Population boundary across an environmental gradient: Effects of quenched disorder

Abstract

Climatic response of population boundaries, known as ecotone, is a classic indicator in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental factors, but also by local heterogeneities in the regional characteristics. Here, we capture the effects of time-independent, quenched spatial heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter. We apply the strongdisorder renormalization group method to calculate the sites occupied with an O(1) probability in the stationary state, readily yielding the population front's position as the outermost site locally as well as globally for the entire boundary. We show that under a quasistatic change of the global environment, mimicking climate change, the front advances intermittently: long quiescent periods are interrupted by rare but long jumps. The characteristics of this intermittent dynamics are found to obey universal scaling laws in terms of the gradient, conjectured to be related to the correlation-length exponent of the model. In the two dimensional case our analysis shows that both the local and global shift of the front exhibit intermittent dynamics and follow the same scaling laws as in one dimension, apart from a logarithmic correction for global shifts. In one dimension, we show that determining the front position is related to an extremal problem of random walks, shedding further light on the origin of the jumps. Our results are in stark contrast to the behavior of the model without disorder, suggesting that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.

Multipartite Entanglement in the Random Ising Chain

“…A potentially promising direction is through the well-known mapping to a random potential representation of the SDRG treatment, similarly to the application in Ref. [34].…”

Advancing and retreating fronts in a changing climate: a percolation model of range shifts

“…We follow the footsteps of these gradient metapopulation models, but combine their elements uniquely, as we analyze the two‐dimensional spatial pattern in the steady state, directly comparing the effect of the spatial and temporal change of the environment. It is worth mentioning that several models of shifting metapopulations (w/wo an environmental gradient) assumed the occurrence of habitat loss, introducing an additional kind of spatial inhomogeneity on a finer spatial scale (Travis 2003, Best et al 2007, Mustin et al 2009, Kubisch et al 2014, Juhász and Kovács 2020). Our present aim is to study the emergent spatial patterns undisturbed by inhomogeneities.…”

“…For example, Travis (2003), Best et al (2007) and McInerny et al (2009) studied habitat tracking in discrete climate windows, set by step functions (that is, not along smooth environmental gradients). Range shifts along environmental gradients have been investigated, for example, by Mustin et al (2009), Turner and Wong (2010), Bocedi et al (2014), Kubisch et al (2014), Tejo et al (2017) and Juhász and Kovács (2020) (see Zeng and Malanson 2006 about an ecotone shift). We follow the footsteps of these gradient metapopulation models, but combine their elements uniquely, as we analyze the two-dimensional spatial pattern in the steady state, directly comparing the effect of the spatial and temporal change of the environment.…”

“…Pattern formation has thoroughly been described in homogeneous CPs, in which the environment was the same in every site (reviewed by Oborny 2007), and also across environmental gradients in a constant climate (Gastner et al 2009, Gastner and Oborny 2012, Oborny 2018, Juhász and Oborny 2020. Juhász and Kovács (2020) and we in this paper add climate change to the gradient contact process. In the forthcoming text, these model types will be abbreviated as hCP (homogeneous), cgCP (constant gradient), and sgCP (shifting gradient) contact processes.…”

“…The effects of various non‐random spatial distributions have been investigated less intensively (see Mendelson 2000 for an example). The study of percolation within those patterns that emerge from (meta)population processes is in the initial stage yet (Milne et al 1996, Oborny et al 2007, Gastner et al 2009, Gastner and Oborny 2012, Oborny 2018, Juhász and Kovács 2020, Juhász and Oborny 2020). A gradient, i.e.…”