Title: When do we have the power to detect biological interactions in spatial point patterns?,
Abstract: 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.