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PubMed1994

Topographic mapping of the visual evoked potential after source derivation.

Visual Evoked Potentials (VEP) have been considered an important complementary diagnostic method for the study of the physiology of the visual pathways and cortex. It is suggested that topographic maps of Visual Evoked Potentials (VEP) generate information related to the anatomy and physiology of the visual cortex. The source derivation technique applied to electroencephalographic signals has been shown to improve the sensitivity and spatial selectivity of the results. Mapping VEP after source derivation was implemented in order to facilitate the interpretation of the VEP signals and as an aid in identifying the distribution of the sources generating them. The signals were obtained from normal individuals stimulated with full-field and half-field pattern reversal checker-boards. The electrode system used (16 channels) was that proposed by Bodis-Wollner; this system concentrates the electrodes in the scalp areas related to the visual cortex. Signals were sampled simultaneously with a 10-bit A/D converter, saved and, thereafter, processed in an IBM/PC compatible microcomputer. After coherently averaging the responses, source derivation considering inter-electrode distances was applied. It was observed that the spatial spreading of the signals was reduced, leading to an improved spatial selectivity, locating the VEP sources in the expected brain regions and suggesting the existence of electrical dipoles.

Adult↗
PubMed1985

The absence of spread of adaptation between rod photoreceptors in turtle retina.

Adaptation by weak backgrounds and the spatial spread of desensitization between rods was studied in the snapping turtle retina, Chelydra serpentina. Intracellular membrane potentials were recorded from these photoreceptors in an eyecup preparation. The kinetics and sensitivity of rod responses were changed significantly by large, very dim backgrounds. For the twenty-five most sensitive rods where the dark-adapted flash sensitivity, SDF, was greater than 1.0 mV/Rh*, Rh* being the number of effective photo-isomerizations per rod, the background intensity required to halve the amplitude of the linear range response averaged 0.21 Rh* s-1. The time-to-peak of the test responses was reduced up to 50% by these dim backgrounds. The desensitizing effects of full field backgrounds of various intensities on the responses to large test spots were measured. The dependence of incremental flash sensitivity, SF, on background intensity, IB, followed the form (FORMULA: SEE TEXT) where I0 is the background intensity which halved SDF. The same intensity dependence held for slit-shaped background fields that desensitized responses to small test spots. The desensitizing effects of large, very dim flashed and continuous backgrounds took several seconds to appear and decay to dark levels. This in conjunction with the sparsity of photons suggests, that the desensitization from a single photoisomerization can persist for several seconds. A comparison of the desensitizing effects of spot and annular backgrounds revealed that small spot backgrounds superimposed on the centered test spots desensitized rods more effectively than annular fields. This finding held true even when annular patterns produced a greater maintained hyperpolarization in the rods. Thus, there was no unique relationship between desensitization and the steady maintained hyperpolarization evoked by a background field. The dependence of adaptation on distance from the impaled rod was determined with slit-shaped background fields placed at different positions across the rod's receptive field. The desensitizing effect of displaced slit stimuli was found to decline much more rapidly with distance than excitation. Displacing the slit by 20 micron from the centre reduced its desensitizing effect by more than 1 log unit. In contrast, excitation fell to about 80% at the same distance (lambda ranging from 50 to 70 micron). The fall off of desensitization with distance matched the calculated fall off with distance of light scatter from a slit. No difference was noted in the kinetics of test responses in the presence of equally desensitizing, superimposed and displaced slits.(ABSTRACT TRUNCATED AT 400 WORDS)

Adaptation, Ocular↗
PubMedDate not supplied

Electrical interactions via the extracellular potential near cell bodies.

Ephaptic interactions between a neuron and axons or dendrites passing by its cell body can be, in principle, more significant than ephaptic interactions among axons in a fiber tract. Extracellular action potentials outside axons are small in amplitude and spatially spread out, while they are larger in amplitude and much more spatially confined near cell bodies. We estimated the extracellular potentials associated with an action potential in a cortical pyramidal cell using standard one-dimensional cable theory and volume conductor theory. Their spatial and temporal pattern reveal much about the location and timing of currents in the cell, especially in combination with a known morphology, and simple experiments could resolve questions about spike initiation. From the extracellular potential we compute the ephaptically induced polarization in a nearby passive cable. The magnitude of this induced voltage can be several mV, does not spread electrotonically, and depends only weakly on the passive properties of the cable. We discuss their possible functional relevance.

