Coexistence of species with different dispersal across landscapes: a critical role of spatial correlation in disturbance

Abstract

Disturbance is key to maintaining species diversity in plant communities. Although the effects of disturbance frequency and extent on species diversity have been studied, we do not yet have a mechanistic understanding of how these aspects of disturbance interact with spatial structure of disturbance to influence species diversity. Here we derive a novel pair approximation model to explore competitive outcomes in a two-species system subject to spatially correlated disturbance. Generally, spatial correlation in disturbance favoured long-range dispersers, while distance-limited dispersers were greatly suppressed. Interestingly, high levels of spatial aggregation of disturbance promoted long-term species coexistence that is not possible in the absence of disturbance, but only when the local disperser was intrinsically competitively superior. However, spatial correlation in disturbance led to different competitive outcomes, depending on the disturbed area. Concerning ecological conservation and management, we theoretically demonstrate that introducing a spatially correlated disturbance to the system or altering an existing disturbance regime can be a useful strategy either to control species invasion or to promote species coexistence. Disturbance pattern analysis may therefore provide new insights into biodiversity conservation.

Keywords: colonization–competition trade-off; pair approximation; spatially correlated disturbance; species dispersal.

Figure 1.

Illustration of species pattern formation just before and after a spatial pulse disturbance event in a landscape with a lattice of size 100 × 100 cells, produced by an individual-based model (IBM) based on the orthogonal neighbouring correlation principle (see details in [31,43]; white, unoccupied/undisturbed sites; green, local dispersers; blue, global dispersers; red, disturbed area). (a) Initial species pattern with two dispersers just before a pulse disturbance: local disperser with global density ρ₁ = 0.2 and intraspecific clumping q_1/1 = 0.75, and global dispersers with ρ₂ = q_2/2 = 0.2 representing a random distribution. (b) A spatially correlated disturbance pattern with disturbed area ρ_d = 0.2 and its spatial aggregation q_d/d = 0.9 (see algorithm in [31,43]). (c) Species pattern just after a pulse disturbance. Figure 1c is the superimposed result of figure 1a and b, with any individuals (in figure 1a) within the disturbed area (red colour in figure 1b) being removed immediately following the pulse.

Figure 2.

Combined effects of disturbance extent (ρ_d) and spatial correlation (q_d/d) on the competitive outcome of a local disperser interacting with a global disperser (red dashed line with ρ_d = q_d/d, randomly structured disturbance; ρ_d < q_d/d, spatially aggregated disturbance; ρ_d > q_d/d, spatially over-dispersed disturbance). Mortality rate for the global disperser: (a) m₂ = 0.011, (b) m₂ = 0.012, (c) m₂ = 0.013 and (d) m₂ = 0.014. Other parameter values: species birth rate α = β = 0.02, mortality rate m₁ = 0.005 (local disperser), disturbance periodicity T = 75, intraspecific competition γ₁₁ = γ₂₂ = 0.02, and interspecific competition γ₁₂ = γ₂₁ = 0. Inaccessible region: see equation (2.2).

Figure 3.

Effect of disturbance periodicity (T) on the competitive outcome of a local disperser interacting with a global disperser, while simultaneously varying both disturbance extent (ρ_d) and spatial aggregation (q_d/d) (red dashed line at ρ_d = q_d/d indicating randomly structured disturbance). (a) T = 50, (b) T = 100, (c) T = 150 and (d) T = 200. Mortality rates: m₁ = 0.005 (local disperser) and m₂ = 0.013 (global disperser). Other parameters: see figure 2. Inaccessible region: see equation (2.2).