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A general framework for invasion cycles in ecology.

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Ecological network interactions can sustain species diversity via cycles. This study links interaction structure to cycle emergence, finding asymmetric interactions promote complex invasion cycles, while symmetric ones suppress them.

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • Ecological networks are theorized to maintain species diversity through oscillatory dynamics.
  • A framework connecting interaction structure to the presence, type, and complexity of these cycles is currently lacking.

Purpose of the Study:

  • To develop an analytical framework linking ecological interaction structure to the emergence and complexity of oscillatory dynamics.
  • To clarify the conditions under which indirect interactions drive cycles in ecological networks.

Main Methods:

  • Developed an analytical toolbox combining invasion graphs with mathematical decomposition of interaction matrices.
  • Analyzed interaction matrices into symmetric (self-limitation) and antisymmetric (competitive asymmetry) components.

Main Results:

  • Symmetric interaction dominance suppresses invasion cycles.
  • Antisymmetric interaction dominance promotes single- and multi-species invasion cycles.
  • Increased asymmetries lead to more complex cycles, but high growth rate variability suppresses cycle potential.

Conclusions:

  • Interaction structure critically determines the emergence and complexity of ecological cycles.
  • A simple ratio assessing symmetric vs. antisymmetric contributions can constrain cycle emergence and species diversity.
  • This framework clarifies the role of indirect interactions in maintaining biodiversity.