Action Potentials↗
PubMed1999

Longitudinal spread of second messenger signals in isolated rod outer segments of lizards.

1. In vertebrate rods activation of the phototransduction cascade by light triggers changes in the concentrations of at least two diffusible intracellular second messengers (cGMP and Ca2+) whose actions depend on how far they spread from their site of production or entry. To address questions about their spatial spread, cell-attached patch current recording and fluorescence imaging of Calcium Green-dextran were used to measure the longitudinal spread of cGMP and Ca2+, respectively, in functionally intact isolated Gecko gecko lizard rod outer segments under whole-cell voltage clamp. 2. The light-evoked changes in cGMP and Ca2+ concentrations decayed with distance from a site of steady focal activation by two-photon absorption of 1064 nm light with similar decay lengths of approximately 3.5 microm. 3. These results can be understood on the basis of a quantitative model of coupled diffusible intracellular messengers, which is likely to have broad relevance for second messenger signalling pathways in general. 4. The decay length for the spread of adaptation from a site of steady local illumination was about 8 microm, i.e. substantially longer than the decay lengths measured for the spread of cGMP and Ca2+. There are a number of factors, however, that could broaden the apparent relationship between functional changes in the light response and the concentration of a diffusible messenger. For these reasons the measured decay length is an upper limit estimate of the spread of adaptation and does not rule out the possibility that Ca2+ and/or cGMP carry the adaptation signal.

Adaptation, Physiological↗
PubMed2000

Reappraising the apparent costs of attending to two separate visual objects.

Support for object-based accounts of visual attention has been drawn from several different types of effect. One effect is found when observers try to restrict their attention to a particular region of a display. Other regions belonging to the same object are often selected as well, suggesting that attention spreads spatially over entire objects. Another effect is found when judging two visual attributes; performance is often less efficient when the attributes belong to separate objects rather than both belonging to a single object. This latter effect has been taken to imply that only one segmented object can be attended at a time. However, it may instead merely be a variant of the first effect. If, as we assume here, attention spreads to task-irrelevant regions of relevant objects, it will encompass a larger spatial region and more information when judging attributes of two objects rather than one. Here we compared judging one versus two objects, while manipulating whether the two objects occupied a wider extent than the single object condition (as in previous work), or not. Costs were found for judging two objects versus one only when together they occupied a wider spatial extent. We conclude that reported difficulties in attending two objects may be due to attention spreading across the entire spatial extent of objects when judging their parts, rather than a fixed inability to process more than object at a time.

Adult↗
PubMedDate not supplied

Comparison of methods to determine electron pencil beam spread in tissue-equivalent media.

This study has intercompared the predictions of Fermi-Eyges theory for the rms spatial spread (sigma) of an electron pencil beam scattering in muscle-, lung- and bone-equivalent media with those of; two range straggling modifications to the theory, Monte Carlo simulations, and an empirical method based on broad beam penumbra. Systematic differences among the results obtained by these methods for the values of sigma have been identified. Monte Carlo simulations are lower than the predictions of Fermi-Eyges theory for sigma at all depths whereas the broad beam penumbra method results are in reasonable agreement with Fermi-Eyges theory at depths less than approximately 0.7 times the range of the incident electrons. All of the methods investigated have an increasing discrepancy from the predictions of Fermi-Eyges theory with depth, especially close to the end of the electron range. The two range-straggling modifications to Fermi-Eyges theory developed for soft tissue do not agree with either measured or Monte Carlo results for sigma in homogeneous scattering media of lung and bone.

Bone and Bones↗
PubMed1997

Nonlinear processing of tactile information in the thalamocortical loop.

