Framework for analyzing ecological trait-based models in multidimensional niche spaces

Area of Science:

• Ecology
• Theoretical Ecology
• Mathematical Biology

Background:

• Ecological niches are fundamental to understanding species coexistence and biodiversity.
• Previous models often simplify niche dimensionality, limiting their applicability to complex trait interactions.
• Analyzing multidimensional niches requires robust theoretical frameworks.

Purpose of the Study:

• To develop a novel theoretical framework for analyzing ecological models with multidimensional niche spaces.
• To incorporate multiple phenotypic traits into niche descriptions using symbolic sequences.
• To provide a method for predicting niche differentiation and population dynamics.

Main Methods:

• Representing ecological niches as sequences of symbols.
• Utilizing Hamming distance to model ecological drivers like competitive exclusion.
• Applying a matrix diagonalization transform to the community interaction matrix.
• Exemplifying the method with Lotka-Volterra equations and an exponential competition kernel.

Main Results:

• The developed framework successfully diagonalizes the community interaction matrix.
• The method allows for the prediction of conditions leading to niche differentiation.
• Asymptotic long-term population distributions of niches can be predicted near instability points.

Conclusions:

• The symbolic sequence approach offers a powerful tool for multidimensional niche analysis.
• This framework enhances the predictive power of ecological models concerning species interactions and coexistence.
• The method provides insights into the mechanisms driving niche differentiation and community structure.