Phase transitions in evolutionary dynamics.

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

Phase transitions in biology: from bird flocks to population dynamics.

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Neural Synchronization, Chimera States and Sleep Asymmetry.

We model the dynamics of sleep states in two connected model brain hemispheres, using groups of coupled individual Hindmarsh-Rose neural oscillators. In a single isloated hemisphere, sleep-promoting neurons and wake-promoting neurons exhibit alternating levels of within-group mean field activity, as well as alternating levels of stochastic phase synchronization, as the system moves between simulated day and night. In a two-hemisphere model, we find differences in the behavior of the sleep-promototing or wake-promoting regions between hemispheres, indicative of chimera-like behavior. We observe phase-cluster states, in which different hemispheres exhibit different bursting dynamics, as well as differences in synchronization between hemispheres. This provides a basis for modeling unihemispheric sleep, which occurs naturally in cetaceans and some bird species, among others, as well as asymmetric sleep, which occurs in human subjects suffering from sleep apnea or experiencing the "first night effect" induced by sleeping in a novel environment.

Phase transition behaviour in yeast and bacterial populations under stress.

Non-equilibrium phase transitions from survival to extinction have recently been observed in computational models of evolutionary dynamics. Dynamical signatures predictive of population collapse have been observed in yeast populations under stress. We experimentally investigate the population response of the budding yeast Saccharomyces cerevisiae to biological stressors (temperature and salt concentration) in order to investigate the system's behaviour in the vicinity of population collapse. While both conditions lead to population decline, the dynamical characteristics of the population response differ significantly depending on the stressor. Under temperature stress, the population undergoes a sharp change with significant fluctuations within a critical temperature range, indicative of a continuous absorbing phase transition. In the case of salt stress, the response is more gradual. A similar range of response is observed with the application of various antibiotics to Escherichia coli, with a variety of patterns of decreased growth in response to antibiotic stress both within and across antibiotic classes and mechanisms of action. These findings have implications for the identification of critical tipping points for populations under environmental stress.

Multiple phase transitions in an agent-based evolutionary model with neutral fitness.

Null models are crucial for understanding evolutionary processes such as speciation and adaptive radiation. We analyse an agent-based null model, considering a case without selection-neutral evolution-in which organisms are defined only by phenotype. Universal dynamics has previously been demonstrated in a related model on a neutral fitness landscape, showing that this system belongs to the directed percolation (DP) universality class. The traditional null condition of neutral fitness (where fitness is defined as the number of offspring each organism produces) is extended here to include equal probability of death among organisms. We identify two types of phase transition: (i) a non-equilibrium DP transition through generational time (i.e. survival), and (ii) an equilibrium ordinary percolation transition through the phenotype space (based on links between mating organisms). Owing to the dynamical rules of the DP reaction-diffusion process, organisms can only sparsely fill the phenotype space, resulting in significant phenotypic diversity within a cluster of mating organisms. This highlights the necessity of understanding hierarchical evolutionary relationships, rather than merely developing taxonomies based on phenotypic similarity, in order to develop models that can explain phylogenetic patterns found in the fossil record or to make hypotheses for the incomplete fossil record of deep time.

Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons.

Chimera states occur when identically coupled groups of nonlinear oscillators exhibit radically different dynamics, with one group exhibiting synchronized oscillations and the other desynchronized behavior. This dynamical phenomenon has recently been studied in computational models and demonstrated experimentally in mechanical, optical, and chemical systems. The theoretical basis of these states is currently under active investigation. Chimera behavior is of particular relevance in the context of neural synchronization, given the phenomenon of unihemispheric sleep and the recent observation of asymmetric sleep in human patients with sleep apnea. The similarity of neural chimera states to neural "bump" states, which have been suggested as a model for working memory and visual orientation tuning in the cortex, adds to their interest as objects of study. Chimera states have been demonstrated in the FitzHugh-Nagumo model of excitable cells and in the Hindmarsh-Rose neural model. Here, we demonstrate chimera states and chimera-like behaviors in a Hodgkin-Huxley-type model of thermally sensitive neurons both in a system with Abrams-Strogatz (mean field) coupling and in a system with Kuramoto (distance-dependent) coupling. We map the regions of parameter space for which chimera behavior occurs in each of the two coupling schemes.

