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Testing the productive-space hypothesis: rational and power

  • Community Ecology
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Abstract

Understanding and explaining the causes of variation in food-chain length is a fundamental challenge for community ecology. The productive-space hypothesis, which suggests food-chain length is determined by the combination of local resource availability and ecosystem size, is central to this challenge. Two different approaches currently exist for testing the productive-space hypothesis: (1) the dual gradient approach that tests for significant relationships between food-chain length and separate gradients of ecosystem size (e.g., lake volume) and per-unit-size resource availability (e.g., g C m−1 year−2), and (2) the single gradient approach that tests for a significant relationship between food-chain length and the productive space (product of ecosystem size and per-unit-size resource availability). Here I evaluate the efficacy of the two approaches for testing the productive-space hypothesis. Using simulated data sets, I estimate the Type 1 and Type 2 error rates for single and dual gradient models in recovering a known relationship between food-chain length and ecosystem size, resource availability, or the combination of ecosystem size and resource ability, as specified by the productive-space hypothesis. The single gradient model provided high power (low Type 2 error rates) but had a very high Type 1 error rate, often erroneously supporting the productive-space hypothesis. The dual gradient model had a very low Type 1 error rate but suffered from low power to detect an effect of per-unit-size resource availability because the range of variation in resource availability is limited. Finally, I performed a retrospective power analysis for the Post et al. (Nature 405:1047–1049, 2000) data set, which tested and rejected the productive-space hypothesis using the dual gradient approach. I found that Post et al. (Nature 405:1047–1049, 2000) had sufficient power to reject the productive-space hypothesis in north temperate lakes; however, the productive-space hypothesis must be tested in other ecosystems before its generality can be fully addressed.

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Acknowledgments

I thank C. A. Layman, L. Oksanen, L.M. Puth, G. Takimoto, J. Trexler, and an anonymous reviewer for comments and suggestions that improved this paper. This research was supported by the National Science Foundation (DEB no. 0316679).

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  1. Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT, 06520-8105, USA

    David M. Post

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  1. David M. Post
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Correspondence to David M. Post.

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Communicated by Joel Trexler.

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Post, D.M. Testing the productive-space hypothesis: rational and power. Oecologia 153, 973–984 (2007). https://doi.org/10.1007/s00442-007-0798-8

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  • DOI: https://doi.org/10.1007/s00442-007-0798-8

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