Summary of my PhD thesis

The Long March for PhD finally came to the end. I am proud of what came out of it. Though all my research projects had quite different motivations originally, they all came together forming a consistent theme: an environment-dependent framework to study how ecological networks maintain or change biodiversity in local ecological communities.

A short background story. My advisor pushed really hard on my PhD proposal. I spent almost an entire semester working on it, rewriting four different versions. But he was still not happy with the outcome and asked me to rewrite it and reschedule the committee meeting. I was, of course, disappointed but, in the meantime, also puzzled by why he cared so much about the PhD proposal: in the end, nobody reads my thesis and why shouldn’t I just paste my papers together and that’s it. However, after finishing the PhD thesis, I now realized that he was right: it is a rare opportunity to think hard and deep what my works together have contributed to the literature.

Hither Thou Shalt Come, But No Further

What determines and maintains biodiversity? This central question in ecology cannot be answered by studying species or organisms individually because no species is an island [1]. Instead, overwhelming observational and experimental evidence supports that species interactions are central for the persistence of almost every form of life on Earth [2, 3]. Thus, ecologists have centered their focus on the scale of local ecological communities—the set of interacting species in a given location and time [4–6]. Ecological communities are everywhere, ranging from the tiny microbiome in our guts to the food webs present in the rain forests. Thus, understanding the dynamics of ecological communities is not only essential to decipher the mechanisms of biodiversity maintenance, but it also has direct relevance for many other scientific fields. For example, understanding the dynamics of the gut microbiome from person to person is essential for human health, and understanding the dynamics of food webs from location to location is essential for ecosystem services.

Importantly, life does not operate in a static vacuum but in a fluctuating natural environment. Thus, a key challenge in the path towards a general understanding of ecological communities is how to deal with pervasive uncertain environmental factors. Broadly speaking, this challenge has been relatively well tackled in the micro-scale (one to two species) and macro-scale communities (hundreds and thousands of species) but less so in the meso-scale (in between micro- and macro-scales). The reason behind this phenomena is the relationship between the scale of the study and the environmental factors [1, 7, 8]: In micro-scale communities, manageable experiments can reveal the causal mechanisms by controlling the environmental factors. In macro-scale communities, statistical patterns emerge despite uncertain environmental factors. Indeed, the majority of successful theories in community ecology have their strongest explanation power in either the dynamics of the micro-scale communities or that of the macro-scale communities. For example, Contemporary Niche Theory [9, 10] and Modern Coexistence Theory [11, 12] work better for the micro-scale communities [13–15], while Neutral Theory [16, 17], and Maximum Entropy Theory [18, 19] work better for the macro-scale communities [20, 21].

The meso-scale communities cannot escape from the claws of uncertain environmental factors. Importantly, a failure in confronting uncertain environmental factors may cause contingency or context-dependency—results are only true under particular circumstances and generalizations may be an unjustifiable extrapolation. Consequently, some community ecologists have suggested that it may be futile to search for any general laws of species coexistence in meso-scale communities [1, 22]. Yet, the meso-scale is the typical characteristic scale of the majority of ecological communities in nature. Then, does it imply that we have to study ecological communities on a case-by-case basis?

The network approach and the emerging debates

In light of this fundamental obstacle established above, an emerging research line focuses on ecological networks—the organization of species interactions within an ecological community. Specifically, an ecological network of an ecological community is built by considering the species as the nodes and the species interactions as the links [23]. The idea of ecological networks is nothing new; Charles Darwin has already proposed the metaphor ``entangled bank’’ to describe an ecological community [24]. Different from the traditional approach, the defining theme in this research line is to uncover the universal patterns of ecological networks in different ecological communities [25–27]. That is, despite the fluctuating environmental factors on each ecological community, ecological networks may still exhibit common backbone structures, which can reveal general mechanisms of species coexistence across different contexts. For example, many ecologists believe that modularity is a universal structure in food webs, while nestedness is a universal structure in mutualistic communities. See Figure 1.

