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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Understanding environmental stochasticity's effect on population dynamics is crucial.
  • Characterizing invariant probability measures in multi-species models with environmental noise is challenging.

Purpose of the Study:

  • To investigate how environmental stochasticity influences long-term population sizes in one- and two-species models.
  • To develop methods for analyzing population dynamics under fluctuating environmental conditions.

Main Methods:

  • Utilizing properties of per-capita growth rates at stationarity for simpler models.
  • Applying a recent result by Cuello to analyze the impact of small noise in complex models.

Main Results:

  • Environmental fluctuations can decrease, increase, or leave unchanged the expected population size.
  • The impact of noise depends on the specific dynamical model and the parameters affected (e.g., growth rate, carrying capacity).
  • The choice of the deterministic baseline significantly influences the observed effects of environmental fluctuations.

Conclusions:

  • Environmental stochasticity has varied effects on population sizes, contingent on ecological models and parameters.
  • The introduction and baseline comparison of noise are critical factors in population dynamics studies.
  • This research provides insights into the complex interplay between environmental variability and species persistence.