timing and speed) in smaller / shorter-lived species (see Cox et al. 2014, Naef-Daenzer & Grüebler 2016), the development of miniaturization is also expected to allow further investigation of post-fledging behavioural maturation in a wider range of bird species. Our understanding of this crucial life phase in different types of species should thus continue to progress in the coming years.

References

Cox W. A., Thompson F. R. III, Cox A. S. & Faaborg J. 2014. Post-fledging survival in passerine birds and the value of post-fledging studies to conservation. Journal of Wildlife Management, 78: 183-193. https://doi.org/10.1002/jwmg.670

Delord K., Weimerskirch H. & Barbraud C. 2023. The challenges of independence: ontogeny of at-sea behaviour in a long-lived seabird. bioRxiv, ver. 6 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2021.10.23.465439

Kays R., Crofoot M. C., Jetz W. & Wikelski M. 2015. Terrestrial animal tracking as an eye on life and planet. Science, 348 (6240). https://doi.org/10.1126/science.aaa2478

Marchetti K: & Price T. 1989. Differences in the foraging of juvenile and adult birds: the importance of developmental constraints. Biological Reviews, 64: 51-70. https://doi.org/10.1111/j.1469-185X.1989.tb00638.x

Naef-Daenzer B., Fruh D., Stalder M., Wetli P. & Weise E. 2005. Miniaturization (0.2 g) and evaluation of attachment techniques of telemetry transmitters. The Journal of Experimental Biology, 208: 4063–4068. https://doi.org/10.1242/jeb.01870

Naef-Daenzer B. & Grüebler M. U. 2016. Post-fledging survival of altricial birds: ecological determinants and adaptation. Journal of Field Ornithology, 87: 227-250. https://doi.org/10.1111/jofo.12157

Oro D. & Martínez-Abraín A. 2009. Ecology and behavior of seabirds. Marine Ecology, pp.364-389.

Ponchon A., Grémillet D., Doligez B., Chambert T., Tveera T., Gonzàles-Solìs J & Boulinier T. 2013. Tracking prospecting movements involved in breeding habitat selection: insights, pitfalls and perspectives. Methods in Ecology and Evolution, 4: 143-150. https://doi.org/10.1111/j.2041-210x.2012.00259.x

Thiebot J.-B., Delord K., Barbraud C., Marteau C. & Weimerskirch H. 2015. 167 individuals versus millions of hooks: bycatch mitigation in longline fisheries underlies conservation of Amsterdam albatrosses. Aquatic Conservation 26: 674-688. https://doi.org/10.1002/aqc.2578

Whitford M & Klimley A. P. An overview of behavioral, physiological, and environmental sensors used in animal biotelemetry and biologging studies. Animal Biotelemetry, 7: 26. https://doi.org/10.1186/s40317-019-0189-z

Wooller R.D., Bradley J. S. & Croxall J. P. 1992. Long-term population studies of seabirds. Trends in Ecology and Evolution, 7: 111-114. https://doi.org/10.1016/0169-5347(92)90143-y

Wunderle J. M. 1991. Age-specific foraging proficiency in birds. Current Ornithology, 8: 273-324.

 Understanding the effects of environmental perturbations on coexistence is a key challenge in ecology, and models have played an important role in structuring our ideas and generating predictions, leading to quantitative hypotheses. In such models, environmental perturbations are often captured by changes in parameter values, such as the intrinsic growth rates of species (1–3). The question then becomes how much one can change these parameters without breaking coexistence and thus losing species (4). 
 
An intuitively appealing approach to address this question is to calculate a model’s feasibility domain (5–7). Loosely defined, it is the fraction of parameter settings leading to the coexistence of all species. Mathematically speaking, it is a high-dimensional triangle, of which one can calculate the size, just as for plain two-dimensional triangles. Parameter settings outside of this triangle break coexistence. Thus, it seems logical that greater feasibility domains would make for more robust ecosystems. However, careful interpretation is key: a greater feasibility domain merely implies that across many attempts at running a model with different random parameter settings, coexistence will be more frequent. It does not necessarily inform us how much one can perturb the parameters of a community with a predefined parameter setting. To get this information, we also need to know the shape of the triangle (7): perturbations more easily knock the parameter setting out of a flat triangle than out of an equilateral triangle. 
 
