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PubMed1998

Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. I. Alpha and beta event-related desynchronization.

Human scalp EEG studies have shown that event-related desynchronization (ERD) in the alpha (8-13 Hz) and beta (15-25 Hz) bands may be used to detect functional activation of sensorimotor cortex. However, in most previous studies somatotopy has not been examined in detail and brief, self-paced movements, focusing on the planning of motor output, have been used. We recorded electrocorticographic (ECoG) signals in five clinical subjects during a visual-motor decision task that was designed to activate the representations of different body parts in sensorimotor cortex. To focus more on execution of motor output than on its planning, subjects were instructed to make sustained isometric muscle contractions in different body parts (tongue protrusion, fist-clenching or foot dorsiflexion) in response to randomized visual stimuli depicting each action. ECoG spectral analysis utilized a mixed-effects analysis of variance model in which within-trial temporal dependencies were taken into account, and the magnitude and statistical significance of alpha and beta ERDs were mapped onto a surface rendering of each subject's brain MRI. Cortical electrical stimulation was performed in all subjects for clinical purposes, and the resulting maps of sensorimotor function were compared with those generated by ECoG spectral analysis. During the early phases of the motor responses, alpha ERD commonly occurred in a diffuse spatial pattern that was not somatotopically specific. During the late phases, the spatial pattern of alpha ERD usually became more focused and somatotopically specific. Maps of alpha ERD were closer to cortical stimulation maps when alpha ERD was sustained throughout the late phases of the motor responses. Thus, the topography of alpha ERD more resembled traditional somatotopy when its temporal profile approximated that of the motor response. The topography of beta ERD was often more discrete and somatotopically specific than that of alpha ERD, but beta ERD was often transient and sometimes absent. Sometimes, unilateral limb movement produced sustained alpha and beta ERD over bilateral sensorimotor cortices, with overlapping patterns for different body parts. The topographical spread of alpha ERD beyond expected functional-anatomical boundaries during early (and sometimes late) phases of motor responses invites a re-examination of traditional assumptions about sensorimotor functional neuroanatomy, as well as the role of alpha ERD as an index of cortical activation. We agree with others that the somatotopic representations of different body parts overlap more than previously thought. Also, unilateral limb movements may be associated with both contralateral and ipsilateral activation of sensorimotor cortex. We conjecture that alpha ERD may reflect activity within a broad synaptic network with distributed cortical representations.

Adult↗

PubMed2005

[Landscape ecological planning of Jiaozuo city].

With the application of the principles of landscape ecology and the techniques of geographic information systems, the landscape of Jiaozuo city was divided into six types, i. e., farmland, garden plot, woodland, residential and industrial area, waters, and others. The landscape diversity, dominance, fragmentation, and isolation indexes were calculated by models and GIS to analyze the spatial patterns of these landscape types. Based on the optimization of landscape spatial patterns, a pattern for developing a rational and natural ecosystem in Jiaozuo city was proposed, i. e., keeping four or five large natural patches, planning small artificial green patches, linking the large and small patches by various corridors to ensure the ecosystem inside the city to circulate well, combining residential areas properly to form a urban troop with Jiaozuo town as the center and with seven surrounding towns joined through highways to form a network city pattern. After doing these, urban built-up areas could be linked each other, and inlayed in a natural ecological matrix. This pattern could strengthen the ecological connection, raise the stability of the ecosystem, and maintain the balance of urban ecological system.

China↗

PubMed1997

Spatial chain patterns of intra-urban migration.

"This research analyzes quantitatively the track of individual chain-type migration of many residents to determine how they move in response to changes in their lives, i.e., whether there is spatial regularity on the chain patterns of intra-urban migration. The study area for this research is the industrial city of Yokkaichi, Japan. The study helps us to understand the state of intra-urban migration at the non-aggregate level for all residents during a 15-year period. Special attention is given to the age at which a resident relocates, and to the interval between two successive movements, i.e., the stationary period."

Age Factors↗

PubMed1997

GABAergic modulation of hippocampal population activity: sequence learning, place field development, and the phase precession effect.

