The fractal organization of ultradian rhythms in avian behavior

Monitoring poultry social dynamics using colored tags: Avian visual perception, behavioral effects, and artificial intelligence precision

Artificial intelligence (AI) in animal behavior and welfare research is on the rise. AI can detect behaviors and localize animals in video recordings, thus it is a valuable tool for studying social dynamics. However, maintaining the identity of individuals over time, especially in homogeneous poultry flocks, remains challenging for algorithms. We propose using differentially colored "backpack" tags (black, gray, white, orange, red, purple, and green) detectable with computer vision (eg. YOLO) from top-view video recordings of pens. These tags can also accommodate sensors, such as accelerometers. In separate experiments, we aim to: (i) evaluate avian visual perception of the different colored tags; (ii) assess the potential impact of tag colors on social behavior; and (iii) test the ability of the YOLO model to accurately distinguish between different colored tags on Japanese quail in social group settings. First, the reflectance spectra of tags and feathers were measured. An avian visual model was applied to calculate the quantum catches for each spectrum. Green and purple tags showed significant chromatic contrast to the feather. Mostly tags presented greater luminance receptor stimulation than feathers. Birds wearing white, gray, purple, and green tags pecked significantly more at their own tags than those with black (control) tags. Additionally, fewer aggressive interactions were observed in groups with orange tags compared to groups with other colors, except for red. Next, heterogeneous groups of 5 birds with different color tags were videorecorded for 1 h. The precision and accuracy of YOLO to detect each color tag were assessed, yielding values of 95.9% and 97.3%, respectively, with most errors stemming from misclassifications between black and gray tags. Lastly using the YOLO output, we estimated each bird's average social distance, locomotion speed, and the percentage of time spent moving. No behavioral differences associated with tag color were detected. In conclusion, carefully selected colored backpack tags can be identified using AI models and can also hold other sensors, making them powerful tools for behavioral and welfare studies.

Review: Environmental enrichment builds functional capacity and improves resilience as an aspect of positive welfare in production animals

The success of the animal in coping with challenges, and in harnessing opportunities to thrive, is central to its welfare. Functional capacity describes the capacity of molecules, cells, organs, body systems, the whole animal, and its community to buffer against the impacts of environmental perturbations. This buffering capacity determines the ability of the animal to maintain or regain functions in the face of environmental perturbations, which is recognised as resilience. The accuracy of physiological regulation and the maintenance of homeostatic balance underwrite the dynamic stability of outcomes such as biorhythms, feed intake, growth, milk yield, and egg production justifying their assessment as indicators of resilience. This narrative review examines the influence of environmental enrichments, especially during developmental stages in young animals, in building functional capacity and in its subsequent expression as resilience. Experience of enriched environments can build skills and competencies across multiple functional domains including but not limited to behaviour, immunity, and metabolism thereby increasing functional capacity and facilitating resilience within the context of challenges such as husbandry practices, social change, and infection. A quantitative method for measuring the distributed property of functional capacity may improve its assessment. Methods for analysing embedded energy (emergy) in ecosystems may have utility for this goal. We suggest functional capacity provides the common thread that links environmental enrichments with an ability to express resilience and may provide a novel and useful framework for measuring and reporting resilience. We conclude that the development of functional capacity and its subsequent expression as resilience is an aspect of positive animal welfare. The emergence of resilience from system dynamics highlights a need to shift from the study of physical and mental states to the study of physical and mental dynamics to describe the positive dimension of animal welfare.

A mathematical model for the role of dopamine-D2 self-regulation in the production of ultradian rhythms

Many self-motivated and goal-directed behaviours display highly flexible, approximately 4 hour ultradian (shorter than a day) oscillations. Despite lacking direct correspondence to physical cycles in the environment, these ultradian rhythms may be involved in optimizing functional interactions with the environment and reflect intrinsic neural dynamics. Current evidence supports a role of mesostriatal dopamine (DA) in the expression and propagation of ultradian rhythmicity, however, the biochemical processes underpinning these oscillations remain to be identified. Here, we use a mathematical model to investigate D2 autoreceptor-dependent DA self-regulation as the source of ultradian behavioural rhythms. DA concentration at the midbrain-striatal synapses is governed through a dual-negative feedback-loop structure, which naturally gives rise to rhythmicity. This model shows the propensity of striatal DA to produce an ultradian oscillation characterized by a flexible period that is highly sensitive to parameter variations. Circadian (approximately 24 hour) regulation consolidates the ultradian oscillations and alters their response to the phase-dependent, rapid-resetting effect of a transient excitatory stimulus. Within a circadian framework, the ultradian rhythm orchestrates behavioural activity and enhances responsiveness to an external stimulus. This suggests a role for the circadian-ultradian timekeeping hierarchy in governing organized behaviour and shaping daily experience through coordinating the motivation to engage in recurring, albeit not highly predictable events, such as social interactions.

