Biology subjects

Lechon-Alonso, P.

Publications and source records attributed to Lechon-Alonso, P..

4 recordsLinked to original sources

bioRxiv2026

Emergent feasibility in random ecological systems with higher-order interactions

A recurring lesson from random ecological models is that coexistence is hard to come by: in the Generalized Lotka-Volterra (GLV) model with pairwise interactions, the probability that randomly sampled parameters admit a positive (feasible) equilibrium - a necessary condition for coexistence - is exactly 1/2n in n species, vanishing rapidly with diversity. This rarity is often read as evidence that coexistence demands specific ecological mechanisms. Real interactions, however, are rarely strictly pairwise: any nonlinear dependence of one species growth rate on anothers abundance, Taylor-expanded, generates higher-order interactions (HOIs) of increasing degree. Treating the interaction order d as a knob that indexes this nonlinearity, we map the random GLV with HOIs onto the Kostlan-Shub-Smale class of random polynomial systems and approximate the probability of feasibility (Pf ) analytically. We find a phase transition at d = 4: below this threshold, Pf decays with diversity as in the pairwise case; above it, the exponential proliferation of equilibria outpaces the probability that any given equilibrium is feasible, and the probability of feasibility increases with n, approaching one. The transition appears to be universal across symmetric coefficient distributions, but vanishes when sign symmetry of the parameter distribution is broken. This work uncovers a route by which feasibility emerges from nonlinearity alone, with no fine-tuning of parameters and no appeal to specific ecological mechanisms.

ecology↗

bioRxiv2026

Tipping points are typical in ecosystems with higher-order interactions

Whether species-rich communities erode gradually or collapse abruptly under environmental change is a central question in ecology [1]. Classical pairwise theory predicts that coexistence is always lost gradually, through smooth declines to extinction [2], yet real ecological interactions are often strongly state-dependent - shaped by nonlinearities that fixed pairwise coefficients cannot capture [3]. Here we show that higher-order (nonlinear) interactions make abrupt, irreversible loss of coexistence a typical route to community collapse: across diverse random communities, the equilibrium supporting coexistence disappears suddenly at a fold bifurcation. Using polynomial homotopy continuation [4] to track equilibria as environmental conditions change, we find that folds progressively dominate the boundary of the coexistence domain as nonlinearity strengthens, replacing the gradual extinctions of pairwise theory. Furthermore, the sign structure of higher-order interactions controls both the onset of tipping-points and whether biodiversity buffers or amplifies collapse. Because higher-order and nonlinear interactions are intimately linked, tipping points also arise generically in pairwise models with strong nonlinearity. Applying our continuation framework to a canonical model of plant-pollinator collapse [5], we formally resolve its bifurcation structure as fold-mediated, and we show that fold bifurcations are typical across published multispecies models spanning mutualistic, competitive, and consumer-resource interactions. These results challenge the expectation that monitoring abundances suffices to anticipate collapse, and unify structural-stability theory, which delineates the safe operating space for coexistence, with critical transition theory, which characterizes the nature of its boundaries.

ecology↗

bioRxiv2024

Robust coexistence in ecological competitive communities

Darwin already recognized that competition is fiercest among conspecifics, a principle that later made intraspecific competition central to ecological theory through concepts such as niche differentiation and limiting similarity. Beyond shaping coexistence, strong intraspecific competition can also stabilize community dynamics by ensuring that populations return to equilibrium after disturbance. Here we investigate a more fundamental question: how intraspecific competition influences the very existence of a steady state (feasibility) in large random ecological communities dominated by competition. We show that, analogous to classical results on stability, there is a critical level of intraspecific competition above which a feasible steady state is guaranteed to exist. We derive a general expression for the probability of feasibility and prove that, asymptotically (as species number grows), the transition to stability occurs before the transition to feasibility with probability one. Thus, in large competitive communities, any feasible equilibrium is automatically stable. This ordering persists even when many species in the initial pool cannot coexist and extinctions occur: the dynamics prune the community, shifting feasibility and stability thresholds but never reversing their order. These results imply that large competitive communities generically converge to a globally stable equilibrium, making sustained oscillations or chaos unlikely--consistent with experimental observations.

ecology↗

bioRxiv2021

No robust coexistence in a canonical model of plant-soil feedbacks

Plant-soil feedbacks (PSFs) are considered a key mechanism generating frequency-dependent dynamics in plant communities. Negative feedbacks, in particular, are often invoked to explain coexistence and the maintenance of diversity in species-rich communities. However, the primary modeling framework used to study PSFs considers only two plant species, and we lack clear theoretical expectations for how these complex interactions play out in communities with natural levels of diversity. Here, we demonstrate that this canonical model for PSFs is equivalent to a well-studied model from evolutionary game theory, and use this equivalence to characterize the dynamics with an arbitrary number of plant species. Surprisingly, we find that coexistence of more than two species is virtually impossible, suggesting that alternative theoretical frameworks are needed to describe feedbacks observed in diverse natural communities. Drawing on our analysis, we discuss future directions for PSF models and implications for experimental study of PSF-mediated coexistence in the field.

ecology↗