arXiv subjects

Jacopo Grilli

Publications and source records attributed to Jacopo Grilli.

At least 19 recordsLinked to original sources

arXiv2025

Unifying Theories in High-Dimensional Biology: Approaches, Challenges and Opportunities

Across biological subdisciplines, the last decade has seen an explosion of high-dimensional datasets, including datasets for cells, species, immune systems, neurons and behaviour. At the ICTS workshop 'Unifying Theories in High-Dimensional Biophysics' we discussed whether this high dimensionality poses a challenge or opportunity for describing, understanding and predicting biological systems theoretically. We discussed methods, models and frameworks that can help with addressing empirical observations based on these high-dimensional datasets. We summarize the challenges and opportunities that emerged in discussions according to individual participants below.

physics.bio-ph↗

arXiv2025

Modeling Spatial Synchronization of Predator-Prey Oscillations via the XY Model under Demographic Stochasticity and Migration

We investigate stochastic predator-prey dynamics and their spatial phase synchronization using the Rosenzweig-MacArthur model coupled across multiple patches. Combining stochastic simulations based on the Gillespie algorithm with analytical methods inspired by the XY model, we uncover fundamental mechanisms through which demographic noise and dispersal shape synchronization and phase transitions. This study offers a theoretical foundation for understanding and managing large-scale ecological synchrony and ecosystem resilience.

q-bio.PE↗

arXiv2025

Cultural tightness and social cohesion under evolving norms

Successful collective action on issues from climate change to the maintenance of democracy depends on societal properties such as cultural tightness and social cohesion. How these properties evolve is not well understood because they emerge from a complex interplay between beliefs and behaviors that are usually modeled separately. Here we address this challenge by developing a game-theoretical framework incorporating norm-utility models to study the coevolutionary dynamics of cooperative action, expressed belief, and norm-utility preferences. We show that the introduction of evolving beliefs and preferences into the Snowdrift game and Prisoner's Dilemma leads to a proliferation of evolutionary stable equilibria, each with different societal properties. In particular, we find that a declining material environment can simultaneously be associated with increased cultural tightness (defined as the degree to which individuals behave in accordance with widely held beliefs) and reduced social cohesion (defined as the degree of social homogeneity i.e. the extent to which individuals belong to a single well-defined group). Loss of social homogeneity occurs via a process of evolutionary branching, in which a population fragments into two distinct social groups with strikingly different characteristics. The groups that emerge differ not only in their willingness to cooperate, but also in their beliefs about cooperation and in their preferences for conformity and coherence of their actions and beliefs. These results have implications for our understanding of the resilience of cooperation and collective action in times of crisis.

physics.soc-ph↗

arXiv2025

Evolutionary learning of microbial populations in partially predictable environments

Populations evolving in fluctuating environments face the fundamental challenge of balancing adaptation to current conditions against preparation for uncertain futures. Here, we study microbial evolution in partially predictable environments using proteome allocation models that capture the trade-off between growth rate and lag time during environmental transitions. We demonstrate that evolution drives populations toward an evolutionary stable allocation strategy that minimizes resource depletion time, thereby balancing faster growth with shorter adaptation delays. In environments with temporal structure, populations evolve to learn the statistical patterns of environmental transitions through proteome pre-allocation, with the evolved allocations reflecting the transition probabilities between conditions. Our framework reveals how microbial populations can extract and exploit environmental predictability without explicit neural computation, using the proteome as a distributed memory system that encodes environmental patterns. This work demonstrates how information-theoretic principles govern cellular resource allocation and provides a mechanistic foundation for understanding learning-like behavior in evolving biological systems.

q-bio.PE↗

arXiv2023

The effect of demographic stochasticity on predatory-prey oscillations

The ecological dynamics of interacting predator and prey populations can display sustained oscillations, as for instance predicted by the Rosenzweig-MacArthur predator-prey model. The presence of demographic stochasticity, due to the finiteness of population sizes, alters the amplitude and frequency of these oscillations. Here we present a method for characterizing the effects of demographic stochasticity on the limit cycle attractor of the Rosenzweig-MacArthur. We show that an angular Brownian motion well describes the frequency oscillations. In the vicinity of the bifurcation point, we obtain an analytical approximation for the angular diffusion constant. This approximation accurately captures the effect of demographic stochasticity across parameter values.

q-bio.PE↗

arXiv2022

Intrinsic dimension estimation for discrete metrics

Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.

