Recently my former group published one paper about the stability of complex food network in the journal ‘Science’. This is not my direction. But I am near enough to understand their ideas of research.
The basic question came from Robert May in the 70s. He found that there is a dilemma between the theory and the observation. People generally believe that the diversity in an ecological system makes it stable. But May showed it mathematically that with increasing connection links and interactive nodes, an ecological system will become more and more unstable. People with the experience of solving large nonlinear differential equations know that the system becomes more and more difficult to have steady states if the number of equations increase. So
Which is correct: our intuition or our model?
In this papery, they used a small trick before the simulation. If there is a steady state in a dynamic system, you can always re-scale the time for different variables to normalize one steady state to an unit vector = (1, 1, …, 1). Then you can do usual stability analysis around this point. Based on Monte Carlo sampling of different parameters, you will know how they effect the stability of the system around this steady state locally.
Using this half-analytical-half-numeric method, they generated 100 million food webs randomly and made a statistic how different factors effect the stability. They found that more connections and more species really de-stabilize the ecological system. That is, in a forest, if trees, birds, insects etc. form more connections and there are more species, the ecological system in this forest will be more inclined to collapse! (Really unintuitive?) The other conclusion is that the food web will be more stable if top predators like lions, tigers die fast, or they can eat more deer when deer population increases.
This kind of idea is actually not new. In 1960s, when Kauffman tried to study the gene regulatory network of the living organism, he did the same thing by creating millions of random networks since the real genetic networks would come decades later (He simply can not wait). Based on his statistics on all these random gene networks, Kauffman concluded that if we need an evolution in Life, we have to have our gene network at the edge of Chaos. That is, it is not either in deterministic system with the fixed number of steady states, nor in totally chaos without any steady states at all. It is just at this delicate zone in between.
Could this complexity analysis with large number of simulations will reveal more ‘emergent properties’ in Life? Let’s just wait and see.
Ref:
Nice post.
The paper is fascinating, and gives new insights into the stability conditions. This relates to the original work of May, in which he surmised weaker average interaction strength is likely to confer stability to large ecosystems with large SC (here N x C). And recent empirical data and models suggest that large systems do have very weak average interaction strength, leading to longer persistence of real ecosystems. However, the relationship between S & C changes from negative to positive (even exponential) when the resolution of component species and their interactions becomes higher. Works by Cohen and Briand described the hyperbolic decline of C with N, whereas more recent, detailed studies showed L increasing exponentially with N. Models incorporating the empirical details also corroborate this relationship.
However, stability analyses of random food web models look into Lyapunov stability of connected systems, although it is now understood that natural systems are seldom stable. No wonder the more realistic model ecosystems will show less and less stability. We should look into the Lagrangian stability, or persistence. Resilience in terms of return time of the system is also important.
I would request the great scientists like you to focus on the resilience and system persistence, rather than stability. I am willing to share my empirical data collected from agroecosystems over 6 years.