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Highlights • Noise can determine invasion success in competition-diffusion models. • Different density dependencies change the impact of noise on wave pinning. • Results are independent on the chosen growth function. • Numerical results show extreme parameter restrictions for wave pinning. • Wave pinning is unstable against environmental perturbations in one dimension. Abstract Numerical results on conditions for the emergence of propagation failure of diffusive fronts in two-species competition models for populations with either logistic growth or strong Allee effect are presented. Particularly, the stability against environmental perturbations is investigated. Two different density dependencies of the noise intensities are considered. They mimic a differential functional response of the competitors to the variable environment. Assuming classical linearly density-dependent noise intensities, stochastic wave pinning can occur. This is an ecologically important finding regarding biological invasion as it means that the invasion speed can be reduced by environmental perturbations even yielding a reversal of the invasion wave. However, this depends on the form of the functional per-capita noise response. [ABSTRACT FROM AUTHOR]

We study an individual-based model in which two spatially distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in terms of reproduction rate. In the second case, resources are not uniformly distributed in space. In the third case, the two species are transported by a fluid flow. In all these cases, at varying the parameters, we observe a transition from a regime in which diffusing faster confers an effective selective advantage to one in which it constitutes a disadvantage. We analytically estimate the magnitude of this advantage (or disadvantage) and test it by measuring fixation probabilities in simulations of the individual-based model. Our results provide a framework to quantify evolutionary pressure for increased or decreased dispersal in a given environment. [ABSTRACT FROM AUTHOR]

• A membrane-bulk model for cell polarization is analyzed in 3 different geometries. • In 1D, a PDE-ODE system exhibits pole-to-pole oscillations of polarity molecule Cdc42. • On the disk, symmetry-breaking instabilities cause rotating waves and Turing patterns. • Assuming a well-mixed bulk leads to a nonlocal PDE system on a 1D circular domain. • The effects of bulk and surface diffusion on spatio-temporal patterning are described. Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov–Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in mass-conserved cell polarity models. [ABSTRACT FROM AUTHOR]