Dietary restriction modulates ultradian rhythms and autocorrelation properties in mice behavior

Animal behavior emerges from integration of many processes with different spatial and temporal scales. Dynamical behavioral patterns, including daily and ultradian rhythms and the dynamical microstructure of behavior (i.e., autocorrelations properties), can be differentially affected by external cues. Identifying these patterns is important for understanding how organisms adapt to their environment, yet unbiased methods to quantify dynamical changes over multiple temporal scales are lacking. Herein, we combine a wavelet approach with Detrended Fluctuation Analysis to identify behavioral patterns and evaluate changes over 42-days in mice subjected to different dietary restriction paradigms. We show that feeding restriction alters dynamical patterns: not only are daily rhythms modulated but also the presence, phase and/or strength of ~12h-rhythms, as well as the nature of autocorrelation properties of feed-intake and wheel running behaviors. These results highlight the underlying complexity of behavioral architecture and offer insights into the multi-scale impact of feeding habits on physiology.

Synchronized locomotion can improve spatial accessibility inside ant colonies

Synchronization is a conspicuous form of collective behaviour that is of crucial importance in numerous biological systems. Ant colonies from the genera Leptothorax and Temnothorax form small colonies, typically made up of only a few hundred workers, and exhibit a form of synchronized behaviour where workers inside colonies' nests become active together in rhythmic cycles that have a period of approximately 20-200 min. However, it is not currently known if these synchronized rhythms of locomotion confer any functional benefit to colonies. By using a combination of multiple image analysis techniques, we show that inactive Leptothorax ants can act as immobile obstacles to moving ants, and that synchronized activity has the potential to reduce the likelihood that individual ants will encounter regions of immobile obstacles that impede access to portions of the nest. We demonstrate qualitatively similar findings using a computational model of confined active particles with oscillating activity.

Are physiological oscillations physiological?

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic β-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory ('pacemaking') mechanisms at the cellular, tissue and system levels.

The relevance of a right scale for sampling when studying high-resolution behavioral dynamics

Many species used in behavioral studies are small vertebrates with high metabolic rates and potentially enhanced temporal resolution of perception. Nevertheless, the selection of an appropriate scales to evaluate behavioral dynamics has received little attention. Herein, we studied the temporal organization of behaviors at fine-grain (i.e. sampling interval ≤1s) to gain insight into dynamics and to rethink how behavioral events are defined. We statistically explored high-resolution Japanese quail (Coturnix japonica) datasets encompassing 17 defined behaviors. We show that for the majority of these behaviors, events last predominately <300ms and can be shorter than 70ms. Insufficient sampling resolution, even in the order of 1s, of behaviors that involve spatial displacement (e.g. walking) yields distorted probability distributions of event durations and overestimation of event durations. Contrarily, behaviors without spatial displacement (e.g. vigilance) maintain non-Gaussian, power-law-type distributions indicative of long-term memory, independently of the sampling resolution evaluated. Since data probability distributions reflect underlying biological processes, our results highlight the importance of quantification of behavioral dynamics based on the temporal scale pertinent to the species, and data distribution. We propose a hierarchical model that links diverse types of behavioral definitions and distributions, and paves the way towards a statistical framework for defining behaviors.

A dynamically coherent pattern of rhythms that matches between distant species across the evolutionary scale

We address the temporal organization of circadian and ultradian rhythms, crucial for understanding biological timekeeping in behavior, physiology, metabolism, and alignment with geophysical time. Using a newly developed five-steps wavelet-based approach to analyze high-resolution time series of metabolism in yeast cultures and spontaneous movement, metabolism, and feeding behavior in mice, rats, and quails, we describe a dynamically coherent pattern of rhythms spanning over a broad range of temporal scales (hours to minutes). The dynamic pattern found shares key features among the four, evolutionary distant, species analyzed. Specifically, a branching appearance given by splitting periods from 24 h into 12 h, 8 h and below in mammalian and avian species, or from 14 h down to 0.07 h in yeast. Scale-free fluctuations with long-range correlations prevail below ~ 4 h. Synthetic time series modeling support a scenario of coexisting behavioral rhythms, with circadian and ultradian rhythms at the center of the emergent pattern observed.

