Jayanth R. Banavar

Emergence of structural and dynamical properties of ecological mutualistic networks

Mutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants has a key role in the organization of ecological communities. Such networks in ecology have generally evolved a nested architecture independent of species composition and latitude; specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species. Despite sustained efforts to explain observed network structure on the basis of community-level stability or persistence, such correlative studies have reached minimal consensus. Here we show that nested interaction networks could emerge as a consequence of an optimization principle aimed at maximizing the species abundance in mutualistic communities. Using analytical and numerical approaches, we show that because of the mutualistic interactions, an increase in abundance of a given species results in a corresponding increase in the total number of individuals in the community, and also an increase in the nestedness of the interaction matrix. Indeed, the species abundances and the nestedness of the interaction matrix are correlated by a factor that depends on the strength of the mutualistic interactions. Nestedness and the observed spontaneous emergence of generalist and specialist species occur for several dynamical implementations of the variational principle under stationary conditions. Optimized networks, although remaining stable, tend to be less resilient than their counterparts with randomly assigned interactions. In particular, we show analytically that the abundance of the rarest species is linked directly to the resilience of the community. Our work provides a unifying framework for studying the emergent structural and dynamical properties of ecological mutualistic networks.

Scale invariance in the dynamics of spontaneous behavior

Typically one expects that the intervals between consecutive occurrences of a particular behavior will have a characteristic time scale around which most observations are centered. Surprisingly, the timing of many diverse behaviors from human communication to animal foraging form complex self-similar temporal patterns reproduced on multiple time scales. We present a general framework for understanding how such scale invariance may arise in nonequilibrium systems, including those that regulate mammalian behaviors. We then demonstrate that the predictions of this framework are in agreement with detailed analysis of spontaneous mouse behavior observed in a simple unchanging environment. Neural systems operate on a broad range of time scales, from milliseconds to hours. We analytically show that such a separation between time scales could lead to scale-invariant dynamics without any fine tuning of parameters or other model-specific constraints. Our analyses reveal that the specifics of the distribution of resources or competition among several tasks are not essential for the expression of scale-free dynamics. Rather, we show that scale invariance observed in the dynamics of behavior can arise from the dynamics intrinsic to the brain.

Information-based fitness and the emergence of criticality in living systems

Significance Recently, evidence has been mounting that biological systems might operate at the borderline between order and disorder, i.e., near a critical point. A general mathematical framework for understanding this common pattern, explaining the possible origin and role of criticality in living adaptive and evolutionary systems, is still missing. We rationalize this apparently ubiquitous criticality in terms of adaptive and evolutionary functional advantages. We provide an analytical framework, which demonstrates that the optimal response to broadly different changing environments occurs in systems organizing spontaneously—through adaptation or evolution—to the vicinity of a critical point. Furthermore, criticality turns out to be the evolutionary stable outcome of a community of individuals aimed at communicating with each other to create a collective entity. Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to flock dynamics. However, a well-founded theory for understanding how and why interacting living systems could dynamically tune themselves to be poised in the vicinity of a critical point is lacking. Here we use tools from statistical mechanics and information theory to show that complex adaptive or evolutionary systems can be much more efficient in coping with diverse heterogeneous environmental conditions when operating at criticality. Analytical as well as computational evolutionary and adaptive models vividly illustrate that a community of such systems dynamically self-tunes close to a critical state as the complexity of the environment increases while they remain noncritical for simple and predictable environments. A more robust convergence to criticality emerges in coevolutionary and coadaptive setups in which individuals aim to represent other agents in the community with fidelity, thereby creating a collective critical ensemble and providing the best possible tradeoff between accuracy and flexibility. Our approach provides a parsimonious and general mechanism for the emergence of critical-like behavior in living systems needing to cope with complex environments or trying to efficiently coordinate themselves as an ensemble.

Evolution and selection of river networks: Statics, dynamics, and complexity

Significance Our focus is on a rich interdisciplinary problem touching on earth science, hydrology, and statistical mechanics—an understanding of the statics and dynamics of the network structures that we observe in the fluvial landscape, and their relation to evolution and selection of recurrent patterns of self-organization. It is an exemplar of how diverse ideas, numerical simulation, and elementary mathematics can come together to help solve the mystery of understanding a ubiquitous pattern of nature. Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal channel networks (OCNs) are feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics—every spanning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation, or climate, and differ significantly from those of the ground state, known exactly. Results are provided on the emergence of criticality through adaptative evolution and on the yet-unexplored range of applications of the OCN concept.

Understanding health and disease with multidimensional single-cell methods.

Current efforts in the biomedical sciences and related interdisciplinary fields are focused on gaining a molecular understanding of health and disease, which is a problem of daunting complexity that spans many orders of magnitude in characteristic length scales, from small molecules that regulate cell function to cell ensembles that form tissues and organs working together as an organism. In order to uncover the molecular nature of the emergent properties of a cell, it is essential to measure multiple-cell components simultaneously in the same cell. In turn, cell heterogeneity requires multiple-cells to be measured in order to understand health and disease in the organism. This review summarizes current efforts towards a data-driven framework that leverages single-cell technologies to build robust signatures of healthy and diseased phenotypes. While some approaches focus on multicolor flow cytometry data and other methods are designed to analyze high-content image-based screens, we emphasize the so-called Supercell/SVM paradigm (recently developed by the authors of this review and collaborators) as a unified framework that captures mesoscopic-scale emergence to build reliable phenotypes. Beyond their specific contributions to basic and translational biomedical research, these efforts illustrate, from a larger perspective, the powerful synergy that might be achieved from bringing together methods and ideas from statistical physics, data mining, and mathematics to solve the most pressing problems currently facing the life sciences.

