Coarse-graining as a downward causation mechanism.

Downward causation is the controversial idea that 'higher' levels of organization can causally influence behaviour at 'lower' levels of organization. Here I propose that we can gain traction on downward causation by being operational and examining how adaptive systems identify regularities in evolutionary or learning time and use these regularities to guide behaviour. I suggest that in many adaptive systems components collectively compute their macroscopic worlds through coarse-graining. I further suggest we move from simple feedback to downward causation when components tune behaviour in response to estimates of collectively computed macroscopic properties. I introduce a weak and strong notion of downward causation and discuss the role the strong form plays in the origins of new organizational levels. I illustrate these points with examples from the study of biological and social systems and deep neural networks.This article is part of the themed issue 'Reconceptualizing the origins of life'.

Sparse code of conflict in a primate society.

Animals living in groups collectively produce social structure. In this context individuals make strategic decisions about when to cooperate and compete. This requires that individuals can perceive patterns in collective dynamics, but how this pattern extraction occurs is unclear. Our goal is to identify a model that extracts meaningful social patterns from a behavioral time series while remaining cognitively parsimonious by making the fewest demands on memory. Using fine-grained conflict data from macaques, we show that sparse coding, an important principle of neural compression, is an effective method for compressing collective behavior. The sparse code is shown to be efficient, predictive, and socially meaningful. In our monkey society, the sparse code of conflict is composed of related individuals, the policers, and the alpha female. Our results suggest that sparse coding is a natural technique for pattern extraction when cognitive constraints and small sample sizes limit the complexity of inferential models. Our approach highlights the need for cognitive experiments addressing how individuals perceive collective features of social organization.

A family of algorithms for computing consensus about node state from network data.

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes-from ranking websites to determining critical species in ecosystems-yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node's state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node's direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus-through breadth or depth- impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes "form opinions" about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.

Policing stabilizes construction of social niches in primates.

All organisms interact with their environment, and in doing so shape it, modifying resource availability. Termed niche construction, this process has been studied primarily at the ecological level with an emphasis on the consequences of construction across generations. We focus on the behavioural process of construction within a single generation, identifying the role a robustness mechanism--conflict management--has in promoting interactions that build social resource networks or social niches. Using 'knockout' experiments on a large, captive group of pigtailed macaques (Macaca nemestrina), we show that a policing function, performed infrequently by a small subset of individuals, significantly contributes to maintaining stable resource networks in the face of chronic perturbations that arise through conflict. When policing is absent, social niches destabilize, with group members building smaller, less diverse, and less integrated grooming, play, proximity and contact-sitting networks. Instability is quantified in terms of reduced mean degree, increased clustering, reduced reach, and increased assortativity. Policing not only controls conflict, we find it significantly influences the structure of networks that constitute essential social resources in gregarious primate societies. The structure of such networks plays a critical role in infant survivorship, emergence and spread of cooperative behaviour, social learning and cultural traditions.

Institutional dynamics and learning networks.

Institutions have been described as 'the humanly devised constraints that structure political, economic, and social interactions.' This broad definition of institutions spans social norms, laws, companies, and even scientific theories. We describe a non-equilibrium, multi-scale learning framework supporting institutional quasi-stationarity, periodicity, and switching. Individuals collectively construct ledgers constituting institutions. Agents read only a part of the ledger-positive and negative opinions of an institution-its "public position" whose value biases one agent's preferences over those of rivals. These positions encode collective perception and action relating to laws, the power of parties in political office, and advocacy for scientific theories. We consider a diversity of complex temporal phenomena in the history of social and research culture (e.g. scientific revolutions) and provide a new explanation for ubiquitous cultural resistance to change and novelty-a systemic endowment effect through hysteresis.

The challenges and scope of theoretical biology.

