Portal:Complex Systems Digital Campus/E-Department on Collective Behavior

Portal:Complex_Systems_Digital_Campus/E-Department_on_Collective Behavior Collective behavior in homogeneous and heterogeneous systems

Introduction From genetic and social networks to the ecosphere, we face systems composed of many distinct units that display collective behavior on space and time scales clearly separated from those of individual units. Among many others, we can mention cellular movements in tissue formation, flock dynamics, social and economic behavior in human societies, speciation in evolution. The complexity of such phenomena manifests itself in the non-trivial properties of the collective dynamics - emerging at the global, population level - with respect to the microscopic level dynamics. Many answers and insights into such phenomena can and have been obtained by analyzing them through the lens of non-linear dynamics and out-of-equilibrium statistical physics. In this framework, the microscopic level is often assumed to consist of identical units. Heterogeneity is, however, present to varying extents in both real and synthetic populations. Therefore, the existing descriptions also need to encompass variability both at the level of the individual units and at the level of the environment they are embedded in, and to describe the structures that emerge at the population level. Similarly, homogeneous environment (medium) is a useful approximation for studying collective dynamics. Yet hardly any real, either natural or artificial, environment is homogeneous, thus deeply influencing the structures, dynamics and fates of a population. The variability of the environment applies both on spatial and temporal scales. Examples include filaments and vortices in fluid media, patches and corridors in landscapes, fluctuating resources. From a methodological point of view, such influences require, at least: the quantification of environmental heterogeneities at different scales; the improvement of the formalization of heterogeneity; the identification of the heterogeneity features that are relevant to the population level and the study of population responses to changes in these heterogeneities. The question of the generation of heterogeneity of biological systems and its possible requirement for further selecting emergent patterns at different scales is of crucial importance for our understanding of biological processes. During early steps of embryogenesis in metazoans, cell diversity is generated from the non-homogeneous distribution of sub-cellular components, cell division and cell environment interaction. Cell diversity is required for further functional differentiation. Collective behaviors of cell populations underlying pattern formation should be coupled with cell diversification and differentiation. Both theoretical and experimental aspects of these questions have been almost completely unexplored so far. Finding how molecular and cellular behaviors are coupled in these processes is a main challenge of developmental biology. Close interaction between nonlinear physicists and biologists, social scientists and computer scientists has proved to be a key ingredient for advances in handling these subjects. Main Challenges 1 Collective dynamics of homogeneous and/or heterogeneous units In the past few years, considerable efforts have been devoted to studying and characterizing the emergence of collective phenomena in observation, experiments and at the theoretical level. Examples can be found in a wide range of different systems, from nano-scales to granular matter behavior, neuronal dynamics and social organizations in the animal kingdom (including human societies). The intrinsic dynamical nature of these phenomena is naturally tackled by the physics of nonlinear systems. As a result, various paths to collective behavior have been identified: phase synchronization in interacting oscillating systems, ordering phase transition in systems of self-propelled agents, self-organization and pattern formation in spatially-extended systems (e.g. ecological systems). However, we are far from fully understanding the relation between microscopic dynamics and macroscopic properties. For instance, the emergence at the global level of nontrivial coherent dynamics out of unlocked microscopic oscillators, characterized by time scales much shorter than the macroscopic one, still lacks a general theoretical framework. While it has been speculated that transport coefficients can be extracted from the long wavelength components of microscopic linear analysis (Lyapunov analysis), no clear connection has been established so far. Systems of self-propelled units seem to display anomalously large number density fluctuations – unknown in ordinary equilibrium matter and observed experimentally in granular media – but current theoretical models only partially account for such phenomena. New insights are expected from the intermediate-scale mesoscopic description that bridges the microscopic and macroscopic levels by coarse-graining relevant quantities over appropriate local length and time scales. Due to the importance of fluctuations in out-of-equilibrium phenomena, the resulting partial differential equations (PDEs) are expected to yield stochastic terms, often multiplicative in the coarse-grained fields. The analysis of such stochastic PDEs is an open challenge for physicists and mathematicians alike, both from the numerical and the analytical point of view, but powerful new techniques, such as the non-perturbative renormalization group, promise to shed new light on this subject in the near future. Although much effort has been devoted so far to systems of homogeneous units, numerous problems of interest deal with systems composed of many different species, such as living systems from single cells to ecosystems. Indeed, fully understanding the emergence of collective phenomena in such systems may require taking into account the interaction between heterogeneous units. Tackling emergence of collective properties in such systems raises numerous questions. To what extent can heterogeneous systems be reduced to homogeneous ones? In other words, is a wide degree of heterogeneity an irreducible feature of certain systems (for instance complex ecological niches), which cannot be efficiently described in terms of simpler and decoupled few-species models? Are the emergent properties of homogeneous systems conserved in heterogeneous ones, and what are the specific features that arise at the collective level from microscopic heterogeneity? How do new emergent properties relate to previous results obtained in a more homogeneous context? Can the theoretical results acquired on homogeneous contexts be extended towards heterogeneous systems? Can we extend tools developed to model the collective dynamic to take heterogeneity into account (agent-based simulation, for example, can be very naturally extended) or do we have to develop new tools specifically? At the theoretical level, the study of simple systems composed by coupled oscillators with heterogeneous frequencies may open new insights into more practical systems, while the important role played by synaptic plasticity in neuronal dynamics has long been recognized. Segregation between different species, on the other hand, can be readily described using heterogeneous agent-based models. On a different scale, cells can be seen as an inhomogeneous fluid. Thus, theoretical results about the behavior of such systems (e.g. phase transition, diffusion in crowed heterogeneous media, etc.) could shed new light on many open questions in molecular and cellular biology, such as the organization of the cell nucleus, diffusion in membranes, signal transduction, regulation of transcription. Finally, it is worth recalling that the theoretical approach must be developed in parallel with experimental observations. Model studies need to provide results in a form that can be compared and validated with experiments at the quantitative level. In particular, spatial reconstruction techniques – allowing to measure the three-dimensional position and trajectory of each unit inside a large group - are proving increasingly useful for extracting information at the microscopic dynamics level. 