Hysteresis Dynamics,Bursting Oscillations and Evolution to Chaotic Regimes

This article describes new aspects of hysteresis dynamics which have been uncovered through computer experiments. There are several motivations to be interested in fast-slow dynamics. For instance, many physiological or biological systems display different time scales. The bursting oscillations which can be observed in neurons, beta-cells of the pancreas and population dynamics are essentially studied via bifurcation theory and analysis of fast-slow systems (Keener and Sneyd, 1998; Rinzel, 1987). Hysteresis is a possible mechanism to generate bursting oscillations. A first part of this article presents the computer techniques (the dotted-phase portrait, the bifurcation of the fast dynamics and the wave form) we have used to represent several patterns specific to hysteresis dynamics. This framework yields a natural generalization to the notion of bursting oscillations where, for instance, the active phase is chaotic and alternates with a quiescent phase. In a second part of the article, we emphasize the evolution to chaos which is often associated with bursting oscillations on the specific example of the Hindmarsh-Rose system. This evolution to chaos has already been studied with classical tools of dynamical systems but we give here numerical evidence on hysteresis dynamics and on some aspects of the wave form. The analytical proofs will be given elsewhere.     

Structural Relaxation During Drying and Rehydration of Food Materials��the Water Effect and the Origin of Hysteresis

The state of water in foodstuffs is a guiding principle in food design, and the equilibrium concept of water activity (Aw) is ubiquitous. It is regarded as a primary variable or “hurdle” in preservation technology, and a key variable influencing chemical reaction during storage. However, the amount of water in any system differs as function of water activity depending whether it is determined by water sorption or desorption. Even though this hysteresis behaviour has already been described in the literature, no physical interpretation of its origin has yet been proposed with respect to detailed molecular organisation. This work shows, for two different food powders, gluten and a milk-based product that the hysteresis disappears when either go through their glass transition. A more complete DSC analysis for gluten during different sorption/desorption cycles demonstrates that the hysteresis is dependent on the ageing of the material, which evolves in the glassy state and is induced by structural relaxation.     

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.     

Historical demography of a wild lemur population (Propithecus verreauxi) in southwest Madagascar

The human colonization of Madagascar is associated with the extinction of numerous lemur species. However, the degree to which humans have negatively influenced the historical population dynamics of extant lemur species is not well understood. This study employs genetic and demographic analyses to estimate demographic parameters relating to the historical population dynamics of a wild lemur population, Verreaux’s sifaka (Propithecus verreauxi). The genetic analyses are used to determine whether this population experienced a historically recent (i.e., within the last 2000 years) population bottleneck, as well as to estimate the historical population growth rate and the timing of any changes in population size in the past. In addition, a retrospective demographic analysis is used to determine sources of variation and covariation in the sifaka life cycle and how variation in life-cycle transitions contributes to variation in population growth rate. The genetic analyses indicate that the sifaka population did not experience a recent population bottleneck; however, the historical population growth rate was negative, indicating that the ancestral population size was much larger than the current size. The timing of the ancestral population decline has a point estimate of 2300 years ago, but with large credible intervals: 3611–1736 years ago. This point estimate corresponds with the first evidence for human arrival to Madagascar. Climatic variation has also likely influenced past (and current) population dynamics due to stochastic annual rainfall patterns and climatic desiccation, the latter of which began in southwestern Madagascar around 4000 years ago. Variation in the survival of 2-year-old animals as well as large adult females makes the largest contribution to variation in population growth rate. In the absence of more explicit models pertaining to historical population dynamics, it is difficult to attribute the negative population growth rate of this species solely to a single factor (e.g., hunting, habitat destruction).     

