The effect of shared vulnerabilities on the survival of complex systems

Abstract

Biological systems are a model of self-correction and stability in the face of disruptions. Yet not all biological systems survive. Studying what distinguishes species that do from those that go extinct can provide insight into the basis of robustness in complex adaptive systems.

We propose to test, via modeling, data analysis and experimentation, a novel multi-species dynamic equilibrium theory we have put forth recently that states that the fate of complex interdependent systems depends on whether they share vulnerabilities to disruptions with competing systems. Sets of systems with shared vulnerabilities will exhibit self-corrective forces that depend on the collective size of the set rather than on that of individual species, and thus individual species will go extinct. Systems with no shared vulnerabilities will, in contrast, exhibit self-corrective forces that are a function of their size and show long-term stability.

1. Overview of the Problem

What makes some systems survive and others break down in complex systems of systems?

• Biodiversity and Human Capital as Critical Resources: Biodiversity is a critical resource, with community ecology emerging as a significant intellectual frontier.
• Biodiversity as a Source of Energy: The global ecosystem is a massive energy harvester; understanding how species function together is vital for designing engineered communities.
• Biodiversity as a Model System: Eco-biological systems are the oldest and most complex systems known, offering insights applicable to other critical infrastructures like human capital.

Biodiversity: A Puzzle of Evolution & Ecology

Why does biodiversity persist despite Darwinian theory suggesting that only the fittest should survive? While standard doctrine suggests competition should drive all but the fittest to extinction, empirical evidence shows that multiple species often coexist within the same niche, and high levels of genetic polymorphism persist within species. This forces a reevaluation of established evolutionary tenets.

2. Proposed R&D

2.1. Technical Approach

We propose to frame the coexistence of genotypes through dynamic equilibrium. We identify parasites as a key force in determining population sizes, as parasite-driven mortality increases with population density. The theory predicts that species sharing vulnerabilities will compete until extinction, whereas those with unique vulnerabilities can coexist stably. This "arms race" against parasites is posited as a primary driver of biodiversity and genetic variation.

2.2. Key R&D Goals and Project Milestones

FY 05: Demonstrating the Theory In Computo

• Oct. 2004: Verify assumptions of disease-related mortality as a function of population size.
• Nov. 2004: Demonstrate stable co-existence equilibria in ecological models.
• Dec. 2004: Test the impact of parasite elimination on biodiversity.
• March 2005: Observe clustering of species in genetic space.
• April 2005: Apply theory to morphogenesis.
• May 2005: Contrast parasitic vs. mutualistic interactions.
• Sept. 2005: Experimental support regarding highly variable genes and disease susceptibility.

FY 06: Modeling Markets as Networks

We aim to extend this theory to economic markets, modeling public corporations as nodes in a network where edges represent significant correlations in stock price fluctuations to analyze system vulnerability.