Desaillais et al. (8) develop a new theory that sheds light on what drives the shape of the feasibility domain. Specifically, they present the probability distribution that tells how close to the edge of the feasibility domain the parameter settings in that domain tend to be. For example, all points in a very flat triangle are close to its edge, while in an equilateral triangle, most points are safely stowed inside. The results show how, in a Lotka-Volterra model, the matrix of species interactions fully defines this distribution, which makes the technique empirically applicable in so far as one can estimate these interactions. The analysis then continues to explore the role of specific species in putative loss of coexistence. Desaillais et al. identify two species-level quantities: the first measures the total influence of the surrounding community on a focal species, while the second is a proxy for how close that focal species is to being lost, should a perturbation occur. While these two quantities are not mathematically independent, their correlation is not perfect, allowing one to categorize species into distinct ecological roles. A dataset of plant communities with different compositions illustrates how to apply this idea and gain some additional insight into the robustness of coexistence. These results pave the way for a number of potentially rewarding applications. How does the robustness of coexistence differ across network types? For which network types do we find back a more diverse set of ecological roles for species, i.e. for which networks are the two quantities least correlated? 

References

1. Baert, J.M., Janssen, C.R., Sabbe, K., and De Laender, F. (2016). Per capita interactions and stress tolerance drive stress-induced changes in biodiversity effects on ecosystem functions. Nat. Commun. 7, 12486. https://doi.org/10.1038/ncomms12486

2. Pásztor, L., Botta-Dukat, Z., Magyar, G., Czaran, T., and Meszéna, G. (2016). Theory-based ecology: A Darwinian approach 1st ed. (Oxford University Press).

3. Cenci, S., Montero-Castaño, A., and Saavedra, S. (2018). Estimating the effect of the reorganization of interactions on the adaptability of species to changing environments. J. Theor. Biol. 437, 115–125. https://doi.org/10.1016/j.jtbi.2017.10.016

4. Spaak, J.W., Baert, J.M., Baird, D.J., Eisenhauer, N., Maltby, L., Pomati, F., Radchuk, V., Rohr, J.R., Van den Brink, P.J., and De Laender, F. (2017). Shifts of community composition and population density substantially affect ecosystem function despite invariant richness. Ecol. Lett. 20, 1315–1324. https://doi.org/10.1111/ele.12828

5. Meszéna, G., Gyllenberg, M., Pásztor, L., and Metz, J.A.J. (2006). Competitive exclusion and limiting similarity: A unified theory. Theor. Popul. Biol. 69, 68–87. https://doi.org/10.1016/j.tpb.2005.07.001

6. Saavedra, S., Rohr, R.P., Bascompte, J., Godoy, O., Kraft, N.J.B., and Levine, J.M. (2017). A structural approach for understanding multispecies coexistence. Ecol. Monogr. 87, 470–486. https://doi.org/10.1002/ecm.1263

7. Grilli, J., Adorisio, M., Suweis, S., Barabás, G., Banavar, J.R., Allesina, S., and Maritan, A. (2017). Feasibility and coexistence of large ecological communities. Nat. Commun. 8. https://doi.org/10.1038/ncomms14389

8. Desallais M, Loreau M, Arnoldi J.F. (2024) The distribution of distances to the edge of species coexistence. bioRxiv, ver.4 peer-reviewed and recommended by PCI Ecology https://doi.org/10.1101/2024.01.21.575550