Modified Wavelet Analyses Permit Quantification of Dynamic Interactions Between Ultradian and Circadian Rhythms

Circadian rhythms provide daily temporal structure to cellular and organismal biological processes, ranging from gene expression to cognition. Higher-frequency (intradaily) ultradian rhythms are similarly ubiquitous but have garnered far less empirical study, in part because of the properties that define them-multimodal periods, non-stationarity, circadian harmonics, and diurnal modulation-pose challenges to their accurate and precise quantification. Wavelet analyses are ideally suited to address these challenges, but wavelet-based measurement of ultradian rhythms has remained largely idiographic. Here, we describe novel analytical approaches, based on discrete and continuous wavelet transforms, which permit quantification of rhythmic power distribution across a broad ultradian spectrum, as well as precise identification of period within empirically determined ultradian bands. Moreover, the aggregation of normalized wavelet matrices allows group-level analyses of experimental treatments, thereby circumventing limitations of idiographic approaches. The accuracy and precision of these wavelet analyses were validated using in silico and in vivo models with known ultradian features. Experiments in male and female mice yielded robust and repeatable measures of ultradian period and power in home cage locomotor activity, confirming and extending reports of ultradian rhythm modulation by sex, gonadal hormones, and circadian entrainment. Seasonal changes in day length modulated ultradian period and power, and exerted opposite effects in the light and dark phases of the 24 h day, underscoring the importance of evaluating ultradian rhythms with attention to circadian phase. Sex differences in ultradian rhythms were more prominent at night and depended on gonadal hormones in male mice. Thus, relatively straightforward modifications to the wavelet procedure allowed quantification of ultradian rhythms with appropriate time-frequency resolution, generating accurate, and repeatable measures of period and power which are suitable for group-level analyses. These analytical tools may afford deeper understanding of how ultradian rhythms are generated and respond to interoceptive and exteroceptive cues.

Network Analysis of Inflammatory Bowel Disease Research: Towards the Interactome

BACKGROUND AND AIMS

Modern views accept that inflammatory bowel diseases [IBD] emerge from complex interactions among the multiple components of a biological network known as the 'IBD interactome'. These diverse components belong to different functional levels including cells, molecules, genes and biological processes. This diversity can make it difficult to integrate available empirical information from human patients into a collective view of aetiopathogenesis, a necessary step to understand the interactome. Herein, we quantitatively analyse how the representativeness of components involved in human IBD and their relationships ha ve changed over time.

METHODS

A bibliographic search in PubMed retrieved 25 971 abstracts of experimental studies on IBD in humans, published between 1990 and 2020. Abstracts were scanned automatically for 1218 IBD interactome components proposed in recent reviews. The resulting databases are freely available and were visualized as networks indicating the frequency at which different components are referenced together within each abstract.

RESULTS

As expected, over time there was an increase in components added to the IBD network and heightened connectivity within and across functional levels. However, certain components were consistently studied together, forming preserved motifs in the networks. These overrepresented and highly linked components reflect main 'hypotheses' in IBD research in humans. Interestingly, 82% of the components cited in reviews were absent or showed low frequency, suggesting that many aspects of the proposed IBD interactome still have weak experimental support in humans.

CONCLUSIONS

A reductionist and fragmented approach to the study of IBD has prevailed in previous decades, highlighting the importance of transitioning towards a more integrated interactome framework.

Practical application of a Bayesian network approach to poultry epigenetics and stress

Background

Relationships among genetic or epigenetic features can be explored by learning probabilistic networks and unravelling the dependencies among a set of given genetic/epigenetic features. Bayesian networks (BNs) consist of nodes that represent the variables and arcs that represent the probabilistic relationships between the variables. However, practical guidance on how to make choices among the wide array of possibilities in Bayesian network analysis is limited. Our study aimed to apply a BN approach, while clearly laying out our analysis choices as an example for future researchers, in order to provide further insights into the relationships among epigenetic features and a stressful condition in chickens (Gallus gallus).

