Diversity and Destructive Oscillations: Camerano, Elton, and May

In a greatly simplified sense, the universe can be conceived as an enormous dynamical system governed by feedbacks that span scales up to, and including, the cosmos. Within this whole-universe perspective, ecology forms an extremely dynamic subset, replete with feedbacks that start from some of the smallest scales (DNA) and extend all the way to the scale of the whole planet. This dynamic volatility, and its accompanying multi-scale feedbacks, makes for a fascinating area of study. While excellent work in ecology has compartmentalized subdisciplines with great success (e.g., population ecology), I want to briefly consider here an area of ecology that attempts to conceptually tackle the ground across ecological subdisciplines, and asks how multi-scale feedbacks govern the dynamics of whole ecological systems. It is the intrepid who tackle such complexity, and yet the very nature of ecology has pushed many scientists to attempt a glimpse into the inner workings of the machinery that comprises a whole set of interacting species within an environmental context (i.e., a food web or ecosystem). In this short piece, I will discuss some of the pioneers of this scientific frontier and the viewpoints that have challenged, and inspired, us to consider ecosystems from a unified perspective. Ecologists have long pondered the interconnectedness of life, and the dynamical implications of this web of interactions. In an early contribution unearthed by Joel Cohen (1994), Lorenzo Camerano (1880) envisioned the ecological network as a massive set of interactions that, when perturbed, yield decaying oscillations that spread through a food web in a manner akin to the way sound resonates through a pipe organ. The interaction of many singular sound frequencies (oscillations) merge into a coherent spectrum of sound, with some frequencies muted and others magnified. It is intriguing that this description from a young naturalist was phrased so abstractly. Here, Camerano (1880) was referring to the spectrum of sound frequencies as a metaphor for the spectrum of population dynamic frequencies that are associated with any given interaction (Fig. 1). Intriguingly, later theoretical development in both population and food web ecology would begin to think about decomposing whole system dynamics into their inherent species frequencies (oscillations), as well as attempt to discern the rules that govern the interactions of the many frequencies that underlie a network. The math of sound waves, whereby waves can add and become more “destructive” (i.e., of greater amplitude), cancel each other out, or create entirely new spectra. … the balance of relatively simple communities of plants and animals is more easily upset than that of richer ones; that is more subject to destructive oscillations in population (Elton 1958). With this, Elton crystalizes the notion of an oscillation as a potentially destructive agent in a whole food web, and simultaneously suggests that a complex, diverse set of interactions may cancel such destructive oscillations in a manner not unlike the way sound waves can cancel each other. We will see that our modern view is not entirely different from this intuitive perspective. The stage was set for a suite of more mathematically trained biologists to run with these metaphors. In the 1970s, Robert May formally considered Elton's intuitive arguments—that is, that simple models were more unstable, while diverse models will be less prone to “destructive oscillations.” May's contributions stemming from this work have had an enormous and continuing impact on ecology. I often think that we, as scientists, can discover things because of our unique personal history. Robert May, for example, studied relatively simple, dynamically rich, nonlinear systems (May 1976); while simultaneously trying to piece the whole ecosystem together using an equilibrium perspective (i.e., the community matrix). This combination meant that his interpretation of the more static whole-systems matrix results was strongly influenced by his understanding of the nonlinear properties (e.g., oscillators) of more simple dynamical systems. This combined perspective led him to make several whole-system conjectures that have proven extremely valuable (e.g., that weak interactions and compartments may be pivotal to maintaining diverse functioning ecosystems). … the fallacy in the intuitive [diversity-stability] argument is that, the greater the size and connectance of a web, the larger the number of modes of oscillations it possesses, since each mode is as likely to be unstable as stable” (May 1973:75). In a sense, May had mentally decomposed the whole food web into a set of many coupled consumer-resource (C-R) oscillators, and argued that, all else equal, this allows us to understand the destabilizing potential of “unstructured” diversity. Specifically, diversity, so unstructured, ought to produce chains of wild, and destructive, coupled oscillators. While May's result seems hard to refute in randomly assembled systems, the results appear to change when interactions of different types are coupled together in a nonrandom manner. Much like Camerano's (1880) spectrum of sound, where sound waves can mute frequencies, we find that diversity accompanied by specific food web structures may not always inspire destructive oscillations, but rather may act to cancel out such destabilizing oscillations. More recent results, including the weak interaction effect, are really just extensions of this notion of coupled oscillators. Specifically, more modern results push this metaphor a little farther by asking how structure can “mute” or “excite” potentially destructive consumer resource oscillations. The weak interaction effect really just acknowledges that weak interactions can deflect energy away from a potentially destructive consumer resource oscillator (i.e., potential, here, means that if the interaction was isolated, it would oscillate violently). Thus, upon inspection, the modern result is really a rather modest extension, or unification, of the historical ideas of Camerano, Elton, and May. One, not all C-R interactions are oscillators (some C-R couplings are nondestructive) and, two, the position of a nondestructive interaction has the ability to mute or cancel the destructive capacity of another interaction.

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