Random walk analysis of ranging patterns of sympatric langurs in a complex resource landscape.

The identification of random walk models to characterize the movement patterns of social groups of primates, and the behavioral processes that give rise to such movement patterns, remain open questions in movement ecology. Movement patterns characterized by a power-law tail with exponent between 1 and 3 (Lévy flight) occur when animals forage on scarce, randomly distributed resources. For primates and similar foragers with memory processes, movements resembling Lévy flights emerge when feeding trees (targets) are randomly distributed and the trunk size distribution of targets follows a power-law. We tested three competing random walk models to describe movement patterns of two langur species. We found a truncated power law to be the most suitable model. The power-law model was poorly supported by the data and hence we found no support for Lévy-flight-like behavior. Moreover, the spatial distribution of feeding trees and the probability distribution of feeding tree size differed from values suggested to result in Lévy-flight-like patterns. We identify intraspecific territoriality, foraging behavior, and the spatial and size distribution of food patches as plausible mechanisms that may have given rise to the observed movement patterns.

Neural computation and the computational theory of cognition.

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism-neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation.

Introduction to Focus Issue: nonlinear and stochastic physics in biology.

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

Synchronization analysis of voltage-sensitive dye imaging during focal seizures in the rat neocortex.

Seizures are often assumed to result from an excess of synchronized neural activity. However, various recent studies have suggested that this is not necessarily the case. We investigate synchronization during focal neocortical seizures induced by injection of 4-aminopyridine (4AP) in the rat neocortex in vivo. Neocortical activity is monitored by field potential recording and by the fluorescence of the voltage-sensitive dye RH-1691. After removal of artifacts, the voltage-sensitive dye (VSD) signal is analyzed using the nonlinear dynamics-based technique of stochastic phase synchronization in order to determine the degree of synchronization within the neocortex during the development and spread of each seizure event. Results show a large, statistically significant increase in synchronization during seizure activity. Synchrony is typically greater between closer pixel pairs during a seizure event; the entire seizure region is synchronized almost exactly in phase. This study represents, to our knowledge, the first application of synchronization analysis methods to mammalian VSD imaging in vivo. Our observations indicate a clear increase in synchronization in this model of focal neocortical seizures across a large area of the neocortex; a sharp increase in synchronization during seizure events was observed in all 37 seizures imaged. The results are consistent with a recent computational study which simulates the effect of 4AP in a neocortical neuron model.

Mutation size optimizes speciation in an evolutionary model.

The role of mutation rate in optimizing key features of evolutionary dynamics has recently been investigated in various computational models. Here, we address the related question of how maximum mutation size affects the formation of species in a simple computational evolutionary model. We find that the number of species is maximized for intermediate values of a mutation size parameter mu; the result is observed for evolving organisms on a randomly changing landscape as well as in a version of the model where negative feedback exists between the local population size and the fitness provided by the landscape. The same result is observed for various distributions of mutation values within the limits set by mu. When organisms with various values of mu compete against each other, those with intermediate mu values are found to survive. The surviving values of mu from these competition simulations, however, do not necessarily coincide with the values that maximize the number of species. These results suggest that various complex factors are involved in determining optimal mutation parameters for any population, and may also suggest approaches for building a computational bridge between the (micro) dynamics of mutations at the level of individual organisms and (macro) evolutionary dynamics at the species level.

Stochastic resonance and the evolution of Daphnia foraging strategy.

