Null model algorithms


Null models have been widely used to analyze the patterns observed in nature in the attempt to understand the ecological and evolutionary mechanisms structuring the biological communities. A null model is a simplified representation of how species would be distributed or biological communities be assembled if specific ecological processes were not operating. Until now, algorithms were designed to create null models using matrix data. The package SESraster covers a current gap by implementing randomization algorithms to build null models using presence/absence raster data.


The data for null model analyses usually consists of a binary presence-absence matrix, in which the entries represent the presence (1) or absence (0) of a particular species in a particular site, rows represent species or taxa, columns represent sites or samples (Ulrich and Gotelli 2012). There are nine major types of null model algorithms for species co-occurrence analysis based on how sums of species (originally rows) and sites (originally columns) are treated (i.e. fixed, equiprobable, or proportional sums; see Table 1; Table 2 of (Gotelli 2000)). When using raster data, layers represent species or taxa and cells represent sites or samples. SESraster currently implements six (green cells in Table 1) of the nine algorithms for co-occurrence analysis summarized by Gotelli (2000).

Table 1. Nine null model algorithms for species co-occurrence analysis listed in Gotelli (2000). Cells in green represent the algorithms currently implemented in SESraster.
Site (Col, Cell)
Equiprobable Proportional Fixed
Species<br>(Row, Layer) Equiprobable SIM1: EE<br>occurrence frequency: E <br> site richness: E SIM6: EP<br>occurrence frequency: E <br> site richness: P SIM3: EF<br>occurrence frequency: E <br> site richness: F
Proportional SIM7: PE<br>occurrence frequency: P <br> site richness: E SIM8: PP<br>occurrence frequency: P <br> site richness: P SIM5: PF<br>occurrence frequency: P <br> site richness: F
Fixed SIM2: FE<br>occurrence frequency: F <br> site richness: E SIM4: FP<br>occurrence frequency: F <br> site richness: P SIM9: FF<br>occurrence frequency: F <br> site richness: F

Spatial null model algorithms in SESraster

Time to get started with SESraster: vignette("spatial-null-models"). See installation instructions and how the implemented null model algorithms work with spatial data.


Gotelli, Nicholas J. 2000. “Null Model Analysis of Species Co-Occurrence Patterns.” Ecology 81 (9): 2606–21.
Ulrich, Werner, and Nicholas J. Gotelli. 2012. “A Null Model Algorithm for Presenceabsence Matrices Based on Proportional Resampling.” Ecological Modelling 244 (October): 20–27.