stat.ML↗

arXiv2022

Stable cooperation emerges in stochastic multiplicative growth

Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we introduce a mechanism for the emergence of cooperation in the presence of fluctuations. We consider agents whose wealth changes stochastically in a multiplicative fashion. Each agent can share part of her wealth as a public good, which is equally distributed among all the agents. We show that, when agents operate with long-time horizons, cooperation produces an advantage at the individual level, as it effectively screens agents from the deleterious effect of environmental fluctuations.

q-bio.PE↗

arXiv2021

Remote teaching data-driven physical modeling through a COVID-19 open ended data challenge

Physics can be seen as a conceptual approach to scientific problems, a method for discovery, but teaching this aspect of our discipline can be a challenge. We report on a first-time remote teaching experience for a computational physics third-year physics laboratory class taught in the first part of the 2020 COVID-19 pandemic (March-May 2020). To convey a ``physics of data" approach to data analysis and data-driven physical modeling we used interdisciplinary data sources, with an openended ``COVID-19 data challenge" project as the core of the course. COVID-19 epidemiological data provided an ideal setting for motivating the students to deal with complex problems, where there is no unique or preconceived solution. Our results indicate that such problems yield qualitatively different improvements compared to close-ended projects, as well as point to critical aspects in using these problems as a teaching strategy. By breaking the students' expectations of unidirectionality, remote teaching provided unexpected opportunities to promote active work and active learning.

physics.ed-ph↗

arXiv2020

Estimating the impact of preventive quarantine with reverse epidemiology

The impact of mitigation or control measures on an epidemics can be estimated by fitting the parameters of a compartmental model to empirical data, and running the model forward with modified parameters that account for a specific measure. This approach has several drawbacks, stemming from biases or lack of availability of data and instability of parameter estimates. Here we take the opposite approach -- that we call reverse epidemiology. Given the data, we reconstruct backward in time an ensemble of networks of contacts, and we assess the impact of measures on that specific realization of the contagion process. This approach is robust because it only depends on parameters that describe the evolution of the disease within one individual (e.g. latency time) and not on parameters that describe the spread of the epidemics in a population. Using this method, we assess the impact of preventive quarantine on the ongoing outbreak of Covid-19 in Italy. This gives an estimate of how many infected could have been avoided had preventive quarantine been enforced at a given time.

q-bio.PE↗

arXiv2018

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively.

physics.soc-ph↗

arXiv2017

The effect of population abundances on the stability of large random ecosystems

Random matrix theory successfully connects the structure of interactions of large ecological communities to their ability to respond to perturbations. One of the most debated aspects of this approach is the missing role of population abundances. Despite being one of the most studied patterns in ecology, and one of the most empirically accessible quantities, population abundances are always neglected in random matrix approaches and their role in determining stability is still not understood. Here, we tackle this question by explicitly including population abundances in a random matrix framework. We obtain an analytical formula that describes the spectrum of a large community matrix for arbitrary feasible species abundance distributions. The emerging picture is remarkably simple: while population abundances affect the rate to return to equilibrium after a perturbation, the stability of large ecosystems is uniquely determined by the interaction matrix. We confirm this result by showing that the likelihood of having a feasible and unstable solution in the Lotka-Volterra system of equations decreases exponentially with the number of species for stable interaction matrices.

q-bio.PE↗

arXiv2017

Reconciling cooperation, biodiversity and stability in complex ecological communities

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.

q-bio.PE↗

arXiv2017

Family-specific scaling laws in bacterial genomes

Among several quantitative invariants found in evolutionary genomics, one of the most striking is the scaling of the overall abundance of proteins, or protein domains, sharing a specific functional annotation across genomes of given size. The size of these functional categories change, on average, as power-laws in the total number of protein-coding genes. Here, we show that such regularities are not restricted to the overall behavior of high-level functional categories, but also exist systematically at the level of single evolutionary families of protein domains. Specifically, the number of proteins within each family follows family-specific scaling laws with genome size. Functionally similar sets of families tend to follow similar scaling laws, but this is not always the case. To understand this systematically, we provide a comprehensive classification of families based on their scaling properties. Additionally, we develop a quantitative score for the heterogeneity of the scaling of families belonging to a given category or predefined group. Under the common reasonable assumption that selection is driven solely or mainly by biological function, these findings point to fine-tuned and interdependent functional roles of specific protein domains, beyond our current functional annotations. This analysis provides a deeper view on the links between evolutionary expansion of protein families and the functional constraints shaping the gene repertoire of bacterial genomes.

