Habitat fragmentation promotes spatial scale separation under resource competition

TL;DR

This work investigates how habitat fragmentation, modeled as a heterogeneous network of patches, shapes intraspecific competition and dispersal under space-limited carrying capacity. It develops a degree-normalized, nonlinear diffusion framework on networks, incorporating asymmetric resource perception through exponents $\sigma_x$ and $\sigma_y$ and a nonlinear carrying-capacity term, with diffusion governed by the random-walk Laplacian $L^{\mathrm{RW}}$. The authors show that spatial segregation naturally emerges: stronger competitors concentrate in network hubs while weaker ones are displaced toward the periphery, with explicit steady-state conditions and a first-order expansion revealing degree-dependent dominance. The framework is generalized to $M$ species with reaction terms including an Allee effect, producing a slow–fast mechanism that yields mosaics of single-species domains and, at saturation, up to $\lfloor 1/\mathcal{A} \rfloor$ coexisting species, reinforcing the core conclusion that fragmentation–driven topology and crowding alone can generate stable, segregated communities with potential implications for speciation.

Abstract

Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals disperse across interconnected patches. We consider an intraspecific competition model, where individuals compete for space while dispersing according to a nonlinear random walk, capturing the heterogeneity of the network. The interplay between asymmetric competition, dispersal dynamics, and spatial heterogeneity leads to nonuniform species distribution: individuals with stronger competitive traits accumulate in central (hub) habitat patches, while those with weaker traits are displaced toward the periphery. We provide analytical insights into this mechanism, supported by numerical simulations, demonstrating how competition and spatial structure jointly influence species segregation. In the large-network limit, this effect becomes extreme, with dominant individuals disappearing from peripheral patches and subordinate ones from central regions, establishing spatial segregation. This pattern may create favorable conditions for speciation, as physical separation can reinforce divergence within the population over time.

Figures (4)

• Figure 1: Representation of the species' final concentrations at steady state. (a) Final concentrations of $x$ (blue) and $y$ (red) across nodes, along with the normalized degree (magenta). The inset shows the ratio of the asymptotic densities $x_i/y_i$ at each node for $\sigma_x = \sigma_y = 1$. (b) and (c) Network layouts showing the absolute concentrations of species $x$ and $y$, respectively. In both (b) and (c), node size is proportional to degree, with larger nodes representing more connected (central) patches. Darker colors indicate higher species concentration, while lighter colors indicate lower values. The network is a scale-free graph generated using the Barabási--Albert (BA) model with parameters $N = 100$, $m_0 = 5$, and $m = 3$, where $N$ is the total number of nodes, $m_0$ the initial seed size, and $m$ the number of preferentially attached links each new node forms. Parameters for the main panels: $\sigma_x = 2.5$, $\sigma_y = 0.5$, $\mathcal{D}_x = \mathcal{D}_y = 30$; initial densities are $x = 0.5$ and $y = 0.2$ uniformly across all nodes.
• Figure 2: Long-term dynamics of a four-species reaction–diffusion model on a network. Panel (a) shows the global population distribution, with nodes colored by the dominant species: $x$ (blue), $y$ (red), $z$ (green), and $w$ (yellow). Nodes in magenta indicate coexistence of at least two species. Panels (b)–(e) depict the subnetworks occupied primarily by species $x$, $y$, $z$, and $w$, respectively. All species are initialized at a density of $0.05$. Diffusion coefficients are set to $\mathcal{D}_x = 5000$, $\mathcal{D}_y = 100$, $\mathcal{D}_z = 500$, and $\mathcal{D}_w = 300$; crowding exponents are $\sigma_x = 4.5$, $\sigma_y = 1.1$, $\sigma_z = 1.3$, and $\sigma_w = 1.8$. The reaction rate is $r = 1$, and the Allee threshold is set to $\mathcal{A} = 0.15$ for all species, consistent with observational in situ studies shepherd1995studies.
• Figure 3: Diffusion-only dynamics on the network and parameter set of Fig. \ref{['fig:fourspecies']}. Nodes are colored by the dominant species: $X$ (blue), $Y$ (red), $Z$ (green), $W$ (yellow); magenta marks coexistence. (a) All species initialized at $0.05$. (b) Identical setup except species $Y$ starts at $0.01$. Reaction terms are switched off ($r=0$). Even under pure diffusion, when all species start equally, the strongest competitor $Y$ colonizes most hubs; with $Y$ reduced, it fails to conquer the largest hub and many medium-degree nodes remain mixed, while the second-strongest $Z$ invades several secondary hubs, in some cases displacing $Y$. Note that the peripheral nodes shown in white (not visible at this color scale) are empty.
• Figure 4: Representation of steady-state species distributions across the network. (a) Final concentrations of species $x$ and $y$ under sublinear movement responses, with $\sigma_x = 0.9$, $\sigma_y = 0.3$, and equal diffusion coefficients $\mathcal{D}_x = \mathcal{D}_y = 30$; initial densities are uniformly set to 0.3. (b) Same network structure, but with parameters chosen to emphasize strong asymmetry: $\sigma_x = 5.5$, $\sigma_y = 0.5$, and a much larger diffusion coefficient for species $x$ ($\mathcal{D}_x = 2000$) to compensate for its high perceived availability. In both panels, the inset shows the corresponding network layout, with node sizes proportional to degree. In panel (b), species $x$ is nearly absent from high-degree nodes—such as nodes 1 and 2—where concentrations fall below $10^{-4}$.