A mathematics paper written by three Taiwan-born researchers outlines a new approach to using predator-prey causal relationships to improve the accuracy of population estimates.
The study was written by Albert Yang (楊智傑) and Peng Chung-kang (彭仲康) of Harvard Medical School’s Beth Israel Deaconess Medical Center and Norden Huang (黃鍔) of National Central University.
The researchers found that a causal-decomposition approach generally applicable to random probability and deterministic systems could be a key mode of causal interactions in models using Lotka-Volterra equations, also known as predator-prey equations, the paper said.
The equations track populations over time.
The trio used statistics from wolf and moose populations in Isle Royale National Park, an island in Lake Superior in the US state of Michigan, as well as a Canada lynx and snowshoe hare time series reconstructed from records provided by Hudson’s Bay Co — a former fur trading business that now owns and operates retail stores — for the study.
The predictive causality approach, as proposed by Nobel laureate Clive Granger, might underestimate the simultaneous and reciprocal nature of interactions between two animal populations, so they took a causal-decomposition approach based on the covariation of cause and effect, they wrote in the introduction to the paper, which was published on Thursday last week in Nature Communications.
“The Granger causality is based on time dependency between cause and effect,” they wrote. “Granger causality is critically dependent on the assumption that cause and effect are separable.”
Their methods identified the dominant causal role of the predator in intrinsic mode functions, the researchers said.
“Previously, the causality of such autonomous differential-equation models was understood only in mathematical terms, because there is no prediction-based causal factor,” they wrote.
The causal decomposition method, using ensemble empirical mode decomposition, is fundamentally different from the spectral extension of Granger’s causality and results in more precise phase and amplitude definition, they wrote.
However, there are limitations to the methodology, in that causal decomposition does not imply true causality, they said, adding that the current model is limited to pair-wise measurements instead of multivariate systems.
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