Fishing through time: population dynamics of plaice (Pleuronectes platessa) in the Kattegat–Skagerrak over a century

Over the past century, advances in technology and historical events such as climate change have resulted in significant changes in the exploitation pattern, population sizes and the potential yield of fish stocks. These variations provide contrast in the data that improves our knowledge on population dynamics and our ability to develop management strategies for long-term sustainable exploitation. In this study, we use a standardized scientific trawl survey to obtain a historical time series (1901–2007) of relative abundance, recruitment and size structure for plaice in the Kattegat–Skagerrak. Our work extends the available time series by more than 80 years so that the evaluation of trends is more informative than is possible from the current assessment. We show that the current adult biomass is approximately 40% of the maximum observed at the beginning of the century and during the 1960s. The average maximum individual length has been reduced by 10 cm over the studied time period. An analysis of trends in mean length indicates that fishing mortality was variable during the first half of the century and has increased steadily over the past 20 years. Recruitment has been the highest on record during recent years, suggesting that the alleged link between coastal environmental degradation and juvenile survival is of low importance. The overall findings of our work will provide managers with a historical perspective on the population dynamics of the stock, which will support the long-term management of plaice in the Kattegat–Skagerrak.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Genome-wide analysis of the structure of the South African Coloured Population in the Western Cape

Admixed populations present unique opportunities to discover the genetic factors underlying many multifactorial diseases. The geographical position and complex history of South Africa has led to the establishment of the unique admixed population known as the South African Coloured. Not much is known about the genetic make-up of this population, and the historical record is patchy. We genotyped 959 individuals from the Western Cape area, self-identified as belonging to this population, using the Affymetrix 500k genotyping platform. This resulted in nearly 75,000 autosomal SNPs that could be compared with populations represented in the International HapMap Project and the Human Genome Diversity Project. Analysis by means of both the admixture and linkage models in STRUCTURE revealed that the major ancestral components of this population are predominantly Khoesan (32–43%), Bantu-speaking Africans (20–36%), European (21–28%) and a smaller Asian contribution (9–11%), depending on the model used. This is consistent with historical data. While of great historical and genealogical interest, this information is also essential for future admixture mapping of disease genes in this population.     

Estimation of population firing rates and current source densities from laminar electrode recordings

This model study investigates the validity of methods used to interpret linear (laminar) multielectrode recordings. In computer experiments extracellular potentials from a synaptically activated population of about 1,000 pyramidal neurons are calculated using biologically realistic compartmental neuron models combined with electrostatic forward modeling. The somas of the pyramidal neurons are located in a 0.4 mm high and wide columnar cylinder, mimicking a stimulus-evoked layer-5 population in a neocortical column. Current-source density (CSD) analysis of the low-frequency part (<500 Hz) of the calculated potentials (local field potentials, LFP) based on the ‘inverse’ CSD method is, in contrast to the ‘standard’ CSD method, seen to give excellent estimates of the true underlying CSD. The high-frequency part (>750 Hz) of the potentials (multi-unit activity, MUA) is found to scale approximately as the population firing rate to the power 3/4 and to give excellent estimates of the underlying population firing rate for trial-averaged data. The MUA signal is found to decay much more sharply outside the columnar populations than the LFP.     

Order Parameter Dynamics of Body-scaled Hysteresis and Mode Transitions in Grasping Behavior

Several experimental studies have shown that human grasping behavior exhibits a transition from one-handed to two-handed grasping when to-be-grasped objects become larger and larger. The transition point depends on the relative size of objects measured in terms of human body-scales. Most strikingly, the transitions between the two different behavioral ‘modes’ of grasping exhibit hysteresis. That is, one-to-two hand transitions and two-to-one hand transitions occur at different relative object sizes when objects are scaled up or down in size. In our study we approach body-scaled hysteresis and mode transitions in grasping by exploiting the notion that human behavior in general results from self-organization and satisfies appropriately-defined order parameter equations. To this end, grasping transitions and grasping hysteresis are discussed from a theoretical perspective in analogy to cognitive processes defined by Haken’s neural network model for pattern recognition. In doing so, issues such as the exclusivity of grasping modes, biomechanical constraints, mode-mode interactions, single subject behavior and population behavior are explored.     

