Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized Lotka-Volterra model to include both spatial structure and environmental fluctuations across space and time. We find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that their combined effects permit arbitrarily many species to stably coexist despite strongly disordered competitive interactions. We analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives an anomalous scaling of abundance fluctuations, known empirically as Taylor's law. At the community level, this manifests as an effective sublinear self-inhibition that renders the community stable and asymptotically neutral in the high-diversity limit. Spatiotemporal noise thus provides a novel resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist.
Natural ecosystems are extraordinarily diverse, with hundreds to thousands of species coexisting across scales, from tropical rainforests and coral reefs to microbial communities [1][2][3][4]. Classical ecological models, however, predict that such diversity is unstable to competitive exclusion [5]. May's diversity-stability paradox sharpens this tension [6]: in large, randomly-interacting communities, adding species makes stable coexistence increasingly unlikely. Consistent with this prediction, when species that co-occur in nature are placed in well-mixed, controlled laboratory conditions, they often fail to coexist and instead competitively exclude [7][8][9][10]. How, then, is stable biodiversity maintained in nature?
Several routes around this paradox have been proposed [11,12]. One approach is to impart a specific structure onto the matrix of interspecific interactions; for example, through sparsity, modularity, or strong correlations [13][14][15][16][17][18][19]. Spatial structure provides further mechanisms: if the interaction coefficients vary as much throughout space as they do between species, then different spatial patches select different winners, and diversity can be maintained at the community level [20,21]. A second approach has been to move beyond static theories, where stationary abundances correspond to stable equilibria of a dynamical system, and instead take account of temporal fluctuations [18,[21][22][23]. Environmental variability, due to fluctuations in abiotic factors such as weather or nutrient availability, has been suggested to create temporal niches that favor coexistence if it acts asymmetrically on different species [11,[24][25][26][27][28][29][30][31]. However, in the disordered competitive setting most directly tied to May’s argument, environmental noise alone does not generically stabilize coexistence [32,33] and can instead accelerate diversity loss by driving rare species toward extinction [34].
A standard setting in which May’s argument is borne * These authors contributed equally to this work.
out is the generalized Lotka-Volterra (gLV) model with random (quenched) interactions [35], which reproduces key dynamical features of laboratory microcosms [10,36,37]. In the recent theoretical literature, it has been typical to focus on weakly-interacting communities, where interaction coefficients are made to vanish as the inverse of the species pool size [20,35,[38][39][40][41]. Although this scaling can generate diverse stable equilibria, it implies that in rich communities, cross-inhibition is negligible compared to self-inhibition. This is at odds with direct measurements in microbial systems [10], and is least plausible precisely where the diversity-stability paradox is most acute-for instance, the coexistence of thousands of very similar phytoplankton on only a handful of resources [42].
In this work, we demonstrate that two ubiquitous features of natural ecosystems, (1) spatial structure and (2) spatiotemporal environmental noise, suffice to stabilize extensive coexistence in strongly-competitive metacommunities. Working in the randomly-interacting generalized Lotka-Volterra framework, we show that neither ingredient alone stabilizes diversity, but that their combination creates a new phase in which arbitrarily many species coexist despite strong competition. The mechanism of this noise-induced transition leaves clear macroecological footprints with empirical backing: spatiotemporal noise generates heavy-tailed abundance distributions [30,43,44], giving rise to a manifestation of Taylor’s law [45][46][47], where abundance fluctuations scale as an anomalous power of the mean. This, in turn, leads to an emergent nonanalytic, sublinear self-inhibition at the community level, which we show to stabilize unbounded diversity [41]. Within the coexistence phase, individual species become progressively less distinguishable as diversity is increased, so that the limiting model approaches neutrality in spite of strongly heterogeneous pairwise interactions. These macroecological patterns are not imposed as modeling choices; they emerge together with the stabilization of richness, strengthening the plausibility of our framework.
To model spatiotemporal noise, we augment the gLV model as follows (Fig. 1a): we implement spatial structure using a metacommunity, comprising a network of “patches” with local interactions within each patch and dispersal between them [18,20,48,49]. We include environmental noise through fluctuations in the species growth rates, which amounts to a multiplicative noise term proportional to the species abundance. This is to be distinguished from demographic noise, which scales as the square root of the abundance. The abundance of species i ∈ 1, . . . , S on patch α ∈ 1, . . . , P then evolves as
where ∂α denotes the neighbors of patch α and c α its connectivity, D is the dispersal rate, and T sets the strength of environmental noise, which is to be interpr
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