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Does deterministic coexistence theory matter in a finite world?

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Deterministic coexistence metrics may be unreliable in nature. This study shows that incorporating invasion growth rates and equilibrium population sizes improves predictions of species coexistence duration in finite, stochastic environments.

Keywords:
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Area of Science:

  • Ecology
  • Population Biology
  • Theoretical Ecology

Background:

  • Contemporary species coexistence studies rely on deterministic models with unrealistic assumptions of continuous densities, infinite landscapes, and infinite time.
  • Real-world species consist of discrete individuals facing demographic stochasticity in finite habitats, leading to finite extinction times.
  • Metrics derived from deterministic theory, such as invasion growth rates and niche/fitness differences, may not accurately predict real-world species coexistence duration.

Purpose of the Study:

  • To test the efficacy of deterministic coexistence metrics in predicting species coexistence duration in finite, stochastic environments.
  • To develop new theoretical and computational methods for estimating coexistence times in stochastic models.
  • To parameterize these models with field data for biologically informed coexistence time estimates.

Main Methods:

  • Developed new theoretical and computational methods to estimate coexistence times in stochastic versions of classic deterministic competition models.
  • Parameterized the model using experimental field data from 90 pairwise combinations of 18 annual plant species.
  • Utilized demographically uncoupled single-species models incorporating invasion growth rates and equilibrium population sizes.

Main Results:

  • Even with only 10 individuals, predicted coexistence times exceeded 1000 years for species expected to deterministically coexist.
  • Invasion growth rates explained 60% of the variation in intrinsic coexistence times, confirming their utility.
  • Integrating invasion growth rates and equilibrium population sizes explained over 99% of the variation in species coexistence times.
  • Increasing niche overlap and fitness differences did not consistently decrease coexistence times, contrary to deterministic predictions.

Conclusions:

  • Deterministic coexistence metrics are useful but require supplementation with equilibrium population size data for accurate duration predictions in finite, stochastic systems.
  • The developed methods and findings support the informed use of deterministic theory while emphasizing the need for stochastic and finite-world considerations.
  • Accurate prediction of species coexistence duration necessitates integrating invasion growth rates with species' equilibrium population sizes.