Search strategies are currently of great interest, with reports on foraging ranging from albatrosses and spider monkeys to microzooplankton. Here, we investigate the role of noise in optimizing search strategies. We focus on the zooplankton Daphnia, which move in successive sequences consisting of a hop, a pause and a turn through an angle. Recent experiments have shown that their turning angle distributions (TADs) and underlying noise intensities are similar across species and age groups, suggesting an evolutionary origin of this internal noise. We explore this hypothesis further with a digital simulation (EVO) based solely on the three central Darwinian themes: inheritability, variability and survivability. Separate simulations utilizing stochastic resonance (SR) indicate that foraging success, and hence fitness, is maximized at an optimum TAD noise intensity, which is represented by the distribution's characteristic width, sigma. In both the EVO and SR simulations, foraging success is the criterion, and the results are the predicted characteristic widths of the TADs that maximize success. Our results are twofold: (1) the evolving characteristic widths achieve stasis after many generations; (2) as a hop length parameter is changed, variations in the evolved widths generated by EVO parallel those predicted by SR. These findings provide support for the hypotheses that (1) sigma is an evolved quantity and that (2) SR plays a role in evolution.

Imaging cortical electrical stimulation in vivo: fast intrinsic optical signal versus voltage-sensitive dyes.

We applied high-temporal-resolution optical imaging utilizing both the fast intrinsic optical signal (fIOS) and voltage-sensitive dyes (VSDs) to observe the spatiotemporal characteristics of rat somatosensory cortex during electrical stimulation. We find that changes in both the fIOS and VSD signals occur rapidly (<30 ms) after the stimulus is applied, suggesting that both membrane depolarization and transmembrane ion movement occur shortly after the stimulus, preceding the more gradual physiological changes in oxygen consumption revealed by the slower component of the intrinsic optical signal. We find that the VSD signal spreads through a much larger area of cortex than the fIOS.

Patch exploitation in two dimensions: from Daphnia to simulated foragers.

We explore the variability that animals display in their movement choices as they forage in a finite-sized food patch with a uniform food distribution, and present a framework for how these choices may be adjusted to optimize foraging efficiency. Inspired by experimental studies of the zooplankton Daphnia, we model foraging animals as "agents" moving in two dimensions in repeated and successive sequences of hops, pauses, and turns. For Daphnia and other species, critical movement parameters such as hop lengths, pause times, and turning angles are typically reported as probability density functions. Similarly, the agents in our simulations choose their movement parameters at random from such distributions. Each distribution is defined by a characteristic width, which we interpret as a "noise width," available to be tuned for increased foraging efficiency. We investigate the sensitivity of the system by measuring the food gathered by the agents as the turning angle and hop length noise widths are varied. In all cases, we find a maximum in food gathered at some particular value of the noise width in question, suggesting that these results can be considered robust examples of natural stochastic resonance.

Transitions between multistable states as a model of epileptic seizure dynamics.

Epileptic seizures are generally considered to result from excess and synchronized neural activity. Additionally, changes in amplitude and frequency are often seen in local field potential or electroencephalogram recordings during a seizure event. To investigate how seizures initiate, and how dynamical changes occur during seizure progression, we develop a neocortical network model based on a model suggested by Wilson [J. Theor. Biol. 200, 375 (1999)]. We propose a possible mechanism for seizure initiation as a bifurcation, and suggest that experimentally observed changes in field potential amplitude and frequency during the course of a seizure may be explained by noise-induced transitions among multistable states.

Frustration, drift, and antiphase coupling in a neural array.

Synchronization among neurons is critical for many processes in the nervous system, ranging from the processing of sensory information to the onset of pathological conditions such as epilepsy. Here, we study synchronization in an array of neurons, each modeled by a set of nonlinear ordinary differential equations. We find that an array of 20x20 coupled neurons undergoes a series of alternating low and high synchronization states, as measured by phase-locking and frequency entrainment, as the coupling constant is tuned. The role of long-range connections in inducing "small-world networks" has recently been of great interest in many physical and biological problems. Since long-range connections do exist in the brain, we investigated the role of such connections in our neural array. Introducing a biologically realistic percentage of long-range connections has no significant effect on synchronization. We find that it is rather the type of coupling and the total number of connections that determine the synchronization state of the array. We also show that some coupling conditions can lead to frustration in the system, resulting from an inability to simultaneously satisfy conflicting phase requirements. This frustration leads to a drift in the overall behavior of the network, which may offer an explanation for transitions between different types of neural oscillations observed experimentally.