Figure 1. Two ecological network structures. Here we present an illustration of two hypothetical network structures. The ecological network is represented as a matrix. The columns correspond to different plant species while the rows correspond to different pollinators (in Panel A) or herbivores (in Panel B). A species interaction is represented as a gray grid. Panel (A) illustrates the nested structure. The defining feature of a nested structure is that highly connected species interact with both highly connected and poorly connected species, while poorly connected species interact almost exclusively with highly connected species. Panel (B) illustrates the modular structure. The defining feature of the modular structure is that in which groups of species have many interactions among them, but few interactions with the rest of the species in the network.

However, this approach has been seriously challenged in the past decade. Take the nested structure in mutualistic interactions as an example. Since its discovery at the beginning of the 21st century [[28]}, the study on the nested pattern has become one of the hottest topics in theoretical ecology [29–37]. However, ecologists struggled to come to a consensus after decades of research. Instead, ecologists have been divided into three schools of thought. The first school, the mainstream, believes that nested structure is a key factor to support biodiversity in mutualistic communities [35, 36, 38]. The second school believes that there is no causal relationship between the nested pattern and biodiversity [34, 39–41]. The third school believes that nested patterns are not universal in observed mutualistic communities [42–44], thus makes the whole question a straw man. Obviously, these three schools of thought are not compatible. Figure 2 illustrates the causal diagrams between nestedness and species coexistence in these three schools of thought. Similar debates also exist in the study of other network structures such as modularity in food webs [45–49].

Figure 2. The debates in the study of ecological networks. Three different schools of thought coexist in linking nestedness and species coexistence in mutualistic communities.

In essence, the debates arise from the fact that many observed ecological networks deviated strongly from these so-called universal structures [44]. Different schools of thought have drastically different attitudes towards these noises. The first school considers these deviations as purely noises. The second school considers these deviations as the evidence that nestedness is a byproduct rather than the cause of biodiversity. The third school considers these deviations so strong that these universal structures themselves should be considered as noise. Thus, while the network approach holds great promise to overcome the contingency in (meso-scale) ecological communities, it does not live up to the naive expectation that all communities would exhibit similar structures.

Thesis statement

The debates on the network approach strongly suggest that the generalities of ecological communities can only be unveiled by viewing environmental factors as general constraints instead of ignoring them. Thus, I propose an environment-dependent perspective. The environment-dependent perspective argues that, instead of considering the deviations from the universal structures as noises, we should consider them as signatures of the differences of environmental factors acting on the ecological communities. Specifically, under the environment-dependent perspective, every ecological network can be decomposed into a universal structure and a particular structure. The universal structure is mainly shaped by biotic constraints while the particular structure is mainly shaped by environmental pressures. Then, by leveraging upon the interplay between the universal and the particular structures, we can find the common ground to reconcile the debates and may lead to general understandings of ecological networks.

This idea of an environment-dependent perspective was inspired by the structuralist view in evolutionary biology [50, 51]. The structuralist view has provided a systematic and probabilistic way of understanding the diversity (or lack of diversity) that we observe in nature. That is, contingency does not necessarily imply intractability but instead calls for a probabilistic way to disentangle the complexity of nature. In line with the key insight of the structuralist view, we argue that the environment-dependent perspective can be naturally framed under the notion of structural stability, which can be conceptualized as the range of tolerance to environmental perturbations on system parameters before losing species coexistence. That is, structural stability provides a probabilistic measure of species coexistence in a world with unpredictable environmental perturbations: the larger the structural stability, the more likely the species can coexist under random environmental perturbations. The first part of this thesis provides a probabilistic, scale-dependent, rigorous framework to formalize the environment-dependent framework.

Figure 3. The causal diagram in the environment-dependent perspective of ecological networks. The nodes denote the key elements in ecological dynamics. The black links represent the ecological processes (denoted in blue) that connect these elements. The chapters of this thesis (denoted in orange) provide theoretical predictions from the environment-dependent framework and the empirical validation.

Building upon the mathematical framework, the environment-dependent perspective provides a general casual diagram to understand and predict the dynamics of ecological communities (Figure 3). The dynamics of a local ecological community is determined by four key elements: the species pool, community structure, environment, species coexistence [5]. The causal links between these elements are important ecological processes. The species pool affects the ecological network via the community assembly process. And the ecological network and species coexistence have a feedback loop. That is, the population dynamics links the ecological network to species coexistence, while the structural transformation links species coexistence back to the ecological network. And the environment is a confounder of the ecological network and species coexistence. That is, the ecological network changes along the environmental gradient, and species coexistence is endangered by environmental stress. The second part of this thesis provides a testable prediction of how the environment-dependent can deepen our understanding of each and every one of these links, along with empirical validation.

