Identifying scales of pattern in ecological data: A comparison of lacunarity, spectral and wavelet analyses

Document Type

Article

Publication Date

3-2005

Department

College of Forest Resources and Environmental Science; Department of Mathematical Sciences

Abstract

Identifying scales of pattern in ecological systems and coupling patterns to processes that create them are ongoing challenges. We examined the utility of three techniques (lacunarity, spectral, and wavelet analysis) for detecting scales of pattern of ecological data. We compared the information obtained using these methods for four datasets, including: surface temperature across space (linear transect), surface temperature across time, understory plant diversity across space (linear transect), and a simulated series of known structure. For temperature and plant diversity across the transect, we expected to find dominant scales of pattern of approximately 220 m and, for plant diversity scales of pattern of > 450 m, corresponding to management activities on the study landscapes. For temperature across time, we predicted a dominant scale of 24 h. The simulated data included a sine wave with a known period of 9.9 units, an edge at approximately 30 units, and a random component. The different analyses provided unique but complementary information. Lacunarity and spectral analyses were most consistent with each other across datasets, both indicating a dominant scale of pattern at 400-500 m (coarser than expected) for the transect temperature series, a lack of dominant scale in the pattern of understory diversity, and scales of pattern at 1.8-5.1 and 8.5-11.1 units (≈wavelength) for the simulated data series. Spectral analysis best approximated an expected, 24 h period in the temporal temperature series. Wavelet variance detected finer scales of pattern (240 m) in transect temperature and suggested patterns in plant diversity at scales of 460 and 1100 m. By retaining locational information, only the wavelet transform and associated position variance detected the abrupt edge in the simulated data series. Wavelet analysis also emphasized variability, even within cyclic phenomena, not identified by spectral or lacunarity analyses, and suggested hierarchical structure in the pattern of understory plant diversity. The appropriate technique for assessing scales of pattern depends on the type of data available, the question being asked, and the detail of information desired. This comparison highlighted the importance of: (1) using multiple techniques to examine scales of pattern in ecological data; (2) interpreting analysis results in concert with examination and ecological knowledge of the original data; and (3) utilizing results to direct subsequent descriptive and experimental examination of features or processes inducing scales of pattern.

Publication Title

Ecological Complexity

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