The Effects of Seasonality on Competition for a Limiting Resource DOI Open Access

Lluc Briganti Wiprachtiger

SIAM Undergraduate Research Online, Journal Year: 2022, Volume and Issue: 15

Published: Jan. 1, 2022

Theoretical studies of PDE/ODE models describing ecosystem dynamics usually ignore seasonality in environmental conditions.In this paper I study a model two generic consumer species that compete for single limiting resource.I first consider constant resource input and then compare it to the case when is dependent on time with seasonal (periodic) pattern.The analysed analytically, by looking at linear stability every equilibrium.The through numerical simulations.Results analysis show has significant effect outcome system, as time, there could be stable coexistence, which not possible under input.Moreover, metastable coexistence states exist both regimes if average fitness difference between small.Finally, times until extinction become longer constant. Introduction.In setting where same resource, one species, even slightest advantage, will dominate over other, cause its competitor.This competitive exclusion principle [9].The dominates kind system determined Tilman's R * rule [16,24], outcompete other can survive less amount available.A substantial research using mathematical been done competition resource.The term "limiting resource" refers limits growth therefore, insufficient quantity, dying out [6,7,16,25].According principle, cannot occur these circumstances [9,17].However, nature commonly observed.The therefore suggests presence coexistence-enabling mechanisms [16].Even no mechanism stabilising present, metastability [8].A state an inherently unstable nevertheless occurs long transient.In context dynamics, have similar fitness.In cases applies, near balance causes process take time.Therefore, transient such cases.Mathematically, characterised small magnitude eigenvalues (or more) model's equilibria [20].This describes slow convergence or divergence from equilibrium, meaning may system.Another enables

Language: Английский

Far-from-Equilibrium Traveling Pulses in Sloped Semiarid Environments Driven by Autotoxicity Effects DOI
Gabriele Grifó, Annalisa Iuorio, Frits Veerman

et al.

SIAM Journal on Applied Mathematics, Journal Year: 2025, Volume and Issue: 85(1), P. 188 - 209

Published: Jan. 27, 2025

Language: Английский

Citations

2
Spatial patterns in ecological systems: from microbial colonies to landscapes DOI
Ricardo Martínez‐García, Corina E. Tarnita, Juan A. Bonachela

et al.

Emerging Topics in Life Sciences, Journal Year: 2022, Volume and Issue: 6(3), P. 245 - 258

Published: June 9, 2022

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial distributions starting from disordered configurations. These form due diverse nonlinear interactions among organisms between their environment, lead the emergence of new (eco)system-level properties unique self-organized systems. Such pattern consequences include higher resilience resistance environmental changes, abrupt ecosystem collapse, hysteresis loops, reversal competitive exclusion. Here, we review exhibiting patterns. We establish two broad categories depending on whether self-organizing process is primarily driven by density-dependent demographic rates or movement. Using this organization, examine a wide range observational scales, microbial colonies whole ecosystems, discuss mechanisms hypothesized underlie observed system-level consequences. For each example, both empirical evidence existing theoretical frameworks developed identify causes patterning. Finally, trace qualitative similarities across propose possible ways developing more quantitative understanding how self-organization operates scales ecology.

Language: Английский

Citations

24
Processes and Predictions in Ecological Models: Logic and Causality DOI Creative Commons
Christian Damgaard

Journal of Forecasting, Journal Year: 2025, Volume and Issue: unknown

Published: Feb. 27, 2025

ABSTRACT To make credible ecological predictions for terrestrial ecosystems in a changing environment and increase our understanding of processes, we need plant models that can be fitted to spatial temporal data. Such based on sufficient processes account the different sources uncertainty. Here, I argue (1) use structural equation hierarchical framework with latent variables (2) specify whether current knowledge relationships among state may categorized primarily as logical (empirical) or causal. will help us continuous progress ability predict dynamics provide local known degree uncertainty are useful generating adaptive management plans. The recommend analogous general epistemological how is obtained.

Language: Английский

Citations

0
Vegetation pattern formation and transition in dryland ecosystems with finite soil resources and inertia DOI Creative Commons
Giancarlo Consolo, Carmela Curró, Gabriele Grifó

et al.

