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Diversity increases the stability of ecosystems.

Francesca Arese Lucini1, Flaviano Morone1, Maria Silvina Tomassone2

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Ecosystem stability increases with species diversity, contrary to the 40-year-old diversity-stability paradox. This study resolves the paradox by introducing nonlinear interactions, showing diversity benefits ecosystems, aligning with empirical evidence.

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • The diversity-stability paradox, proposed by Robert May in 1972, suggests increased species diversity destabilizes ecosystems.
  • This paradox arose from mathematical models with linear species interactions, contradicting empirical observations.
  • Despite its theoretical basis, the paradox has persisted for over four decades.

Purpose of the Study:

  • To re-evaluate the diversity-stability relationship by addressing the limitations of linear models.
  • To demonstrate how nonlinear interactions resolve the diversity-stability paradox.
  • To provide a theoretical framework supporting the beneficial role of diversity in ecosystem stability.

Main Methods:

  • Analysis of a mathematical model with linear species interactions, identifying the neglect of fixed-point solutions as a key issue.
  • Development and analysis of a new model incorporating nonlinear species interactions, using a saturating term analogous to a Hill function.
  • Application of k-core percolation to find the exact fixed-point solution of the nonlinear model.

Main Results:

  • Linear models lead to paradoxical predictions of ecosystem instability with increasing diversity due to ill-posed solutions.
  • The nonlinear model demonstrates that increased species diversity enhances ecosystem stability.
  • The exact fixed-point solution derived from k-core percolation confirms the disappearance of the paradox.

Conclusions:

  • The diversity-stability paradox is an artifact of linear modeling assumptions.
  • Nonlinear interactions are crucial for accurately representing ecosystem dynamics and stability.
  • This research theoretically validates the long-observed empirical evidence that biodiversity enhances ecosystem stability.