A Statistical Test for Ripley’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>Function Rejection of Poisson Null Hypothesis

Abstract

Ripley’s<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:math>function 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 the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:math>value 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.