A geometric approach to scaling individual distributions to macroecological patterns

Nao Takashina, Buntarou Kusumoto, Yasuhiro Kubota, Evan P. Economo

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Understanding macroecological patterns across scales is a central goal of ecology and a key need for conservation biology. Much research has focused on quantifying and understanding macroecological patterns such as the species-area relationship (SAR), the endemic-area relationship (EAR) and relative species abundance curve (RSA). Understanding how these aggregate patterns emerge from underlying spatial pattern at individual level, and how they relate to each other, has both basic and applied relevance. To address this challenge, we develop a novel spatially explicit geometric framework to understand multiple macroecological patterns, including the SAR, EAR, RSA, and their relationships. First, we provide a general theory that can be used to derive the asymptotic slopes of the SAR and EAR, and demonstrates the dependency of RSAs on the shape of the sampling region. Second, assuming specific shapes of the sampling region, species geographic ranges, and individual distribution patterns therein based on theory of stochastic point processes, we demonstrate various well-documented macroecological patterns can be recovered, including the tri-phasic SAR and various RSAs (e.g., Fisher's logseries and the Poisson lognormal distribution). We also demonstrate that a single equation unifies RSAs across scales, and provide a new prediction of the EAR. Finally, to demonstrate the applicability of the proposed model to ecological questions, we provide how beta diversity changes with spatial extent and its grain over multiple scales. Emergent macroecological patterns are often attributed to ecological and evolutionary mechanisms, but our geometric approach still can recover many previously observed patterns based on simple assumptions about species geographic ranges and the spatial distribution of individuals, emphasizing the importance of geometric considerations in macroecological studies.

Original languageEnglish
Pages (from-to)170-188
Number of pages19
JournalJournal of Theoretical Biology
Publication statusPublished - Jan 14 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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