Overview of the thesis

The thesis is organized into Methods and Applications:


  • Cenci*, Song*, Saavedra. Ecology & Evolution (2018) (Chapter 1) discusses in detail why we need an environment-dependent perceptive to analyze ecological networks. The importance of a network structure changes as a function of the environmental perturbations acting on a community at any given point in time. Thus, there is no one better network structure than others in general, but all is in the eyes of the local environment.
  • Song & Saavedra. Ecology (2018) (Chapter 2) discusses the importance of the intrinsic growth rates as an environment-mediates demographic parameters. We show that a long-standing debate in ecology was originated from the underestimation of the association of the parameter space of intrinsic growth rates with species coexistence. Thus, a more systematic exploration of the feasible parameter space of intrinsic growth rates is necessary to derive general conclusions about the coexistence patterns of ecological communities.
  • Song, Rohr, Saavedra. J. of Theoretical Biology (2018) (Chapter 3) builds the mathematical framework of structural stability. We develop a quantitative estimation of structural stability for arbitrary ecological network structures with any interaction type and trophic constraints. Importantly, this methodology works for a large class of nonlinear population dynamics and scales.


  • Song, Rohr, Saavedra. J. of Animal Ecology (2017) (Chapter 4) shows how the environment-dependent framework reconcile the contrasting views on nestedness in mutualistic communities (environmental gradient in Fig 3). The environment-dependent framework predicts that more nested network structures can increase the structural stability, which should be more advantageous and occur more often in locations subject to random environmental perturbations. The empirical mutualistic networks show that higher levels of nestedness are indeed associated with a higher temperature seasonality.
  • [Song & Saavedra. PLoS Comp. Biology (2020)] (Chapter 5) shows how the environment-dependent framework solves a central computational challenge to tell apart antagonistic and mutualistic networks (environmental gradient in Fig 3). It is widely believed that the network structures encode unique features for different species interaction types. Michalska-Smith and Allesina (2019) showed it was practically impossible to differentiate ecological interactions based on network structures. This differentiation becomes possible by adding the local environmental information where the networks were sampled.
  • Song, Rohr, Vasseur, Saavedra. J. of Ecology (2020) (Chapter 6) shows how the environment-dependent framework can disentangle the environmental stress (environmental stress in Fig 3). We show a general trade-off: increasing the tolerance to perturbations in intrinsic growth rates typically decreases the tolerance in competition strengths. We find empirical evidence that the tolerance to perturbations in intrinsic growth rates is maximized instead of that to perturbations in competition strengths in the studied annual plant communities.
  • Song & Saavedra. Proc. Roy. Soc. B (2018) (Chapter 7) shows how the environment-dependent framework can consistently predict the phenological events (structural transformation in Fig 3). We test our measure of structural stability as a predictor of changes in species richness recorded on a daily basis in a high-arctic plant-pollinator community during two spring seasons. We find that the structural stability is the only consistent predictor of changes in species richness among different ecological and environmental variables.
  • Song, Altermatt, Pearse, Saavedra. Ecology Letters (2018) (Chapter 8) shows how the environment-dependent framework can decipher the assembly rules (community assembly in Fig 3). By leveraging on the trend of how the structural stability changes as the community assembles, we can identify the most likely assembly rules from observational data. Using the registry of the last 2000 years of plant introductions and their novel herbivores encountered in Central Europe, we find that the order of arrival of closely-related (but not of distantly-related) plant species is the key assembly rule.
  • Song, Von Ahn, Rohr, Saavedra. Trends in Ecology & Evolution (2020) (Chapter 9) shows how the environment-dependent framework can help understand the context-dependency of species interactions (population dynamics in Fig 3). Empirical studies have shown that an interaction class between two species may switch to a different class depending on the biotic and abiotic contexts. We propose an overarching theoretical framework, by integrating probabilistic and structural approaches, to establish null expectations about switches of interaction classes across environmental contexts.


