Micro‐CT reconstruction reveals the colony pattern regulations of four dominant reef‐building corals

Abstract Colonies are the basic geometric building blocks of coral reefs. However, the forming regulations of both colonies and reefs are still not understood adequately. Therefore, in this study, we reconstructed 25 samples using high‐resolution micro‐computed tomography to investigate coral growth patterns and parameters. Our skeleton and canal reconstructions revealed the characteristics of different coral species, and we further visualized the growth axes and growth rings to understand the coral growth directions. We drew a skeleton grayscale map and calculated the coral skeleton void ratios to ascertain the skeletal diversity, devising a method to quantify coral growth. On the basis of the three‐dimensional (3D) reconstructions and growth parameters, we investigated the growth strategies of different coral species. This research increases the breadth of knowledge on how reef‐building corals grow their colonies, providing information on reef‐forming regulations. The data in this paper contain a large amount of coral growth information, which can be used in further research on reef‐forming patterns under different conditions. The method used in this study can also be applied to animals with porous skeletons.

Conventional studies on reef-building corals have concentrated on the physiology, ecology, statistics, and multi-omics of corals, allowing us to understand the biological characteristics of coral polyps and symbiont zooxanthellae. At the heart of healthy reefs is the sustained formation of the calcium carbonate skeletons of many coral species; therefore, it is important to understand how corals grow their skeletons. The structure, distribution, volume ratio, and other useful patterns of the canals in coral skeletons are also important to understand, as they play key roles in coral growth (Li et al., 2021).
Traditional biological analysis techniques, such as scanning electron microscopy (SEM) and grinding sections, necessitate a high workload and complex operability (Giuseppe et al., 2019;Odum & Odum, 1955). They provide limited evidence due to their non-transparent coral skeletons, which restrict the direct observation of the structures and related parameters in coral colonies (Marfenin, 2015).
In recent years, computed tomography (CT) has been applied to study reef-building coral skeletons (Beuck et al., 2007;Gutiérrez-Heredia et al., 2015;Knackstedt et al., 2006;Kruszyński et al., 2007;Kruszynski et al., 2006;Pinzón et al.,2014). With the development and popularization of high-resolution micro-computed tomography (HRCT), research on coral skeletons has revealed the morphological and internal structures of coral branchlets, and also investigated coral skeletal structures (Ivankina et al., 2020;Urushihara et al., 2016) and exogenous influences on coral skeletons, including water currents (Chindapol et al., 2013), the marine environment , and ocean acidification (Enochs et al., 2016;Fordyce et al., 2020). However, there are various challenges in studying coral growth patterns regulation using CT sectional slices that are singly dependent on skeleton reconstruction. Consequently, we created a novel method of canal reconstruction, which used HRCT to study coral growth pattern regulation in Pocillopora damicornis, visualizing its calice networks, budding signals, polyp relationships, colony growth directions, and coral branching regulations (Li et al., 2020). Furthermore, to fill in current knowledge gaps, we expanded this method to determine the growth pattern in much more predominant reef-building coral gen- including lumen reconstructions of the canal system in each colony, growth axis formation, growth ring visualization, grayscale gradient maps, and growth parameters quantification, to obtain the formation mechanism and related parameters for our colony samples.
According to the canal reconstructions and measured growth parameters, we investigated different growth strategies of the major species to define how corals grow their skeletons and how skeletal growth varies among species. This work also provides some useful methods and extends our understanding of the digging growth information of coral colonies.