2. Collective dynamics in heterogeneous environments The complexity of collective dynamics is rooted both in individual properties and interactions and in the structure of their environment. Assessing the impact of environmental heterogeneity onto the population is a central challenge in many fields, including biology, geosciences, computer and social sciences. The complex systems approach should provide a unifying framework for investigating the effect of environmental heterogeneity on population dynamics. In particular, progress is needed in the following directions: Multiscale analyses: observation and measurement of environmental heterogeneity requires new tools for its detection against a noisy background and its analysis at multiple scales. Here, theoretical frameworks are useful to interpret the multiscale heterogeneity behaviors detected. In landscape ecology, for example, the need to capture the scaling sensitivity of mosaic heterogeneity has often been mentioned, while technical tools for this purpose are still lacking. A similar problem arises in plankton studies: turbulence structures the spatial and temporal distribution of the population in scales ranging from centimeters to the oceanic basin, and from minutes to years, but observations currently cover only portions of this range. Formalization: the capture of heterogeneity within models requires the introduction of novel formalization and representation approaches. Equations, algorithms and geometric representations must encompass environmental heterogeneity at different scales and describe and couple the environment with the dynamics of population units. For example, long-range hydrodynamical interactions should be included in models describing the collective motion of bacteria swimming in viscous fluids. Evolution of the vegetal cover has been formalized using differential equations for continuous diffusion processes or percolation-centered approaches. Yet a mathematical formalization of more discontinuous environments, either in terms of environment heterogeneity or of constituting units, remains to be achieved. Identification of key environmental features: models cannot include a description of all possible sources of heterogeneity. It will therefore be of key importance to identify the aspects of heterogeneity that are most relevant for the chosen description of the system. Heterogeneity can be examined in terms of concepts such as information, texture, correlation parameters and coherent structures that have to be selected for the collective dynamics under study. For example, landscape structures may exhibit different heterogeneity, depending on the properties influencing the collective dynamics: contrast often highlights barrier effects, while connectivity highlights preferential pathways in the mosaic. In a fluid, transport barriers and mixing regions organize the spatial distribution of tracers; nonlinear methods make it possible to extract such structures from the velocity field and to shed light on the interaction between turbulence and biochemical tracers. Changing environments: heterogeneity is often not defined once and for all, but can change over the course of time. Such changes can occur on time scales faster than those of the collective dynamics, or manifest themselves as slow drifts in the environmental properties. An example is provided by microbiological populations that live in environments where food availability and temperature are subject to intense fluctuations. Describing the adaptation and evolution of collective behavior requires us to take such fluctuations into account. When the environmental modifications are induced by the population itself, it is the feedback between collective behavior and environmental heterogeneity that shapes the coupled population-environment dynamics, as in the case of the biota-earth interaction in the wake of climate change. 3. Emergence of heterogeneity and differentiation processes, dynamical heterogeneity, information diffusion From genetic networks to social networks and ecospheres, we face systems that seem to display endogenous heterogeneity: heterogeneity that emerges from the very functioning of the system. Among others, we can mention cell differentiation in ontogeny, social and economic differentiation in human societies and speciation in evolution. The origin and role of this heterogeneity in the viability and maintenance of these large systems is still largely unknown. Yet its importance is recognized in the emergence of topological macro-structures underlying the global functioning of the system. The understanding of the emergence of heterogeneity and its maintenance is thus a challenge for our understanding, management and, possibly, control of complex systems. From a simple homogeneous structure (multiple copies of the same object or uniform topological space) there are four main types of emergence of heterogeneity, which can be classified in terms of both their Kolmogorov complexity and their logical depth (a measure of "organizational complexity" introduced by Charles Bennett). (a) Random emergence: noise upon a regular simple structure (random perturbation). One observes an increase in Kolmogorov complexity, but no increase in organizational complexity. (b) Coordinated or strongly constrained evolution. Example: the duplication of a gene gives two genes, allowing the divergence of their function; varying individuals in a social structure (specialization, new functions, etc.). It is not necessarily associated with a significant increase in Kolmogorov complexity, but with an increase in organizational complexity ("crystallization of a computation"). (c) Mixed emergence: randomness and constraints play a role in the dynamical process of emergence. Examples: whole molecular and genetic modules are re-used and evolve, leading to morphogenetic and functional diversity; speciation by isolation and adaptation to various geographical constraints; several copies of an entity subjected to various conditions diverge by learning or mutual adjustment. There is an increase in both Kolmogorov complexity and organizational complexity. (d) Emergence by "computation/expression of a pre-existing program". If the "computation" is fast and non-random, there is no increase in Kolmogorov complexity, nor in organizational complexity.