Results

Chickens raised under control conditions (n = 22) and chickens exposed to a social isolation protocol (n = 24) were used to identify differentially methylated regions (DMRs). A total of 60 DMRs were selected by a threshold, after bioinformatic pre-processing and analysis. The treatment was included as a binary variable (control = 0; stress = 1). Thereafter, a BN approach was applied: initially, a pre-filtering test was used for identifying pairs of features that must not be included in the process of learning the structure of the network; then, the average probability values for each arc of being part of the network were calculated; and finally, the arcs that were part of the consensus network were selected. The structure of the BN consisted of 47 out of 61 features (60 DMRs and the stressful condition), displaying 43 functional relationships. The stress condition was connected to two DMRs, one of them playing a role in tight and adhesive intracellular junctions in organs such as ovary, intestine, and brain.

Conclusions

We clearly explain our steps in making each analysis choice, from discrete BN models to final generation of a consensus network from multiple model averaging searches. The epigenetic BN unravelled functional relationships among the DMRs, as well as epigenetic features in close association with the stressful condition the chickens were exposed to. The DMRs interacting with the stress condition could be further explored in future studies as possible biomarkers of stress in poultry species.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04800-0.

A Bayesian network structure learning approach to identify genes associated with stress in spleens of chickens

Differences in the expression patterns of genes have been used to measure the effects of non-stress or stress conditions in poultry species. However, the list of genes identified can be extensive and they might be related to several biological systems. Therefore, the aim of this study was to identify a small set of genes closely associated with stress in a poultry animal model, the chicken (Gallus gallus), by reusing and combining data previously published together with bioinformatic analysis and Bayesian networks in a multi-step approach. Two datasets were collected from publicly available repositories and pre-processed. Bioinformatics analyses were performed to identify genes common to both datasets that showed differential expression patterns between non-stress and stress conditions. Bayesian networks were learnt using a Simulated Annealing algorithm implemented in the software Banjo. The structure of the Bayesian network consisted of 16 out of 19 genes together with the stress condition. Network structure showed CARD19 directly connected to the stress condition plus highlighted CYGB, BRAT1, and EPN3 as relevant, suggesting these genes could play a role in stress. The biological functionality of these genes is related to damage, apoptosis, and oxygen provision, and they could potentially be further explored as biomarkers of stress.

The Fractal Tapestry of Life: II Entailment of Fractional Oncology by Physiology Networks

This is an essay advocating the efficacy of using the (noninteger) fractional calculus (FC) for the modeling of complex dynamical systems, specifically those pertaining to biomedical phenomena in general and oncological phenomena in particular. Herein we describe how the integer calculus (IC) is often incapable of describing what were historically thought to be simple linear phenomena such as Newton's law of cooling and Brownian motion. We demonstrate that even linear dynamical systems may be more accurately described by fractional rate equations (FREs) when the experimental datasets are inconsistent with models based on the IC. The Network Effect is introduced to explain how the collective dynamics of a complex network can transform a many-body noninear dynamical system modeled using the IC into a set of independent single-body fractional stochastic rate equations (FSREs). Note that this is not a mathematics paper, but rather a discussion focusing on the kinds of phenomena that have historically been approximately and improperly modeled using the IC and how a FC replacement of the model better explains the experimental results. This may be due to hidden effects that were not anticapated in the IC model, or to an effect that was acknowledged as possibly significant, but beyond the mathematical skills of the investigator to Incorporate into the original model. Whatever the reason we introduce the FRE used to describe mathematical oncology (MO) and review the quality of fit of such models to tumor growth data. The analytic results entailed in MO using ordinary diffusion as well as fractional diffusion are also briefly discussed. A connection is made between a time-dependent fractional-order derivative, technically called a distributed-order parameter, and the multifractality of time series, such that an observed multifractal time series can be modeled using a FRE with a distributed fractional-order derivative. This equivalence between multifractality and distributed fractional derivatives has not received the recognition in the applications literature we believe it warrants.

