Mean Nearest-neighbor Distance Research Articles

Habitat structure and animal movement: the behaviour of bumble bees in uniform and random spatial resource distributions.

Foraging organisms (like bumble bees) move between resource points (like flowers) whose natural distributions vary enormously: from hyperdispersed to random to clumped. These differences in habitat structure may significantly influence the fitness of both plant and pollinator. To examine the effect of habitat structure on pollinator movement and fitness, we observed captive worker bumble bees collecting nectar from artificial flowers containing equal volumes of reward and arranged in two spatial configurations: a hexagonal array with constant distances between flowers ("constant"), and an "exploded hexagonal" array, with variable distances between flowers ("variable"). The mean nearest-neighbour distance was the same in both arrays, as was the general hexagonal appearance. The experiment therefore compares how resource dispersion, independent of nearest-neighbour distance, influences bee behaviour. Bees in the variable array showed decreased directionality, higher revisitation frequencies, and greater inter-flower flight distances than shown in the constant array. As a consequence, bees in the variable array had a 19% lower gross rate of nectar collection. Our results suggest that wild-foraging bees should prefer regularly spaced flowers (when all else, including mean nearest-neighbour distance, is equal), and that plants can decrease self-pollination by regular spacing between flowers, inflorescences, or individuals.

Further Evidence of Abnormal Cytoarchitecture of the Entorhinal Cortex in Schizophrenia Using Spatial Point Pattern Analyses

Previous studies have reported cytoarchitectural abnormalities in superficial laminae of rostral portions of the entorhinal cortex in schizophrenia, including decreased densities of neurons, poorly formed layer II neuron islands, and apparent displacement of layer II-type neurons deep into layer III; however, findings have been controversial, given the qualitative nature of the descriptions and the normal heterogeneity of cytoarchitecture of the region. The x, y coordinates of Nissl-stained neurons were mapped in layers II, III, and V of entorhinal subdivision ER in 8 prospectively accrued patients with schizophrenia and 8 nonneuropsychiatric controls. Indices of neuron dispersion, nearest neighbor distances, and effective radius were determined. An abnormally clustered dispersion of neurons in layer III was present in schizophrenics compared to controls along with a reduced neuron effective radius, whereas the mean nearest-neighbor distance was normal. In layer II, there was a significantly increased effective radius, whereas other indices were normal. No between-group differences were noted in layer V for any variable. These data provide further evidence for subtle aberrant cytoarchitecture in superficial laminae of the entorhinal cortex in schizophrenia and are consistent with neurodevelopmental models of abnormal neuronal pruning, “miswiring,” and/or migration in the illness.

Scale of observation and distribution of adult conspecifics: their influence in assessing passive and active settlement mechanisms in the barnacle Balanus crenatus (Brugière)

The settlement behaviour of Balanus crenatus (Brugière) was examined in field experiments in relation to different patterns of distribution of adult conspecifics. The study was carried out in August 1994 in Anse du Petit Mitis, Québec, Canada. Flat panels supporting random, aggregated, and uniform distributions of adult conspecifics or ceramic mimics were moored vertically on 3 lines. Panels were placed at random 2.5 m below the water surface. Settlement only occurred on panels supporting barnacles. Over 30% of the observed settlement occurred on adult conspecifics. ANOVAs showed no significant effects of distribution on number of settlers at the scale of the panel. Settlement tended to become homogenized over the panel with uniform distributions, while it became aggregated on panels with random and aggregated adult distributions. Mean nearestneighbour distances of spat did not vary among spatial patterns tested. When settling on adults, cyprids settled preferentially on the rostrum, facing current flow. A nested ANOVA carried out on the number of spat per adult on a given panel showed no effect of adult distribution. Differences in spat distribution among replicate panels, barnacle individuals, and positions were observed, suggesting that settlement of B. crenatus was affected by variations of the hydrodynamic environment at the scale of the adult barnacle. Flume experiments using inert particles and the same field panels were carried out to determine the position of initial contact on the panel. Comparison of field and flume results suggests that it is the small-scale behaviour taking place after initial contact on the panel and prior to permanent attachment that determines the patterns of spat distribution.

