This research involves three components: The dynamics of coral reefs, a continuum model for coral reefscapes and a coupled societal-coral reef agent-based model. Collaborators: Marlene Brito Millán and Dylan McNamara.
Spatial patterning of coral reef sessile benthic organisms can constrain competitive and demographic rates, with implications for dynamics over a range of time scales. However, techniques for quantifying and analysing reefscape behaviour, particularly at short to intermediate time scales (weeks to decades), are lacking. An analysis of the dynamics of coral reefscapes simulated with a lattice model shows consistent trends that can be categorized into four stages: a repelling stage that moves rapidly away from an unstable initial condition, a transient stage where spatial rearrangements bring key competitors into contact, an attracting stage where the reefscape decays to a steady-state attractor, and an attractor stage. The transient stage exhibits nonlinear dynamics, whereas the other stages are linear. The relative durations of the stages are affected by the initial spatial configuration as characterized by coral aggregation—a measure of spatial clumpiness, which together with coral and macroalgae fractional cover, more completely describe modelled reefscape dynamics. Incorporating diffusional processes results in aggregated patterns persisting in the attractor. Our quantitative characterization of reefscape dynamics has possible applications to other spatio-temporal systems and implications for reef restoration: high initial aggregation patterns slow losses in herbivore-limited systems and low initial aggregation configurations accelerate growth in herbivore-dominated systems.
Marlene Brito Millán and BT Werner, A continuum model for the dynamics of coral reefscapes
Coral reefs are ecosystems comprised of a diverse array of spatially interacting organisms nonlin- early linked to a range of spatio-temporal processes and emergent patterns. Because of the complex and multi-scale nature of reefs, computer modeling has played a role in investigating reef change and its link to the interactions influencing foundational calcifying coral reef organisms. However, most models have failed to treat or properly characterize the impact of the intense competition for two-dimensional benthic space that is the foundational mechanism of coral reef formation and development. To address this gap and to develop the capability to model coral reef dynamics on the scale of islands and beyond, here we describe and explore a continuum model derived by averaging the processes operating in a lattice model of coral reef dynamics. Thirteen fields that vary in space and time self-consistently characterize the reefscape; the fractional cover of four main functional groups on the reef (coral (CO), macroalgae (MA), turf algae (TA), and crustose coralline algae (CCA); length of interaction boundaries of the possible six inter-group combinations (CO- MA, CO-TA, CO-CCA,MA-TA,MA-CCA,TA-CCA); mean coral colony size; mean squared coral colony size; and fish biomass representing an herbivore population coupled to the benthic commu- nity. Spatial averaging of reef processes results in twelve corresponding partial differential equations solved numerically using a finite difference predictor-corrector scheme. Comparisons between the continuum model and the lattice model show considerable correspondence in behavior but some differences in time scales and variable values in the attractors. These differences are attributable to differing treatment of the development of coral colony size, which affects CO-MA competition, and the effect of distributions of small-scale variables on nonlinear terms in the continuum model equa- tions. An initial investigation of the spatial pattern forming capabilities of the continuum model yields the development of predator-prey-type cyclical attractors that form reaction-diffusion-type spatial patterns.
Marlene Brito Millán and BT Werner, Dynamical Behavior of a Coupled Indigenous Societal-Reef System