arXiv subjects

Ada Altieri

Publications and source records attributed to Ada Altieri.

At least 19 recordsLinked to original sources

arXiv2026

The role of nestedness and saturating feedback in bipartite ecological systems

Large ecosystems balance competition and cooperation, yet standard generalized Lotka--Volterra models make mutualism destabilizing by amplifying disorder and driving unbounded growth. We show that Monod-like saturation resolves this paradox: dynamical mean-field theory and random-matrix analysis reveal a broader stable phase and enhanced survival. Network architecture provides a second control mechanism, but nestedness offers no intrinsic stability advantage. Instead, it is a byproduct of degree distributions with high connectivity necessary for stability.

q-bio.PE↗

arXiv2026

Dynamical systems on ultra small-world networks

Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside of this regime, to make them easier to treat analytically. Here we derive a framework to apply the powerful dynamical mean-field theory on highly heterogeneous networks that is able to account for more of the degree correlations naturally arising from network constraints, known as structural cut-offs. We apply this framework to the well-studied and understood disordered Lotka-Volterra model, and show typically reported observables such as survival rates and stability for these systems on ultra small-world networks. We find much better agreement for these variables for all ranges of exponents for simulated power-law networks as well as empirically sourced networks.

cond-mat.dis-nn↗

arXiv2025

Random motility regulation as a generic mechanism of community formation

The self-organization of microbial ecosystems involves a large variety of mechanisms, ranging from biochemical signaling to population dynamics. Among these, the role of motility regulation has been little studied, despite the importance of active migration processes. Here we show how weak, random motility regulation suffices to induce complex forms of organization in bacterial mixtures comprising a large number of coexisting strains. First, we simulate microscopic models of run-and-tumble bacteria whose self-propulsion speeds are weakly regulated by the local density of each strain, mimicking the impact of weak, random metabolic interactions. Our simulations reveal that, as the heterogeneity of the interaction network increases, the system undergoes a phase transition leading to the emergence of distinct, spatially segregated communities. To account for these results and assess their robustness, we use random-matrix theory to analyze the hydrodynamic description of the bacterial mixture, obtaining a quantitative agreement with our microscopic simulations. Our results hold for a variety of motility-regulation mechanisms and highlight the need to characterize the role of motility regulation in experimentally relevant situations.

cond-mat.stat-mech↗

arXiv2025

Les Houches lectures on Theoretical Ecology: High-dimensional models and extreme events

The study of ecological systems is gaining momentum in modern scientific research, driven by an abundance of empirical data and advancements in bioengineering techniques. However, a full understanding of their dynamical and thermodynamical properties, also in light of the ongoing biodiversity crisis, remains a formidable endeavor. From a theoretical standpoint, modeling the interactions within these complex systems -- such as bacteria in microbial communities, plant-pollinator networks in forests, or starling murmurations -- presents a significant challenge. Given the characteristic high dimensionality of the datasets, alternative elegant approaches employ random matrix formalism and techniques from disordered systems. In these lectures, we will explore two cornerstone models in theoretical ecology: the MacArthur/Resource-Consumer model, and the Generalized Lotka-Volterra model, with a special focus on systems composed of a large number of interacting species. In the second part, we will highlight timely directions, particularly to bridge the gap with empirical observations and detect macroecological patterns.

q-bio.PE↗

arXiv2024

Higher-order Ising model on hypergraphs

Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the ordered and the disordered phase. By a mean-field treatment, we show that the transition is continuous when only three-body interactions are considered but becomes abrupt when interactions of higher orders are introduced. Using a Georges-Yedidia expansion to go beyond a na\"ive mean-field approximation, we reveal a quantitative shift in the critical point of the phase transition, which does not affect the universality class of the model. Finally, we compare our results with traditional $p$-spin models with many-body interactions. Our work unveils new collective phenomena on complex interacting systems, revealing the importance of investigating higher-order systems beyond three-body interactions.

cond-mat.stat-mech↗

arXiv2024

Nonreciprocal Spin-Glass Transition and Aging

Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical Sherrington-Kirpatrick model that describes the antagonistic coupling between two identical complex agents modeled as macroscopic spin glasses. Our dynamical mean field theory calculations reveal an exceptional-point mediated transition from a static disorder phase to an oscillating amorphous phase as well as non-reciprocal aging with slow dynamics and oscillations.