Factors Influencing Burrowing Owl (Speotyto cunicularia) Nest Densities and Numbers in Western Nebraska

-Burrowing owls (Speotyto cunicularia) were studied at 21 prairie dog towns in native prairie and 17 native prairie pastures with badger (Taxidea taxus) burrows in the Nebraska panhandle in the spring and summer from 1989-1991. The number of nesting burrowing owl pairs ranged from 1-20 in prairie dog (Cynomys ludovicianus) towns and from 1-4 in pastures with badger burrows. Burrowing owl densities in small prairie dog towns ( 35 ha) prairie dog towns ranged from 0.9-2.5 owls/ha. Mean nearest-neighbor distance (?SE) in clusters within large (?35 ha) prairie dog towns was 125.0 m + 4.6, whereas the mean distance between owl nests in small towns (<35 ha), where owls did not have the space to cluster, was 105.1 m + 7.4. Mean nearest-neighbor distance for owls nesting in pastures with badger burrows was 240.2 m ? 39.2. No relationship was found between owl numbers and number of active or inactive prairie dog burrows. In 1990 burrowing owl density was inversely related to active burrow density, but no relationship was found in 1991. Burrow availability may be a limiting factor for owls nesting in pastures with badger burrows. As the size (ha) of prairie dog towns increased, burrowing owls occurred in higher numbers but lower densities.

The Role of Tessellation Methods in the Analysis of Three-Dimensional Spatial Point Patterns

This paper concerns the analysis of three-dimensional spatial point patterns using the Dirichlet tessellation. The tessellation method is illustrated by means of a case study in which spatial patterns of chromosomes in cells of a plant hybrid called Leontodon hispidus x L. taraxacoides are investigated. The objective of the analysis is to determine if chromosomes originating from the two species that produce the hybrid occupy separate spatial domains within the cell. The Dirichlet tessellation is used to construct a test for random labelling of chromosome locations by parent species. An alternative test based on the mean nearest-neighbor distance between chromosomes of different types is also illustrated. The tessellation test leads to rejection of the null hypothesis of random labelling whereas the test based on the mean nearest-neighbor distance does not. The reasons for the differences between the results of the two approaches are explored.

Use of Space by Nesting Black-billed GullsLarus bulleri: Behavioural Changes During the Reproductive Cycle

Black-billed Gulls Larus bulleri nesting in seven colonies in braided rivers in New Zealand were studied in 1990. These habitats are subject to frequent floods following heavy rain or snow melts. While a colony contained only incubating birds, the gulls nested close together (mean nearest neighbour distance 45-80 cm in six colonies) but once chicks began to hatch and to wander into nearby territories, families required more space. Parents and families moved outside the original colony and, eventually, to the water's edge. Aggression levels were low for incubating birds, increased for parents with chicks still in the colony and decreased when parents with their chicks moved to the water's edge. Parents with territories at the water's edge benefitted from increased space, lower aggression rates, and decreased food piracy while they were feeding their chicks. For chicks, the advantages were decreased aggression from neighbours and the ability to escape to the water when a ground or aerial predator approached.

The Distribution of Ant Colonies in a Semiarid Landscape: Implications for Community and Ecosystem Processes

We studied the spatial distribution of harvester ants (Pogonomyrmex occidentalis) across multiple scales in the shortgrass-steppe of northeastern Colorado, USA. Using low-level aerial photographs (1: 2000 scale), we mapped the locations of ant colonies in five areas (65-130 ha) that differed in topography and grazing intensity by domestic cattle. Ant colonies were also mapped in field plots to verify data obtained from aerial photographs. Densities of ant colonies were analyzed by subdividing each of the areas by soil map units and 1-ha quadrats. We performed simulations to examine dispersion patterns at different scales using the 1st-10th nearest-neighbor distances (NND). Overall ant densities ranged from 6 to 16 colonies/ha among the five study areas. Local densities varied more widely among 1-ha quadrats (0-50 colonies/ha) and among soils (0-18 colonies/ha). Variability in colony density was greatest in areas with rolling topography and lowest under heavy grazing. Dispersion patterns obtained from the distribution of 1st NND showed regular and clumped departures from random at different parts of the distribution. Over broader scales, analyses of the 1st-10th mean NND showed a regular or random dispersion at the 1st or 2nd NND and a clumped pattern at the 3rd NND and beyond. Across the 1st-10th NND, quantitative patterns of dispersion differed among the five study areas. Ant distributions are likely influenced both by fine-scale factors such as neighborhood interactions and by broad-scale factors such as soils, topography, and grazing. Whether due to natural factors or land use, broad-scale variability in the distribution of ant populations may have important consequences to behavioral, community and ecosystem processes.

