Scale transition theory with special reference to species coexistence in a variable environment

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Understanding how population dynamics change across spatial and temporal scales is crucial.
• Emergent properties on larger scales arise from interactions between nonlinearities and variation on smaller scales.
• Species coexistence mechanisms, like the storage effect, are often linked to temporal fluctuations.

Purpose of the Study:

• To present scale transition theory as a mathematical framework for analyzing population dynamics.
• To explain how nonlinear functions and variation interact to produce scale-dependent phenomena.
• To elucidate the mechanisms of species coexistence driven by temporal fluctuations.

Main Methods:

• Applying statistical theory for averaging nonlinear functions.
• Utilizing spatial models where larger-scale variables are averages of smaller-scale ones.
• Analyzing temporal averages of per capita growth rates to understand long-term population trends.

Main Results:

• Scale transition theory provides a method to understand emergent properties from small-scale interactions.
• The theory explains species coexistence through temporal fluctuations and nonlinear dynamics.
• Key coexistence mechanisms identified include the storage effect and nonlinear competitive variance.

Conclusions:

• Scale transition theory offers a robust mathematical approach to ecological scaling problems.
• Understanding the interplay between nonlinearity and variation is key to predicting population dynamics.
• The theory clarifies the role of temporal fluctuations in maintaining species diversity.