Rats explore tangible objects in a manner such that, at any given moment in time, multiple facial whiskers simultaneously contact the surface of the object. Although both thalamic and cortical neurons responsible for processing such tactile information have large, multiwhisker receptive fields, it remains unclear what kinds of computations can be carried out by these neuronal populations when behaviorally relevant multiwhisker stimuli are used. By simultaneously recording the activity of up to 78 cortical and thalamic neurons per animal, we observed that the magnitude of sensory responses and the spatial spread of ensemble activity increased in a nonlinear fashion according to the extent and spatial orientation of the multiwhisker stimuli. Supralinear responses were seen more frequently with vertically than with horizontally oriented stimuli. These data suggest that thalamocortical interactions in the rat somatosensory system can generate complex spatial transformations of multiwhisker stimuli that go beyond the classic inhibitory interactions previously observed.

Animals↗
PubMedDate not supplied

Estimating exposure to volatile organic compounds from municipal water-supply systems: use of a better computational model.

The Southington, Connecticut, water-supply system is characterized by a distribution network that contains more than 1 700 pipeline segments of varying diameters and construction materials, more than 186 mi (299 km) of pipe, 9 groundwater extraction wells capable of pumping more than 4 700 gal/min (0.2965 m3/s), and 3 municipal reservoirs. Volatile organic compounds, which contaminated the underlying groundwater reservoir during the 1970s, contaminated the water-supply system and exposed the town's residents to volatile organic chemicals. We applied a computational model to the water-supply system to characterize and quantify the distribution of volatile organic compounds in the pipelines, from which we estimated the demographic distribution of potential exposure to the town's residents. Based on results from modeling analyses, we concluded the following: (a) exposure to volatile organic compound contamination may vary significantly from one census block to another, even when these census blocks are adjacent to each other within a specified radius; (b) maximum spatial spread of contamination in a water-distribution system may not occur under peak demand conditions, and, therefore, maximum spatial distribution of the exposed population also may not correspond to peak demand conditions, and (c) use of the proposed computational model allows for a more refined and rigorous methodology with which to estimate census-block-level contamination for exposure assessment and epidemiologic investigations.

Algorithms↗
PubMed2002

Spreading of fatigue-related effects from active to inactive parts in the medial gastrocnemius muscle of the cat.

In the medial gastrocnemius muscle of the decerebrate cat, the spatial spread of fatigue between active and inactive muscle parts was studied. Conditioning fatiguing stimulation (CFS) was applied to a part of the muscle to test whether it had an effect on the contraction efficiency in an unstimulated part. To exclude somato-sympathetic reflexes during CFS, a full rhizotomy of the lumbo-sacral spinal cord was performed. The same ipsilateral ventral root, either L7 or S1, was divided into seven filaments, one of which was used for the test stimulation, and four or five for CFS. The CFS consisted of 12 s sessions of distributed stimulation of five (or four) filaments at a rate of 40 s(-1), the sessions were repeated, every 40 s, 15 or more times. The test consisted of 12 s of regular stimulation at a rate of 10 s(-1), preceded and followed by a single stimulus. The tests applied just after CFS showed a strong decline of both tension and electromyogram (EMG), amounting to only [mean (SD)] 0.45 (0.18) and 0.51 (0.19) (n = 15), respectively, of the corresponding values in the tests before CFS. It thus turned out that depressive fatigue-related effects could spread within the muscle. At the same time, control reactions recorded in the lateral gastrocnemius during stimulation of its cut nerve did not change. Subsequent repetitions of the tests usually revealed a tendency towards restoration. The EMG reactions recovered more quickly than tension. The depression of EMG after CFS was accompanied by a slowing of the constituent M-waves; their latencies decreased during restoration. Distinct changes in the systemic blood pressure were observed during CFS. These changes were usually correlated well with muscle tension changes. The factors possibly underlying the observed effects may include diffusion of metabolites from active to inactive muscle fibres, lowering of the efficiency of neuro-muscular transmission due to squeezing of efferent motor terminals and changes in outer metabolite content, as well as local hypoxia due to increases in intramuscular pressure.

Animals↗
PubMed2000

Fast imaging in two dimensions resolves extensive sources of Ca2+ sparks in frog skeletal muscle.

