Regeneration pattern analysis of Quercus liaotungensis in a temperate forest using two-dimensional wavelet analysis

This paper introduces the two-dimensional (2D) wavelet analysis as a general interrogative technique for the detection of spatial structure in lattice data. The 2D wavelet analysis detects components of hierarchical structure and displays the locational information of the components. Patches and gaps of different spatial scales in graphical presentation of wavelet coefficients can be linked to the local ecological processes that determine patterns at stand or landscape scales. Derived from the 2D wavelet transform function, the calculation of wavelet variance can reduce the four-dimensional data of wavelet coefficients to a two-dimensional wavelet variance function and quantify the contribution of the given scale to the overall pattern. We illustrate the use of the 2D wavelet analysis by analyzing two simulated patterns and identifying the regeneration pattern of the Quercus liaotungensis in a warm temperate forest in north China. Our results indicate that the recruitment of Q. liaotungensis occurs in an overlapping area between the patch of adult and canopy gap at scales of 45 m×45 m–70 m×70 m and 20 m×20 m–30 m×30 m. The regeneration pattern of Q. liaotungensis can be mainly ascribed to a trade-off between two ecological processes: recruitment around parent trees and the physiological light requirements of seedlings and saplings. Our results provide a general portrayal of the regeneration pattern for the dispersal-limited and shade-intolerant Quercus species. We find that the two-dimensional wavelet analysis efficiently characterizes the scale-specific pattern of Q. liaotungensis at different life-history stages.