Impulsive Fire Disturbance in a Savanna Model: Tree-Grass Coexistence States, Multiple Stable System States, and Resilience

Is resilience a unifying concept for the biological sciences?

There is increasing interest in applying resilience concepts at different scales of biological organization to address major interdisciplinary challenges from cancer to climate change. It is unclear, however, whether resilience can be a unifying concept consistently applied across the breadth of the biological sciences, or whether there is limited capacity for integration. In this review, we draw on literature from molecular biology to community ecology to ascertain commonalities and shortcomings in how resilience is measured and interpreted. Resilience is studied at all levels of biological organization, although the term is often not used. There is a suite of resilience mechanisms conserved across biological scales, and there are tradeoffs that affect resilience. Resilience is conceptually useful to help diverse researchers think about how biological systems respond to perturbations, but we need a richer lexicon to describe the diversity of perturbations, and we lack widely applicable metrics of resilience.

Pattern Formation in Mesic Savannas

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.

Emergent structure and dynamics of tropical forest-grassland landscapes

Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback that is not easily reversed. A hypothesized mechanism for such bistability is feedback between fire and vegetation, where fire spreads as a contagion process on grass patches. Theoretical models have largely implemented this mechanism implicitly, by assuming a threshold dependence of fire spread on flammable vegetation. Here, we show how the nonlinear dynamics and bistability emerge spontaneously, without assuming equations or thresholds for fire spread. We find that the forest geometry causes the nonlinearity that induces bistability. We demonstrate this in three steps. First, we model forest and fire as interacting contagion processes on grass patches, showing that spatial structure emerges due to two counteracting effects on the forest perimeter: forest expansion by dispersal and forest erosion by fires originating in adjacent grassland. Then, we derive a landscape-scale balance equation in which these two effects link forest geometry and dynamics: Forest expands proportionally to its perimeter, while it shrinks proportionally to its perimeter weighted by adjacent grassland area. Finally, we show that these perimeter quantities introduce nonlinearity in our balance equation and lead to bistability. Relying on the link between structure and dynamics, we propose a forest resilience indicator that could be used for targeted conservation or restoration.

An immuno-epidemiological model for transient immune protection: A case study for viral respiratory infections

The dynamics of infectious disease in a population critically involves both within-host pathogen replication and between host pathogen transmission. While modeling efforts have recently explored how within-host dynamics contribute to shaping population transmission, fewer have explored how ongoing circulation of an epidemic infectious disease can impact within-host immunological dynamics. We present a simple, influenza-inspired model that explores the potential for re-exposure during a single, ongoing outbreak to shape individual immune response and epidemiological potential in non-trivial ways. We show how even a simplified system can exhibit complex ongoing dynamics and sensitive thresholds in behavior. We also find epidemiological stochasticity likely plays a critical role in reinfection or in the maintenance of individual immunological protection over time.