1. Lawton, J. H. (1999). Are there general laws in ecology? Oikos, 84, 177–192.

2. Thompson, J. N. (2005). The geographic mosaic of coevolution. University of Chicago Press, Chicago, IL.

3. Grant, P. R., & Grant, B. R. (2014). 40 years of evolution. Darwin’s finches on daphne major island. Princeton Univ. Press, Princeton.

4. Hutchinson, G. E. (1978). An introduction to population ecology. Yale University Press.

5. Vellend, M. (2016). The theory of ecological communities. Princeton University Press, Princeton, NJ.

6. Levine, J. M., Bascompte, J., Adler, P. B., & Allesina, S. (2017). Beyond pairwise mechanisms of species coexistence in complex communities. Nature, 546, 56.

7. Levin, S. A. (1992). The problem of pattern and scale in ecology: The Robert H. MacArthur award lecture. Ecology, 73(6), 1943–1967.

8. Wang, S. (2018). Simplicity from complex interactions. Nature Ecology and Evolution, 2(8), 1201–1202.

9. Tilman, D. (1982). Resource competition and community structure. Princeton University Press, Princeton, NJ.

10. Chase, J. M., & Leibold, M. A. (2003). Ecological niches: Linking classical and contemporary approaches. University of Chicago Press.

11. Chesson, P. (2000). Mechanisms of maintenance of species diversity. Annual Review of Ecology, Evolution, and Systematics, 31(1), 343–366.

12. Adler, P. B., HilleRisLambers, J., & Levine, J. M. (2007). A niche for neutrality. Ecology Letters, 10(2), 95–104.

13. Letten, A. D., Ke, P.-J., & Fukami, T. (2017). Linking modern coexistence theory and contemporary niche theory. Ecological Monographs, 87(2), 161–177.

14. Barabás, G., D’Andrea, R., & Stump, S. M. (2018). Chesson’s coexistence theory. Ecological Monographs, 88(3), 277–303.

15. Song, C., Barabás, G., & Saavedra, S. (2019). On the consequences of the interdependence of stabilizing and equalizing mechanisms. The American Naturalist, 194(5), 627–639.

16. Hubbell, S. P. (1997). A unified theory of biogeography and relative species abundance and its application to tropical rain forests and coral reefs. Coral reefs, 16(5), S9–S21.

17. Zhou, S.-R., & Zhang, D.-Y. (2008). A nearly neutral model of biodiversity. Ecology, 89(1), 248–258.

18. Harte, J. (2011). Maximum entropy and ecology : A theory of abundance, distribution, and energetics. Oxford: Oxford University Press.

19. Harte, J., & Newman, E. A. (2014). Maximum information entropy: A foundation for ecological theory. Trends in Ecology and Evolution, 29(7), 384–389.

20. Azaele, S., Suweis, S., Grilli, J., Volkov, I., Banavar, J. R., & Maritan, A. (2016). Statistical mechanics of ecological systems: Neutral theory and beyond. Reviews of Modern Physics, 88(3), 35003.

21. O?Dwyer, J. P., Rominger, A., & Xiao, X. (2017). Reinterpreting maximum entropy in ecology: A null hypothesis constrained by ecological mechanism. Ecology letters, 20(7), 832–841.

22. Currie, D. J. (2019). Where newton might have taken ecology. Global Ecology and Biogeography, 28(1), 18–27.

23. May, R. M. (2006). Network structure and the biology of populations. Trends in Ecology and Evolution, 21(7), 394–399.

24. Darwin, C. (1909). The origin of species. P. F. Collier & Son.

25. Garlaschelli, D., Caldarelli, G., & Pietronero, L. (2003). Universal scaling relations in food webs. Nature, 423(6936), 165–168.

26. Proulx, S. R., Promislow, D. E., & Phillips, P. C. (2005). Network thinking in ecology and evolution. Trends in Ecology and Evolution, 20(6), 345–353.

27. Bascompte, J. (2010). Structure and dynamics of ecological networks. Science, 329(5993), 765–766.

28. Bascompte, J., Jordano, P., Melián, C. J., & Olesen, J. M. (2003). The nested assembly of plant–animal mutualistic networks. Proceedings of the National Academy of Sciences, 100(16), 9383–9387.