Scientific theories seek to provide simple explanations for significant empirical regularities based on fundamental physical and mechanistic constraints. Biological theories have rarely reached a level of generality and predictive power comparable to physical theories. This discrepancy is explained through a combination of frozen accidents, environmental heterogeneity, and widespread non-linearities observed in adaptive processes. At the same time, model building has proven to be very successful when it comes to explaining and predicting the behavior of particular biological systems. In this respect biology resembles alternative model-rich frameworks, such as economics and engineering. In this paper we explore the prospects for general theories in biology, and suggest that these take inspiration not only from physics, but also from the information sciences. Future theoretical biology is likely to represent a hybrid of parsimonious reasoning and algorithmic or rule-based explanation. An open question is whether these new frameworks will remain transparent to human reason. In this context, we discuss the role of machine learning in the early stages of scientific discovery. We argue that evolutionary history is not only a source of uncertainty, but also provides the basis, through conserved traits, for very general explanations for biological regularities, and the prospect of unified theories of life.

Inductive game theory and the dynamics of animal conflict.

Conflict destabilizes social interactions and impedes cooperation at multiple scales of biological organization. Of fundamental interest are the causes of turbulent periods of conflict. We analyze conflict dynamics in an monkey society model system. We develop a technique, Inductive Game Theory, to extract directly from time-series data the decision-making strategies used by individuals and groups. This technique uses Monte Carlo simulation to test alternative causal models of conflict dynamics. We find individuals base their decision to fight on memory of social factors, not on short timescale ecological resource competition. Furthermore, the social assessments on which these decisions are based are triadic (self in relation to another pair of individuals), not pairwise. We show that this triadic decision making causes long conflict cascades and that there is a high population cost of the large fights associated with these cascades. These results suggest that individual agency has been over-emphasized in the social evolution of complex aggregates, and that pair-wise formalisms are inadequate. An appreciation of the empirical foundations of the collective dynamics of conflict is a crucial step towards its effective management.

Challenges for complexity measures: A perspective from social dynamics and collective social computation.

We review an empirically grounded approach to studying the emergence of collective properties from individual interactions in social dynamics. When individual decision-making rules, strategies, can be extracted from the time-series data, these can be used to construct adaptive social circuits. Social circuits provide a compact description of collective effects by mapping rules at the individual level to statistical properties of aggregates. This defines a simple form of social computation. We consider the properties that complexity measures would need to have to best capture regularities at different level of analysis, from individual rules to circuits to population statistics. One obvious benefit of using the properties and structure of biological and social systems to guide the development of complexity measures is that it is more likely to produce measures that can be applied to data. Principled but pragmatic measures would allow for a rigorous investigation of the relationship between adaptive features at the micro, meso, and macro scales, a long standing goal of evolutionary theory. A second benefit is that empirically grounded complexity measures would facilitate quantitative comparisons of strategies, circuits, and aggregate properties across social systems.

The information theory of individuality.

Despite the near universal assumption of individuality in biology, there is little agreement about what individuals are and few rigorous quantitative methods for their identification. Here, we propose that individuals are aggregates that preserve a measure of temporal integrity, i.e., "propagate" information from their past into their futures. We formalize this idea using information theory and graphical models. This mathematical formulation yields three principled and distinct forms of individuality-an organismal, a colonial, and a driven form-each of which varies in the degree of environmental dependence and inherited information. This approach can be thought of as a Gestalt approach to evolution where selection makes figure-ground (agent-environment) distinctions using suitable information-theoretic lenses. A benefit of the approach is that it expands the scope of allowable individuals to include adaptive aggregations in systems that are multi-scale, highly distributed, and do not necessarily have physical boundaries such as cell walls or clonal somatic tissue. Such individuals might be visible to selection but hard to detect by observers without suitable measurement principles. The information theory of individuality allows for the identification of individuals at all levels of organization from molecular to cultural and provides a basis for testing assumptions about the natural scales of a system and argues for the importance of uncertainty reduction through coarse-graining in adaptive systems.

Collective Computation in Animal Fission-Fusion Dynamics.

