Finding continuity and discontinuity in fish schools via integrated information theory

Fish communicate with water flow to enhance a school's social network

Schooling fish rely on a social network created through signaling between its members to interact with their environment. Previous studies have established that vision is necessary for schooling and that flow sensing by the lateral line system may aid in a school's cohesion. However, it remains unclear to what extent flow provides a channel of communication between schooling fish. Based on kinematic measurements of the speed and heading of schooling tetras (Petitella rhodostoma), we found that compromising the lateral line by chemical treatment reduced the mutual information between individuals by ∼13%. This relatively small reduction in pairwise communication propagated through schools of varying size to reduce the degree and connectivity of the social network by more than half. Treated schools additionally showed more than twice the spatial heterogeneity of fish with unaltered flow sensing. These effects were much more substantial than the changes that we measured in the nearest-neighbor distance, speed and intermittency of individual fish by compromising flow sensing. Therefore, flow serves as a valuable supplement to visual communication in a manner that is revealed through a school's network properties.

Upper bounds for integrated information

Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated information quantifies how much of the causal powers of a subset of units in a state, also referred to as a mechanism, cannot be accounted for by its parts. If the causal powers of the mechanism can be fully explained by its parts, it is reducible and its integrated information is zero. Here, we study the upper bound of this measure and how it is achieved. We study mechanisms in isolation, groups of mechanisms, and groups of causal relations among mechanisms. We put forward new theoretical results that show mechanisms that share parts with each other cannot all achieve their maximum. We also introduce techniques to design systems that can maximize the integrated information of a subset of their mechanisms or relations. Our results can potentially be used to exploit the symmetries and constraints to reduce the computations significantly and to compare different connectivity profiles in terms of their maximal achievable integrated information.

A measure centrality index for systematic empirical comparison of consciousness theories

Consciousness science is marred by disparate constructs and methodologies, making it challenging to systematically compare theories. This foundational crisis casts doubts on the scientific character of the field itself. Addressing it, we propose a framework for systematically comparing consciousness theories by introducing a novel inter-theory classification interface, the Measure Centrality Index (MCI). Recognizing its gradient distribution, the MCI assesses the degree of importance a specific empirical measure has for a given consciousness theory. We apply the MCI to probe how the empirical measures of the Global Neuronal Workspace Theory (GNW), Integrated Information Theory (IIT), and Temporospatial Theory of Consciousness (TTC) would fare within the context of the other two. We demonstrate that direct comparison of IIT, GNW, and TTC is meaningful and valid for some measures like Lempel-Ziv Complexity (LZC), Autocorrelation Window (ACW), and possibly Mutual Information (MI). In contrast, it is problematic for others like the anatomical and physiological neural correlates of consciousness (NCC) due to their MCI-based differential weightings within the structure of the theories. In sum, we introduce and provide proof-of-principle of a novel systematic method for direct inter-theory empirical comparisons, thereby addressing isolated evolution of theories and confirmatory bias issues in the state-of-the-art neuroscience of consciousness.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with ρ - 1 / 4 . On the other hand, they tend to be monofractal, and their average scales with ρ - 1 / 2 for high fish densities. These two regimes overlap at critical density ρ c , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

On the non-uniqueness problem in integrated information theory

Integrated Information Theory (IIT) 3.0 is among the leading theories of consciousness in contemporary neuroscience. The core of the theory relies on the calculation of a scalar mathematical measure of consciousness, Φ, which is inspired by the phenomenological axioms of the theory. Here, we show that despite its widespread application, Φ is not a well-defined mathematical concept in the sense that the value it specifies is non-unique. To demonstrate this, we introduce an algorithm that calculates all possible Φ values for a given system in strict accordance with the mathematical definition from the theory. We show that, to date, all published Φ values under consideration are selected arbitrarily from a multitude of equally valid alternatives. Crucially, both [Formula: see text] and [Formula: see text] are often predicted simultaneously, rendering any interpretation of these systems as conscious or not, non-decidable in the current formulation of IIT.

When do parts form wholes? Integrated information as the restriction on mereological composition

Under what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivial restriction on composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens under no or all conditions. In this paper, we provide a self-contained introduction to the integrated information theory (IIT) of consciousness. We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT restriction to existing proposals and argue that the IIT restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system.

