Coexistence and Spread of Competitors in Heterogeneous Landscapes

Abstract

Competition between species is ubiquitous in nature and therefore widely studied in ecology through experiment and theory. One of the central questions is under which conditions a (rare) invader can establish itself in a landscape dominated by a resident species at carrying capacity. Applying the same question with the roles of the invader and resident reversed leads to the principle that "mutual invasibility implies coexistence." A related but different question is how fast a locally introduced invader spreads into a landscape (with or without competing resident), provided it can invade. We explore some aspects of these questions in a deterministic, spatially explicit model for two competing species with discrete non-overlapping generations in a patchy periodic environment. We obtain threshold values for fragmentation levels and dispersal distances that allow for mutual invasion and coexistence even if the non-spatial competition model predicts competitive exclusion. We obtain exact results when dispersal is governed by a Laplace kernel. Using the average dispersal success, we develop a mathematical framework to obtain approximate results that are independent of the exact dispersal patterns, and we show numerically that these approximations are very accurate.

Scale-Dependent Community Theory for Streams and Other Linear Habitats

“…Addressing the Janzen-Connell hypothesis, Stump and Chesson (2015) show clear effects of the amount of dispersal on the coexistence of tropical trees. Focusing on spatially periodic environmental change, Samia and Lutscher (2010) and Snyder andChesson (2003, 2004) find, in agreement with this article, that coexistence depends on the scales of dispersal and environmental change. Similar dependence of coexistence on spatial and temporal scales is found by Aiken and Navarrete (2014), in a model where the necessary numerical and physiological separation is generated by variation in connectivity rather than by local environmental conditions.…”

“…Numerous models have addressed spatial coexistence mechanisms in terms of life-history trade-offs (e. g., Hastings 1980;Hanski 1983;Tilman 1994;Amarasekare et al 2004;Miller and Chesson 2009;Muller-Landau 2010;Samia and Lutscher 2010). In general, they draw a sharp distinction between local interactions and regional coexistence.…”

Spreading speeds for stage structured plant populations in fragmented landscapes

“…The existing analytical methods have been successful in their agreement with simulations of IDEs, but are limited to non stage-structured populations and either (i) to a particular choice of kernel, which does not accurately describe the dispersal patterns of all species, e.g. [35], or (ii) to cases in which dispersal occurs at scales much larger than the distance between patches (Figure 1a), see [33,35]. However, many fragmented habitats [36] such as calcareous grassland in Dorset, UK [9] and woodland in Wisconsin [37], as well as natural habitats such as vernal pools in California [38], do not conform to this pattern and are composed of small habitat fragments separated by distances which have sufficient length to make inter-patch dispersal rare.…”

Effects of long-range taxis and population pressure on the range expansion of invasive species in heterogeneous environments

“…Whereas most theoretical studies on biological invasion have assumed that environments are homogeneous (Skellam 1951; for review, see Shigesada and Kawasaki 1997;Okubo and Levin 2001;Lewis et al 2016), recent theoretical developments have increasingly been directed toward more realistic situations involving environmental heterogeneity, temporal variability, or interactions with other species (Chesson 2000;Hastings et al 2005). Specifically, in the case of environments that change periodically in space, the spatio-temporal process of biological invasion has been investigated intensively in the framework of a reaction-diffusion equation (RDE model) or integro-difference equation (IDE model) to provide various new insights into the range expansion pattern and its spreading speed (RDE model: Shigesada et al 1986;Weinberger 2002;Kinezaki et al 2003Kinezaki et al , 2010Berestycki et al 2005a, b;Roques and Stoica 2007;IDE model: Kawasaki and Shigesada 2007;Lutscher 2008;Weinberger et al 2008;Dewhirst and Lutscher 2009;Samia and Lutscher 2010;Gilbert et al 2014;Musgrave and Lutscher 2014;Musgrave et al 2015;Bengfort et al 2016). More recently, increasing attention has been focused on the effects of directed movement toward more favorable habitats (taxis) on biological invasion (Mistro et al 2005;Lutscher et al 2006;Cantrell et al 2006;Kawasaki et al 2012;Vergni et al 2012;Lutscher 2013, 2015;Li et al 2015;Shigesada et al 2015).…”