New derivation reduces bias and increases power of Ripley's L index

The development of distance-dependent growth and survival models depends on an understanding of the spatial distribution of the population in question . Ripley's L index (L-R) has found wide application for examining the spati al dispersion of plants. L-R is calculated as the square root of a weighted sum of the number of observed plant pairs that are less than a certain dis tance apart. The weighting used by L-R inflates the pair count sum to compe nsate for reduced pair counts for plants near the plot boundary. Using Mont e Carlo simulations, we show that the variance in the observed number of tr ee pairs is not stabilized by the square root transformation at low expecte d counts. The non-linearity of the square root transformation introduces a consistent bias in both the first and second moments of the tree pair distr ibution. We present a derived estimator for Ripley's analytical L index (L- A) that provides a more accurate estimate of variance and mean. This new ap proach, based on a true Poisson variate, includes a modification of the pre vious edge correction method that incorporates a global estimate of mean pa ir density, rather than local values. This reduces variance caused by stoch astic placement of point pairs near the boundary. Monte Carlo simulations v erified the predictions of this model over a wide range of population sizes (25-1400). Simulation results showed that the L-R numerical estimate of th e confidence limit was overly conservative by nearly a factor of two. The i mproved power and accuracy provided by L-A suggest that it would be fruitfu l to reexamine population spatial dispersion data in the literature using t he analytical estimator (L-A). As an illustration, the power and accuracy o f L-R and L-A to detect non-random spatial dispersions is compared using ge nerated populations and six stands of mapped trees in Connecticut. (C) 1999 Elsevier Science B.V. All rights reserved.