Ca2+ sparks were monitored by confocal laser-scanning microscopy of fluo-3 at video rates, in fast twitch muscle fibres, stimulated by exposure to caffeine and/or low [Mg2+]. Scanning was in two spatial dimensions ('2D') or 2D plus time, at 4 ms per image frame. Sparks were identified in 2D images of normalized fluorescence by an automatic procedure, which also evaluated the event's location and morphometric parameters. Most sparks were circular, but some were elongated, especially in caffeine. Separation of the spark from circular symmetry was quantified by its eccentricity (length/width - 1). In an internal solution with 0.4 mM [Mg2+], sparks (989 events in 4 cells) had amplitude 0.73, width 1.94 microm, length 2.12 microm and eccentricity not significantly different from 0. Upon application of 1 mM caffeine, length (of 2578 events in the same cells) increased significantly (by 0.41 microm, or 19 %), width increased by 0.18 microm (9 %) and amplitude decreased slightly. The eccentricity became significantly different from 0, and the sparks' long axis predominantly oriented parallel to the plane of the Z disks. More than 10 % of the events in caffeine had length greater than 4 microm, a relatively flat top, and a sharp termination at both ends of the major axis. Additionally, there was only a weak correlation between eccentricity and amplitude. These properties suggest that the elongated events are produced by simultaneous opening of multiple channels within a junction, rather than anisotropic diffusion of Ca2+ or random overlap of round sparks. Elongated events often increased in eccentricity early in their evolution. Then, most remained elongated during their rise and decay, while others spread spatially in the plane of the Z disks. In 1-2 % of the events, the centre of mass migrated in space, over time, at approximately 0.1 microm x ms(-1). These spatio-temporal features require the involvement of multiple release channels, at spatially resolvable locations. Because sources often spread over distances greater than 1 or 2 microm, and arrays of junctional elements (couplons) are at most 1.2 microm long, it must be possible for activation of release to propagate between neighbouring couplons, especially under the influence of caffeine and/or low [Mg2+].

Aniline Compounds↗
PubMed1994

A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems.

The detective quantum efficiency (DQE) is a system parameter that can be used to accurately describe image noise transfer characteristics through many imaging systems. A simpler approach used by some investigators, particularly when evaluating new ideas and system designs, is to describe the system as a series of cascaded stages. Each stage may correspond to either an increase in the number of quanta (e.g., conversion from x-ray to optical quanta in a radiographic screen), or a loss (a detection or coupling probability). The number of secondary quanta at each stage per incident primary quantum is given by the product of all preceding gains, and can be displayed graphically for convenient interpretation. The stage with the fewest quanta is called the "quantum sink," limiting the pixel signal-to-noise ratio to less than the square root of the number of quanta per pixel. This conventional zero-spatial-frequency "quantum accounting diagram" (QAD), however, neglects the spatial spreading of secondary quanta and can seriously underestimate image noise. It is shown that this problem is avoided with the introduction of a spatial-frequency dependent QAD, expressed as the product of the gains and squared modulation-transfer functions (MTF) of each stage. A generalized expression is developed for the DQE of a cascaded imaging system that is dependent only on the gain, gain Poisson excess (related to the variance), and MTF, of each stage. A direct relationship is then shown to exist between the DQE and values in the QAD. The QAD of a hypothetical system consisting of a charge-coupled device camera and a scintillating screen is evaluated as an illustrative example. The conventional zero-frequency analysis suggests two quantum sinks occur with approximately equal importance: one in the number of x rays, and one in the number of optical quanta. The spatial-frequency dependent analysis, however, shows the optical quantum sink becomes severe and dominates at nonzero frequencies. The necessary increase in gain or optical numerical aperture required to prevent the optical quantum sink for spatial frequencies of interest is determined from the QAD analysis. The visual impact of this nonzero spatial-frequency quantum sink is shown in images generated using a Monte Carlo simulation of the cascading process.

Algorithms↗
PubMed1988

Effects of blur and eccentricity on differential spatial displacement discrimination.