Physica D Nonlinear Phenomena, Journal Year: 2025, Volume and Issue: unknown, P. 134601 - 134601

Published: March 1, 2025

Language: Английский

Citations

0
Enhanced species coexistence in Lotka-Volterra competition models due to nonlocal interactions DOI

Gabriel Andreguetto Maciel,

Ricardo Martínez‐García

Journal of Theoretical Biology, Journal Year: 2021, Volume and Issue: 530, P. 110872 - 110872

Published: Aug. 20, 2021

Language: Английский

Citations

20
Large Amplitude Radially Symmetric Spots and Gaps in a Dryland Ecosystem Model DOI Creative Commons

Eleanor Byrnes,

Paul Carter, Arjen Doelman

et al.

Journal of Nonlinear Science, Journal Year: 2023, Volume and Issue: 33(6)

Published: Sept. 21, 2023

Abstract We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics geometric singular perturbation theory. draw connections between the geometry with that traveling stationary front same model. In particular, we demonstrate instability spots large radius by deriving an asymptotic relationship critical eigenvalue associated coefficient which encodes sideband nearby front. Furthermore, are unstable to range perturbations intermediate wavelength angular direction, provided is not too small. Our results accompanied numerical simulations spectral computations.

Language: Английский

Citations

7
A Stabilizing Effect of Advection on Planar Interfaces in Singularly Perturbed Reaction-Diffusion Equations DOI
Paul Carter

SIAM Journal on Applied Mathematics, Journal Year: 2024, Volume and Issue: 84(3), P. 1227 - 1253

Published: June 10, 2024

Language: Английский

Citations

2
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework DOI Creative Commons
Yifei Li, Pascal R. Buenzli, Matthew J. Simpson

et al.

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, Journal Year: 2022, Volume and Issue: 478(2262)

Published: June 1, 2022

Understanding whether a population will survive or become extinct is central question in biology. One way of exploring this to study dynamics using reaction-diffusion equations, where migration usually represented as linear diffusion term, and birth-death with nonlinear source term. While most commonly employed migration, there are several limitations approach, such the inability diffusion-based models predict well-defined front. overcome generalize constant diffusivity,

Language: Английский

Citations

8
Resource-Mediated Competition Between Two Plant Species with Different Rates of Water Intake DOI
Chunyi Gai, Théodore Kolokolnikov

SIAM Journal on Applied Mathematics, Journal Year: 2023, Volume and Issue: 83(2), P. 576 - 602

Published: April 27, 2023

.We propose an extension of the well-known Klausmeier model vegetation to two plant species that consume water at different rates. Rather than competing directly, plants compete through their intake water, which is a shared resource between them. In semiarid regions, produces spot patterns. We are interested in how competition for affects coexistence and stability patches species. consider types—a "thirsty" "frugal" species—that only differ by amount they per unit growth, while being identical other aspects. find there finite range precipitation rate can coexist. Outside (when either sufficiently low or high), frugal out-competes thirsty As decreased, sequence thresholds such first die off, spots remain resilient longer. The pattern consisting most resilient. next consists all-thirsty patches, with mixed less homogeneous also examine numerically what happens very large high rate, takes over entire range, out-competing plant.Keywordsspecies coexistencestability analysisKlausmeier modelresource-mediated competitionreaction-diffusion systemspattern formationMSC codes35B3535B3635B4035Q92

Language: Английский

Citations

4
Pattern dynamics of a predator-prey system with Ivlev-type functional response DOI Open Access
Liu Yang,

Zuolin Shen,

Junjie Wei

et al.

Discrete and Continuous Dynamical Systems - B, Journal Year: 2024, Volume and Issue: 29(9), P. 3802 - 3823

Published: Jan. 1, 2024

In this paper, we study the dynamics and pattern formation of a reaction-diffusion system with Ivlev-type functional response homogeneous Neumann boundary conditions. We first consider global existence boundedness nonnegative solutions then discuss stability steady states. By using energy estimates Leray-Schauder degree theory, prove nonexistence nonconstant positive states respectively. Finally, show some interesting spatiotemporal dynamical behaviors in numerical simulations. Our result is consistent 'activation-inhibition' mechanism, where prey treated as an activator predator inhibitor. When diffusion rate much lower than that predator, patterns may be generated.

Language: Английский

Citations

1