A detailed biophysical model of hippocampal region CA3 was constructed to study how GABAergic modulation influences place field development and the learning and recall of sequence information. Simulations included 1,000 multicompartmental pyramidal cells, each consisting of seven intrinsic and four synaptic currents, and 200 multicompartmental interneurons, consisting of two intrinsic and four synaptic currents. Excitatory rhythmic septal input to the apical dendrites of pyramidal cells and both excitatory and inhibitory input to interneurons at theta frequencies provided a cellular basis for the development of theta and gamma frequency oscillations in population activity. The fundamental frequency of theta oscillations was dictated by the driving rhythm from the septum. Gamma oscillation frequency, however, was determined by both the decay time of the gamma-aminobutyric acid-A (GABA(A))-receptor-mediated synaptic current and the overall level of excitability in interneurons due to alpha-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid and N-methyl-D-aspartate (NMDA)-receptor-gated channel activation. During theta population activity, total GABA(B)-receptor-mediated conductance levels were found to gradually rise and fall in rhythmic fashion with the predominant population frequency (theta rhythm). This resulted in periodic GABA(B)-receptor-mediated suppression of excitatory synaptic transmission at recurrent collaterals (intrinsic fibers) of pyramidal cells and suppression of inhibitory synaptic transmission to both pyramidal cells and interneurons. To test the ability of the model to learn and recall temporal sequence information, a completion task was employed. During learning, the network was presented a sequence of nonorthogonal spatial patterns. Each input pattern represented a spatial "location" of a simulated rat running a specific navigational path. Hebbian-type learning was expressed as an increase in postsynaptic NMDA-receptor-mediated conductances. Because of several factors including the sparse, asymmetric excitatory synaptic connections among pyramidal cells in the model and a sufficient degree of random "background" firing unrelated to the input patterns, repeated simulated runs resulted in the gradual emergence of place fields where a given cell began to respond to a contiguous segment of locations on the path. During recall, the simulated rat was placed at a random location on the previously learned path and tested to see whether the sequence of locations could be completed on the basis of this initial position. Periodic GABA(B)-receptor-mediated suppression of excitatory and inhibitory transmission at intrinsic but not afferent fibers resulted in sensory information about location being dominant during early portions of each theta cycle when GABA(B)-receptor-related effects were highest. This suppression declined with levels of GABA(B) receptor activation toward the end of a theta cycle, resulting in an increase in synaptic transmission at intrinsic fibers and the subsequent recall of a segment of the entire location sequence. This scenario typically continued across theta cycles until the full sequence was recalled. When the GABA(B)-receptor-mediated suppression of excitatory and inhibitory transmission at intrinsic fibers was not included in the model, place field development was curtailed and the network consequently exhibited poor learning and recall performance. This was, in part, due to increased competition of information from intrinsic and afferent fibers during early portions of each theta cycle. Because afferent sensory information did not dominate early in each cycle, the current location of the rat was obscured by ongoing activity from intrinsic sources. (ABSTRACT TRUNCATED)

Animals↗

PubMed2005

Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging.

BACKGROUND: Cancer mortality maps are used by public health officials to identify areas of excess and to guide surveillance and control activities. Quality of decision-making thus relies on an accurate quantification of risks from observed rates which can be very unreliable when computed from sparsely populated geographical units or recorded for minority populations. This paper presents a geostatistical methodology that accounts for spatially varying population sizes and spatial patterns in the processing of cancer mortality data. Simulation studies are conducted to compare the performances of Poisson kriging to a few simple smoothers (i.e. population-weighted estimators and empirical Bayes smoothers) under different scenarios for the disease frequency, the population size, and the spatial pattern of risk. A public-domain executable with example datasets is provided. RESULTS: The analysis of age-adjusted mortality rates for breast and cervix cancers illustrated some key features of commonly used smoothing techniques. Because of the small weight assigned to the rate observed over the entity being smoothed (kernel weight), the population-weighted average leads to risk maps that show little variability. Other techniques assign larger and similar kernel weights but they use a different piece of auxiliary information in the prediction: global or local means for global or local empirical Bayes smoothers, and spatial combination of surrounding rates for the geostatistical estimator. Simulation studies indicated that Poisson kriging outperforms other approaches for most scenarios, with a clear benefit when the risk values are spatially correlated. Global empirical Bayes smoothers provide more accurate predictions under the least frequent scenario of spatially random risk. CONCLUSION: The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of mortality rates into the mapping of risk values and the quantification of the associated uncertainty, while being easier to implement than a full Bayesian model. The availability of a public-domain executable makes the geostatistical analysis of health data, and its comparison to traditional smoothers, more accessible to common users. In future papers this methodology will be generalized to the simulation of the spatial distribution of risk values and the propagation of the uncertainty attached to predicted risks in local cluster analysis.

