Figure 1.
Computed Tomography (CT) scans of scleractinian coral Pocillopora verrucosa.
(A) A controlled coral exposed to ambient current with the average near-bottom velocity of 5 cm s−1 [46]. (B) A coral that was grown in an in situ controlled flume setup with “reduced flow” condition (∼1 cm s−1) (C–E) Corals were grown in the in-situ controlled flumes setup with “enhanced flow” condition (15–20 cm s−1) [32]. Arrows indicate flow direction. The labels of the CT scans are located at the bottom of each figure (see Table 1).
Figure 2.
Schematic diagram of the simulation.
(A) A spherical object represents an initial growth state of the simulation (first growth step) (B) A simulation phase involves solving the Navier-Stokes equations (i) and the advection-diffusion equation (ii). (C) Accretion phase translocates absorbed nutrients from previous simulation phase to a new growth layer hence, after a few consecutive growth steps, spontaneous branching occurs.
Figure 3.
An example of three consecutive accretive growth steps.
(A–C) Accretive growth steps; vertex vi represents a simulated corallite. The new layer is constructed along the direction of normal vector ni of the vertex vi. A, B and C are three consecutive growth steps where triangles are inserted once the surface of the object increases.
Figure 4.
Finite element meshes representation of the environment around the simulated coral.
The arrow indicates the direction of the flow.
Table 1.
Parameters used for simulations and parameters used to calculate Pe number, surface/volume ratio and symmetry magnitude.
Figure 5.
(A) A skeleton graph with the increased level of occlusion of the volumetric data in the background, (B–C) Visualization of spheres used for calculating morphometric traits - diameter of a sphere at the terminal branch is defined as terminal branch thickness –dc, (D) A visualization of the volumetric data of TS_002 coral (See Table 1 for label), (E) Visualization of symmetry angles hangle and vangle
, (F) Visualization of the associated vectors used for calculation of symmetry vector smmag.
Figure 6.
(A) Simulated coral in a no-flow condition. (B–F) Simulated corals from various flow simulations (B) Pe_branch = 0.00113, (C) Pe_branch = 0.0105, (D) Pe_branch = 0.0970, (E) Pe_branch = 1.13, (F) Pe_branch∼11.3, Arrow indicates flow direction. The labels of the simulated corals are located on the bottom of each figure (See Table 1 for labels).
Figure 7.
Qualitative comparison between the real (A, C) and simulated coral (B, D) (CT_455 and SIM_FLOW_D3, see Table 1).
Figure 8.
z-plane Slices (z = 0.07) of the flow pattern around the simulated corals, the slices were taken from the middle part of the colony.
(A) SIM_FLOW_D1, Pe_branch = 0.00113, (B) SIM_FLOW_D2, Pe_branch = 0.0105 (C) SIM_FLOW_D3, Pe_branch = 0.097 (D) SIM_FLOW_D4, Pe_branch = 1.13 (E) SIM_FLOW_D5, Pe_branch∼11.3. Slices of a different z-plane can be found in Supplementary Figure S3 (See Table 1 for the labels).
Figure 9.
Visualization of the volume rendering of the simulated corals with their associated histograms of the local morphometric traits.
Red lines indicate projected branches vector on the substratum plane (visualized from the bottom up perspective). For the simulation with flow, flow is directed from right to left. The morphometric traits measured here are as follow: symmetry angles hangle and vangle, and the symmetry attitude smmag (see table 1 for labels). (A) SIM_NO_FLOW, Pe_branch = 0, (B) SIM_FLOW_D1, Pe_branch = 0.00113, (C) SIM_FLOW_D2, Pe_branch = 0.0105 (D) SIM_FLOW_D3, Pe_branch = 0.097 (E) SIM_FLOW_D4, Pe_branch = 1.13.
Figure 10.
Visualization of the volume rendering of the CT-scanned corals with their associated histograms of the local morphometric traits.
Red lines indicate projected branches vector on the substratum plane (visualized from the bottom up perspective). For the in situ flow-controlled corals, flow direction is from right to left. The morphometric traits measured here are as follow: symmetry angles hangle and vangle, and the symmetry attitude smmag (see table 1 for labels). (A) controlled coral CT_456, Pe_branch = 0.136, (B) reduced flow coral (TS_002), Pe_branch = 0.0163 (C), enhanced-flow coral TS_001, Pe_branch = 0.188, (D) enhanced-flow coral TS_003, Pe_branch = 0.227, and (E) enhanced-flow coral CT455, Pe_branch = 0.288.
Figure 11.
Mean values of symmetry angles hangle and vangle versus Pe_branch for simulated corals (A) and CT-scanned corals (B).
Error bars indicate 95% confidence interval. (C–D) shows regression plot of skewness and kurtosis against Pe_branch for both the simulated and CT-scanned corals.
Figure 12.
Mean values of symmetry magnitude smmag versus Pe_branch for simulated corals (A) and CT-scanned (B) corals.
Error bars indicate 95% confidence interval. (C-D) surface/volume ratio of simulated and CT-scanned corals versus Pe_branch.