<![CDATA[Biodiversity has traditionally been assessed through species richness, yet this approach often fails to capture the functional roles that determine ecosystem processes and resilience. Increasing ecological evidence indicates that ecosystems with similar species counts may differ substantially in functional composition, leading to divergent ecological outcomes. This study aims to develop a mathematical ecology framework that quantifies functional biodiversity by integrating trait-based analysis with nonlinear modeling. The research employs a quantitative design combining secondary ecological datasets, multidimensional trait space construction, and computational modeling to evaluate relationships between functional diversity and ecosystem performance. Results demonstrate that functional richness, evenness, and divergence significantly predict ecosystem productivity and stability, while species richness shows limited explanatory power. Nonlinear analysis reveals threshold effects and complex interactions, indicating that functional trait composition governs ecosystem responses to environmental change. Functional diversity also shapes network structure, enhancing system resilience through redundancy and complementarity among traits. The study concludes that functional biodiversity provides a more comprehensive and predictive measure of ecological complexity than species richness alone. Integration of mathematical ecology with trait-based approaches offers a robust analytical framework for advancing biodiversity research and informing conservation strategies.]]>
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