Population history reconstruction,based on craniometry I. The backtracking approach and initial results

This study reports on the initial results of an investigation into the taxonomic efficacy of different subsets of craniometric variables. Taxonomic performances of such subsets were evaluated in relation to a benchmark of expected results. This evaluation was allowed through the use of recent Eskaleut skeletal groups having an essentially known population historical relationship to one another. Exploratory data analysis revealed a provisionally optimal trait subset, i.e. one which produced a matrix of inter-group generalized biological distances in closest congruence with the “expected” model. This taxonomically efficacious, 18-trait battery (B18) was derived from a larger (B36) subset, comprised of 36 traits identified as the most powerful multivariate discriminators. In formulating the B18 battery, the B36 parent list was culled of measurements identified as being the most prone to error or noise stemming from imprecision, lack of morphometric efficacy, age regression, and minor cranial deformation. Also, and importantly, adaptive traits were culled if they covered craniofacial regions which are physiologically responsive, or biomechanically related, to the function of mastication. These results are gratifying, for they suggest that if proper consideration is given to various quality control criteria, computed intergroup biological distances have a greater likelihood of expressing information on population history relationships. While the provisional results reported here on taxonomic optimality are particular to the region under study, the underlying (“Backtracking”) approach is generalizable. Steps are outlined whereby this approach to population history reconstruction can be undertaken for any geographic region which meets stated prerequisites concerning materials and methods.     

‘Good-genes’ and ‘compatible-genes’ effects in an Alpine whitefish and the information content of breeding tubercles over the course of the spawning season

Abies ziyuanensis is a highly endangered fir species endemic to South China. Unlike other Abies species that are distributed in areas with cold climates, A. ziyuanensis is restricted to several isolated island-like localities at subtropical mountains. In this study, we used dominant amplified fragment length polymorphism (AFLP) and co-dominant simple sequence repeats (SSR) markers to infer the genetic structure of A. ziyuanensis. Seven populations consisting of 139 individuals were sampled across their whole distribution. A. ziyuanenesis has a relatively low level of genetic variation, with a mean genetic diversity per population (He) of 0.136 (AFLP) and 0.337 (SSR), which is lower than that of other reported endemic species based on the same kind of marker. We observed high population differentiation, with Gst = 0.482 (AFLP) and Fst = 0.250 (SSR), among the seven populations. AMOVA also detected significant differentiation among populations (Φst (AFLP) = 0.550 and Φst (SSR) = 0.289) and among regions (Φct (AFLP) = 0.139 and Φct (SSR) = 0.135) in both marker types. Both ongoing evolutionary forces (e.g., genetic drift resulting from small population size) and historical events (e.g., population contraction and fragmentation during and after the Quaternary glacial cycles) may have contributed to the genetic structure in A. ziyuanensis.     

A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system

A quantitative, physiology-based model of the ascending arousal system is developed, using continuum neuronal population modeling, which involves averaging properties such as firing rates across neurons in each population. The model includes the ventrolateral preoptic area (VLPO), where circadian and homeostatic drives enter the system, the monoaminergic and cholinergic nuclei of the ascending arousal system, and their interconnections. The human sleep-wake cycle is governed by the activities of these nuclei, which modulate the behavioral state of the brain via diffuse neuromodulatory projections. The model parameters are not free since they correspond to physiological observables. Approximate parameter bounds are obtained by requiring consistency with physiological and behavioral measures, and the model replicates the human sleep-wake cycle, with physiologically reasonable voltages and firing rates. Mutual inhibition between the wake-promoting monoaminergic group and sleep-promoting VLPO causes ;;flip-flop' behavior, with most time spent in 2 stable steady states corresponding to wake and sleep, with transitions between them on a timescale of a few minutes. The model predicts hysteresis in the sleep-wake cycle, with a region of bistability of the wake and sleep states. Reducing the monoaminergic-VLPO mutual inhibition results in a smaller hysteresis loop. This makes the model more prone to wake-sleep transitions in both directions and makes the states less distinguishable, as in narcolepsy. The model behavior is robust across the constrained parameter ranges, but with sufficient flexibility to describe a wide range of observed phenomena.     

