Intermittent precipitation and spatial Allee effects drive irregular vegetation patterns in semiarid ecosystems

TL;DR

This paper tackles how intermittent precipitation and local Allee effects shape irregular vegetation patterns in semiarid ecosystems. It develops an individual-based model (IBM) where rainfall pulses transiently modulate facilitation and competition, generating pulse-driven clustering and extinction dynamics. Key findings show that the frequency and duration of favorable periods govern long-term persistence, with resilience arising from local spatial covariance and neighborhood density rather than total biomass, and that mean-field approaches substantially underestimate persistence by neglecting spatial refugia. The work provides a mechanistic, spatially explicit framework for assessing desertification risk under climate‑driven changes in rainfall intermittency, linking micro-scale processes to landscape-scale patterns through the pair-correlation function and related metrics.

Abstract

Vegetation in semi-arid ecosystems frequently organizes into spatially heterogeneous mosaics that regulate ecosystem functioning, productivity, and resilience. These patterns arise from local biological interactions, including facilitation among neighboring plants and competition for limiting resources. Classical theoretical approaches have attributed such organization to scale-dependent feedbacks, predicting regular spatial patterns and abrupt transitions to collapse. However, growing empirical and theoretical evidence reveal that environmental variability and demographic stochasticity can fundamentally reshape spatial organization, driving irregular clusters, dynamic mosaics, and gradual rather than catastrophic vegetation declines. In drylands, rainfall variability is a dominant source of environmental forcing: precipitation typically occurs in short, irregular pulses that transiently enhance survival and recruitment before competitive interactions again dominate. Near persistence thresholds, ecosystem dynamics are therefore governed not only by average climatic conditions but also by the timing and spatial coincidence of favorable events. Under these conditions, positive density dependence and local facilitation can critically determine whether vegetation patches persist, expand, or collapse. Here, we develop an individual-based model that integrates intermittent precipitation with local Allee effects to examine how stochastic rainfall shapes spatial organization and persistence. We show that the interaction between pulsed resource availability and density-dependent survival generates irregular cluster structures and strongly modulates extinction risk, with resilience emerging from local spatial covariance and neighborhood density rather than from total biomass alone. These results highlight the importance of individual-level, stochastic processes in determining ecosystem resilience.

Figures (7)

• Figure 1: Examples of irregular clusters of vegetation. Horseshoe Bend, Arizona (36.875470º N, 111.504602º W). Pinacate Desert, Sonora (31.534861º N, 114.189449º W). Southern Chad-Niger border (14.695937º N, 13.751921º E).
• Figure 2: Emergence and quantification of spatial clustering in the individual-based model (IBM) with precipitation-modulated competition. (a) Trajectory of the normalized population density $\rho(t)$ over time. Pink shaded regions denote "wet" periods ($d=50$) where competition is reduced ($\psi_{c\_}$), mirroring rainfall pulses. (b–d) Spatial snapshots of individual plants at specific time points (indicated in panel a), showing the rapid formation of clusters during wet phases and their gradual thinning during dry intervals. (e) Pair-correlation function $C(\xi)$ calculated for snapshots (b)–(d); values $C(\xi) > 1$ at short distances indicate significant spatial aggregation (clustering) compared to complete spatial randomness (CSR). (f) Spatiotemporal evolution of the PCF for various distances $\xi$, highlighting how the local Allee effect maintains structural heterogeneity throughout the pulse-decay cycle.
• Figure 3: Absence of large-scale clustering in the logistic model under intermittent precipitation.. (a) Population density trajectory using a logistic model \ref{['eq:logistic rates']}. (b–d) Spatial snapshots showing a near-uniform distribution of individuals; while small, transient groups appear due to short-range dispersal, no large-scale clusters emerge. (e) The PCF remains near 1 across most distances, suggesting little spatial correlation. (f) Time-resolved PCF confirms that without positive density-dependent feedback, vegetation cannot self-organize into structured patterns despite environmental fluctuations.
• Figure 4: Dynamics of average population density under different precipitation regimes, with precipitation coupled both to competition and facilitation. (a,c) Trajectories for a fixed rainfall frequency ($\lambda = 0.1$) with varying pulse durations ($d$). Short durations lead to rapid extinction, while longer durations allow the Allee effect to amplify growth sufficiently to bridge dry intervals. (b,d) Trajectories for a fixed duration ($d = 40$) with varying frequencies ($\lambda$). Higher frequencies (shorter inter-pulse intervals) promote survival by preventing the population from dropping below the critical Allee threshold. The results are the average of $100$ realizations for a $50\cross50$ spatial domain, and the remaining parameter values used in the simulations are indicated in \ref{['tab:parameter_values']}. The shaded areas corresponding to 95% confidence intervals are not visible. Individual realizations for some parameter values are shown in the Supplementary\ref{['fig:individual_realizations_allee_competition', 'fig:individual_realizations_allee_facilitation']}.
• Figure 5: Survival probability of vegetation as a function of precipitation frequency ($\lambda$) and duration ($d$). The phase space reveals a sharp transition between certain extinction (yellow, low $\lambda$ and $d$) and reliable persistence (green, high $\lambda$ and $d$). The diagonal transition zone illustrates a compensatory mechanism: frequent short rainfall events can sustain the ecosystem as effectively as rare, long-lasting pulses. The black dashed line represents a power-law fit to the critical threshold, capturing the nonlinear boundary imposed by the spatial Allee effect. The phase diagram and the transition from extinction to persistence are largely insensitive to precipitation coupling-whether through increased facilitation or decreased competition-and remain robust to rainfall stochasticity. Other parameter values are indicated in \ref{['tab:parameter_values']}.