Intrinsic optical signal imaging of neocortical seizures: the 'epileptic dip'.

Focal neocortical seizures, induced by injection of 4-aminopyridine, were imaged in the rat neocortex using the intrinsic optical signal, with incident light at various wavelengths. We observed focal, reproducible and prolonged reflectance drops following seizure onset, regardless of wavelength, in the ictal onset zone. A persistent drop in light reflectance with incident orange light, which corresponds to a decrease in oxygenated hemoglobin, was observed. We describe this phenomenon as an 'epileptic dip' as it is reminiscent of the 'initial dip' observed using the intrinsic optical signal, and also with blood oxygen level-dependent functional magnetic resonance imaging, after normal sensory processing, although with much longer duration. This persistent ictal ischemia was confirmed by direct measurement of tissue oxygenation using oxygen-sensitive electrodes.

Blood volume and hemoglobin oxygenation response following electrical stimulation of human cortex.

Our understanding of perfusion-based human brain mapping techniques relies on a detailed knowledge of the relationship between neuronal activity and cerebrovascular hemodynamics. We performed optical imaging of intrinsic signals at wavelengths sensitive to total hemoglobin (Hbt; which correlate with cerebral blood volume (CBV)) and deoxygenated hemoglobin (Hbr) directly in humans during neurosurgical operations and investigated the optical signals associated with bipolar cortical stimulation at a range of amplitudes. Cortical stimulation elicited a rapid focal increase in Hbr (initial dip) in all subjects. An equally rapid increase in Hbt (<200 ms), with a slightly higher signal-to-noise ratio, was also highly localized for <2 s in spite of the non-columnar nature of the stimulus, after which the signal spread to adjacent gyri. A later decrease in Hbr (>3 s), which is relevant to the blood oxygen level dependent (BOLD) signal, was poorly localized. Increasing the stimulus amplitude elicited a linear increase in the area of the optical signal for Hbt and the initial dip but not the late decrease in Hbr, and a nonlinear increase in optical signal amplitude with a plateau effect for initial dip, Hbt and late decrease in Hbr.

Temporal dependence in uncoupling of blood volume and oxygenation during interictal epileptiform events in rat neocortex.

We investigated the dynamic spatiotemporal relationships of cerebral blood volume (CBV), deoxygenated hemoglobin (Hbr), and light scatter (LS) associated with interictal epileptiform events with multiwavelength optical recording of intrinsic signals and simultaneous field potential recording. Interictal spikes (IISs) were induced with iontophoresis of bicuculline methiodide in rat neocortex. Intrinsic signal changes appeared as early as 100 msec after the IIS at all wavelengths and could be appreciated after only a single IIS. Initially, the largest signal arose from a focal increase in deoxygenation, which lasted for approximately 2 sec, consistent with an "initial dip." An equally early focal increase in CBV had a smaller amplitude than the Hbr signal until >2 sec after the IIS, when its amplitude surpassed that of the Hbr signal but also spread to a larger, less focal area. The most spatially restricted and smallest amplitude signal was produced by LS. A later hyperoxygenation, or increase in blood oxygenation level-dependent signal, was often seen in the draining veins but inconsistently seen in the IIS focus. An inverted optical signal was recorded at all wavelengths from multiple regions in the surrounding cortex within 100 msec of the IIS. We therefore conclude that the IIS induces a rapid increase in metabolic demand, which cannot be met by a rapid, initially focal but small increase in CBV that results in a prolonged increase in Hbr (epileptic dip in oxygenated hemoglobin). The inverted optical signal in the surround arises from a decrease in CBV and a decrease in Hbr, likely resulting from a combination of shunting of CBV to the focus and decreased metabolic demand resulting from decreased neuronal activity, consistent with "surround inhibition."