Polyp oriented modelling of coral growth

A generalized numerical model for clonal growth in scleractinian coral colonies

Coral reefs, vital ecosystems supporting diverse marine life, are primarily shaped by the clonal expansion of coral colonies. Although the principles of coral clonal growth, involving polyp division for spatial extension, are well-understood, numerical modelling efforts are notably scarce in the literature. In this article, we present a parsimonious numerical model based on the cloning of polyps, using five key parameters to simulate a range of coral shapes. The model is agent-based, where each polyp represents an individual. The colony's surface expansion is dictated by the growth mode parameter (s), guiding the preferred growth direction. Varying s facilitates the emulation of diverse coral shapes, including massive, branching, cauliflower, columnar and tabular colonies. Additionally, we introduce a novel approach for self-regulatory branching, inspired by the intricate mesh-like canal system and internode regularity observed in Acropora species. Through a comprehensive sensitivity analysis, we demonstrate the robustness of our model, paving the way for future applications that incorporate environmental factors, such as light and water flow. Coral colonies are known for their high plasticity, and understanding how individual polyps interact with each other and their surroundings to create the reef structure has been a longstanding question in the field. This model offers a powerful framework for studying these interactions, enabling a future implementation of environmental factors and the possibility of identifying the key mechanisms influencing coral colonies' morphogenesis.

Parallel evolution of gravity sensing

Omnipresent gravity affects all living organisms; it was a vital factor in the past and the current bottleneck for future space exploration. However, little is known about the evolution of gravity sensing and the comparative biology of gravity reception. Here, by tracing the parallel evolution of gravity sensing, we encounter situations when assemblies of homologous modules result in the emergence of non-homologous structures with similar systemic properties. This is a perfect example to study homoplasy at all levels of biological organization. Apart from numerous practical implementations for bioengineering and astrobiology, the diversity of gravity signaling presents unique reference paradigms to understand hierarchical homology transitions to the convergent evolution of integrative systems. Second, by comparing gravisensory systems in major superclades of basal metazoans (ctenophores, sponges, placozoans, cnidarians, and bilaterians), we illuminate parallel evolution and alternative solutions implemented by basal metazoans toward spatial orientation, focusing on gravitational sensitivity and locomotory integrative systems.

Stochastic diffusion characterizes early colony formation in Mediterranean coral Corallium rubrum

The colony formation in Mediterranean coral Corallium rubrum is initiated by a larva that metamorphoses into the first polyp of the emerging colony approximately two weeks after settlement. The primary polyp then sets up a slow process that eventually, at least after several years, gives rise to a tree-like rigid colony structure on which other polyps flourish. For a mature colony, this axial skeleton provides support for new polyps. However, the first emergence of the characteristic axial skeleton takes two to four years from the larva stage. The early colony morphology, instead, is shaped exclusively by the polyps' abundant deposition of sclerites, a magnesian calcite biomineral that has a different granularity from the distinctive red-coloured skeleton. With the appearance of the first polyp, a growing sclerite heap in a mesoglea layer provides a base for the emerging colony. In this paper, to elucidate the mechanical processes of early skeleton development in C. rubrum colonies, we present a computational model whereby the mesoglea layer provides a diffusion medium for the sclerites that the polyps deposit. We show that our stochastic model with three parameters captures the dynamic variability observed in measurements on living colonies. Our simulation results provide evidence for a diffusion process whereby the interplay between polyp budding and sclerite deposition are the main determinants of structure in early colony formation. Our model demonstrates that the frequency of budding events in an early colony can be described as a function of the available mesoglea surface whereas the number of polyps on the colony plays a secondary role in determining this frequency. We show that these model predictions are confirmed by direct observations on the colonies in our sample. Moreover, our results indicate that diffusion is a prevalent mechanism of colony development also at later stages of a colony's life span.

Survival in branching cellular populations

We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical model that captures the essential features of the dynamics. Using simulations and analytic approaches, we show that the survival probability of strains within the growing population is sensitive to the branching geometry: Branch bifurcations enhance survival probability due to an overall population growth (i.e., "inflation"), while branch termination and the small effective population size at the growing branch tips increase the probability of strain extinction. We show that the evolutionary dynamics may be captured on a wide range of branch geometries parameterized just by the branch diameter N₀ and branching rate b. We find that the survival probability of neutral cell strains is largest at an "optimal" branching rate, which balances the effects of inflation and branch termination. We find that increasing the selective advantage s of the cell strain mitigates the inflationary effect by decreasing the average time at which the mutant cell fate is determined. For sufficiently large selective advantages, the survival probability of the advantageous mutant decreases monotonically with the branching rate.

Space-filling and benthic competition on coral reefs

Reef-building corals are ecosystem engineers that compete with other benthic organisms for space and resources. Corals harvest energy through their surface by photosynthesis and heterotrophic feeding, and they divert part of this energy to defend their outer colony perimeter against competitors. Here, we hypothesized that corals with a larger space-filling surface and smaller perimeters increase energy gain while reducing the exposure to competitors. This predicted an association between these two geometric properties of corals and the competitive outcome against other benthic organisms. To test the prediction, fifty coral colonies from the Caribbean island of Curaçao were rendered using digital 3D and 2D reconstructions. The surface areas, perimeters, box-counting dimensions (as a proxy of surface and perimeter space-filling), and other geometric properties were extracted and analyzed with respect to the percentage of the perimeter losing or winning against competitors based on the coral tissue apparent growth or damage. The increase in surface space-filling dimension was the only significant single indicator of coral winning outcomes, but the combination of surface space-filling dimension with perimeter length increased the statistical prediction of coral competition outcomes. Corals with larger surface space-filling dimensions (Ds > 2) and smaller perimeters displayed more winning outcomes, confirming the initial hypothesis. We propose that the space-filling property of coral surfaces complemented with other proxies of coral competitiveness, such as life history traits, will provide a more accurate quantitative characterization of coral competition outcomes on coral reefs. This framework also applies to other organisms or ecological systems that rely on complex surfaces to obtain energy for competition.

Morphometric and allometric rules of polyp's landscape in regular and chimeric coral colonies of the branching species Stylophora pistillata

BACKGROUND

Most studies on architectural rules in corals have focused on the branch and the colony level, unveiling a variety of allometric rules. Working on the branching coral Stylophora pistillata, here we further extend the astogenic directives of this species at the polyp level, to reveal allometric and morphometric rules dictating polyps' arrangement.

RESULTS

We identified a basic morphometric landscape as a six-polyp circlet developed around a founder polyp, with established distances between polyps (six equilateral triangles), reflecting a strong genetic-based background vs high plasticity on the population level. Testing these rules in regular and chimeric S. pistillata colonies, we revealed similar morphometric/allometric rules developed via a single astogenic pathway. In regular colonies, this pathway was driven by the presence/absence of intra-circlet budding polyps, while in chimeras, by the distances between the two founder polyps. In addition, we identified the intra-circlet budding as the origin of first branching, if BPC distances are kept <1.09 ± 0.25 mm.

CONCLUSIONS

The emerged allometric/morphometric rules indicate the existence of a positional information paradigm for polyps' landscape distribution, where each polyp creates its own positional field of morphogen gradients through six inductive sites, thus forming six positional fields for the development of the archetypal "six-polyp crown".

Phenotypic determinism and contingency in the evolution of hypothetical tree-like organisms

Whether evolutionary history is mostly contingent or deterministic has been given much focus in the field of evolutionary biology. Studies addressing this issue have been conducted theoretically, based on models, and experimentally, based on microcosms. It has been argued that the shape of the adaptive landscape and mutation rate are major determinants of replicated phenotypic evolution. In the present study, to incorporate the effects of phenotypic plasticity, we constructed a model using tree-like organisms. In this model, the basic rules used to develop trees are genetically determined, but tree shape (described by the number and aspect ratio of the branches) is determined by both genetic components and plasticity. The results of the simulation show that the tree shapes become more deterministic under higher mutation rates. However, the tree shape became most contingent and diverse at the lower mutation rate. In this situation, the variances of the genetically determinant characters were low, but the variance of the tree shape is rather high, suggesting that phenotypic plasticity results in this contingency and diversity of tree shape. The present findings suggest that plasticity cannot be ignored as a factor that increases contingency and diversity of evolutionary outcomes.

Interplay of model ingredients affecting aggregate shape plasticity in diffusion-limited aggregation

We analyze the combined effect of three ingredients of an aggregation model--surface tension, particle flow and particle source--representing typical characteristics of many aggregation growth processes in nature. Through extensive numerical experiments and for different underlying lattice structures we demonstrate that the location of incoming particles and their preferential direction of flow can significantly affect the resulting general shape of the aggregate, while the surface tension controls the surface roughness. Combining all three ingredients increases the aggregate shape plasticity, yielding a wider spectrum of shapes as compared to earlier works that analyzed these ingredients separately. Our results indicate that the considered combination of effects is fundamental for modeling the polymorphic growth of a wide variety of structures in confined geometries and/or in the presence of external fields, such as rocks, crystals, corals, and biominerals.

Role of differential adhesion in cell cluster evolution: from vasculogenesis to cancer metastasis

Cell-cell and cell-matrix adhesions are fundamental to numerous physiological processes, including angiogenesis, tumourigenesis, metastatic spreading and wound healing. We use cellular potts model to computationally predict the organisation of cells within a 3D matrix. The energy potentials regulating cell-cell (JCC) and cell-matrix (JMC) adhesive interactions are systematically varied to represent different, biologically relevant adhesive conditions. Chemotactically induced cell migration is also addressed. Starting from a cluster of cells, variations in relative cell adhesion alone lead to different cellular patterns such as spreading of metastatic tumours and angiogenesis. The combination of low cell-cell adhesion (high JCC) and high heterotypic adhesion (low JMC) favours the fragmentation of the original cluster into multiple, smaller cell clusters (metastasis). Conversely, cellular systems exhibiting high-homotypic affinity (low JCC) preserve their original configuration, avoiding fragmentation (organogenesis). For intermediate values of JCC and JMC (i.e. JCC/JMC ∼ 1), tubular and corrugated structures form. Fully developed vascular trees are assembled only in systems in which contact-inhibited chemotaxis is activated upon cell contact. Also, the rate of secretion, diffusion and sequestration of chemotactic factors, cell deformability and motility do not significantly affect these trends. Further developments of this computational model will predict the efficacy of therapeutic interventions to modulate the diseased microenvironment by directly altering cell cohesion.

Modelling growth and form of the scleractinian coral Pocillopora verrucosa and the influence of hydrodynamics

The growth of scleractinian corals is strongly influenced by the effect of water motion. Corals are known to have a high level of phenotypic variation and exhibit a diverse range of growth forms, which often contain a high level of geometric complexity. Due to their complex shape, simulation models represent an important option to complement experimental studies of growth and flow. In this work, we analyzed the impact of flow on coral's morphology by an accretive growth model coupled with advection-diffusion equations. We performed simulations under no-flow and uni-directional flow setup with the Reynolds number constant. The relevant importance of diffusion to advection was investigated by varying the diffusion coefficient, rather than the flow speed in Péclet number. The flow and transport equations were coupled and solved using COMSOL Multiphysics. We then compared the simulated morphologies with a series of Computed Tomography (CT) scans of scleractinian corals Pocillopora verrucosa exposed to various flow conditions in the in situ controlled flume setup. As a result, we found a similar trend associated with the increasing Péclet for both simulated forms and in situ corals; that is uni-directional current tends to facilitate asymmetrical growth response resulting in colonies with branches predominantly developed in the upstream direction. A closer look at the morphological traits yielded an interesting property about colony symmetry and plasticity induced by uni-directional flow. Both simulated and in situ corals exhibit a tendency where the degree of symmetry decreases and compactification increases in conjunction with the augmented Péclet thus indicates the significant importance of hydrodynamics.

Nutritional resources as positional information for morphogenesis in the stony coral Stylophora pistillata

We are interested in deciphering the mechanisms for morphogenesis in the Red Sea scleractinian coral Stylophora pistillata with the help of mathematical models. Previous mathematical models for coral morphogenesis assume that skeletal growth is proportional to the amount of locally available energetic resources like diffusible nutrients and photosynthetic products. We introduce a new model which includes factors like dissolved nutrients and photosynthates, but these resources do not serve as building blocks for growth but rather provide some kind of positional information for coral morphogenesis. Depending on this positional information side branches are generated, splittings of branches take place and branch growth direction is determined. The model results are supported by quantitative comparisons with experimental data obtained from young coral colonies.

A comparison between coral colonies of the genus Madracis and simulated forms

In addition to experimental studies, computational models provide valuable information about colony development in scleractinian corals. Using our simulation model, we show how environmental factors such as nutrient distribution and light availability affect growth patterns of coral colonies. To compare the simulated coral growth forms with those of real coral colonies, we quantitatively compared our modelling results with coral colonies of the morphologically variable Caribbean coral genus Madracis. Madracis species encompass a relatively large morphological variation in colony morphology and hence represent a suitable genus to compare, for the first time, simulated and real coral growth forms in three dimensions using a quantitative approach. This quantitative analysis of three-dimensional growth forms is based on a number of morphometric parameters (such as branch thickness, branch spacing, etc.). Our results show that simulated coral morphologies share several morphological features with real coral colonies (M. mirabilis, M. decactis, M. formosa and M. carmabi). A significant correlation was found between branch thickness and branch spacing for both real and simulated growth forms. Our present model is able to partly capture the morphological variation in closely related and morphologically variable coral species of the genus Madracis.

Critical evaluation of branch polarity and apical dominance as dictators of colony astogeny in a branching coral

The high morphological resemblance between branching corals and trees, can lead to comparative studies on pattern formation traits, best exemplified in plants and in some cnidarians. Here, 81 branches of similar size of the hermatypic coral Stylophora pistillata were lopped of three different genets, their skeletons marked with alizarin red-S, and divided haphazardly into three morphometric treatment groups: (I) upright position; (II) horizontal position, intact tip; and (III) horizontal position, cut tip. After 1 y of in-situ growth, the 45 surviving ramets were brought to the laboratory, their tissues removed and their architectures analyzed by 22 morphological parameters (MPs). We found that within 1 y, isolated branches developed into small coral colonies by growing new branches from all branch termini, in all directions. No architectural dissimilarity was assigned among the three studied genets of treatment I colonies. However, a major architectural disparity between treatment I colonies and colonies of treatments II and III was documented as the development of mirror structures from both sides of treatments II and III settings as compared to tip-borne architectures in treatment I colonies. We did not observe apical dominance since fragments grew equally from all branch sides without documented dominant polarity along branch axis. In treatment II colonies, no MP for new branches originating either from tips or from branch bases differed significantly. In treatment III colonies, growth from the cut tip areas was significantly lower compared to the base, again, suggesting lack of apical dominance in this species. Changes in branch polarity revealed genet associated plasticity, which in one of the studied genets, led to enhanced growth. Different genets exhibited canalization flexibility of growth patterns towards either lateral growth, or branch axis extension (skeletal weight and not porosity was measured). This study revealed that colony astogeny in S. pistillata is a regulated process expressed through programmed events and not directly related to simple energy trade-off principles or to environmental conditions, and that branch polarity and apical dominance do not dictate colony astogeny. Therefore, plasticity and astogenic disparities encompass a diversity of genetic (fixed and flexible) induced responses.

Modelling the skeletal architecture in a sponge with radiate accretive growth

A mathematical model of the skeletogenesis and the influence of the physical environment on the morphogenesis of a branching sponge, for example, Haliclona oculata or Lubomirskia baikalensis, is presented. In the model, we assume that the radiate accretive growth process is nutrient limited. With this model we can generate in a simulated accretive growth process branching objects with a similarity to the branching sponges.

How plastic can phenotypic plasticity be? The branching coral Stylophora pistillata as a model system

Phenotypic plasticity enables multicellular organisms to adjust morphologies and various life history traits to variable environmental challenges. Here, we elucidate fixed and plastic architectural rules for colony astogeny in multiple types of colonial ramets, propagated by cutting from genets of the branching coral Stylophora pistillata from Eilat, the Red Sea. We examined 16 morphometric parameters on 136 one-year old S. pistillata colonies (of seven genotypes), originating from small fragments belonging, each, to one of three single-branch types (single tips, start-up, and advanced bifurcating tips) or to structural preparative manipulations (representing a single or two growth axes). Experiments were guided by the rationale that in colonial forms, complexity of evolving phenotypic plasticity can be associated with a degree of structural modularity, where shapes are approached by erecting iterative growth patterns at different levels of coral-colony organization. Analyses revealed plastic morphometric characters at branch level, and predetermined morphometric traits at colony level (only single trait exhibited plasticity under extreme manipulation state). Therefore, under the experimental manipulations of this study, phenotypic plasticity in S. pistillata appears to be related to branch level of organization, whereas colony traits are controlled by predetermined genetic architectural rules. Each level of organization undergoes its own mode of astogeny. However, depending on the original ramet structure, the spherical 3-D colonial architecture in this species is orchestrated and assembled by both developmental trajectories at the branch level, and traits at the colony level of organization. In nature, branching colonial forms are often subjected to harsh environmental conditions that cause fragmentation of colony into ramets of different sizes and structures. Developmental traits that are plastic, responding to fragment structure and are not predetermine in controlling astogeny, allow formation of species-specific architecture product through integrated but variable developmental routes. This adaptive plasticity or regeneration is an efficient mechanism by which isolated fragments of branching coral species cope with external environmental forces.

Skeletal variability of the coral Favia gravida (Verrill, 1868) from Brazil

The skeletal variability of the coral Favia gravida, a species endemic to Brazil, was quantitatively described including populations from three locations: Tamandaré (state of Pernambuco), Abrolhos (state of Bahia), and Santa Cruz (state of Espírito Santo). Ten colonies were collected from each population and fourteen morphological characters were measured from ten corallites per colony. The results of univariate (among 14 skeletal characters, 7 showed p < 0.05) analysis provide evidence to suggest that F. gravida has considerable morphological plasticity, which may explain its ability to adapt to different ecological conditions. The species also displays polymorphism within and between colonies of each population. Intercolony variation within populations was relevant for most of the variables measured. Canonical discriminant analysis (r = 0.8648) showed that the population farthest offshore (Abrolhos) was distinct from the other two (Tamandaré and Santa Cruz), which have been affected by terrigenous sediments carried from the coast. Specimens from Santa Cruz displayed the highest degree of meandrinization.

Morphogenesis of the branching reef coral Madracis mirabilis

Understanding external deciding factors in growth and morphology of reef corals is essential to elucidate the role of corals in marine ecosystems, and to explain their susceptibility to pollution and global climate change. Here, we extend on a previously presented model for simulating the growth and form of a branching coral and we compare the simulated morphologies to three-dimensional (3D) images of the coral species Madracis mirabilis. Simulation experiments and isotope analyses of M. mirabilis skeletons indicate that external gradients of dissolved inorganic carbon (DIC) determine the morphogenesis of branching, phototrophic corals. In the simulations we use a first principle model of accretive growth based on local interactions between the polyps. The only species-specific information in the model is the average size of a polyp. From flow tank and simulation studies it is known that a relatively large stagnant and diffusion dominated region develops within a branching colony. We have used this information by assuming in our model that growth is entirely driven by a diffusion-limited process, where DIC supply represents the limiting factor. With such model constraints it is possible to generate morphologies that are virtually indistinguishable from the 3D images of the actual colonies.

Do plants and animals differ in phenotypic plasticity?

This paper compares the flexibility in the nexus between phenotype and genotype in plants and animals. These taxa although considered to be fundamentally different are found to be surprisingly similar in the mechanisms used to achieve plasticity. Although non-cognitive behaviour occurs in plants, its range is limited, while morphological and developmental plasticity also occur to a considerable extent in animals. Yet both plants and animals are subject to unique constraints and thus need to find unique solutions to functional problems. A true comparison between the plant and animal phenotype would be a comparison between plants and sessile photosynthesizing colonial invertebrates. Such comparisons are lacking. However, they would provide important insights into the adaptive significance of plasticity in these groups. It is also suggested that a comparison of inflexible traits in these groups would provide an understanding of the constraints, as well as the costs and benefits,of a plastic versus non-plastic phenotype in plants and animals.