Using the Goldilocks Principle to model coral ecosystem engineering

Abstract

The occurrence and proliferation of reef-forming corals is of vast importance in terms of the biodiversity they support and the ecosystem services they provide. The complex three-dimensional structures engineered by corals are comprised of both live and dead coral, and the function, growth and stability of these systems will depend on the ratio of both. To model how the ratio of live : dead coral may change, the 'Goldilocks Principle' can be used, where organisms will only flourish if conditions are 'just right'. With data from particle imaging velocimetry and numerical smooth particle hydrodynamic modelling with two simple rules, we demonstrate how this principle can be applied to a model reef system, and how corals are effectively optimizing their own local flow requirements through habitat engineering. Building on advances here, these approaches can be used in conjunction with numerical modelling to investigate the growth and mortality of biodiversity supporting framework in present-day and future coral reef structures.

Keywords: Goldilocks Principle; Lophelia pertusa; coral; flow velocity; particle image velocimetry; smoothed-particle hydrodynamics modelling.

Figure 1.

Curve of the theoretical prey capture rates of L. pertusa at different current velocities against time. Bisecting layer (rectangle) indicates a ‘survival threshold’ based on prey capture. Coral polyps not surpassing this threshold would die, leaving exposed ‘dead’ framework. Given adequate time, this modelled threshold can be surpassed either through prey capture in optimal or suboptimal conditions. (Online version in colour.)

Figure 2.

Examples of the complex three-dimensional matrix structure of cold-water coral reef frameworks in the NE Atlantic showing live coral (white/orange colour) and dead coral framework (grey). Live coral typically sits on the top of dead coral framework. (a) SE Rockall Bank (Changing Oceans 2012) and (b–d) Norwegian cold-water habitats imaged by JAGO in cruises POS525 and PS_ARK22-1a [37]. (Online version in colour.)

Figure 3.

Experimental set-up and visualized disruption of water flow by corals. Left panels demonstrate experimental set-ups in flume tanks with L. pertusa colonies and nubbins. Middle and right panels demonstrate average flow velocity vector fields and velocity magnitudes around L. pertusa nubbins during 2 min PIV recordings at 10 Hz. Top row—nubbin exposed to 2 cm s⁻¹ free-stream flow. Middle row—nubbin placed behind a larger colony exposed to 2 cm s⁻¹ free-stream flow. Bottom row—nubbin located behind a larger colony exposed to 30 cm s⁻¹ free-stream flow. The solid black/white areas indicate no available data. (Online version in colour.)

Figure 4.

Water flow velocities at L. pertusa nubbin tips in flume experiments ± s.e. ‘Exposed’ nubbins were in full boundary layer flow, ‘behind colony’ nubbins had one colony placed in front of them and ‘between colonies’ had one colony in front and one behind it. The grey area indicates the broad region of optimum flow speeds for L. pertusa capture of zooplankton (approx. 2–6 cm s⁻¹ [–35]).

Figure 5.

SPH models of coral growth. Top layer flows from the left to right side at 50 cm s⁻¹ as indicated by the red arrows. Growth rates of coral were one particle for every growth-step if steady-state surrounding velocities were optimal between 3 and 6 cm s⁻¹. Live coral is denoted in red, dead coral is grey and water particles in blue. Numbers in each of the three panels indicate simulation growth-step (e.g. 20, 80, 140, 230). (a) Coral growth with no death rule applied, (b) coral growth with a death rule applied if coral does not experience optimal flow for five growth-steps. (c) Coral growth with a death rule applied if coral does not experience optimal flow for 30 growth-steps. (Online version in colour.)