Single generation cycles and delayed feedback cycles are not separate phenomena

We study a simple model for generation cycles, which are oscillations with a period of one or a few generation times of the species. The model is formulated in terms of a single delay-differential equation for the population density of an adult stage, with recruitment to the adult stage depending on the intensity of competition during the juvenile phase. This model is a simplified version of a group of models proposed by Gurney and Nisbet, who were the first to distinguish between single-generation cycles and delayed-feedback cycles. According to these authors, the two oscillation types are caused by different mechanisms and have periods in different intervals, which are one to two generation times for single-generation cycles and two to four generation times for delayed-feedback cycles. By abolishing the strict coupling between the maturation time and the time delay between competition and its effect on the population dynamics, we find that single-generation cycles and delayed-feedback cycles occur in the same model version, with a gradual transition between the two as the model parameters are varied over a sufficiently large range. Furthermore, cycle periods are not bounded to lie within single octaves. This implies that a clear distinction between different types of generation cycles is not possible. Cycles of all periods and even chaos can be generated by varying the parameters that determine the time during which individuals from different cohorts compete with each other. This suggests that life-cycle features in the juvenile stage and during the transition to the adult stage are important determinants of the dynamics of density limited populations.     

The importance of control populations for the identification and management of genetic diversity

A fundamental criterion for recognizing species or populations as potentially endangered is the presence/absence of genetic diversity. However, the lack of control populations in many studies of natural systems deprives one from unambiguous criteria for evaluating the genetic effects of small population size and its potential effects on fitness. In this study, I present an example of how the lack of adequate controls may lead to erroneous conclusions for understanding the role that population size may play in the preservation of genetic diversity and fitness of natural populations. The genetic analysis of a population of greater prairie chickens from Illinois, USA, between two time periods (1974–1987 and 1988–1993) in which the studied population experienced a substantial reduction in size and fitness showed no apparent associations between population size and genetic diversity. However, genetic analysis of museum specimens from early this century indicated that Illinois prairie chickens had originally higher levels of genetic diversity, which suggest the Illinois population was already bottlenecked by the 1970s. This study emphasizes the importance of using historical controls to evaluate the temporal dynamics of genetic variability in natural populations. The large number of museum collections worldwide may provide a valuable source of genetic information from past populations, particularly in species currently endangered as a result of human activities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Unprecedented long-term genetic monomorphism in an endangered relict butterfly species

Multi-locus monomorphism in microsatellites is practically non-existent, with one notable exception, the island fox (Urocyon littoralis dickeyi) population on San Nicolas island off the coast of southern California, having been called “the most monomorphic sexually reproducing animal population yet reported”. Here, we present the unprecedented long-term monomorphism in relict populations of the highly endangered Parnassius apollo butterfly, which is protected by CITES and classified as “threatened” by the IUCN. The species is disjunctly distributed throughout the western Palaearctic and has occurred in several small remnant populations outside its main distribution area. We screened 78 individuals from 1 such relict area (Mosel valley, Germany) at 16 allozyme and 6 microsatellite loci with the latter known to be polymorphic in this species elsewhere. From the same area, we also genotyped 55 museum specimens sampled from 1895 to 1989 to compare historical and present levels of genetic diversity. However, none of all these temporal populations yielded any polymorphism. Thus, present and historical butterflies were completely monomorphic for the same fixed allele. This is the second study to report multi-locus monomorphism for microsatellites in an animal population and the first one to prove this monomorphism not to be the consequence of recent factors. Possible explanations for our results are a very low long-term effective population size and/or a strong historic bottleneck or founder event. Since the studied population has just recovered from a recent population breakdown (second half of twentieth century) and no signs of inbreeding depression have been detected, natural selection might have purged the population of weakly deleterious alleles, thus rendering it less susceptible to the usual negative corollaries of high levels of homozygosity and low effective population size.     

GABAergic disinhibition changes the recovery cycle of bat inferior collicular neurons

