[Paper Review] Periodic temporal environmental variations induce coexistence in resource competition models

Tom Burkart, Willeke, Jan+1 more|arXiv (Cornell University)|Feb 23, 2022

Evolution and Genetic Dynamics4 citations

TL;DR

This paper demonstrates that periodic temporal environmental variations—such as seasonal or diurnal cycles—can enable stable coexistence among competing microbial species in resource-limited ecosystems, overturning the competitive exclusion principle. Using time-scale separation and a generalized Monod-type growth model, the authors show that when environmental fluctuations are fast relative to population dynamics, Tilman’s R* rule can be extended, and coexistence emerges due to non-equilibrium dynamics, even in systems where one species would otherwise dominate in a constant environment.

ABSTRACT

Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in environmental conditions, such as resource abundance. Here, we use a generic population dynamics model to study how, and under what conditions, a periodic temporal environmental variation can alter an ecosystem's composition and biodiversity. We demonstrate that using time scale separation allows one to qualitatively predict the long-term population dynamics of interacting species in varying environments. We show that the notion of Tilman's R* rule, a well-known principle that applies for constant environments, can be extended to periodically varying environments if the time scale of environmental changes (e.g., seasonal variations) is much faster than the time scale of population growth (doubling time in bacteria). When these time scales are similar, our analysis shows that a varying environment deters the system from reaching a steady state, and stable coexistence between multiple species becomes possible. Our results posit that biodiversity can in part be attributed to natural environmental variations.

Motivation & Objective

• To understand how periodic environmental variations—such as seasonal or diurnal cycles—affect species coexistence in microbial ecosystems.
• To extend Tilman’s R* rule, which applies in constant environments, to periodically varying environments.
• To identify the conditions under which competitive exclusion is overcome due to temporal environmental fluctuations.
• To provide an intuitive, physically grounded explanation for biodiversity enhancement via environmental periodicity, complementing complex theoretical frameworks like Chesson’s coexistence theory.

Proposed method

• A generalized resource competition model is formulated using Monod-type growth functions with time-dependent resource availability.
• Time-scale separation is applied to analyze long-term population dynamics when environmental changes are fast relative to population growth.
• The system is analyzed under periodic switching of resource abundance, simulating seasonal or circadian cycles.
• Steady-state population dynamics are derived using asymptotic trajectories for dominant species, enabling reduction to pairwise competition models.
• Invasion analysis is performed by tracking net population growth over one environmental period to assess long-term survival or extinction.
• Numerical simulations are used to classify outcomes as coexistence, exclusion of opportunist, or exclusion of gleaner based on log-population change thresholds.

Experimental results

Research questions

• RQ1 Under what conditions does periodic environmental variation enable stable coexistence between competing microbial species in a resource-limited system?
• RQ2 How does the time scale of environmental variation relative to population growth affect long-term ecosystem composition?
• RQ3 Can Tilman’s R* rule for species exclusion in constant environments be extended to periodically varying environments?
• RQ4 What mechanism allows a non-equilibrium environment to prevent competitive exclusion and promote biodiversity?
• RQ5 To what extent can pairwise competition dynamics accurately represent the long-term behavior of multi-species ecosystems under time-dependent conditions?

Key findings

• When environmental fluctuations are fast compared to population growth, the system can be described by an effective time-averaged R* rule, extending the classical theory to periodic environments.
• Coexistence becomes possible when the time scales of environmental variation and population growth are comparable, as the system fails to reach a steady state.
• In systems where one species would otherwise dominate under constant conditions, periodic environmental changes can lead to stable coexistence by altering the effective growth rates.
• The competitive exclusion principle is overcome not by differences in resource affinity, but by non-equilibrium dynamics arising from time-dependent environmental forcing.
• Pairwise competition analysis is sufficient to predict long-term dynamics in multi-species systems, even under time-dependent conditions, due to the dominance of one species in shaping total population size.
• Numerical simulations confirm that coexistence is robust when environmental cycles are fast enough to prevent system equilibration, with extinction thresholds based on net population growth over one cycle.