Density dependence on multiple spatial scales maintains spatial variation in both abundance and traits

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Population density significantly impacts individual fitness through factors like mate availability and competition.
• Density-dependent effects can operate at various spatial scales, influencing different life-history processes.
• Understanding the interplay between local and regional density is crucial for ecological and evolutionary dynamics.

Purpose of the Study:

• To investigate how local and nearby patch densities jointly influence spatial variation in population abundance and phenotypic traits.
• To explore the emergence and maintenance of spatial heterogeneity in population density.
• To examine how eco-evolutionary feedbacks, driven by trait diversification, affect long-term population densities.

Main Methods:

• Utilized a two-patch model governed by coupled ordinary differential equations.
• Employed phase-space analysis and mathematical stability analysis to determine system behavior.
• Incorporated traits and mutations to study diversification under varying selection pressures.

Main Results:

• Mutual density effects between patches can establish and sustain distinct low and high-density patches.
• Divergent selection pressures in differing density patches promote phenotypic diversification.
• Eco-evolutionary feedbacks can alter equilibrium population densities, leading to divergence even when patches are initially identical.

Conclusions:

• Interactions between spatially connected populations can generate spatial heterogeneity in density and traits.
• Trait diversification, driven by density-dependent selection, can lead to distinct evolutionary trajectories in different patches.
• This model demonstrates how ecological and evolutionary processes interact to create and maintain spatial variation within and between populations.