Differential spatial displacement discrimination thresholds were determined for stimuli consisting of blobs with Gaussian spatial and temporal contrast envelopes. The stimuli were presented at detection threshold luminance contrast. The tasks were similar to the two-point discrimination acuity task and the three-dot alignment hyperacuity task. Thresholds were determined as a function of eccentricity along the horizontal meridian of the visual field (from 45 degrees nasal to 65 degrees temporal). The spatial spread or blur parameter of the blobs was adopted as a scale parameter. The results show that the performance of the visual system in differential spatial displacement discrimination tasks becomes progressively more homogeneous for a progressive increase in the blur parameter of the stimuli. Scaling (i) the three-blob alignment results with estimates of the cortical magnification factor and (ii) the two-blob separation discrimination results with their corresponding neural blur parameter shows an impressive isotropy and blur scale-invariance for the mechanisms mediating differential spatial displacement discrimination across the visual field. These results are interpreted in terms of a scaled sampling lattice model of the visual system, in combination with an automatic scale-selection mechanism.

Adult↗
PubMed1993

A quantitative study of the lateral spread of Müller cell responses to retinal lesions in the rabbit.

A wide variety of retinal pathology is associated with an increase in Müller glial cell expression of glial fibrillary acidic protein (GFAP). In this study the time course and spatial spread of the Müller cell GFAP response following argon laser photocoagulation lesions was examined in wholemounted rabbit retina. At 24 hours single focal lesions were surrounded by GFAP positive Müller cell end feet which declined in density with distance but extended as far as 2-3 mm from the lesion. The Müller cell reaction reached a maximal spread of 4-5 mm at 14 to 21 days and had started to contract by 30 days, leaving a core of GFAP positive processes immediately around the lesion site at 60 days. This zone of spread was much larger than the area of disrupted pigment epithelium. Isodensity plots did not reveal any correlation with the trajectory of retinal ganglion cell axons. The spread of reaction was more confined for lesions within the visual streak than in the dorsal or ventral retinal periphery. Multiple lesions within a focal region of retina resulted in a greater density of GFAP reactive end feet with a corresponding greater spread. However, when five to ten lesions were made in a horizontal row, the Müller cells over the entire retina became GFAP immunoreactive. This pan-retinal reaction took several days to spread, peaked at 7-14 days, and contracted back to the primary lesion sites by 2 months. This spread of Müller cell reactivity may be triggered by the diffusion of substances released by injury or it may be due to direct cellular communication. The extensive indirect effect on Müller cells of laser irradiation might be an important component of the clinical effect of laser photocoagulation and indicates a long distance communication mechanism between retinal glia which is poorly understood. This study also shows the importance of the time at which the Müller cell response is assessed.

Animals↗
PubMedDate not supplied

[AIDS epidemic dynamics in the municipality of Rio de Janeiro, Brazil, 1988-1996: Spatial-temporal statistic modeling].

This study uses a spatial-temporal model to analyze the spatial spread of the AIDS epidemic (adult cases) in the municipality of Rio de Janeiro, Brazil, during three periods: 1988-1990, 1991-1993, and 1994-1996. City districts were used as the geographic units of analysis. A spatial analysis was also performed for pediatric AIDS cases due to vertical HIV transmission, according to period of birth, 1985-90 and 1991-96. For total adult AIDS cases, the initial period was characterized by a polygonal cluster located around the harbor area, which expanded from west to east. Among homosexual cases, in situ growth predominated, and a decrease in the intensity of the diffusion process was observed from the second to the final period. Among heterosexual cases, the epidemic displayed a relevant geographic spread, mainly from 1988-1990 to 1991-1993. Among female cases in the final time period, a cluster of high incidence rates was found towards the northwest, including very poor areas. Among pediatric cases in 1991-1996, a significant correlation was found between AIDS incidence rates and poverty levels in the respective municipal districts. The results suggest that a more complete understanding of AIDS spatial-temporal dynamics can make a major contribution to preventive measures.

Acquired Immunodeficiency Syndrome↗
PubMed2001

How predation can slow, stop or reverse a prey invasion.

