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Modelling the species-area relationship using extreme value theory.

Luís Borda-de-Água1,2,3,4, M Manuela Neves5, Luise Quoss6,7

  • 1CIBIO/InBio, Centro de Investigação em Biodiversidade e Recursos Genéticos, Laboratório Associado, Universidade do Porto; Campus Agrário de Vairão, 4485-661, Vairão, Portugal. lbagua@gmail.com.

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We developed a new theory for the species-area relationship (SAR) using extreme value theory. Our model explains the three distinct phases of species accumulation with increasing area, linking them to species geographical distributions.

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Area of Science:

  • Ecology
  • Biodiversity Science
  • Spatial Statistics

Background:

  • The species-area relationship (SAR) describes how species richness increases with sampling area.
  • Nested SARs show consistent patterns across different scales and taxa, but theoretical underpinnings are incomplete.
  • Existing models do not fully explain the observed three-phase pattern of species accumulation.

Purpose of the Study:

  • To develop a novel theoretical framework for the nested species-area relationship.
  • To explain the underlying mechanisms driving the distinct phases observed in SARs.
  • To provide a method for estimating species richness at phase transitions.

Main Methods:

  • Developed a new theory for SAR based on extreme value theory.
  • Modeled SAR as a mixture of minimum distance distributions for species from a focal point.
  • Used Global Biodiversity Information Facility (GBIF) data for empirical validation.

Main Results:

  • The theory successfully explains the three distinct phases of SAR: rapid increase at small areas, slower growth at intermediate scales, and faster rise at large scales.
  • Each phase is determined by the geographical distribution (range) of species relative to the sampling focal point.
  • A formula was derived to estimate species numbers at phase transitions, validated with empirical data from various continents and taxa.

Conclusions:

  • Extreme value theory provides a robust framework for understanding SAR patterns.
  • Species geographical distributions are key determinants of SAR phases.
  • The developed theory and methods are general and applicable to diverse ecological systems with spatial features.