On the generality of stability–complexity relationships in Lotka–Volterra ecosystems

The Effects of Smoking on Human Pharynx Microbiota Composition and Stability

The oral microbiota is essential to the health of the host, yet little is known about how it responds to disturbances. We examined the oropharyngeal microbiota of 30 individuals over 40 weeks. As the oropharynx is an important gateway to pathogens, and as smoking is associated with increased incidence and severity of respiratory infections, we compared the microbiota of smokers and nonsmokers to shed light on its potential for facilitating infections. We hypothesized that decreased species diversity, decreased community stability, or increased differences in community structure could facilitate invading pathogens. We found that smoking is associated with reduced alpha diversity, greater differences in community structure, and increased environmental filtering. The effects of short-term perturbations (antibiotic use and participants exhibiting cold symptoms) were also investigated. Antibiotic use had a negative effect on alpha diversity, irrespective of smoking status, and both antibiotic use and cold symptoms were associated with highly unique bacterial communities. A stability analysis of models built from the data indicated that there were no differences in local or global stability in the microbial communities of smokers, compared to nonsmokers, and that their microbiota are equally resistant to species invasions. Results from these models suggest that smoker microbiota are perturbed but characterized by alternative stable states that are as stable and invasion-resistant as are the microbiota of nonsmokers. Smoking is unlikely to increase the risk of infectious disease through the altered composition and ecological function of the microbiota; this is more likely due to the effects of smoking on the local and systemic immune system. IMPORTANCE Smoking is associated with an increased risk of respiratory infections. Hypothetically, the altered community diversity of smokers' pharyngeal microbiota, together with changes in their ecological stability properties, could facilitate their invasion by pathogens. To address this question, we analyzed longitudinal microbiota data of baseline healthy individuals who were either smokers or nonsmokers. While the results indicate reduced biodiversity and increased species turnover in the smokers' pharyngeal microbiota, their ecological stability properties were not different from those of the microbiota of nonsmokers, implying, in ecological terms, that the smokers' microbial communities are not less resistant to invasions. Therefore, the study suggests that the increased propensity of respiratory infections that is seen in smokers is more likely associated with changes in the local and systemic immune system than with ecological changes in the microbial communities.

Complexity-stability trade-off in empirical microbial ecosystems

May's stability theory, which holds that large ecosystems can be stable up to a critical level of complexity, a product of the number of resident species and the intensity of their interactions, has been a central paradigm in theoretical ecology. So far, however, empirically demonstrating this theory in real ecological systems has been a long-standing challenge with inconsistent results. Especially, it is unknown whether this theory is pertinent in the rich and complex communities of natural microbiomes, mainly due to the challenge of reliably reconstructing such large ecological interaction networks. Here we introduce a computational framework for estimating an ecosystem's complexity without relying on a priori knowledge of its underlying interaction network. By applying this method to human-associated microbial communities from different body sites and sponge-associated microbial communities from different geographical locations, we found that in both cases the communities display a pronounced trade-off between the number of species and their effective connectance. These results suggest that natural microbiomes are shaped by stability constraints, which limit their complexity.

Component response rate variation underlies the stability of highly complex finite systems

The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the relationship between system properties and stability, the effect of variation in response rate across system components remains unconsidered. Here I vary the component response rates (γ) of randomly generated complex systems. I use numerical simulations to show that when component response rates vary, the potential for system stability increases. These results are robust to common network structures, including small-world and scale-free networks, and cascade food webs. Variation in γ is especially important for stability in highly complex systems, in which the probability of stability would otherwise be negligible. At such extremes of simulated system complexity, the largest stable complex systems would be unstable if not for variation in γ. My results therefore reveal a previously unconsidered aspect of system stability that is likely to be pervasive across all realistic complex systems.

Pools versus Queues: The Variable Dynamics of Stochastic "Steady States"

Mathematical models in ecology and epidemiology often consider populations "at equilibrium", where in-flows, such as births, equal out-flows, such as death. For stochastic models, what is meant by equilibrium is less clear--should the population size be fixed or growing and shrinking with equal probability? Two different mechanisms to implement a stochastic steady state are considered. Under these mechanisms, both a predator-prey model and an epidemic model have vastly different outcomes, including the median population values for both predators and prey and the median levels of infection within a hospital (P < 0.001 for all comparisons). These results suggest that the question of how a stochastic steady state is modeled, and what it implies for the dynamics of the system, should be carefully considered.

Reconciling the omnivory-stability debate

Despite attempts at reconciliation, the role of omnivory in food web stability remains unclear. Here we develop a novel community matrix approach that is analogous to the bifurcation method of modular food web theory to show that the stability of omnivorous food chains depends critically on interaction strength. We find that there are only six possible ways that omnivorous interaction strengths can influence the stability of linear food chains. The results from these six cases suggest that: (1) strong omnivory is always destabilizing, (2) stabilization by weak to intermediate omnivorous interaction strengths dominates the set of possible stability responses, and, (3) omnivory can be occasionally strictly destabilizing or intermittently destabilizing. We then revisit the classical results of Pimm and Lawton to show that although their parameterization tends to produce a low percentage of stable omnivorous webs, the same parameterization shows strong theoretical support for the weak interaction effect. Finally, we end by arguing that our current empirical knowledge of omnivory resonates with this general theory.