Observations on Mount St Helens indicate that the spread of recolonizing lupin plants has been slowed due to the presence of insect herbivores and it is possible that the spread of lupins could be reversed in the future by intense insect herbivory [Fagan, W. F. and J. Bishop (2000). Trophic interactions during primary sucession: herbivores slow a plant reinvasion at Mount St. Helens. Amer. Nat. 155, 238-251]. In this paper we investigate mechanisms by which herbivory can contain the spatial spread of recolonizing plants. Our approach is to analyse a series of predator-prey reaction-diffusion models and spatially coupled ordinary differential equation models to derive conditions under which predation pressure can slow, stall or reverse a spatial invasion of prey. We focus on models where prey disperse more slowly than predators. We comment on the types of functional response which give such solutions, and the circumstances under which the models are appropriate.

Animals↗
PubMed1989

A model for spatiotemporal frequency responses in the X cell pathway of the cat's retina.

A linear model is described for the cat eye's signal-processing pathway, from the visual stimulus at the cornea, to cones, to X-type ganglion cells. The model contains elements representing the eye's optics, phototransduction, gain control, spatiotemporal processing by cell layers, and pure delay. Centre-surround antagonism in the model arises through the presence of a centre element producing a small spatial spread of signals, and an antagonistic element producing a larger spread. Two arrangements were tried, feedforward and feedback, in which the antagonistic element's output was subtracted from the centre element's output, and input, respectively. The model was fitted to empirical spatial and temporal frequency responses collected by Frishman et al. (1987), and accounted qualitatively for these data in the feedback, but not the feedforward, arrangement. The model's centre pathway comprises a cascade of low-pass spatial filters, as does the surround pathway. As a consequence, the spatial frequency responses for these two pathways closely approximate Gaussian functions of spatial frequency, and the spatial frequency response of the complete model at low temporal frequency closely matches that of the difference of Gaussians model.

Adaptation, Ocular↗
PubMedDate not supplied

Background contrast modulates kinetics and lateral spread of responses to superimposed stimuli in outer retina.

Surround enhancement (sensitization) is a poorly understood form of network adaptation in which the kinetics of the responses of retinal neurons to test stimuli become faster, and absolute sensitivity of the responses increases with increasing level of steady, surrounding light. Surround enhancement has been observed in all classes of retinal neurons in lower vertebrates except cones, in some primate retinal ganglion cells, and in human psychophysical studies. In theory, surround enhancement could be mediated by two broad classes of mechanisms, which are not mutually exclusive: one in which the kinetics of the transduction linking cone voltage to postsynaptic current in second-order neurons is modulated, and another in which the transformation of postsynaptic current to membrane voltage is modulated. We report here that both classes of mechanism play a role in surround enhancement measured in turtle horizontal cells (HCs). We stimulated the retina by modulating sinusoidally the illuminance of a bar placed at various positions in the HC receptive field. The bar was surrounded by either equally luminant or dim, steady light. Interpretation of responses in the context of a model for the cone-HC network led to the conclusion that the speeding up of response kinetics--due to selective increase in response gain at high temporal frequencies--by surround illuminance is almost completely accounted for by the change in the kinetics of the transduction linking cone membrane potential to HC postsynaptic current. However, surround illuminance also had an additional, surprising effect on the transformation between postsynaptic current and voltage: the space constant for signal spread in the HC network for the dim-surround condition was roughly twice as large as that for the bright-surround condition. Thus, increasing surround illuminance had analogous effects in the spatial and temporal domains: it restricted the time course and the spatial spread of signal. Both effects were dependent on the contrast between the mean bar illuminance and that of the surround, rather than on overall light level. When the stimulus with the bright surround was dimmed uniformly by a neutral density filter, the space constant did not increase, and response gain at high temporal frequencies did not decrease. Pharmacological experiments performed with dopamine and various agonists and antagonists indicated that, although exogenous dopamine can influence surround enhancement, endogenous dopamine does not play an important role in surround enhancement. We conclude that contrast in background light modulates the spatiotemporal properties of signal processing in the outer retina, and does so by a non-dopaminergic mechanism.

Adaptation, Physiological↗
PubMed2000

Modeling and analysis of stochastic invasion processes.

In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyse two basic properties of the invasion. The first property is 'permanence of form' in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, phi which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population.

Animals↗