Abstract
Ripley’sKfunction is the classical tool to characterize the spatial structure of point patterns. It is widely used in vegetation studies. Testing its values against a null hypothesis usually relies on Monte-Carlo simulations since little is known about its distribution. We introduce a statistical test against complete spatial randomness (CSR). The test returns thePvalue to reject the null hypothesis of independence between point locations. It is more rigorous and faster than classical Monte-Carlo simulations. We show how to apply it to a tropical forest plot. The necessary R code is provided.
Highlights
The commonest tool used to characterize the spatial structure of a point set is Ripley’s K statistic [1, 2]
Since little is known about the distribution of the K function, the test of rejection of the null hypothesis relies on Monte-Carlo simulations
The test is valid for one distance but using it repeatedly for all distances where the K function is calculated dramatically increases the risk to reject the null hypothesis by error [8]
Summary
The commonest tool used to characterize the spatial structure of a point set is Ripley’s K statistic [1, 2]. It has been widely used in ecology and other scientific fields and is well referenced in handbooks [3,4,5,6,7]. Since little is known about the distribution of the K function, the test of rejection of the null hypothesis relies on Monte-Carlo simulations. The test is valid for one distance but using it repeatedly for all distances where the K function is calculated dramatically increases the risk to reject the null hypothesis by error [8]. Loosmore and Ford proposed a goodness-of-fit test to eliminate this error, but still rely on Monte-Carlo simulations
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