In this meta-analysis, Shivani et al. [1] investigate 1) whether dominance and reproductive success are generally associated across social mammals and 2) whether this relationship varies according to a) life history traits (e.g., stronger for species with large litter size), b) ecological conditions (e.g., stronger when resources are limited) and c) the social environment (e.g., stronger for cooperative breeders than for plural breeders). Generally, the results are consistent with their predictions, except there was no clear support for this relationship to be conditional on the ecological conditions. considered

As I have previously recommended the preregistration of this study [2,3], I do not have much to add here, as such recommendation should not depend on the outcome of the study. What I would like to recommend is the whole scientific process performed by the authors, from preregistration sent for peer review, to preprint submission and post-study peer review. It is particularly recommendable to notice that this project was a Masters student project, which shows that it is possible and worthy to preregister studies, even for such rather short-term projects. I strongly congratulate the authors for choosing this process even for an early career short-term project. I think it should be made possible for short-term students to conduct a preregistration study as a research project, without having to present post-study results. I hope this study can encourage a shift in the way we sometimes evaluate students’ projects.

I also recommend the readers to look into the whole pre- and post- study reviewing history of this manuscript and the associated preregistration, as it provides a better understanding of the process and a good example of the associated challenges and benefits [4]. It was a really enriching experience and I encourage others to submit and review preregistrations and registered reports!

References

[1] Shivani, Huchard, E., Lukas, D. (2022). The effect of dominance rank on female reproductive success in social mammals. EcoEvoRxiv, rc8na, ver. 10 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.32942/osf.io/rc8na

[2] Shivani, Huchard, E., Lukas, D. (2020). Preregistration - The effect of dominance rank on female reproductive success in social mammals In principle acceptance by PCI Ecology of the version 1.2 on 07 July 2020. https://dieterlukas.github.io/Preregistration_MetaAnalysis_RankSuccess.html

[3] Paquet, M. (2020) Why are dominant females not always showing higher reproductive success? A preregistration of a meta-analysis on social mammals. Peer Community in Ecology, 100056. https://doi.org/10.24072/pci.ecology.100056

[4] Parker, T., Fraser, H., & Nakagawa, S. (2019). Making conservation science more reliable with preregistration and registered reports. Conservation Biology, 33(4), 747-750. https://doi.org/10.1111/cobi.13342

In his 1972 paper “Will a Large Complex System Be Stable?” [1], May challenges the idea that large communities are more stable than small ones. This was the beginning of a fundamental debate that still structures an entire research area in ecology: the diversity-stability debate [2]. The most salient strength of May’s work was to use a mathematical argument to refute an idea based on the observations that simple communities are less stable than large ones. Using the formalism of dynamical systems and a major results on the distribution of the eigen values for random matrices, May demonstrated that the addition of random interactions destabilizes ecological communities and thus, rich communities with a higher number of interactions should be less stable. But May also noted that his mathematical argument holds true only if ecological interactions are randomly distributed and thus concluded that this must not be true! This is how the contradiction between mathematics and empirical observations led to new developments in the study of ecological networks.
Since 1972, the theoretical corpus of ecology has advanced, building on the formalism of dynamical systems, ecologists have revealed that ecological interactions are indeed not randomly distributed [3,4], but general rules are still missing and we are far from understanding what determine the exact network topology of a given community. One promising avenue is to understand the relationship between different facets of the concept of stability [5,6]. Indeed, the classical approach to determine whether a system is stable is qualitative: if a system returns to its equilibrium when it is slightly moved away from it, then the system is considered stable. But there are several other aspects that are worth scrutinizing. For instance, when a system returns to its equilibrium, one can characterize the corresponding transient dynamics [7,8], that is asking fundamental questions such as: what is the trajectory of return? How long does it take to return to the equilibrium? Another fundamental question is whether the system remains qualitatively stable when the distributions of interactions strengths change? From a biological standpoint, all of these questions matter as all these aspects of stability may partially explain the actual structure of ecological networks, and hence, frameworks that integrate several facets of stability are much needed.
The study by Arnoldi et al. [9] is a significant step towards such a framework. The strength of their formalism is threefold. First, instead of considering separately the system and its perturbations, they considering the fluctuations of a perturbed ecological systems and thus, perturbations are parts of the ecological system. Second, they use of a broad definition of perturbation that encompasses the types of perturbations (whether the individual respond synchronously or not), their intensity and their direction (how the perturbations are correlated across species). Third, they quantify the instability of the system using variability which integrates the consequences of perturbations over the whole set of species of a community: such a measure is comparable across communities and accounts for the trivial effect of the perturbations on the system dynamics.
Using this framework, the authors show that interactions within a stable community leads to a general relationship between variability and the abundance of individually perturbed species: if individuals of species respond in synchrony to a perturbation, then the more abundant the species perturbed the higher the variability of the system, but the relationship is reverse when individual respond asynchronously. A direct implications of these results for the classical debate is that the diversity-stability relationship is negative for the former type of perturbations (as in May’s seminal paper) but positive for the latter type. Hence, the rigorous work of Arnoldi and colleagues sheds a new light upon the classical debate: the nature of the perturbation regime prevailing within a community affects the slope of the diversity-stability relationships and given the vast diversity of ecological communities, this may very well be one of the reasons why the debate still endures.
From a historical perspective, it is interesting that ecologists have gone from looking at random webs to structured webs and now, in a sense, Arnoldi et al. are unpacking the role of differentially structured perturbations. The work they achieved will doubtlessly be followed by further theoretical investigations. One natural research avenue is to revisit the role of the topology of ecological networks with this framework: how the distribution of interactions and their strength affect the general relationship they unravel? Finally, this study demonstrate that the impact of the abundance of a species on the variability of the system depends on the nature of the perturbation regime and so the distribution of species abundances within a community should be determined by the prevailing perturbation regime which is a prediction that remains to be tested.

