Spatial convergent cross mapping to detect causal relationships from short time series

Authors

  • Adam Thomas Clark,

    Corresponding author
    1. University of Minnesota, Department of Ecology, Evolution, and Behavior, 1987 Upper Buford Circle, Saint Paul, Minnesota 55108 USA
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  • Hao Ye,

    1. Scripps Institution of Oceanography, University of California–San Diego, 9500 Gilman Drive, La Jolla, California 92093 USA
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  • Forest Isbell,

    1. University of Minnesota, Department of Ecology, Evolution, and Behavior, 1987 Upper Buford Circle, Saint Paul, Minnesota 55108 USA
    2. Department of Plant Biology, 2502 Miller Plant Sciences, University of Georgia, Athens, Georgia 30602 USA
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  • Ethan R. Deyle,

    1. Scripps Institution of Oceanography, University of California–San Diego, 9500 Gilman Drive, La Jolla, California 92093 USA
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  • Jane Cowles,

    1. University of Minnesota, Department of Ecology, Evolution, and Behavior, 1987 Upper Buford Circle, Saint Paul, Minnesota 55108 USA
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  • G. David Tilman,

    1. University of Minnesota, Department of Ecology, Evolution, and Behavior, 1987 Upper Buford Circle, Saint Paul, Minnesota 55108 USA
    2. Bren School of Environmental Science and Management, University of California, 2400 Bren Hall, Santa Barbara, California 93106 USA
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  • George Sugihara

    1. Scripps Institution of Oceanography, University of California–San Diego, 9500 Gilman Drive, La Jolla, California 92093 USA
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  • Corresponding Editor: B. D. Inouye.

Abstract

Recent developments in complex systems analysis have led to new techniques for detecting causal relationships using relatively short time series, on the order of 30 sequential observations. Although many ecological observation series are even shorter, perhaps fewer than ten sequential observations, these shorter time series are often highly replicated in space (i.e., plot replication). Here, we combine the existing techniques of convergent cross mapping (CCM) and dewdrop regression to build a novel test of causal relations that leverages spatial replication, which we call multispatial CCM. Using examples from simulated and real-world ecological data, we test the ability of multispatial CCM to detect causal relationships between processes. We find that multispatial CCM successfully detects causal relationships with as few as five sequential observations, even in the presence of process noise and observation error. Our results suggest that this technique may constitute a useful test for causality in systems where experiments are difficult to perform and long time series are not available. This new technique is available in the multispatialCCM package for the R programming language.

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