Point pattern analysis and size – point and disc null models for stomata distribution.


Size matters: point pattern analysis biases the estimation of spatial properties of stomata distribution

by Naulin P. I., Valenzuela G., Estay S. A. (2016)

  1. Facultad de Ciencias, Instituto de Ciencias Ambientales y Evolutivas, Universidad Austral de Chile, Valdivia, Chile
  2. Center of Applied Ecology and Sustainability, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Santiago, Chile
Paulette I. Naulin Gysling, Universidad de Chile, La Pintana, Santiago

Gerardo Valenzuela,

Sergio Andrés Estay Cabrera, Universidad Austral de Chile, Valdivia, Chile

in New Phytologist, Online Version of Record published before inclusion in an issue – DOI: 10.1111/nph.14305 – 



  • Stomata distribution is an example of biological patterning. Formal methods used to study stomata patterning are generally based on point-pattern analysis, which assumes that stomata are points and ignores the constraints imposed by size on the placement of neighbors. The inclusion of size in the analysis requires the use of a null model based on finite-size object geometry.
  • In this study, we compare the results obtained by analyzing samples from several species using point and disc null models.
  • The results show that depending on the null model used, there was a 20% reduction in the number of samples classified as uniform; these results suggest that stomata patterning is not as general as currently reported. Some samples changed drastically from being classified as uniform to being classified as clustered. In samples of Arabidopsis thaliana, only the disc model identified clustering at high densities of stomata.
  • This reinforces the importance of selecting an appropriate null model to avoid incorrect inferences about underlying biological mechanisms. Based on the results gathered here, we encourage researchers to abandon point-pattern analysis when studying stomata patterning; more realistic conclusions can be drawn from finite-size object analysis.

Published by

Willem Van Cotthem

Honorary Professor of Botany, University of Ghent (Belgium). Scientific Consultant for Desertification and Sustainable Development.

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