cond-mat.dis-nn↗

arXiv2024

Microbiomes Through The Looking Glass: Linking species interactions to dysbiosis through a disordered Lotka-Volterra framework

The rapid advancement of environmental sequencing technologies, such as metagenomics, has significantly enhanced our ability to study microbial communities. The eubiotic composition of these communities is crucial for maintaining ecological functions and host health. Species diversity is only one facet of a healthy community organization; together with abundance distributions and interaction structures, it shapes reproducible macroecological states, i.e., joint statistical fingerprints that summarize whole-community behavior. Despite recent developments, a theoretical framework connecting empirical data with ecosystem modeling is still in its infancy, particularly in the context of disordered systems. Here, we present a novel framework that couples statistical physics tools for disordered systems with metagenomic data, explicitly linking diversity, interactions, and stability to define and compare these macroecological states. By employing the generalized Lotka-Volterra model with random interactions, we reveal two different emergent patterns of species interaction networks and species abundance distributions for healthy and diseased microbiomes. On the one hand, healthy microbiomes have similar community structures across individuals, characterized by strong species interactions and abundance diversity consistent with neutral stochastic fluctuations. On the other hand, diseased microbiomes show greater variability driven by deterministic factors, thus resulting in less ecologically stable and more divergent communities. Our findings suggest the potential of disordered system theory to characterize microbiomes and to capture the role of ecological interactions on stability and functioning.

cond-mat.dis-nn↗

arXiv2024

Interactions and migration rescuing ecological diversity

How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for the survival of diversity-rich ecosystems in the presence of demographic fluctuations. For a single species, one finds a continuous phase transition between an extinction and a survival state, that falls into the universality class of Directed Percolation. Here we show that the case of many species with heterogeneous interactions is different and richer. By merging theory and simulations, we demonstrate that with sufficiently strong demographic noise, the system exhibits behavior akin to the single-species case, undergoing a continuous transition. Conversely, at low demographic noise, we observe unique features indicative of the ecosystem's complexity. The combined effects of the heterogeneity in the interaction network and migration enable the community to thrive, even in situations where demographic noise would lead to the extinction of isolated species. The emergence of mutualism induces the development of global bistability, accompanied by sudden tipping points. We present a way to predict the catastrophic shift from high diversity to extinction by probing responses to perturbations as an early warning signal.

q-bio.PE↗

arXiv2023

Loop expansion around the Bethe approximation through the $M$-layer construction

For every physical model defined on a generic graph or factor graph, the Bethe $M$-layer construction allows building a different model for which the Bethe approximation is exact in the large $M$ limit and it coincides with the original model for $M=1$. The $1/M$ perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat-diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice but are either qualitatively different or absent in the corresponding fully connected case. In this case the standard approach based on a perturbative expansion around the naive mean field theory (essentially a fully connected model) fails. On physical grounds, we expect that when the construction is applied to a lattice in finite dimension there is a small region of the external parameters close to the Bethe critical point where strong deviations from mean-field behavior will be observed. In this region, the $1/M$ expansion for the corrections diverges and it can be the starting point for determining the correct non-mean-field critical exponents using renormalization group arguments. In the end, we will show that the critical series for the generic observable can be expressed as a sum of Feynman diagrams with the same numerical prefactors of field theories. However, the contribution of a given diagram is not evaluated associating Gaussian propagators to its lines as in field theories: one has to consider the graph as a portion of the original lattice, replacing the internal lines with appropriate one-dimensional chains, and attaching to the internal points the appropriate number of infinite-size Bethe trees to restore the correct local connectivity of the original model.

cond-mat.dis-nn↗

arXiv2023

An Introduction to the Theory of Spin Glasses

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method, and the dynamical mean-field theory. In the second part, we deal with the description of low-dimensional systems, mostly in three spatial dimensions, which are mostly studied through numerical simulations. We conclude by mentioning some of the main open problems in the field.

cond-mat.dis-nn↗

arXiv2022

Glassy features and complex dynamics in ecological systems

In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.