Journal Article↗

PubMed2005

Local forest environment largely affects below-ground growth, clonal diversity and fine-scale spatial genetic structure in the temperate deciduous forest herb Paris quadrifolia.

Paris quadrifolia (herb Paris) is a long-lived, clonal woodland herb that shows strong differences in local population size and shoot density along an environmental gradient of soil and light conditions. This environmentally based structuring may be mediated by differences in clonal growth and seedling recruitment through sexual reproduction. To study the interrelationship between environmental conditions and spatial patterns of clonal growth, the spatial genetic structure of four P. quadrifolia populations growing in strongly contrasting sites was determined. In the first place, plant excavations were performed in order to (i) determine differences in below-ground growth of genets, (ii) investigate connectedness of ramets and (iii) determine total genet size. Although no differences in internode length were found among sites, clones in moist sites were much smaller (genets usually consisted of 1-3 interconnected shoots, most of them flowering) than genets in dry sites, which consisted of up to 15 interconnected shoots, the majority of which were vegetative. Further, amplified fragment length polymorphism (AFLP) markers were used. Clonal diversity was higher in populations located in moist and productive ash-poplar forests compared to those found in drier and less productive mixed forest sites (G/N: 0.27 and 0.14 and Simpson's D: 0.84 and 0.75, respectively). Patterns of spatial population genetic structure under dry conditions revealed several large clones dominating the entire population, whereas in moist sites many small genets were observed. Nevertheless, strong spatial genetic structure of the genet population was observed. Our results clearly demonstrate that patterns of clonal diversity and growth form of P. quadrifolia differ among environments. Limited seedling recruitment and large clone sizes due to higher connectedness of ramets explain the low clonal diversity in dry sites. In moist sites, higher levels of clonal diversity and small clone sizes indicate repeated seedling recruitment, whereas strong spatial genetic structure suggests limited seed dispersal within populations.

Belgium↗

PubMed2000

New Frontiers in the Study of Dispersal and Spatial Analysis of Epidemics Caused by Species in the Genus Phytophthora.

Diseases caused by species in the genus Phytophthora are responsible for significant economic losses on a wide range of host plants. Spatial pattern is one of the most characteristic ecological properties of a species, and reflects environmental and genetic heterogeneity and reproductive population growth acting on the processes of reproduction, dispersal, and mortality. Species of Phytophthora can be dispersed either in soil, via surface water movement down rows, from rain splash dispersal, by air, or via movement by humans or invertebrate activity. Dispersal results in patchiness in patterns of disease or inoculum in soil. In this chapter we discuss the mechanisms of dispersal of members of this important genus and describe several methods that can be used to statistically analyze data for which spatial coordinates are known. The methods include testing spatial autocorrelation for binary data or continuous data, semivariograms, and regression models for spatial data. The goal of spatial pattern analysis is to gain an understanding of the mechanisms of dispersal of propagules and to sort out the physical and biological factors that are important for spread of plant pathogens and ultimately, for disease management.

Phytophthora diseases↗

PubMed1980

A developmental study of interhemispheric transfer in children aged five to ten.

In light of anatomical evidence that the corpus callosum does not become fully mature until about age 10, the present study attempted to find evidence of a developmental increase in the efficiency with which information is transferred between the 2 hands (hemispheres). Children were tested at ages 5, 7, and 9 on a battery of 4 tasks which measured the interhemispheric transfer of information necessary to (1) perform a simple size discrimination, (2) reproduce a temporal pattern, (3) reproduce a linear motor movement, and (4) reconstruct a 2-dimensional spatial pattern. All tasks were performed without visual guidance and utilized unilateral tactual and/or kinesthetic input and a 1-handed response. 2 tasks--the motor movement task and the spatial pattern task--showed evidence of a developmental increase in interhemispheric transfer, but the developmental pattern seen on these 2 tasks differed. Possible reasons for the between-task differences are discussed as well as their possible developmental implications.

Cerebral Cortex↗

PubMed2004

On the logic of hypothesis testing in functional imaging.

