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The textural discontinuity hypothesis (TDH) is based on the observation that animal body mass distributions exhibit discontinuities that may reflect the texture of the landscape available for exploitation. This idea has been extended to other complex systems, hinting that the identification and quantification of discontinuities in the distributions of appropriate variables may provide clues to emergent system properties such as resilience. We propose a discontinuity index, based on the vector norm of the full assemblage of observed discontinuities, as a means to quantify and compare this characteristic among systems. We also evaluate four methods to identify the number and location of the most prominent discontinuities. Although results of the four methods are similar, they are not identical, and we conclude that this problem is best addressed with a consistent operationally defined approach in an adaptive inference framework.