Spatial dynamics and impacts of Pissodes terminalis (Coleoptera: Curculionidae) in regenerating stands of lodgepole pine

The spatial distribution of lodgepole pines attacked by Pissodes terminalis Hopping was analysed in spaced and unspaced plots located in the Interior Douglas-fir biogeoclimatic zone in south central British Columbia. The mean area potentially available (APA) described by Voronoi polygons around all attacked trees (7.2 ± 0.2 m 2) was significantly greater than the mean APA of unattacked trees (5.5 ± 0.2 m 2) in the spaced plot. The mean nearest neighbor distance of attacked trees also was significantly greater than that of unattacked trees in the spaced plot. In the unspaced plot, all trees in the plot (attacked and unattacked), and just attacked trees, approached a clumped distribution. In the spaced plot the attack pattern in any given year was clumped, but cumulatively, the trees attacked by P. terminalis approached a random distribution. The largest trees were most likely to be attacked and the most noticeable defect was a crook. Height loss due to weevil attack was 31.4% of the annual potential height increment in the year of attack, and 17% in the year following attack. Trees with ample growing areas are more likely to sustain severe damage due to weevil attacks. Delaying spacing until trees are > 15 years old is recommended to reduce the impact of weevil attack.

Discrimination of fish layers using the three-dimensional information obtained by a split-beam echo-sounder

This study attempts to illustrate the three-dimensional pattern of a “pelagic” and a “benthic” layer of fish using single-target information obtained using a split-beam echo-sounder. Parameters such as the nearest-neighbour distance and separation angle between the two nearest neighbours around a reference fish were used to discriminate between the two layers. The parameters estimated were found to be significantly different between the two layers. The mean nearest-neighbour distance estimated was 6.3 m and 8.8 m for the “benthic” and the “pelagic” layers, respectively, and the mean separation angle between neighbours around a reference fish was 68° and 74°, respectively. The estimated mean target strength (TS) was found to be significantly different for the two layers and conforms to the theoretical TS calculated from the diurnal species and size composition of the layers. It was concluded that illustration and discrimination between the two layers was possible using parameters related to the relative position of targets.

Simulating forest and habitat change in south‐east Alaska with the landscape model PAYSAGE

We used the landscape model PAYSAGE to demonstrate the use of GIS and simulation models for ecosystem management over a portion of Mitkof Island in the Tongass National Forest. The objectives of the study were to: 1) depict the natural heterogeneity in environment and resource distributions across the study area; 2) quantify changes in vegetation and vertebrate habitats (brown creeper, orange‐crowned warbler, marten) during the period of commercial timber harvest (1954 to the present); and 3) simulate likely long‐term changes in vegetation and vertebrate habitat under three management scenarios – the Tongass Forest Plan, the wildlife habitat conservation strategy, and the Pacific Fisheries Task Force strategy. The results indicated that productive forest lands and vertebrate habitats are naturally patchy in the study area due to topography and climate. This natural fragmentation was exacerbated by past logging, which targeted high‐productivity old growth stands. This stand type was reduced in area by 76 per cent from 1954 to 1994. Patch density and mean patch size decreased during this time while mean nearest neighbour distance increased. Simulations of the three management scenarios for a 200‐year period projected relatively minor differences in landscape patterns among the scenarios. This is because the forest plan scenario is relatively restrictive in timber harvest and because most of the area protected in the other two scenarios does nor currently support old growth. We discuss the role of decision‐support tools such as PAYSAGE in adaptive ecosystem management and evaluate limitations of the model.

Spatial properties of retinal mosaics: an empirical evaluation of some existing measures.

Mosaics of neurons are usually quantified by methods based on nearest-neighbor distance (NND). The commonest indicator of regularity has been the ratio of the mean NND to the standard deviation, here termed the 'conformity ratio.' However, an accurate baseline value of this ratio for bounded random samples has never been determined; nor was its sampling distribution known, making it impossible to test its significance. Instead, significance was assessed from goodness-of-fit to a Rayleigh distribution, or from another ratio, that of the observed mean NND to an expected mean predicted by theory, termed the dispersion index. Neither approach allows for boundary effects that are common in experimental mosaics. Equally common are 'missing' neurons, whose effects on the statistics have not been studied. To address these deficiencies, random patterns and real neuronal mosaics were analyzed statistically. Ns independent random-point samples of size Np were generated for 13 Np values between 25 and 6400, where Ns x Np > or = 144,000. Samples were generated with rectangular boundaries of aspect ratio 1:1, 1:5, and 1:10 to examine the influence of sample geometry. NND distributions, conformity ratios, and dispersion indices were computed for the resulting 45,997 independent random patterns. From these, empirical sampling distributions and critical values were determined. NND distributions for small-to-medium, bounded, random populations were shown to differ significantly from Rayleigh distributions. Thus, goodness-of-fit tests are invalid for most experimental mosaics. Charts are presented from which the significance of conformity ratios or dispersion indices can be read directly. The conformity ratio reacts conservatively to extremes of sample geometry, and provides a useful and safe test. The dispersion index is nonconservative, making its use problematic. Tests based on the theoretical distribution of the dispersion index are unreliable for all but the largest samples. Random deletions were also made from 33 real retinal ganglion cell mosaics. The mean NND, conformity ratio, and dispersion index were determined for each original mosaic and 36 independent samples at each of nine sampling levels, retaining between 90% and 10% of the original population. An exclusion radius, based on a spatial autocorrelogram, was also calculated for each of these 10,725 mosaic samples. The mean NND was moderately insensitive to undersampling, rising smoothly. The exclusion radius was remarkably insensitive. The conformity ratio and dispersion index fell steeply, sometimes failing to reach significance while half of the cells still remained. For the same 33 original mosaics, linear regression showed the exclusion radius to be 62 +/- 3% of the mean NND.