cond-mat.dis-nn↗

arXiv2022

Well-mixed Lotka-Volterra model with random strongly competitive interactions

The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive interaction case. We investigate different scalings for the distribution of the interactions with the number of species and try to bridge the gap with previous works. Our results show two different behaviors for the mean abundance at zero and finite temperature respectively, with a continuous crossover between the two. We confirm and extend previous results obtained for weak interactions: at zero temperature, even in the strong competitive interaction limit, the system is in a multiple-equilibria phase, whereas at finite temperature only a unique stable equilibrium can exist. Finally, we establish the qualitative phase diagrams in both cases and compare the two species abundance distributions.

cond-mat.dis-nn↗

arXiv2021

Effects of intraspecific cooperative interactions in large ecosystems

We analyze the role of the Allee effect, a positive correlation between population density and mean individual fitness, for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the case of the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviours of ecosystems.

cond-mat.dis-nn↗

arXiv2020

Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise

In this letter we study a reference model in theoretical ecology, the disordered Lotka-Volterra model for ecological communities, in the presence of finite demographic noise. Our theoretical analysis, which takes advantage of a mapping to an equilibrium disordered system, proves that for sufficiently heterogeneous interactions and low demographic noise the system displays a multiple equilibria phase, which we fully characterize. In particular, we show that in this phase the number of stable equilibria is exponential in the number of species. Upon further decreasing the demographic noise, we unveil a "Gardner" transition to a marginally stable phase, similar to that observed in jamming of amorphous materials. We confirm and complement our analytical results by numerical simulations. Furthermore, we extend their relevance by showing that they hold for others interacting random dynamical systems, such as the Random Replicant Model. Finally, we discuss their extension to the case of asymmetric couplings.

cond-mat.dis-nn↗

arXiv2020

Dynamical Mean-Field Theory and Aging Dynamics

Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin interactions, we show how to incorporate the mean-field theory of aging within dynamical mean-field theory. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking (1RSB) phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase. For the former, we show that the effective temperature of the slow degrees of freedom is fixed by requiring critical dynamical behavior on short time-scales, i.e. marginality. For the latter, we find that aging on an infinite number of slow time-scales is governed by a stochastic equation where the clock for dynamical evolution is fixed by the change of effective temperature, hence obtaining a dynamical derivation of the stochastic equation at the basis of the FRSB phase. Our results extend the realm of the mean-field theory of aging to all situations where DMFT holds.

cond-mat.dis-nn↗

arXiv2019

Mean field stability map of hard-sphere glasses

The response of amorphous solids to an applied shear deformation is an important problem, both in fundamental and applied research. To tackle this problem, we focus on a system of hard spheres in infinite dimensions as a solvable model for colloidal systems and granular matter. The system is prepared above the dynamical glass transition density, and we discuss the phase diagram of the resulting glass under compression, decompression, and shear strain, expanding on previous results [P. Urbani and F. Zamponi, Phys.Rev.Lett. 118, 038001 (2017)]. We show that the solid region is bounded by a "shear jamming" line, at which the solid reaches close packing, and a "shear yielding" line, at which the solid undergoes a spinodal instability towards a liquid, flowing phase. Furthermore, we characterize the evolution of these lines upon varying the glass preparation density. This work aims to provide a general overview of yielding and jamming phenomena in hard-sphere systems by a systematic exploration of the phase diagram.

cond-mat.stat-mech↗

arXiv2018

Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.

cond-mat.dis-nn↗

arXiv2018

Microscopic theory of two-step yielding in attractive colloids

Attractive colloids display two distinct amorphous solid phases: the attractive glass, due to particle bonding, and the repulsive glass, due to the hard core repulsion. By means of a microscopic mean field approach, we analyze their response to a quasi-static shear strain. We find that the presence of two distinct interaction length scales may result in a sharp two-step yielding process, which can be associated with a hysteretic stress response, or with a reversible but non-monotonic stress-strain curve. We derive a generic phase diagram characterized by two distinct yielding lines, an inverse yielding, and a critical point separating the hysteretic and reversible regimes. Our results should be applicable to a large class of glassy materials characterized by two distinct interaction length scales.

cond-mat.soft↗