Recent work suggests that collective computation of social structure can minimize uncertainty about the social and physical environment, facilitating adaptation. We explore these ideas by studying how fission-fusion social structure arises in spider monkey (Ateles geoffroyi) groups, exploring whether monkeys use social knowledge to collectively compute subgroup size distributions adaptive for foraging in variable environments. We assess whether individual decisions to stay in or leave subgroups are conditioned on strategies based on the presence or absence of others. We search for this evidence in a time series of subgroup membership. We find that individuals have multiple strategies, suggesting that the social knowledge of different individuals is important. These stay-leave strategies provide microscopic inputs to a stochastic model of collective computation encoded in a family of circuits. Each circuit represents an hypothesis for how collectives combine strategies to make decisions, and how these produce various subgroup size distributions. By running these circuits forward in simulation we generate new subgroup size distributions and measure how well they match food abundance in the environment using transfer entropies. We find that spider monkeys decide to stay or go using information from multiple individuals and that they can collectively compute a distribution of subgroup size that makes efficient use of ephemeral sources of nutrition. We are able to artificially tune circuits with subgroup size distributions that are a better fit to the environment than the observed. This suggests that a combination of measurement error, constraint, and adaptive lag are diminishing the power of collective computation in this system. These results are relevant for a more general understanding of the emergence of ordered states in multi-scale social systems with adaptive properties-both natural and engineered.

Scaling theory of armed-conflict avalanches.

Armed conflict data display features consistent with scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching armed conflict model to relate the multiple properties to one another. The model incorporates a fractal lattice on which conflict spreads, uniform dynamics driving conflict growth, and regional virulence that modulates local conflict intensity. The quantitative constraints on scaling and universal dynamics we use to develop our minimal model serve more generally as a set of constraints for other models for armed conflict dynamics. We show how this approach akin to thermodynamics imparts mechanistic intuition and unifies multiple conflict properties, giving insight into causation, prediction, and intervention timing.

Conflicts of interest improve collective computation of adaptive social structures.

In many biological systems, the functional behavior of a group is collectively computed by the system's individual components. An example is the brain's ability to make decisions via the activity of billions of neurons. A long-standing puzzle is how the components' decisions combine to produce beneficial group-level outputs, despite conflicts of interest and imperfect information. We derive a theoretical model of collective computation from mechanistic first principles, using results from previous work on the computation of power structure in a primate model system. Collective computation has two phases: an information accumulation phase, in which (in this study) pairs of individuals gather information about their fighting abilities and make decisions about their dominance relationships, and an information aggregation phase, in which these decisions are combined to produce a collective computation. To model information accumulation, we extend a stochastic decision-making model-the leaky integrator model used to study neural decision-making-to a multiagent game-theoretic framework. We then test alternative algorithms for aggregating information-in this study, decisions about dominance resulting from the stochastic model-and measure the mutual information between the resultant power structure and the "true" fighting abilities. We find that conflicts of interest can improve accuracy to the benefit of all agents. We also find that the computation can be tuned to produce different power structures by changing the cost of waiting for a decision. The successful application of a similar stochastic decision-making model in neural and social contexts suggests general principles of collective computation across substrates and scales.

Dual Coding Theory Explains Biphasic Collective Computation in Neural Decision-Making.

A central question in cognitive neuroscience is how unitary, coherent decisions at the whole organism level can arise from the distributed behavior of a large population of neurons with only partially overlapping information. We address this issue by studying neural spiking behavior recorded from a multielectrode array with 169 channels during a visual motion direction discrimination task. It is well known that in this task there are two distinct phases in neural spiking behavior. Here we show Phase I is a distributed or incompressible phase in which uncertainty about the decision is substantially reduced by pooling information from many cells. Phase II is a redundant or compressible phase in which numerous single cells contain all the information present at the population level in Phase I, such that the firing behavior of a single cell is enough to predict the subject's decision. Using an empirically grounded dynamical modeling framework, we show that in Phase I large cell populations with low redundancy produce a slow timescale of information aggregation through critical slowing down near a symmetry-breaking transition. Our model indicates that increasing collective amplification in Phase II leads naturally to a faster timescale of information pooling and consensus formation. Based on our results and others in the literature, we propose that a general feature of collective computation is a "coding duality" in which there are accumulation and consensus formation processes distinguished by different timescales.

Control of finite critical behaviour in a small-scale social system.