Nearest-neighbor statistics in a one-dimensional random sequential adsorption process.

The probability of finding a nearest neighbor at some radial distance from a reference point in many-particle systems is of fundamental importance in a host of fields in the physical as well as biological sciences. We have derived exact analytical expressions for nearest-neighbor probability functions for particles deposited on a line during a random sequential adsorption process for all densities, i.e., up to the jamming limit. Using these results, we find the mean nearest-neighbor distance \ensuremath{\lambda} as a function of the packing fraction, and discuss it in light of recent theorems derived for general ergodic and isotropic packings of hard spheres. \textcopyright{} 1996 The American Physical Society.

SPATIAL DYNAMICS OF A HIMANTHALIA ELONGATA (FUCALES, PHAEOPHYTA) POPULATION

ABSTRACT In dense monospecific stands of plants intraspecific competition usually results in self‐thinning, the concurrent increase in biomass and decrease in density over time. Self‐thinning may also result in a change in the spatial pattern of individuals, but so far the spatial dynamics of marine plants has not been investigated. The brown alga Himanthalia elongata (L.) S. F. Gray forms dense monospecific stands on many northern temperate rocky shores, and various attributes (including its simple form) facilitated the study of the spatial dynamics of this species. The spatial pattern of settling zygotes was examined in the laboratory. In the absence of water movement, substratum heterogeneity, and a point source, zygotes usually settled in clumps rather than randomly. Within the clumps zygotes appeared to be regularly distributed at a scale similar to the size of the zygotes themselves. Furthermore, the clumps themselves seemed to be regularly distributed. On the shore, well‐established stands of “button‐stage” Himanthalia populations were examined during a period of extensive growth and self‐thinning. Individual plants were initially highly regular in spatial pattern but became less so over time. The pattern of plants dying during self‐thinning was also highly regular and probably reflected existing spatial regularity. However, using a hypothesis of mortality as a random event, I found that smaller plants had a less than average survival potential, while larger plants had a greater than average chance. A consideration of the spatial pattern of plants alive at the end of the study revealed regularity at a scale of 2–7 mm but a random spatial pattern at larger scales, which might indicate a small sphere of influence of competing individuals. The best predictor of mean nearest neighbor distances in the populations was mean plant diameter.

The diet and breeding density of Common BuzzardsButeo buteoin relation to indices of prey abundance

The diet and breeding density of 19 pairs of Common Buzzard Buteo buteo¸ were studied in relation to indices of lagomorph and vole abundance during June July 1993 in a range of habitats in southern Scotland. Lagomorphs, voles and birds formed over 70% of the food items analysed from prey remains and pellets collected at nest sites. Indices of prey abundance differed significantly between habitat types. The percentage of lagomorph in Buzzard diet in different localities was significantly correlated with the index of lagomorph abundance; no such correlation was found between the percentage of vole in Buzzard diet and an index of vole abundance. The mean nearest-neighbour distance between Buzzard nests was 1.9 km. There was a significant negative correlation between nearest-neighbour distance and lagomorph abundance. It appears that lagomorphs were the primary prey which influenced the diet and breeding density of Buzzards in the study area.

