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Species-habitat associations are present if species are specialized to small-scale environmental conditions (Tilman & Pacala, 1993) and are more common within suitable habitats (Comita et al., 2007; Harms et al., 2001). Following, species-habitat associations show the importance of abiotic processes on the spatial patterning of plant populations (Garzon-Lopez et al., 2014).

There are mainly two methods that can be found in the literature to analyse such small-scale species-habitat associations, namely the gamma-test (Plotkin et al., 2000) and the torus-translation test (Harms et al., 2001). Both methods require data on the locations of plants (as spatstat::ppp point pattern) and on the environmental conditions (classified into discrete habitats as raster::raster). To show significance species-habitat associations, both methods randomize one of the components. Because the locations of plants as well as the habitats are most likely auto-correlated, the spatial structure must be kept while randomizing the data (Wiegand & Moloney, 2014).

All methods compare the abundance within a habitat between the observed data and the randomized null model data. If the count is below or above a pre-set threshold (e.g. the 2.5th and 97.5th quantiles), negative or positive associations, respectively, are present.

## Randomize environmental data

The following two methods randomize the environmental data, i.e. the RasterLayer data, while keeping the point pattern data fixed.

### Torus-translation-test

The torus-translation test (Harms et al. 2001) shifts the habitat map in all four cardinal directions around a torus. This is only possible for square rasters. To use this method in shar use translate_raster().

### Randomized-habitats procedure

The randomze-habitats procedure (Harms et al. 2001) is also possible for non-square raster and randomizes the habitats using a random-walk algorithm. To use this method in shar use randomize_raster().

## Randomize point pattern data

Contrastingly to the two methods described above, the following two methods randomize the point pattern data, while keeping the environmental data fixed.

### Gamma-test

The gamma-test (Plotkin et al. 2000) randomizes the data by fitting a point process model to the observed data and simulation n random point patterns using the fitted point process model. However, the method only works for point patterns that can be described by a theoretical point process model. To use this method in shar use fit_point_process().

### Pattern reconstruction

Pattern reconstruction (Tscheschel & Stoyan 2006) randomizes the point pattern using simulated annealing (Kirkpatrick et al. 1983). This allows to randomize also complex point patterns without a theoretical point process model. To use this method in shar use reconstruct_pattern().

### References

Comita, L.S., Condit, R., Hubbell, S.P., 2007. Developmental changes in habitat associations of tropical trees. Journal of Ecology 95, 482–492. https://doi.org/10.1111/j.1365-2745.2007.01229.x

Garzon-Lopez, C.X., Jansen, P.A., Bohlman, S.A., Ordonez, A., Olff, H., 2014. Effects of sampling scale on patterns of habitat association in tropical trees. Journal of Vegetation Science 25, 349–362. https://doi.org/10.1111/jvs.12090

Harms, K.E., Condit, R., Hubbell, S.P., Foster, R.B., 2001. Habitat associations of trees and shrubs in a 50-ha neotropical forest plot. Journal of Ecology 89, 947–959. https://doi.org/10.1111/j.1365-2745.2001.00615.x

Kirkpatrick, S., Gelatt, C.D.Jr., Vecchi, M.P., 1983. Optimization by simulated annealing. Science 220, 671–680. https://doi.org/10.1126/science.220.4598.671

Plotkin, J.B., Potts, M.D., Leslie, N., Manokaran, N., LaFrankie, J.V., Ashton, P.S., 2000. Species-area curves, spatial aggregation, and habitat specialization in tropical forests. Journal of Theoretical Biology 207, 81–99. https://doi.org/10.1006/jtbi.2000.2158

Tilman, D., Pacala, S.W., 1993. The maintenance of species richness in plant communities, in: Ricklefs, R.E., Schluter, D. (Eds.), Species Diversity in Ecological Communities. University of Chicago Press, Chicago, pp. 13–25. ISBN 978-0-226-71823-1

Tscheschel, A., Stoyan, D., 2006. Statistical reconstruction of random point patterns. Computational Statistics and Data Analysis 51, 859–871. https://doi.org/10.1016/j.csda.2005.09.007

Wiegand, T., Moloney, K.A., 2014. Handbook of spatial point-pattern analysis in ecology. Chapman and Hall/CRC Press, Boca Raton. ISBN 978-1-4200-8254-8