Statistical mechanics of ecological systems: Neutral theory and beyond

It is of societal importance to advance the understanding of emerging patterns of biodiversity from biological and ecological systems. The neutral theory offers a statistical-mechanical framework that relates key biological properties at the individual scale with macroecological properties at the community scale. This article surveys the quantitative aspects of neutral theory and its extensions for physicists who are interested in what important problems remain unresolved for studying ecological systems.

Towards a unified descriptive theory for spatial ecology: predicting biodiversity patterns across spatial scales

A key challenge for both ecological researchers and biodiversity managers is the measurement and prediction of species richness across spatial scales. Typically, biodiversity is assessed at fine scales (e.g. in quadrats or transects) for practical reasons, but often we are interested in coarser-scale (field, regional, global) diversity issues. Moreover, the pressures affecting biodiversity patterns are often scale specific, making multiscale assessment a crucial methodological priority. As species richness is not additive, it is difficult to translate from the scale of measurement to the scale(s) of interest. A number of methods have been proposed to tackle this problem, but most are too model specific or too rigid to allow general application. Here, we present a general framework (and a specific implementation of it) that allows such scale translations to be performed. Building on the intrinsic relationships among patterns of species richness, abundance and spatial turnover, we introduce a framework that links and predicts the profile of the species-area relationship and the species-abundance distributions across scales when a limited number of fine-scale scattered samples are available. Using the correlation in species abundances between pairs of samples as a function of the distance between them, we are able to link the effects of aggregation, similarity decay, species richness and species abundances across scales. Our approach allows one to draw inferences about biodiversity scaling under very general assumptions pertaining to the nature of interactions, the geographical distributions of individuals and ecological processes. We demonstrate the accuracy of our predictions using data from two well-studied forest stands and also demonstrate the potential value of such methods by examining the effects of management on farmland insects across scales. The framework has important applications to biodiversity research and conservation practice.

From Cellular Characteristics to Disease Diagnosis: Uncovering Phenotypes with Supercells

Cell heterogeneity and the inherent complexity due to the interplay of multiple molecular processes within the cell pose difficult challenges for current single-cell biology. We introduce an approach that identifies a disease phenotype from multiparameter single-cell measurements, which is based on the concept of “supercell statistics”, a single-cell-based averaging procedure followed by a machine learning classification scheme. We are able to assess the optimal tradeoff between the number of single cells averaged and the number of measurements needed to capture phenotypic differences between healthy and diseased patients, as well as between different diseases that are difficult to diagnose otherwise. We apply our approach to two kinds of single-cell datasets, addressing the diagnosis of a premature aging disorder using images of cell nuclei, as well as the phenotypes of two non-infectious uveitides (the ocular manifestations of Behçets disease and sarcoidosis) based on multicolor flow cytometry. In the former case, one nuclear shape measurement taken over a group of 30 cells is sufficient to classify samples as healthy or diseased, in agreement with usual laboratory practice. In the latter, our method is able to identify a minimal set of 5 markers that accurately predict Behçets disease and sarcoidosis. This is the first time that a quantitative phenotypic distinction between these two diseases has been achieved. To obtain this clear phenotypic signature, about one hundred CD8+ T cells need to be measured. Although the molecular markers identified have been reported to be important players in autoimmune disorders, this is the first report pointing out that CD8+ T cells can be used to distinguish two systemic inflammatory diseases. Beyond these specific cases, the approach proposed here is applicable to datasets generated by other kinds of state-of-the-art and forthcoming single-cell technologies, such as multidimensional mass cytometry, single-cell gene expression, and single-cell full genome sequencing techniques.

Effect of localization on the stability of mutualistic ecological networks

The relationships between the core–periphery architecture of the species interaction network and the mechanisms ensuring the stability in mutualistic ecological communities are still unclear. In particular, most studies have focused their attention on asymptotic resilience or persistence, neglecting how perturbations propagate through the system. Here we develop a theoretical framework to evaluate the relationship between the architecture of the interaction networks and the impact of perturbations by studying localization, a measure describing the ability of the perturbation to propagate through the network. We show that mutualistic ecological communities are localized, and localization reduces perturbation propagation and attenuates its impact on species abundance. Localization depends on the topology of the interaction networks, and it positively correlates with the variance of the weighted degree distribution, a signature of the network topological heterogeneity. Our results provide a different perspective on the interplay between the architecture of interaction networks in mutualistic communities and their stability.

An allometry-based approach for understanding forest structure, predicting tree-size distribution and assessing the degree of disturbance

Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, whereas the metabolic scaling theory suggests that the tree number scales universally as −2 power of diameter. Here, we propose a simple functional scaling model in which these two opposing results are reconciled. Basic principles related to crown shape, energy optimization and the finite-size scaling approach were used to define a set of relationships based on a single parameter that allows us to predict the slope of the tree-size distributions in a steady-state condition. We tested the model predictions on four temperate mountain forests. Plots (4 ha each, fully mapped) were selected with different degrees of human disturbance (semi-natural stands versus formerly managed). Results showed that the size distribution range successfully fitted by the model is related to the degree of forest disturbance: in semi-natural forests the range is wide, whereas in formerly managed forests, the agreement with the model is confined to a very restricted range. We argue that simple allometric relationships, at an individual level, shape the structure of the whole forest community.