Entropy and Fractal Techniques for Monitoring Fish Behaviour and Welfare in Aquacultural Precision Fish Farming-A Review

In a non-linear system, such as a biological system, the change of the output (e.g., behaviour) is not proportional to the change of the input (e.g., exposure to stressors). In addition, biological systems also change over time, i.e., they are dynamic. Non-linear dynamical analyses of biological systems have revealed hidden structures and patterns of behaviour that are not discernible by classical methods. Entropy analyses can quantify their degree of predictability and the directionality of individual interactions, while fractal dimension (FD) analyses can expose patterns of behaviour within apparently random ones. The incorporation of these techniques into the architecture of precision fish farming (PFF) and intelligent aquaculture (IA) is becoming increasingly necessary to understand and predict the evolution of the status of farmed fish. This review summarizes recent works on the application of entropy and FD techniques to selected individual and collective fish behaviours influenced by the number of fish, tagging, pain, preying/feed search, fear/anxiety (and its modulation) and positive emotional contagion (the social contagion of positive emotions). Furthermore, it presents an investigation of collective and individual interactions in shoals, an exposure of the dynamics of inter-individual relationships and hierarchies, and the identification of individuals in groups. While most of the works have been carried out using model species, we believe that they have clear applications in PFF. The review ends by describing some of the major challenges in the field, two of which are, unsurprisingly, the acquisition of high-quality, reliable raw data and the construction of large, reliable databases of non-linear behavioural data for different species and farming conditions.

The ambiguous feeling between "mine" and "not-mine" measured by integrated information theory during rubber hand illusion

Human body awareness is adaptive to context changes. The illusory sense of body ownership has been studied since the publication of the rubber hand illusion, where ambiguous body ownership feeling was first defined. Phenomenologically, the ambiguous body ownership is attributed to a conflict between feeling and judgement: it characterises a discrepancy between first- and third-person processes. Although Bayesian inference can explain this malleability of body image, it still fails to relate the subjective feeling to physiological data. This study attempts to explain subjective experience during rubber hand illusions by using integrated information theory (IIT). The integrated information [Formula: see text] in IIT measures the difference between the whole system and its subsystems. By analysing seven different time-series of physiological data representing a small body-brain system, we demonstrate that the integrity of the whole system during the illusion decreases, while the integrity of its subsystems increases. These general tendencies agree with many brain-image analyses and subjective reports; furthermore, we found that subjective ratings as ambiguous body ownership were associated with [Formula: see text]. Our result suggests that IIT can explain the general tendency of the sense of ownership illusions and individual differences in subjective experience during the illusions.

Different Approximation Methods for Calculation of Integrated Information Coefficient in the Brain during Instrumental Learning

The amount of integrated information, Φ, proposed in an integrated information theory (IIT) is useful to describe the degree of brain adaptation to the environment. However, its computation cannot be precisely performed for a reasonable time for time-series spike data collected from a large count of neurons.. Therefore, Φ was only used to describe averaged activity of a big group of neurons, and the behavior of small non-brain systems. In this study, we reported on ways for fast and precise Φ calculation using different approximation methods for Φ calculation in neural spike data, and checked the capability of Φ to describe a degree of adaptation in brain neural networks. We show that during instrumental learning sessions, all applied approximation methods reflect temporal trends of Φ in the rat hippocampus. The value of Φ is positively correlated with the number of successful acts performed by a rat. We also show that only one subgroup of neurons modulates their Φ during learning. The obtained results pave the way for application of Φ to investigate plasticity in the brain during the acquisition of new tasks.

Zebrafish automatic monitoring system for conditioning and behavioral analysis

Studies using zebrafish (Danio rerio) in neuro-behavioural research are growing. Measuring fish behavior by computational methods is one of the most efficient ways to avoid human bias in experimental analyses, extending them to various approaches. Sometimes, thorough analyses are difficult to do, as fish can behave unpredictably during an experimental strategy. However, the analyses can be implemented in an automated way, using an online strategy and video processing for a complete assessment of the zebrafish behavior, based on the detection and tracking of fish during an activity. Here, a fully automatic conditioning and detailed analysis of zebrafish behavior is presented. Microcontrolled components were used to control the delivery of visual and sound stimuli, in addition to the concise amounts of food after conditioned stimuli for adult zebrafish groups in a conventional tank. The images were captured and processed for automatic detection of the fish, and the training of the fish was done in two evaluation strategies: simple and complex. In simple conditioning, the zebrafish showed significant responses from the second attempt, learning that the conditioned stimulus was a predictor of food presentation in a specific space of the tank, where the food was dumped. When the fish were subjected to two stimuli for decision-making in the food reward, the zebrafish obtained better responses to red light stimuli in relation to vibration. The behavior change was clear in stimulated fish in relation to the control group, thus, the distances traveled and the speed were greater, while the polarization was lower in stimulated fish. This automated system allows for the conditioning and assessment of zebrafish behavior online, with greater stability in experiments, and in the analysis of the behavior of individual fish or fish schools, including learning and memory studies.

Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis

Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system's cause-effect structure from spatio-temporal grain and reveals the system's irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from Δ t = 5 / 120 to Δ t = 120 / 120 s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.