Collective Rhythm as an Emergent Property During Human Social Coordination

The literature on social interactions has shown that participants coordinate not only at the behavioral but also at the physiological and neural levels, and that this coordination gives a temporal structure to the individual and social dynamics. However, it has not been fully explored whether such temporal patterns emerge during interpersonal coordination beyond dyads, whether this phenomenon arises from complex cognitive mechanisms or from relatively simple rules of behavior, or which are the sociocultural processes that underlie this phenomenon. We review the evidence for the existence of group-level rhythmic patterns that result from social interactions and argue that the complexity of group dynamics can lead to temporal regularities that cannot be predicted from the individual periodicities: an emergent collective rhythm. Moreover, we use this interpretation of the literature to discuss how taking into account the sociocultural niche in which individuals develop can help explain the seemingly divergent results that have been reported on the social influences and consequences of interpersonal coordination. We make recommendations on further research to test these arguments and their relationship to the feeling of belonging and assimilation experienced during group dynamics.

Short- and long-term dynamics of the physiological and behavioral response to heat stress and thymol supplementation in Japanese quail

Organisms have evolved endogenous timing systems that enable them to predict temporal changes and to coordinate complex internal processes. However, temporal dynamics of biological responses are most often ignored in fields such as dietary supplementation of farm animals exposed to artificial environmental challenges. Herein, we hypothesized that the potential for thymol (2-isopropyl-5-methylphenol) to alleviate physiological and behavioral consequences of heat stress is time-dependent on both long-term (i.e. weeks) and short-term (i.e. within day) time scales. First, during 3-weeks adult female Japanese quail (Coturnix japonica) were exposed daily to 9h of increased environmental temperature (34.2 ± 0.1 °C). Controls remained at standard temperatures (23.6 ± 0.1 °C). Simultaneously, half received thymol dietary supplementation and the other half a control basal diet. On day 4, both thymol and heat stress decreased body weight and feed intake respect to controls (basal, standard temperature). After three weeks, feed intake recovered for thymol groups. Therefore, we performed a second experiment focused on the critical first week of treatment, sampling variables three times a day. The beneficial effects of thymol supplementation were mainly observed during the morning, including prevention of high respiratory rates and reduction in the weight of droppings induced by heat stress, and increased walking under both temperatures. In summary, thymol's potential for alleviating heat stress consequences is time-dependent, and can be conceived as an emergent property resulting from the complex interplay between the dynamics of the biological response to thymol and heat stress. Findings highlight the importance of considering time-related factors when developing supplementation protocols to mitigate environmental challenges.

C. elegans episodic swimming is driven by multifractal kinetics

Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.

An appreciation of the prescience of Don Gilbert (1930-2011): master of the theory and experimental unravelling of biochemical and cellular oscillatory dynamics

We review Don Gilbert's pioneering seminal contributions that both detailed the mathematical principles and the experimental demonstration of several of the key dynamic characteristics of life. Long before it became evident to the wider biochemical community, Gilbert proposed that cellular growth and replication necessitate autodynamic occurrence of cycles of oscillations that initiate, coordinate and terminate the processes of growth, during which all components are duplicated and become spatially re-organised in the progeny. Initiation and suppression of replication exhibit switch-like characteristics, that is, bifurcations in the values of parameters that separate static and autodynamic behaviour. His limit cycle solutions present models developed in a series of papers reported between 1974 and 1984, and these showed that most or even all of the major facets of the cell division cycle could be accommodated. That the cell division cycle may be timed by a multiple of shorter period (ultradian) rhythms, gave further credence to the central importance of oscillatory phenomena and homeodynamics as evident on multiple time scales (seconds to hours). Further application of the concepts inherent in limit cycle operation as hypothesised by Gilbert more than 50 years ago are now validated as being applicable to oscillatory transcript, metabolite and enzyme levels, cellular differentiation, senescence, cancerous states and cell death. Now, we reiterate especially for students and young colleagues, that these early achievements were even more exceptional, as his own lifetime's work on modelling was continued with experimental work in parallel with his predictions of the major current enterprises of biological research.

Aggressive dominance can decrease behavioral complexity on subordinates through synchronization of locomotor activities

Social environments are known to influence behavior. Moreover, within small social groups, dominant/subordinate relationships frequently emerge. Dominants can display aggressive behaviors towards subordinates and sustain priority access to resources. Herein, Japanese quail (Coturnix japonica) were used, given that they establish hierarchies through frequent aggressive interactions. We apply a combination of different mathematical tools to provide a precise quantification of the effect of social environments and the consequence of dominance at an individual level on the temporal dynamics of behavior. Main results show that subordinates performed locomotion dynamics with stronger long-range positive correlations in comparison to birds that receive few or no aggressions from conspecifics (more random dynamics). Dominant birds and their subordinates also showed a high level of synchronization in the locomotor pattern, likely emerging from the lack of environmental opportunities to engage in independent behavior. Findings suggest that dominance can potentially modulate behavioral dynamics through synchronization of locomotor activities.

