Analyses of three-dimensional species associations reveal departures from neutrality in a tropical forest.

The study of community spatial structure is central to understanding diversity patterns over space and species co-occurrence at local scales. Although most analytical approaches consider horizontal and vertical dimensions separately, in this study we introduce a three-dimensional spatial analysis that simultaneously includes horizontal and vertical species associations. Using tree census data (2000-2016) and allometries from the Luquillo forest plot in Puerto Rico, we show that spatial organization becomes less random over time as the forest recovered from land-use legacy effects and hurricane disturbance. Tree species vertical segregation is predominant in the forest with almost all species that co-occur in the horizontal plane avoiding each other in the vertical dimension. Horizontal segregation is less common than vertical, whereas three-dimensional aggregation (a proxy for direct tree competition) is the least frequent type of spatial association. Furthermore, dominant species are involved in more non-random spatial associations, implying that species co-occurrence is facilitated by species segregation in space. This novel three-dimensional analysis allowed us to identify and quantify tree species spatial distributions, how interspecific competition was reduced through forest structure, and how it changed over time after disturbance, in ways not detectable from two-dimensional analyses alone.