Statistics is nowadays the customary language of functional imaging. It is common to express an experimental setting as a set of null hypotheses over complex models and to present results as maps of p-values derived from sophisticated probability distributions. However, the growing interest in the development of advanced statistical algorithms is not always paralleled by similar attention to how these techniques may regiment the ways in which users draw inferences from their data. This article investigates the logical bases of current statistical approaches in functional imaging and probes their suitability to inductive inference in neuroscience. The frequentist approach to statistical inference is reviewed with attention to its two main constituents: Fisherian "significance testing" and Neyman-Pearson "hypothesis testing". It is shown that these conceptual systems, which are similar in the univariate testing case, dissociate into two quite different methods of inference when applied to the multiple testing problem, the typical framework of functional imaging. This difference is explained with reference to specific issues, like small volume correction, which are most likely to generate confusion in the practitioner. Further insight into this problem is achieved by recasting the multiple comparison problem into a multivariate Bayesian formulation. This formulation introduces a new perspective where the inferential process is more clearly defined in two distinct steps. The first one, inductive in form, uses exploratory techniques to acquire preliminary notions on the spatial patterns and the signal and noise characteristics. The (smaller) set of likely spatial patterns generated is then tested with newer data and a more rigorous multiple hypothesis testing technique (deductive step).

Algorithms↗

PubMed2003

Trafficking and activation of eNOS in epithelial cells.

In mammalian cells, formation of nitric oxide (NO) is catalysed by a family of enzymes termed NO synthases (NOS). There are three isoforms of this enzyme, NOS I, II and III. NOS III was originally cloned and identified in endothelial cells; thus this isoform is commonly called endothelial NOS (eNOS). The physiological role of NO produced by eNOS has been documented in most organs, including the brain, lung, cardiovascular system, kidney, liver, gastrointestinal tract and reproductive organs. The bioavailability of NO in these tissues is determined by the balance between its rate of production and degradation. The rate of NO production by eNOS is ultimately dependent on the activity of the enzyme. In the past years, co- and post-translational modifications such as myristoylation, palmitoylation, phosphorylation, protein-protein interactions and subcellular localization have been shown to play an important role in determining eNOS activity. In order to maintain specificity, the production of most signalling molecules occurs in an organized spatial and temporal pattern. Spatial localization of eNOS has been shown to be regulated by different mechanisms that control its targeting from the Golgi apparatus to the plasma membrane, correct compartmentalization within the membrane, and internalization from the plasma membrane to the cytoplasm after activation. Thus, regulated localization and trafficking of eNOS may be essential in regulating enzyme activity and maintaining the spatial and temporal organization of NO signalling in different cell types.

Cell Membrane↗

PubMed1999

Linking spontaneous activity of single cortical neurons and the underlying functional architecture.

The relation between the activity of a single neocortical neuron and the dynamics of the network in which it is embedded was explored by single-unit recordings and real-time optical imaging. The firing rate of a spontaneously active single neuron strongly depends on the instantaneous spatial pattern of ongoing population activity in a large cortical area. Very similar spatial patterns of population activity were observed both when the neuron fired spontaneously and when it was driven by its optimal stimulus. The evoked patterns could be used to reconstruct the spontaneous activity of single neurons.

Action Potentials↗

PubMed2006

Intrinsic activated microglia map to the peri-infarct zone in the subacute phase of ischemic stroke.

BACKGROUND AND PURPOSE: Microglial activation is an important component of the neuroinflammatory response to ischemic stroke. Experimental studies have outlined such patterns temporally and spatially. In vivo studies in stroke patients have relied on positron emission tomography and (R)-PK11195, a ligand that binds peripheral benzodiazepine binding sites. In this study we sought to establish temporal and spatial patterns of microglial activation in ischemic stroke with particular emphasis on a defined peri-infarct zone. METHODS: Using this technique, we studied carotid territory ischemic stroke patients in 3 time windows up to 30 days after ictus. Controls were studied in a single session. [11C](R)-PK11195 injection was followed by 3-dimensional acquisition over 60 minutes. Cerebral blood volume (CBV) was measured afterward with the use of standard C15O paradigms. Analysis employed the reference tissue model in which ipsilateral cerebellum was used to generate parametric binding potential maps corrected for CBV. Data were coregistered to T1-based MRI. Using control data to identify 99% confidence limits, a region of interest analysis was applied to identify significant binding in core infarction, contralateral hemisphere, and within a defined peri-infarct zone. RESULTS: Four patients (mean age, 66 years) were imaged across 9 sessions. Four age-matched controls were studied. Within this model, ipsilateral cerebellum was validated as a reference tissue. With the use of control-derived confidence limits and correction for CBV, significant binding potential rises were identified beyond 72 hours and extending to 30 days in core infarction, contralateral hemisphere, and peri-infarct zone. CONCLUSIONS: In ischemic stroke patients, minimal activation of microglia is seen before 72 hours. Beyond this, binding potential rises in core infarction, peri-infarct zone, and contralateral hemisphere to 30 days. This may represent a therapeutic opportunity that extends beyond time windows traditionally reserved for neuroprotection.

