Spatiotemporal dynamics of coastal Mediterranean ecosystems

Throughout evolution, species have developed mechanisms to adapt and survive in extreme environments. While these adaptations are often studied at the individual level, many survival strategies emerge collectively. In particular, the spontaneous organization of populations can lead to the formation of structures that optimize resource distribution, facilitate waste degradation, or enhance interactions with other species. These structures often result from self-organizing processes, arising from interactions between individuals without external intervention. This phenomenon contributes to increased resilience and enhanced survival rates across populations.

This thesis investigates the formation of structures in marine ecosystems, focusing on two native species from the Mediterranean coasts: \textit{Posidonia oceanica} and \textit{Paramuricea clavata}. Both species are characterized by slow growth, a crucial role as keystone species in coastal ecosystems, and vulnerability to human activities. To analyze these systems, we employed mathematical models based on partial differential equations, which are well-suited for describing population dynamics when individual fluctuations are negligible and environmental conditions are homogeneous. Despite these simplifications, the results are consistent with previous observations and have practical implications for marine ecology.

In the first part of this thesis we explore the concept of excitability applied to \textit{P. oceanica} meadows. We discovered that locally increasing plant density leads to the emergence of traveling structures that reduce competition between individuals and enhance meadow resilience against adverse conditions. These structures were first analyzed from a purely mathematical perspective to uncover the mechanisms underlying their formation. Later, we applied these findings to an ecological model to identify the biological factors necessary for the emergence of excitability in plant populations. This analysis opens new avenues for understanding self-organization in other ecological systems.

The second part of this thesis explores interactions between marine plant species. We propose a model that includes a dependence of the sign and magnitude of species interactions on plant density. Although this aspect has been largely overlooked, it proves crucial for understanding ecosystem transitions and dynamics. This finding highlights the importance of considering nonlinear interactions in the study of marine communities.

Finally, we analyze population dynamics in gorgonian forests, specifically in P. clavata. These organisms form communities of colonies that compete for resources in a hostile environment. In this case, pattern formation is linked to the distribution of colony sizes. Using a simplified model, we successfully reproduced phenomena like "self-thinning" and atypical colony size distributions commonly observed in these ecosystems.

The results of this thesis represent a significant contribution to the study of spatiotemporal dynamic systems, marine ecology, and environmental sciences. Furthermore, they shed light on intricate natural processes and provide practical tools for developing conservation and restoration strategies for threatened coastal ecosystems.