References

[1] May, Robert M (1972). Will a Large Complex System Be Stable? Nature 238, 413–414. doi: 10.1038/238413a0
[2] McCann, Kevin Shear (2000). The Diversity–Stability Debate. Nature 405, 228–233. doi: 10.1038/35012234
[3] Rooney, Neil, Kevin McCann, Gabriel Gellner, and John C. Moore (2006). Structural Asymmetry and the Stability of Diverse Food Webs. Nature 442, 265–269. doi: 10.1038/nature04887
[4] Jacquet, Claire, Charlotte Moritz, Lyne Morissette, Pierre Legagneux, François Massol, Philippe Archambault, and Dominique Gravel (2016). No Complexity–Stability Relationship in Empirical Ecosystems. Nature Communications 7, 12573. doi: 10.1038/ncomms12573
[5] Donohue, Ian, Helmut Hillebrand, José M. Montoya, Owen L. Petchey, Stuart L. Pimm, Mike S. Fowler, Kevin Healy, et al. (2016). Navigating the Complexity of Ecological Stability. Ecology Letters 19, 1172–1185. doi: 10.1111/ele.12648
[6] Arnoldi, Jean-François, and Bart Haegeman (2016). Unifying Dynamical and Structural Stability of Equilibria. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 472, 20150874. doi: 10.1098/rspa.2015.0874
[7] Caswell, Hal, and Michael G. Neubert (2005). Reactivity and Transient Dynamics of Discrete-Time Ecological Systems. Journal of Difference Equations and Applications 11, 295–310. doi: 10.1080/10236190412331335382
[8] Arnoldi, J-F., M. Loreau, and B. Haegeman (2016). Resilience, Reactivity and Variability: A Mathematical Comparison of Ecological Stability Measures. Journal of Theoretical Biology 389, 47–59. doi: 10.1016/j.jtbi.2015.10.012
[9] Arnoldi, Jean-Francois, Michel Loreau, and Bart Haegeman. (2019). The Inherent Multidimensionality of Temporal Variability: How Common and Rare Species Shape Stability Patterns.” BioRxiv, 431296, ver. 3 peer-reviewed and recommended by PCI Ecology. doi: 10.1101/431296