| Canal reconstructions revealing coral growth patterns
The 3D skeletal structures of 25 samples were reconstructed by HRCT at both the macroscopic and microscopic levels ( Figure S1).
The images in Figure 1 and Figure S1 show the complete forms of the original coral skeletons, including the surface morphology and internal structural characteristics, which facilitated an analysis of the coral colony pattern regulation. To obtain the coral growth information from skeletal structures, we reconstructed the canals inside the sample skeletons. The complex canal reconstructions can mainly be divided into three parts: the lumen in calices (where coral polyps live and grow), the inter-septal space, and the gastrovascular canal system. The gastrovascular canal system connects all polyps in a colony, and the movement of fluids in it can transport materials to different parts of the colony, as required (Pearse & Muscatine, 1971). The axial canal is a unique canal within the axial corallite along the branches in an Acropora colony, and its extension reveals the branch growth directions. It belongs to the gastrovascular canal system, and there is also a polyp that lives at the tip of this canal (Li et al., 2021). Cycloseris vaughani is a monostomatous corallum, with only one large polyp in its mouth (1-2 cm in diameter). Calices of P. lutea and M. turgescens are exceedingly small (1 mm in diameter), closely packed and united by the walls (almost no space among calices), while adjacent polyps connect through their porous corallite walls and septa. Calices of F. speciosa are large (6-10 mm in diameter) and polygonal, and some inter-septal space (1 mm in diameter) distribute around the calices. Colonies of species in e-h have simple canal systems. Calices of P. meandrina and P. verrucosa are small (0.5-1 mm in diameter), and their corallite walls touch each other. The inter-septal spaces arrange neatly in columns. Calices of S. hystrix are round and slightly hooded (0.5 mm in diameter), while each lumen in calice corresponds to a small sphere inter-septal space (0.1 mm in diameter) located in the center of the branch. The canal system in M. foliosa is different from M. turgescens, and the calices of M. foliosa (0.5-1 mm in diameter) are well separated by the coenosteum. Gastrovascular canal system and coenosteum connect the polyps in separated calices. Acropora species in i-k have complex canal system. Their calices (1 mm in diameter) are connected by the gastrovascular canal system, while axial canal is a unique structure in the canal system of these Acropora species. Scale bars: 1 mm colonies integrate the coral body like a circulatory system in higher animals (Figure 1i (Li et al., 2020). Every newly budded polyp forms a small calice, with inverted cone-shaped lumen inside (e.g., interseptal space No. 1 in Figure 2c), while the later-formed calices contain larger inverted truncated cone spaces (e.g., inter-septal space No. 2-4 and the lumen in calice No. 5 in Figure 2c). These inverted cone-shaped spaces can be regarded as a reminder for polyps budding in the canal system of a P. verrucosa colony, making it possible F I G U R E 2 3D canal reconstructions of four typical reef-building corals. (a) The gastrovascular canal system connects the axial canal and the lumen in calices (where polyps stay) in an Acropora muricata colony like a net. All these canals integrate the coral branch into an entirety like the circulatory system in higher animals. (b) In Montipora foliosa, the gastrovascular canal system forms a basic network, and the lumen in calices (with polyps inside) are regularly arranged in it. (c) Forming sequence and budding sites of the inter-septal spaces and lumen in calices in Pocillopora verrucosa canal system. The newly budding polyp has a small inverted cone-shaped inter-septal space No. 1, and the following ones are grown into larger inverted truncated cones gradually (inter-septal space No. 2-4 and lumen in calice No. 5). These inverted coneshaped spaces can be regarded as a kind of reminding information for polyp budding in the canal system of P. verrucosa colony, making it possible to capture the behaviors of all polyps in one colony of P. verrucosa by reconstruction. The budding sites can be accurately recorded regardless of the fate of certain individual polyp (Li et al., 2020). (d) The double-layer canal system in Seriatopora hystrix is arranged spirally along with branch growth direction. Scale bars: 1 mm to capture the behaviors of all polyps in one corallum of P. verrucosa by canal reconstruction, whereby budding sites can be accurately recorded regardless of the fate of the individual polyps ( Figure 2c).
In S. hystrix colonies, calices contain cup-shaped lumens with a larger volume, each corresponding to their smaller droplet-like inter-septal spaces. There are no obvious connections between the lumens in calices and inter-septal spaces, and both canals are arranged spirally along the growth direction of the coral branches. The inter-septal spaces generally appear in groups, arranged in the form of three to four independent droplet-like canals that are gathered together. For each group of internal canals, there is a group of surrounding calices (with polyps inside) of a similar quantity (Figure 2d).
It has been found that all polyps in one P. verrucosa colony participate in multiple biological processes through the canal system, including the budding, branching, mineralization, and movement trajectory of polyps (Li et al., 2020). In P. verrucosa, the polyp network is supported by the coenosteum and the network of inter-septal spaces that connects all polyps in one colony, which is universal in Pocillopora Figure 2c). In Acropora and Montipora, the polyp network is more complex because more canal types are involved. The gastrovascular canal system connects all polyps in a holistic network to collaboratively perform biological processes in a single coral colony.