q-bio.GN↗

arXiv2016

Collapse of Resilience Patterns in Generalized Lotka-Volterra Dynamics and Beyond

Recently, a theoretical framework aimed at separating the roles of dynamics and topology in multi-dimensional systems has been developed (Gao et al, \textit{Nature}, Vol 530:307 (2016)). The validity of their method is assumed to hold depending on two main hypothesis: $(i)$ The network determined by the the interaction between pairs of nodes has negligible degree correlations; $(ii)$ The node activities are uniform across nodes on both the drift and pair-wise interaction functions. Moreover, the authors consider only positive (mutualistic) interactions. Here we show the conditions proposed by Gao and collaborators are neither sufficient nor necessary to guarantee that their method works in general, and validity of their results are not independent of the model chosen within the class of dynamics they considered. Indeed we find that a new condition poses effective limitations to their framework and we provide quantitative predictions of the quality of the one dimensional collapse as a function of the properties of interaction networks and stable dynamics using results from random matrix theory. We also find that multi-dimensional reduction may work also for interaction matrix with a mixture of positive and negative signs, opening up application of the framework to food-webs, neuronal networks and social/economic interactions.

physics.gen-ph↗

arXiv2016

Relevant parameters in models of cell division control

A recent burst of dynamic single-cell growth-division data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different modeling frameworks were used to infer specific mechanisms from such data, but the links between frameworks are poorly explored, with relevant consequences for how well any particular mechanism can be supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with a simple physical analogue. By perturbative expansion around the mean initial size (or inter-division time), we show explicitly how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulation, the available data are characterized with great precision by the first-order approximation of this expansion. Hence, a single dimensionless parameter defines the strength and the action of the division control. However, this parameter may emerge from several mechanisms, which are distinguished only by higher-order terms in our perturbative expansion. An analytical estimate of the sample size needed to distinguish between second-order effects shows that this is larger than what is available in the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

q-bio.CB↗

arXiv2015

Cooperation, competition and the emergence of criticality in communities of adaptive systems

The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between exceedingly ordered and too noisy states. We here present a model, based on information theory and statistical mechanics, illustrating how and why a community of agents aimed at understanding and communicating with each other converges to a globally coherent state in which all individuals are close to an internal critical state, i.e. at the borderline between order and disorder. We study --both analytically and computationally-- the circumstances under which criticality is the best possible outcome of the dynamical process, confirming the convergence to critical points under very generic conditions. Finally, we analyze the effect of cooperation (agents try to enhance not only their fitness, but also that of other individuals) and competition (agents try to improve their own fitness and to diminish those of competitors) within our setting. The conclusion is that, while competition fosters criticality, cooperation hinders it and can lead to more ordered or more disordered consensual solutions.

q-bio.PE↗

arXiv2015

The geometry of coexistence in large ecosystems

The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the interactions are altered (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strenghts and ecological network structure on the volume of parameter space leading to feasible equilibria, i.e., ones in which all populations have positive abundances. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence in both mutualistic and consumer-resource systems. Using analytical and numerical methods, we show that feasibility is determined by just a handful of quantities describing the interactions, yielding a nontrivial complexity-feasibility relationship. Analyzing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted by means of a null model of random interactions, whereas food webs are characterized by smaller coexistence domains than those expected by chance. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions. Interestingly, the structure of mutualistic interactions leads to very heterogeneous responses to perturbations, making those systems more fragile than expected by chance.

q-bio.PE↗

arXiv2015

Statistical Mechanics of Ecological Systems: Neutral Theory and Beyond

The simplest theories often have much merit and many limitations, and in this vein, the value of Neutral Theory (NT) has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain pervasive patterns observed in the organization of ecosystems. Its originally tepid reception among ecologists contrasted starkly with the excitement it caused among physicists and mathematicians. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented towards ecologists, our goal here is to review the quantitative results of NT and its extensions for physicists who are interested in learning what NT is, what its successes are and what important problems remain unresolved. Furthermore, we hope that this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. We propose to make these more accessible by extracting them and presenting them in a logical fashion. We conclude the review by discussing how one might introduce realistic non-neutral elements into the current models.

q-bio.PE↗