This study examines the contribution of GABAergic inhibition to the discharge pattern and recovery properties of 110 bat inferior collicular neurons by means of bicuculline application to their recording sites. When stimulated with single pulses, 74 (67%) neurons discharged one or two impulses (phasic responders), 19 (17%) discharged three to ten impulses (phasic bursters) and 17 (16%) discharged impulses throughout the entire stimulus duration (tonic responders). Bicuculline application changed phasic responders into phasic bursters or tonic responders, increased the number of impulses by 10–2000% and shortened the response latency of most neurons. When stimulated with pairs of sound pulses, the recovery cycles of these neurons can be described as: (1) long inhibition (n = 49, 45%); (2) short inhibition (n = 41, 37%); and (3) fast recovery (n = 20, 18%) based upon the 50% recovery time that was either longer than 20 ms, between 10 and 20 ms or shorter than 10 ms. Bicuculline application shortened the 50% recovery time of most neurons by 11–2350% allowing them to respond to pairs of sound pulses at very short interpulse intervals. These data demonstrate that GABAergic inhibition contributes significantly to auditory temporal processing. Accepted: 18 April 1997     

Emergent oscillations in networks of stochastic spiking neurons

Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework.     

The Loss of Genetic Diversity in Sichuan Taimen as Revealed by DNA Fingerprinting

Species endangerment often derives from the “endangerment” of genetic diversity, thus loss of genetic diversity is an important cause of species extinction. Since historical specimens were unavailable, previous studies mainly described the genetic diversity status in the current population rather than the loss of genetic variation over time. In this study, we collected samples during1998–1999 and obtained historical specimens from 1957 to 1958. Based on the two sets of fish, we determined the changes in genetic diversity of Sichuan taimen using DNA fingerprinting. The differences in genetic parameters between the present samples and historical taimens revealed their loss of genetic variation. As a result, the existing populations have lower viability, and proper management has to be implemented to preserve genetic diversity.     

Biogeography and conservation in Southeast Asia: how 2.7 million years of repeated environmental fluctuations affect today’s patterns and the future of the remaining refugial-phase biodiversity

Understanding the historical biogeography of this global biodiversity hotspot is as important to long-term conservation goals as ecology and evolution are to understanding current patterns and processes. Today’s geography is, however, misleading and typical of only ~2% of the last million years; >90% of that time the region’s land area was 1.5–2.0 times larger as mean sea levels were 62 m below today’s, climates were cooler, and extensive forests and savanna covered the emerged Sunda plains. The region’s land area varied two-fold as sea levels fluctuated up to ±50 m with each of ~50 Pleistocene glacial cycles, and forests expanded and contracted with oscillations in land area and seasonality. This dynamic geographic history is relevant to the development of biogeographic regionalism and shows that it is today’s forests that are refugial, not those of the Last Glacial Maximum. This history affects how species will adapt or shift their ranges in response to global warming and further decreases in land area (submergence of low-lying coastal areas) during the 21st century. The alternative is mass species extinction. The biota is also threatened by the continued destruction of forest, destruction of Mekong River flood-pulse based ecosystems, and continued human population growth. Human biogeography will become more important in conservation planning as tens of millions of people who depend on protected area forests, riverine ecosystems, and coastal habitats become environmental refugees. Conservation scientists need to become more involved in regional ecological education, environmental stewardship, and ecosystem-based adaptation to sustain as much as possible of this rich biota and the ecological services it provides.     

Hysteresis in an experimental phytoplankton population

The road to recovery of a deteriorated system is often different, and fraught with more barriers, than the path to the system's deterioration. This phenomenon is called hysteresis, and is inherent to systems presenting alternative stable states. In such systems, the stability of a given state is the product of positive feedback loops. A broad range of natural systems have been predicted to show hysteretic behaviour, but hysteresis has so far only been unambiguously demonstrated at cellular or metabolic levels, not yet at the population or ecosystem level. To extend our understanding of hysteresis at the population level, we performed an experiment on light‐stressed cyanobacteria and found hysteresis between alternative stable states. Furthermore, during the experiment, the cyanobacteria adapted physiologically to high light levels, and deviated from their theoretically predicted pathway of hysteresis, therewith also avoiding extinction. Our experiment confirmed that a population that loses resilience due to deteriorating external conditions can show a delayed – hysteretic – recovery‐response when conditions are improved. This population‐level study also indicates that the slowness of these systems may obscure the true state they are in, which is important to factor into ecosystem monitoring. Additionally, we show that adaptation can drastically alter the systems’ predicted behaviour to ecosystem management. Flexibility of species and slowness should, therefore, be included in the monitoring and prediction of ecosystem responses to environmental changes.