| Growth axis and ring visualization based on 3D reconstruction
The canal reconstruction revealed that coral colonies follow specific growth axes (Li et al., 2020); this can accurately reflect how coral reefs are formed. To illustrate the coral growth direction at the level of polyp proliferation and skeletal dynamic accretion, we visualized the growth axes of various colonies through the 3D reconstruction of canal systems. This regulation cannot be observed directly in coral skeletons and their primary morphology ( Figure 3 and Figure   S2). Growth direction reconstruction in corals following axial growth, such as A. muricata and S. hystrix, can be simply accomplished using basic morphological information. A. muricata growth follows its axial canal ( Figure 2A and Figure S2A), and the gastrovascular canal system in S. hystrix plays a similar role (Figure 2d). However, the growth axes following radial-or lateral-growth coral, such as in P. verrucosa and M. foliosa, are not obvious. To analyze the growth axes of radialgrowth coral, for instance, P. verrucosa, we reconstructed the calices from the branching point to the uppermost tips of each branchlet ( Figure S2B). M. foliosa is a typical lateral-growth coral lacking an axis canal, so we improved our former reconstruction method to explore its growth axis ( Figure S2C,D). An M. foliosa branch expands outward in a foliose shape, and the canal reconstruction from the proximal bifurcating point to the distal edge revealed that the growth direction forms a foliose-shaped branch. Using this method, we reconstructed the entire growth axis of an M. foliosa colony, which reflected a regular dichotomous type (Figure 3). The reconstruction results show that the investigated growth axes of reef-building corals can be divided into three types: dichotomous, polytomous, and divergent ( Figure S2E). The dichotomous growth axis (P. verrucosa, A. digitifera, and M. foliosa) bifurcates at all forks, whether on the main branch or branchlets. The polytomous growth axis (A. muricata and S. hystrix) divides into two or more parts during the branching process. The divergent growth axis (A. millepora and P. meandrina) has no main branches.
Growth rings reflect the details of coral growth and were obtained through the 3D reconstructions of canal systems and growth axes. These rings can divide one coral branch into multiple layers, showing the entire process of the growth pattern ( Figure S3). In the M. foliosa sample, the initial growth ring was quite small, which then proliferated along with the growth axis through the canal system ( Figure S3A). The mature growth rings of A. digitifera and S. hystrix maintained a similar volume throughout branch growth ( Figure   S3B,D). In P. verrucosa, the volumes of the growth rings varied and depended on temporal ecological factors ( Figure S3C).
In summary, the 3D reconstructions showed that the coral growth patterns were regulated by a hierarchy of canal systems, growth axes, and growth rings, while the canal system was its basic foundation. The canals within reef-building coral colonies have regulator distributions, and the colony pattern or growth model can be traced by investigating this kind of regulation.

| Coral growth parameter analyses based on 3D reconstruction
According to our 3D reconstructions, the growth parameters -including skeletal density and the skeleton void ratio -can be ob-  (Table 1). In A. muricata and S. hystrix, the density of new growth skeletons is lower than that of old ones (Figure 4a,d and Table 1). However, the case for M. foliosa and P. verrucosa is the opposite (Figure 4b,c and Table 1). Coral colonies are filled with canals, and it is difficult to precisely measure coral skeleton void ratios (the proportion of skeletal material to the total volume) (Naumann et al., 2009). To mitigate this issue, we designed a method to calcu-

