Quantifying α-diversity as a continuous function of location-a case study of a temperate forest

& alpha;-diversity describes species diversity at local scales. The Simpson's and Shannon-Wiener indices are widely used to characterize & alpha;-diversity based on species abundances within a fixed study site (e.g., a quadrat or plot). Although such indices provide overall diversity estimates that can be analyzed, their values are not spatially continuous nor applicable in theory to any point within the study region, and thus they cannot be treated as spatial covariates for analyses of other variables. Herein, we extended the Simpson's and Shannon-Wiener indices to create point estimates of & alpha;-diversity for any location based on spatially explicit species occurrences within different bandwidths (i.e., radii, with the location of interest as the center). For an arbitrary point in the study region, species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function, with occurrences closer to the center having greater weight than more distant ones. These novel kernel-based & alpha;-diversity indices were tested using a tree dataset from a 400 m x 400 m study region comprising a 200 m x 200 m core region surrounded by a 100-m width buffer zone. Our newly extended & alpha;-diversity indices did not disagree qualitatively with the traditional indices, and the former were slightly lower than the latter by < 2% at medium and large bandwidths. The present work demonstrates the feasibility of using kernel-based & alpha;-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies. Spatially continuous & alpha;-diversity indices are useful to compare and monitor species trends in space and time, which is valuable for conservation practitioners.