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Keywords:

  • Curve fitting;
  • goodness-of-fit;
  • macroecology;
  • power function;
  • random field;
  • rarefaction;
  • saturation function;
  • simulation;
  • species–area relationship;
  • species–sampling relationship

Abstract

Aim  Scheiner (Journal of Biogeography, 2009, 36, 2005–2008) criticized several issues regarding the typology and analysis of species richness curves that were brought forward by Dengler (Journal of Biogeography, 2009, 36, 728–744). In order to test these two sets of views in greater detail, we used a simulation model of ecological communities to demonstrate the effects of different sampling schemes on the shapes of species richness curves and their extrapolation capability.

Methods  We simulated five random communities with 100 species on a 64 × 64 grid using random fields. Then we sampled species–area relationships (SARs, contiguous plots) as well as species–sampling relationships (SSRs, non-contiguous plots) from these communities, both for the full extent and the central quarter of the grid. Finally, we fitted different functions (power, quadratic power, logarithmic, Michaelis–Menten, Lomolino) to the obtained data and assessed their goodness-of-fit (Akaike weights) and their extrapolation capability (deviation of the predicted value from the true value).

Results  We found that power functions gave the best fit for SARs, while for SSRs saturation functions performed better. Curves constructed from data of 322 grid cells gave reasonable extrapolations for 642 grid cells for SARs, irrespective of whether samples were gathered from the full extent or the centre only. By contrast, SSRs worked well for extrapolation only in the latter case.

Main conclusions  SARs and SSRs have fundamentally different curve shapes. Both sampling strategies can be used for extrapolation of species richness to a target area, but only SARs allow for extrapolation to a larger area than that sampled. These results confirm a fundamental difference between SARs and area-based SSRs and thus support their typological differentiation.