| Reef colony forming strategy comparison based on 3D reconstructions
The canal system in the skeleton of a colony is the basic foundation for coral growth (Figure 2), while the type and direction of F I G U R E 3 Growth axis reconstruction of Montipora foliosa. The growth axis reconstruction of our lateral growth sample, M. foliosa, was dichotomous type. The growth axis extends to the perimeter from the center of M. foliosa colony, and foliose-shaped skeletons are formed along the direction of the growth axis. The growth axis and coral branch will both split into two parts at the branching point, while new branches will keep growing along the direction of the new growth axis. Thus, we call it the "dichotomous type". This net-like growth axis ensures that this lateral growth species can maximize the use of light resources (Li et al., 2020). Scale bars: 1 cm  Table f corresponds to each colored rectangle in the histogram e. Scale bars: 2 mm the growth axis determine the branching pattern and growth direction of the colony, respectively (Figure 3, Figure S2). According to the canal reconstructions in this study, we investigated different growth strategies of four representative species to define how corals grow their skeleton and how skeletal growth varies among species.

F I G U R E 5
Growth parameter analysis through colony reconstruction. (a) By outlining the edges of the reconstructed branches in the slices, we calculated the total acreage of skeleton and canals in each slice. The length of edge line shows the perimeter of coral branch in each slice. (b) We defined the direction of growth axis as Z-axis in the 3D coordinate system of coral reconstruction, and the X-Y plane is the radial cross-section perpendicular to Z-axis. The skeleton ratio along Z-axis of coral colony was shown in the line charts. (c) The skeleton ratio of the coral samples in Montipora foliosa, Acropora muricata, Pocillopora verrucosa, and Seriatopora hystrix. Each coral genera contain three samples. Standard deviation is shown as the value of σ in the histogram.

TA B L E 1 Grayscale ranges for coral samples
The corals of each species have their own unique reef forming strategies. The density of new skeletons in M. foliosa and P. verrucosa is higher than that of old ones, while the patterns in A. muricata and S. hystrix are just the opposite (Figure 4, Table 1). Montipora foliosa is a lateral-growth coral, with thinner skeletons at colony edge that are susceptible to physical damage. Therefore, the density of new skeletons formed at the colony edge is higher, ensuring its mechanical strength (Figure 4b). For P. verrucosa, a radial-growth coral with fragile dissepiments, the new skeletons with high densities are mineralized on the surface of the colony to protect inner structures ( Figure 4C). Further, axial-growth corals -such as A. muricata and S. hystrix -form new skeletons with lower densities, because the protection of entire colony is not dependent on the growth area at the branch tip (Figure 4a,d).
Montipora foliosa colonies have the lowest skeleton ratios (47.0%) of the four major species (Figure 5c). This is primarily because its horizontal growth pattern is less affected by sea waves, while its high skeleton density (Figure 4e,f) also helps maintain the mechanical strength of the colony. Thus, the rigidity and strength of the coral colony can be sacrificed to speed up the expansion of its growth rings, increasing its capacity for occupying ecological niches. The other three longitudinally growing genera require higher skeletal ratios to maintain their strength. As S. hystrix colonies are normally found in habitats exposed to wave action, a higher skeleton ratio We believe that the pattern of coral growth rings is related to the growth axis and coenosteum. The growth rate of polyps that share coenosteums in a colony is synchronized, and the polyps mineralize their coenosteums along the direction of the growth axis. As the environment will affect the morphology and density of skeletons mineralized at different time periods, there are multiple 'rings' of different skeletons in one colony, each corresponding to a specific time period. The growth rings are more specific in species with solid coenosteums, like P. verrucosa. In P. verrucosa, different environmental conditions -such as light -affect the canal and skeletal structures of each growth ring within the colony (Li et al., 2020). The related growth parameters can be obtained by reconstructing and measuring the inter-septal spaces in each growth ring, and performing cluster analysis to infer the light conditions received by the colony when this part of the skeleton is formed. The skeletal density of the P. lutea colony is found to be related to seawater temperature, rainfall, and sunshine hours, while the density of skeletons in each growth ring fluctuates quasi-12-month periodically (Shi et al., 2004). Therefore, the grayscale gradient map can be compared to the growth ring reconstructions to study the monthly and yearly influence of the marine environment on coral skeletons. To quantify the specific correlations among the growth ring, coral skeleton, and environmental factors, more experimentation and comparisons are necessary.
In prior studies, researchers found that the atolls in the South China Sea have similar features that indicate forming regulation by basic coral colonies (Liu et al., 2019). We found that the pattern regulation of the M. foliosa colony is similar to that of atolls ( Figure   S3A)