29. Bastolla, U., Lssig, M., Manrubia, S. C., & Valleriani, A. (2005). Biodiversity in model ecosystems, i: Coexistence conditions for competing species. J. Theor. Biol., 235, 521–530.

30. Montoya, J. M., Pimm, S. L., & Solé, R. V. (2006). Ecological networks and their fragility. Nature, 442(7100), 259–264.

31. Thébault, E., & Fontaine, C. (2010). Stability of ecological communities and the architecture of mutualistic and trophic networks. Science, 329(5993), 853–856.

32. Saavedra, S., Stouffer, D. B., Uzzi, B., & Bascompte, J. (2011). Strong contributors to network persistence are the most vulnerable to extinction. Nature, 478(7368), 233–235.

33. Allesina, S., & Tang, S. (2012). Stability criteria for complex ecosystems. Nature, 483(7388), 205–208.

34. James, A., Pitchford, J. W., & Plank, M. J. (2012). Disentangling nestedness from models of ecological complexity. Nature, 487(7406), 227–230.

35. Suweis, S., Simini, F., Banavar, J. R., & Maritan, A. (2013). Emergence of structural and dynamical properties of ecological mutualistic networks. Nature, 500(7463), 449.

36. Rohr, R. P., Saavedra, S., & Bascompte, J. (2014). On the structural stability of mutualistic systems. Science, 345(6195), 1253497.

37. Guimarães Jr, P. R., Pires, M. M., Jordano, P., Bascompte, J., & Thompson, J. N. (2017). Indirect effects drive coevolution in mutualistic networks. Nature, 550(7677), 511.

38. Bastolla, U., Fortuna, M. A., Pascual-Garcı́a, A., Ferrera, A., Luque, B., & Bascompte, J. (2009). The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature, 458(7241), 1018–1020.

39. James, A., Pitchford, J. W., & Plank, M. J. (2013). James et al. Reply. Nature, 500(7463), E2–E3.

40. Barabás, G., J. Michalska-Smith, M., & Allesina, S. (2016). The effect of intra-and interspecific competition on coexistence in multispecies communities. The American Naturalist, 188(1), E1–E12.

41. Valverde, S., Piñero, J., Corominas-Murtra, B., Montoya, J., Joppa, L., & Solé, R. (2018). The architecture of mutualistic networks as an evolutionary spandrel. Nature Ecology and Evolution, 2(1), 94–99.

42. Staniczenko, P. P., Kopp, J. C., & Allesina, S. (2013). The ghost of nestedness in ecological networks. Nature Communications, 4(1), 1–6.

43. Payrató-Borràs, C., Hernández, L., & Moreno, Y. (2019). Breaking the spell of nestedness: The entropic origin of nestedness in mutualistic systems. Physical Review X, 9(3), 31024.

44. Michalska-Smith, S., Matthew J. AND Allesina. (2019). Telling ecological networks apart by their structure: A computational challenge. PLoS Computational Biology, 15(6), 1–13.

45. May, R. M. (1972). Will a large complex system be stable? Nature, 238(5364), 413.

46. Solow, A. R., Costello, C., & Beet, A. (1999). On an early result on stability and complexity. The American Naturalist, 154(5), 587–588.

47. Stouffer, D. B., & Bascompte, J. (2011). Compartmentalization increases food-web persistence. Proceedings of the National Academy of Sciences, 108(9), 3648–3652.

48. Grilli, J., Rogers, T., & Allesina, S. (2016). Modularity and stability in ecological communities. Nature Communications, 7(1), 1–10.

49. Cenci, S., Song, C., & Saavedra, S. (2018). Rethinking the importance of the structure of ecological networks under an environment-dependent framework. Ecology and Evolution, 8(14), 6852–6859.

50. Alberch, P. (1989). The logic of monsters: Evidence for internal constraint in development and evolution. Geobios, 22, 21–57.

51. Gould, S. J. (2002). The structure of evolutionary theory. Harvard University Press, Cambridge, MA.

Chuliang Song
Chuliang Song
(Incoming) Asssistant Professor

I am a quantitative ecologist driven by the curiosity of how biodiversity is generated and maintained.

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