A geometric approach to scaling individual distributions to macroecological patterns

Area of Science:

• Macroecology
• Spatial Ecology
• Conservation Biology

Background:

• Macroecological patterns (species-area relationship [SAR], endemic-area relationship [EAR], relative species abundance [RSA]) are central to ecology and conservation.
• Understanding how these aggregate patterns emerge from individual-level spatial distributions and relate to each other is crucial.

Purpose of the Study:

• To develop a novel, spatially explicit geometric framework for understanding multiple macroecological patterns and their interrelationships.
• To provide a theoretical basis for deriving SAR and EAR slopes and understanding RSA dependencies on sampling region shape.

Main Methods:

• Developed a general theory for deriving asymptotic slopes of SAR and EAR.
• Utilized stochastic point processes to model species ranges and individual distributions within specific sampling region shapes.
• Applied the framework to unify RSAs across scales and predict EAR.

Main Results:

• Recovered well-documented macroecological patterns, including tri-phasic SAR and various RSAs (e.g., Fisher's logseries, Poisson lognormal).
• Demonstrated a single equation unifies RSAs across scales.
• Provided a new prediction for the EAR and showed how beta diversity changes with spatial extent and grain.

Conclusions:

• A geometric approach, using simple assumptions about species ranges and individual distributions, can recover many observed macroecological patterns.
• Emphasizes the significant role of geometric considerations in macroecological studies, complementing traditional ecological and evolutionary explanations.