| Skeleton-canal reconstruction as a method for studying animals with porous skeletons
In this study, we determined the growth pattern regulation of major reef-building coral species through 3D reconstructions of canals and skeletons using HRCT. These canal systems and skeleton data support further studies on reef-building corals and improve upon the knowledge base of coral biology, including structural features, growth regulation, mineralization traits, and polyp networks (Li et al., 2020). At the surface of a reef-building coral branch, all polyps are interconnected like a vertebrate's dermal system (Dubininkas, 2017) by tissue, making up an apparent polyp network. Here, we found that there is another type of polyp network supported by the canal system within a skeletal system that maintains coral growth processes.
The canal reconstructions allowed us to obtain the mechanism behind coral growth, budding, branching, and mineralizing, which helped visualize the growth process, summarize growth strategies, and ascertain growth models (Figures 1-3). Following the growth direction shown in the canal systems, we reconstructed the growth axis of coral colonies, particularly M. foliosa, which seems to grow irregularly. This research could provide a solid basis for coral classification ( Figure S2). To obtain a deep understanding of coral growth patterns at the monthly, seasonal, and yearly time scales, reconstructing the growth pattern hierarchy of canal system, growth axes, and growth rings is of great importance ( Figure S2E, Figure   S3). Additionally, we reconstructed coral skeletons through HRCT to draw grayscale gradient maps, revealing the density differences of coral skeletons in each colony and quantifying the volume ratio of skeletons within specific density intervals, which reflected the differentiated mineralization strategies (Figure 4). On this basis, we calculated the reconstructed skeletons layer-by-layer to obtain the growth parameters, including coral mineralization, surface areas, and skeleton ratios, which help quantify coral growth ( Figure 5). The related data contain a large amount of information on coral growth, which can be used for further research on coral growth patterns in different conditions or time periods.
A large number of animals have skeletons with complex canal systems, similar to reef-building corals. In a manner mimicking the annual rings of a tree, these skeletons and canal systems contain significant amounts of growth information, including calcification strategies and growth patterns. Based on the reconstructions of these skeletons and canals, we can easily obtain growth parameters, summarize growth regulations, and visualize the growth process, laying the foundation for the construction of animal models.
Thus, we believe that the above-mentioned skeleton-canal reconstruction method is not only suitable for studying most coral species, but can also be applied to numerous animals with porous skeletons.

| Sample collection
The

| Coral culture system
Our coral samples were cultured with the laboratory auto-calibration Around 20 kg of live rocks, which were also collected from the South China Sea, was placed in the coral tank. These live rocks provided the structure of the growth environment and some necessary microorganisms. We also added minerals to the tank weekly, including Mg, Ca, KH, K, I, and Fe.

| HRCT test
We

| Internal canal reconstruction
Slice data derived from the scans were then analyzed and manipulated using VG software. The 3D reconstructions were created in Mimics (v20.0) software and VG Studio Max (v3.3.0), following the method as previously described (Li et al., 2020).

| Coral-growth quantitative analysis
We randomly selected three coral branches from colony reconstruction results of M. foliosa, A. muricata, P. verrucosa, and S. hystrix.
We defined the direction of growth axis as Z-axis in the 3D coordinate system of coral reconstruction, and the X-Y plane is the radial cross-section perpendicular to Z-axis. Then, we exported each reconstructed branch as a set of slices perpendicular to the Z-axis

This study was supported by the Open Research Fund Program of
Guangxi Key Lab of Mangrove Conservation and Utilization (Grant No. GKLMC-202002).

CO N FLI C T O F I NTE R E S T
The authors declare no competing interests.

DATA AVA I L A B I L I T Y S TAT E M E N T
The HRCT data that support the findings of this study are available to share. You may download the HRCT reconstruction data through following sharing links: