Periodic Reporting for period 1 - CoralMath (MATHEMATICAL MODELS FOR CORAL REEFS: TOWARDS AN INTERDISCIPLINARY AND CONSERVATION-FOCUSED RESEARCH)
Periodo di rendicontazione: 2023-09-01 al 2025-02-28
Coral reefs are among the most biodiverse ecosystems on the planet, yet they are rapidly declining due to global warming and local anthropogenic pressures. This interdisciplinary project applies non-linear physics and complex systems modeling to improve our understanding of coral reef dynamics and inform marine conservation strategies.By combining ecological knowledge with methods from statistical mechanics, non-equilibrium systems, and numerical simulations, the project develops scalable models of coral growth and reef-scale interactions. These models bridge spatial scales—from individual coral colonies to entire reef structures—and offer new theoretical insights into coral self-organization and spatial pattern formation. Two main applications are addressed: the formation of grazing halos—circular bare zones around reefs driven by herbivory—modeled as emergent spatial phenomena to evaluate reef health; and the optimization of coral restoration efforts by identifying spatial configurations that enhance survival and reduce costs. The outcomes support evidence-based strategies for conservation and restoration, contributing to the goals of the EU Biodiversity Strategy for 2030 by promoting the sustainable management of marine ecosystems and enhancing coastal resilience.
Work Performed and Main Achievements
This project combines non-linear physics and mathematical modeling to better understand the complex dynamics of coral reef ecosystems. Significant progress has been made in three main areas: coral growth, grazing dynamics, and restoration strategies.
Coral Growth Modeling
A three-dimensional model was developed to simulate coral colony growth based on clonal reproduction at the polyp level. Using a minimal set of parameters, the model successfully reproduces a wide variety of natural coral shapes, such as table, massive, and branching forms. This approach provides a flexible framework to explore how different growth rules and environmental conditions influence coral morphology. In addition to a scientific publication and a book chapter, the model is being validated with field data to reinforce its applicability in real-world settings. A complementary two-dimensional agent-based model is also under development to study reef-scale patterns and their interaction with ocean flow dynamics.
Grazing Dynamics
A model was created to investigate the formation and variability of reef halos—bare zones around coral patches shaped by herbivore activity. By incorporating interactions between herbivores and seagrass, and calibrating the model with observed data, the simulations accurately reflect halo sizes and seagrass coverage as seen in satellite imagery. The model also captures seasonal changes and introduces a new explanation for the appearance of corridors connecting isolated halos. These findings offer new insights into how grazing behavior can influence spatial structure in reef environments and highlight the potential of halo patterns as indicators of ecosystem health.
Restoration Strategies
Building on the coral growth framework, the project is advancing toward practical applications in coral restoration. New simulations are being developed to incorporate environmental variables such as light and water flow, in collaboration with researchers in computational modeling. These enhancements aim to improve our understanding of how coral colonies develop under different environmental conditions and to support more effective and resource-efficient restoration efforts.
Overall, the scientific work performed has led to the development of new tools and models that enhance our understanding of coral reef systems and provide valuable guidance for their conservation and restoration.
This project combines non-linear physics and mathematical modeling to better understand the complex dynamics of coral reef ecosystems. Significant progress has been made in three main areas: coral growth, grazing dynamics, and restoration strategies.
Coral Growth Modeling
A three-dimensional model was developed to simulate coral colony growth based on clonal reproduction at the polyp level. Using a minimal set of parameters, the model successfully reproduces a wide variety of natural coral shapes, such as table, massive, and branching forms. This approach provides a flexible framework to explore how different growth rules and environmental conditions influence coral morphology. In addition to a scientific publication and a book chapter, the model is being validated with field data to reinforce its applicability in real-world settings. A complementary two-dimensional agent-based model is also under development to study reef-scale patterns and their interaction with ocean flow dynamics.
Grazing Dynamics
A model was created to investigate the formation and variability of reef halos—bare zones around coral patches shaped by herbivore activity. By incorporating interactions between herbivores and seagrass, and calibrating the model with observed data, the simulations accurately reflect halo sizes and seagrass coverage as seen in satellite imagery. The model also captures seasonal changes and introduces a new explanation for the appearance of corridors connecting isolated halos. These findings offer new insights into how grazing behavior can influence spatial structure in reef environments and highlight the potential of halo patterns as indicators of ecosystem health.
Restoration Strategies
Building on the coral growth framework, the project is advancing toward practical applications in coral restoration. New simulations are being developed to incorporate environmental variables such as light and water flow, in collaboration with researchers in computational modeling. These enhancements aim to improve our understanding of how coral colonies develop under different environmental conditions and to support more effective and resource-efficient restoration efforts.
Overall, the scientific work performed has led to the development of new tools and models that enhance our understanding of coral reef systems and provide valuable guidance for their conservation and restoration.
This project has led to the development of a generalised mathematical model that captures the shape-specific growth of clonal coral colonies. By integrating geometric growth rules with ecological principles, the mode It accounts for colony morphology and spatial competition, providing a novel framework to better understand how coral colonies grow. A key achievement is the model’s ability to replicate the distinctive shapes of different coral colonies—ranging from massive to branching forms—within a unified framework. This opens the door to using the model as a diagnostic tool to assess coral health and predict the resilience of various morphologies under environmental stress. It also enables the testing of hypotheses about coral recovery and adaptation, offering valuable support for reef restoration planning and conservation strategies.
In parallel, the project has advanced our understanding of grazing halos—ring-like bare zones that form around coral patches or reef structures due to the spatially constrained foraging behavior of herbivorous fish. By combining field observations with spatial modelling, we showed how seasonal fluctuations in environmental conditions and seagrass productivity influence the formation and dynamics of these halos. The model reveals how fish movement, refuge availability, and habitat quality interact to shape these visible seascape patterns. These insights deepen our understanding of predator-prey interactions, habitat connectivity, and the ecological processes that structure reef ecosystems at larger scales.
Potential Impacts
The results have implications across several domains. First, in basic science, the models created contributes to the growing field of mathematical ecology, particularly in understanding modular organisms like corals and their interactions with the surrounding ecosystem. Second, in applied conservation, it offers tools to simulate how coral colonies and associated habitat patterns may respond to climate change, disturbances, or restoration efforts. This can guide reef management decisions, particularly in regions where herbivory plays a key role in ecosystem resilience.
Key Needs for Further Uptake and Success
To fully realise the potential of this work, several steps are needed:
-Further research: Expanding the model to include environmental drivers (e.g. temperature, light, nutrient availability), inter-species dynamics, and stochastic events would enhance realism and applicability.
-Access to funding: Continued financial support will be essential to scale the model’s capabilities and move from research development to field-ready tools.
-International collaboration: Engaging partners across diverse reef systems will test the model under different ecological and sociopolitical contexts, increasing global relevance.
-Policy interface: Translating findings into actionable recommendations for conservation and spatial planning can help bridge the gap between research and impact on the ground.
Overall, this project lays the foundation for a new generation of spatially explicit models that connect the biology of individual coral colonies to broader reef-scale patterns and processes. With the right support and continued interdisciplinary collaboration, the tools and insights developed here can contribute meaningfully to coral reef resilience and management in a changing world.
In parallel, the project has advanced our understanding of grazing halos—ring-like bare zones that form around coral patches or reef structures due to the spatially constrained foraging behavior of herbivorous fish. By combining field observations with spatial modelling, we showed how seasonal fluctuations in environmental conditions and seagrass productivity influence the formation and dynamics of these halos. The model reveals how fish movement, refuge availability, and habitat quality interact to shape these visible seascape patterns. These insights deepen our understanding of predator-prey interactions, habitat connectivity, and the ecological processes that structure reef ecosystems at larger scales.
Potential Impacts
The results have implications across several domains. First, in basic science, the models created contributes to the growing field of mathematical ecology, particularly in understanding modular organisms like corals and their interactions with the surrounding ecosystem. Second, in applied conservation, it offers tools to simulate how coral colonies and associated habitat patterns may respond to climate change, disturbances, or restoration efforts. This can guide reef management decisions, particularly in regions where herbivory plays a key role in ecosystem resilience.
Key Needs for Further Uptake and Success
To fully realise the potential of this work, several steps are needed:
-Further research: Expanding the model to include environmental drivers (e.g. temperature, light, nutrient availability), inter-species dynamics, and stochastic events would enhance realism and applicability.
-Access to funding: Continued financial support will be essential to scale the model’s capabilities and move from research development to field-ready tools.
-International collaboration: Engaging partners across diverse reef systems will test the model under different ecological and sociopolitical contexts, increasing global relevance.
-Policy interface: Translating findings into actionable recommendations for conservation and spatial planning can help bridge the gap between research and impact on the ground.
Overall, this project lays the foundation for a new generation of spatially explicit models that connect the biology of individual coral colonies to broader reef-scale patterns and processes. With the right support and continued interdisciplinary collaboration, the tools and insights developed here can contribute meaningfully to coral reef resilience and management in a changing world.