Acute Disease↗

PubMedDate not supplied

Optical recording analysis of olfactory response of the procerebral lobe in the slug brain.

We studied the oscillatory properties and the olfactory responses of the procerebral (PC) lobe of the cerebral ganglion in the terrestrial mollusc Limax marginatus. The PC lobe, a central olfactory organ in Limax, is a highly interconnected network of local interneurons that receives olfactory inputs from the inferior and superior tentacular noses. We used an optical recording technique with a voltage-sensitive dye to record the activity of the PC lobe from either the posterior or the dorsal surface. The recordings revealed that almost all PC interneurons showed spontaneous oscillatory activities that had been entrained with each other. Upon presentation to the nose of odors to which the slugs had been aversively conditioned, the basal level of the oscillation changed biphasically. In the early phase of the response, depolarization in the basal level of the oscillation occurred in one or more belt-shaped regions parallel to the dorsoventral axis. In the late phase of the response, hyperpolarization of basal potential level of the PC lobe oscillations occurred in a wider area. Such spatial and temporal modulation was not observed when the unpaired control odors were presented to the preparation, whereas the same preparations responded to the aversively conditioned stimuli. Thus, it was considered that the spatial and temporal response in the basal level of oscillation was specific to the aversively conditioned odors. Furthermore, the spatial pattern of the depolarization modulation in the early phase was repeatable in multiple trials performed using the same odor, although different odors produced different spatial patterns of the modulation. From these results, we conclude that in the PC lobe learned odors are represented as spatial and temporal activity patterns of oscillators that constitute a coherent network.

Animals↗

PubMed1999

Spatial and temporal patterns of evoked neural activity from auditory nuclei in chick brainstem detected by optical recording.

In order to detect the spatial patterning of the auditory projection of the embryonic chick brainstem, anatomical methods such as orthograde transport of horseradish peroxidase have been used. However, these methods do not provide the continuous information required about the absolute value and time-course of varying neural excitement. Furthermore, the use of conventional electrophysiological methods makes it difficult or impossible to detect the transmembrane voltage change because of the small size and fragility of the cells of the young chick brainstem. We thus believe that optical measurement of membrane potential might be beneficial in circumstances where electrodes are difficult to use for reasons of cell size, complexity, or membrane topology. In the present work, we therefore examined the feasibility of an optical method for delineating the synaptic transmission of afferent input in the auditory nuclei in the chick brainstem. We used embryonic chick brainstem slice preparations featuring an intact eighth nerve, and loaded depolarizing square current pulses from tungsten microelectrodes into the auditory nerve for stimulation of these preparations. In this approach, we used a multiple-site optical recording system comprising a 16 x 16-element photodiode array and a voltage sensitive dye (NK-2761). Neural excitation evoked by stimulation to the left auditory nerve was propagated to the dorsal side of the brainstem. This area in which the optical signal was detected is located on the auditory nuclei. Since the physiological spatial patterning of the auditory nerve projection could be roughly estimated by the optical technique, the technique is considered useful for examining the electrical activity generated from auditory nuclei in the brainstem. This is the first report of spatial patterning of auditory neurons in the embryonic chick brainstem generated through optical recording.

Animals↗

PubMed2026

Spectral Transforms as a Tool to Optimize Digital Phenotyping in Biological Images.

