1/f Noise in spatial patterns of Dipterocarpaceae trees in a tropical rainforest, Sarawak, Malaysia

Background/Question/Methods The spatial pattern of individual trees of a species is a joint outcome of species’ specific seed dispersals and environmental conditions where they grow. As already described by Condit et al (2000), most tropical tree species in the six forest dynamics plots, including our focal 52-ha plot in Sarawak, represented aggregated spatial patterns. To expand on the work of Condit et al, we investigated spatial patterns of 73 dipterocarp species containing rare species with N> 9 individuals, by applying two dimensional Fourier transforms (FT) and 1/f noise to the data of number of conspecific individuals that were enumerated in a 20m x 20m area and arranged in a 25-by-52 matrix. Denoting the frequency and power spectral density in FT by f and P(f), respectively, 1/f noise is written in the form, P(f) = K f ^{- a}, where K and a are coefficients specific to species. When a = 1.0, the rule of 1/f noise holds, suggesting aggregated patterns. Random and Brownian motion like patterns are expressed by a = 0.0 and a = 2.0, respectively. We determined a for each species to understand the degree of aggregation. In addition to species’ patterns, the patterns of topography and soil were similarly analyzed.

Results/Conclusions The FT analysis of spatial data resulted in power spectral density P(f) arranged in a 16-by-32 matrix specific to species. We used the regression equation of log P(f) = log K – a₁logf₁ – a₂logf₂ for the description of a species specific fluctuation in P(f), in which f₁ represents the frequency for row elements, while f₂ for column elements in the matrix. The uniform (or regular) spatial distribution, which is characterized by P(f) = 0 for all sets of f₁ and f₂, was not detected. The a₁ was not always similar to a₂ even in a given species, reflecting directional biases of spatial patterns. The a₁ and a₂ for respective species were in a range between 0.0005107 (random) and 1.283, 0.4215 (aggregated) in mean, and 0.08489 in variance. The correlation coefficients (r) of P(f)s between paired species were calculated for comparing species dependent spatial patterns. The r was also calculated between P(f) of species’ spatial patterns and that of environmental factors (topography, soil texture and wood decomposition rates), leading to a provisional conclusion that spatial patterns of individual tree distribution are highly correlative with patterns of environmental factors in frequency domains.