When do we have the power to detect biological interactions in spatial point patterns?
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Determining the relative importance of environmental factors, biotic interactions and stochasticity in assembling and maintaining species-rich communities remains a major challenge in ecology. In plant communities, interactions between individuals of different species are expected to leave a spatial signature in the form of positive or negative spatial correlations over distances relating to the spatial scale of interaction. Most studies using spatial point process tools have found relatively little evidence for interactions between pairs of species. More interactions tend to be detected in communities with fewer species. However, there is currently no understanding of how the power to detect spatial interactions may change with sample size, or the scale and intensity of interactions. We use a simple 2-species model where the scale and intensity of interactions are controlled to simulate point pattern data. In combination with an approximation to the variance of the spatial summary statistics that we sample, we investigate the power of current spatial point pattern methods to correctly reject the null model of bivariate species independence. We show that the power to detect interactions is positively related to the abundances of the species tested, and the intensity and scale of interactions. Increasing imbalance in abundances has a negative effect on the power to detect interactions. At population sizes typically found in currently available datasets for species-rich plant communities we find only a very low power to detect interactions. Differences in power may explain the increased frequency of interactions in communities with fewer species. Furthermore, the community-wide frequency of detected interactions is very sensitive to a minimum abundance criterion for including species in the analyses.
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