Modern livestock breeding has mastered genotyping. Genome-wide association studies, genomic selection, and SNP arrays enable genetic merit prediction at lower cost. However, phenotyping remains the bottleneck, as manual measurement is slow, expensive, subjective, and unable to capture spatial or temporal trait organization. Digital phenotyping via artificial intelligence could resolve this, but deep learning requires thousands of labelled examples, impractical when phenotyping cost itself limits datasets to hundreds of individuals. This creates a paradox: AI could accelerate phenotyping but requires large numbers of samples to train the models. Here, we demonstrate that integrating computer vision with machine learning offers sample-efficient digital phenotyping using eggshell colour as a model system. Rather than learning features from scratch (deep learning), we engineer physically motivated features via Wavelet transforms that decompose images into multi-scale spatial components. Wavelet features captured 14.2 percentage points more variance (R2 = 0.976 vs. 0.834, p < 0.001) than standard colorimetry, with 50% better sample efficiency (achieving at n = 60 what colorimetry required n = 120). Variance decomposition revealed 77% of discriminative capacity derives from spatial patterns (bands, spots, gradients) invisible to scalar averages. Additionally, we identified "cryptic phenotypes" (3.3%) where spatial patterns contradicted average colour, cases where colorimeters failed but Wavelets succeeded. The underlying principle-that spatial decomposition can recover organizational information lost by scalar averaging-may be applicable to other traits with spatial or temporal structure, such as marbling, dermatitis, or pigmentation rhythms, although whether comparable performance gains would be observed remains to be tested empirically. Hence, for breeding programs implementing genomic selection, computer vision-based digital phenotyping captures complex trait variation without massive training datasets, addressing the bottleneck that increasingly limits genetic progress as genotyping becomes trivial.

Wavelet transform↗

PubMed1987

Reading twisted text: implications for the role of saccades.

These experiments investigated how the quality of saccadic skill limits the acquisition of visual information during a reading task. Subjects read text in which the spatial pattern of saccades was varied by reversing the order of words in a line, the order of letters in a word, or both. Some of these transformations drastically altered the customary visual appearance of words. To distinguish visual from oculomotor influences on reading, letters, in some conditions, were rotated 180 deg to produce text in which the customary visual appearance of words was destroyed while the order of words and letters remained unchanged. We found that the directional pattern of saccades had relatively modest effects on reading speed under the instruction to read accurately. The size of saccades had large effects on reading speed. Text in which familiar patterns of letters were destroyed, either by changing letter-order or letter-orientation, was read by sequences of small (less than 30') saccades made to look at every letter, or every alternate letter. Separate tests of letter recognition showed that these small saccades were necessary because recognition of letters drops sharply as a function of eccentricity in the absence of familiar letter patterns. Frequent small saccades slowed reading in that durations of the pauses before saccades increased when saccade size fell below 30-60'. We found a similar pattern of increased saccadic latency with decreasing saccade size when subjects used saccades to track a point whose motion mimicked their own reading eye movement patterns. The long latencies before small saccades in the point-tracking task showed that saccadic programming difficulties contributed to the long pause durations before small saccades during reading. The observed difficulty in programming small saccades means that valid inferences about the duration of visual or cognitive processes cannot be drawn from the temporal pattern of saccades unless the relative difficulty and time required to program different spatial patterns of saccades is taken into account.

Eye Movements↗

PubMed2003

Metapopulation dynamics with quasi-local competition.

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.

Competitive Behavior↗

PubMed1990

Spatial harmonics and pattern specification in early Drosophila development. Part I. Bifurcation sequences and gene expression.

Molecular probes have now provided an unprecedented wealth of detail revealing the changing spatial patterns of gene products in early Drosophila development. This is examined for dynamic properties which might provide insights into the underlying behaviour of the patterning process. What emerges is that transcripts and protein products of members of the major categories of zygotically active genes involved in segmentation pass through transient spatial patterns that are suggestive of harmonic sequences arising from spatial frequency-doubling bifurcations. That is to say, these patterns are typically periodic in space and show a doubling in the number of domains of spatial expression as development proceeds. One of these patterns reflects the primary functional role of the gene in the establishment of the spatial pattern. The different categories of segmentation gene pass through these transients at different rates, those with the longest functional wavelength progressing most slowly. Each gene in a category has its own unique phase relationship to other members, as well as particular variations on the harmonic sequence theme. The result is that the developing embryo experiences a spatial hierarchy of phase-shifted patterning influences that span the range from the whole embryo to single segments, providing progressively more spatial resolution in the patterning process. The characteristic transients and the dynamic relationships between genes of the different categories suggest that gene products expressed in longer-wavelength patterns act as bifurcation parameters on the dynamic system generating the next shorter wavelength category. Such parametric influences are known to result in frequency-doubling bifurcations in Turing reaction-diffusion systems. A general model is proposed of a hierarchically-nested set of quasi-autonomous dynamic systems involving gene activities that can generate the progressively finer spatial order that emerges during embryogenesis. This model has implications for the general stability properties of evolving epigenetic systems.

Animals↗