Many adaptive systems sit near a tipping or critical point. For systems near a critical point small changes to component behaviour can induce large-scale changes in aggregate structure and function. Criticality can be adaptive when the environment is changing, but entails reduced robustness through sensitivity. This tradeoff can be resolved when criticality can be tuned. We address the control of finite measures of criticality using data on fight sizes from an animal society model system (Macaca nemestrina, n=48). We find that a heterogeneous, socially organized system, like homogeneous, spatial systems (flocks and schools), sits near a critical point; the contributions individuals make to collective phenomena can be quantified; there is heterogeneity in these contributions; and distance from the critical point (DFC) can be controlled through biologically plausible mechanisms exploiting heterogeneity. We propose two alternative hypotheses for why a system decreases the distance from the critical point.

Collective memory in primate conflict implied by temporal scaling collapse.

In biological systems, prolonged conflict is costly, whereas contained conflict permits strategic innovation and refinement. Causes of variation in conflict size and duration are not well understood. We use a well-studied primate society model system to study how conflicts grow. We find conflict duration is a 'first to fight' growth process that scales superlinearly, with the number of possible pairwise interactions. This is in contrast with a 'first to fail' process that characterizes peaceful durations. Rescaling conflict distributions reveals a universal curve, showing that the typical time scale of correlated interactions exceeds nearly all individual fights. This temporal correlation implies collective memory across pairwise interactions beyond those assumed in standard models of contagion growth or iterated evolutionary games. By accounting for memory, we make quantitative predictions for interventions that mitigate or enhance the spread of conflict. Managing conflict involves balancing the efficient use of limited resources with an intervention strategy that allows for conflict while keeping it contained and controlled.

Quantifying collectivity.

In biological function emerges from the interactions of components with only partially aligned interests. An example is the brain-a large aggregation of neurons capable of producing unitary, coherent output. A theory for how such aggregations produce coherent output remains elusive. A first question we might ask is how collective is the behavior of the components? Here we introduce two properties of collectivity and illustrate how these properties can be quantified using approaches from information theory and statistical physics. First, amplification quantifies the sensitivity of the large scale to information at the small scale and is related to the notion of criticality in statistical physics. Second, decomposability reveals the extent to which aggregate behavior is reducible to individual contributions or is the result of synergistic interactions among components forming larger subgroups. These measures facilitate identification of causally important components and subgroups that might be experimentally manipulated to study the evolution and controllability of biological circuits and their outputs.

Social structure, robustness, and policing cost in a cognitively sophisticated species.

Conflict management is one of the primary requirements for social complexity. Of the many forms of conflict management, one of the rarest and most interesting is third-party policing, or intervening impartially to control conflict. Third-party policing should be hard to evolve because policers personally pay a cost for intervening, while the benefits are diffused over the whole group. In this study we investigate the incidence and costs of policing in a primate society. We report quantitative evidence of non-kin policing in the nonhuman primate, the pigtailed macaque. We find that policing is effective at reducing the intensity of or terminating conflict when performed by the most powerful individuals. We define a measure, social power consensus, that predicts effective low-cost interventions by powerful individuals and ineffective, relatively costly interventions by low-power individuals. Finally, we develop a simple probabilistic model to explore whether the degree to which policing can effectively reduce the societal cost of conflict is dependent on variance in the distribution of power. Our data and simple model suggest that third-party policing effectiveness and cost are dependent on power structure and might emerge only in societies with high variance in power.

Robustness mechanisms in primate societies: a perturbation study.

Conflict management mechanisms have a direct, critical effect on system robustness because they mitigate conflict intensity and help repair damaged relationships. However, robustness mechanisms can also have indirect effects on system integrity by facilitating interactions among components. We explore the indirect role that conflict management mechanisms play in the maintenance of social system robustness, using a perturbation technique to 'knockout' components responsible for effective conflict management. We explore the effects of knockout on pigtailed macaque (Macaca nemestrina) social organization, using a captive group of 84 individuals. This system is ideal in addressing this question because there is heterogeneity in performance of conflict management. Consequently, conflict managers can be easily removed without disrupting other control structures. We find that powerful conflict managers are essential in maintaining social order for the benefit of all members of society. We show that knockout of components responsible for conflict management results in system destabilization by significantly increasing mean levels of conflict and aggression, decreasing socio-positive interaction and decreasing the operation of repair mechanisms.