Sperm physiology varies according to ultradian and infradian rhythms

The spermatozoon must be physiologically prepared to fertilize the egg, process called capacitation. Human sperm samples are heterogeneous in their ability to capacitate themselves, which leads to variability between samples from the same or different donors, and even along the seasons. Here we studied sperm variation in the capacitation state according to the ability of capacitated spermatozoa to acrosome react upon stimulation (% ARi) and to be recruited by chemotaxis (% Chex). Both indirect indicators of sperm capacitation increased along the incubation time with fluctuations. Those capacitated sperm recruited by chemotaxis showed an ultradian rhythm with a cycle every 2 h, which might be influenced by unknown intrinsic sperm factors. Two infradian rhythms of 12 months for the % ARi and of 6 months for % Chex were observed, which are associated with the joint action of temperature and photoperiod. Thus, to avoid false negative results, human sperm samples are recommended to be incubated for a long period (e.g. 18 h) preferably in spring time. This innovative point of view would lead to better comprehend human reproductive biology and to think experimental designs in the light of sperm cyclicity or to improve sperm aptitude for clinical purposes.

Temporal metabolic partitioning of the yeast and protist cellular networks: the cell is a global scale-invariant (fractal or self-similar) multioscillator

Britton Chance, electronics expert when a teenager, became an enthusiastic student of biological oscillations, passing on this enthusiasm to many students and colleagues, including one of us (DL). This historical essay traces BC's influence through the accumulated work of DL to DL's many collaborators. The overall temporal organization of mass-energy, information, and signaling networks in yeast in self-synchronized continuous cultures represents, until now, the most characterized example of in vivo elucidation of time structure. Continuous online monitoring of dissolved gases by direct measurement (membrane-inlet mass spectrometry, together with NAD(P)H and flavin fluorescence) gives strain-specific dynamic information from timescales of minutes to hours as does two-photon imaging. The predominantly oscillatory behavior of network components becomes evident, with spontaneously synchronized cellular respiration cycles between discrete periods of increased oxygen consumption (oxidative phase) and decreased oxygen consumption (reductive phase). This temperature-compensated ultradian clock provides coordination, linking temporally partitioned functions by direct feedback loops between the energetic and redox state of the cell and its growing ultrastructure. Multioscillatory outputs in dissolved gases with 13 h, 40 min, and 4 min periods gave statistical self-similarity in power spectral and relative dispersional analyses: i.e., complex nonlinear (chaotic) behavior and a functional scale-free (fractal) network operating simultaneously over several timescales.

The fractal organization of ultradian rhythms in avian behavior

Living systems exhibit non-randomly organized biochemical, physiological, and behavioral processes that follow distinctive patterns. In particular, animal behavior displays both fractal dynamics and periodic rhythms yet the relationship between these two dynamic regimens remain unexplored. Herein we studied locomotor time series of visually isolated Japanese quails sampled every 0.5 s during 6.5 days (>10⁶ data points). These high-resolution, week-long, time series enabled simultaneous evaluation of ultradian rhythms as well as fractal organization according to six different analytical methods that included Power Spectrum, Enright, Empirical Mode Decomposition, Wavelet, and Detrended Fluctuation analyses. Time series analyses showed that all birds exhibit circadian rhythms. Although interindividual differences were detected, animals presented ultradian behavioral rhythms of 12, 8, 6, 4.8, 4 h and/or lower and, irrespective of visual isolation, synchronization between these ultradian rhythms was observed. Moreover, all birds presented similar overall fractal dynamics (for scales ∼30 s to >4.4 h). This is the first demonstration that avian behavior presents fractal organization that predominates at shorter time scales and coexists with synchronized ultradian rhythms. This chronobiological pattern is advantageous for keeping the organism’s endogenous rhythms in phase with internal and environmental periodicities, notably the feeding, light-dark and sleep-wake cycles.