Court Site Constancy, Dispersion, Male Survival and Court Ownership in the Male Tooth-billed Bowerbird,Scenopoeetes dentirostris(Ptilonorhynchidae)

SummaryThe Tooth-billed Bowerbird Scenopoeetes dentirostris was studied over 16 consecutive display seasons in 50 ha of upland rainforest on the Paluma Range, north Queensland. Eighty-two courts were plotted during the first 12 seasons. Of these an average of 55 were attended each Season and 39 were attended for at least ten consecutive seasons at a mean nearest neighbour distance (NND) of 68 m. Court sites, particularly long-established ones, were more densely distributed on hill-tops and contiguous slopes or ridges. On hill-tops mean NND was 50 m. The dispersion of sites was similar each season. Data indicate the probability of males at courts forming exploded leks on higher topography, but court distributions in any one season showed a dispersion intermediate between an even spread over suitable habitat and true (i.e. exclusive) clumping (true lek). There was an average of one court per ha with an overall mean NND of 61 m. Ownership of 21 court sites involving 24 individually marked males were examined during 16 seasons. Of 24 males involved, 12 survived ten or more seasons, mean annual survival rate was 88% and mean expectancy of further life after banding was 8.1 years. Fidelity by individual males to a single court or court site was extremely high: 71% of marked birds attended only one site during the study. Males with paler mouth pigmentation (presumed to be younger individuals) established courts near, or between, long-established sites, and then sought to occupy the adjacent, long-established court sites of older, black-mouthed, males. The behaviour of younger males attempting to enter groups of immediately neighbouring older males and interactions between the age classes suggested females seek more experienced, older, males as indicated to them by court/male quality and court position/leaf decoration numbers. Several older males showed reluctance to relinquish a traditional court location by returning to one, having been kept from it by tree falls, after several years.

Nearest-neighbor statistics for packings of hard spheres and disks

The probability of finding a nearest neighbor at some radial distance from a given particle in a system of interacting particles is of fundamental importance in a host of fields in the physical as well as biological sciences. A procedure is developed to obtain analytical expressions for nearest-neighbor probability functions for random isotropic packings of hard D-dimensional spheres that are accurate for all densities, i.e., up to the random close-packing fraction. Using these results, the mean nearest-neighbor distance \ensuremath{\lambda} as a function of the packing fraction is computed for such many-body systems and compared to rigorous bounds on \ensuremath{\lambda} derived here. Our theoretical results are found to be in excellent agreement with available computer-simulation data.

Structure of thin cobalt films on Copper studied by EXAFS and analyzed with the FEFF code

A polarization dependent first shell analysis of the EXAFS spectra shows that cobalt grows on Cu(100) and Cu(111) in perfect epitaxy: the mean nearest neighbour distance between cobalt atoms parallel to the surface is 2.55 A (same value as in bulk copper) and the interlayer bond length is 2.50 A. The contraction of the lattice parameter perpendicular to the surface is in agreement with the continuum elasticity theory. The analysis of further neighbour shells is done with the FEFF code (multiple scattering) modified to take into account the structural anisotropy. Simulations are compared to experiments and show anumbiguously that cobalt has an fcc tetragonal structure on Cu 100, but a distorted hcp structure on Cu(111)

Crystallographic structure of cobalt films on Cu(001): elastic deformation to a tetragonal structure

The stable structure of cobalt is hexagonal closed-packed (hcp), but cobalt can be stabilized in a distorted face-centered cubic structure (fcc) by epitaxy on Cu(001). The deviation from the isotropic fcc structure is determined by surface-extended X-ray absorption fine structure (EXAFS). A polarization dependent first shell analysis of the EXAFS spectra shows that the Co/Cu(001) films have a face-centered tetragonal structure (fct): the mean nearest-neighbour distance parallel to the surface is 2.55Å(same value as in bulk copper) and the interlayer bond length is 2.50Å: the films are in perfect epitaxy on copper (001) with a contraction of the lattice parameter perpendicular to the surface of 4%, in agreement with the continuum elasticity theory. A constant tetragonalization is observed for films of 2 to 15 monolayers. A simulation of the EXAFS spectra is also done using the FEFF code. In order to simulate the polarization dependence of the experimental spectra, we have introduced in this theoretical calculation a polarization dependence of the paths (single scattering and multiple scattering ones) based on a plane wave approximation. This simple model gives a good agreement between calculated and experimental polarization dependent EXAFS spectra both on bulk hcp cobalt and on the face-centered tetragonal films Co/Cu(001); this agreement confirms the structure determined from the first shell analysis.

Nest Site Selection by Eared Grebes in Minnesota

This study examined nest site selection within Eared Grebe (Podiceps nigricollis) colonies in terms of nesting synchrony, nearest-neighbor distances, vegetation, exposure, and nest success. Nests in 11 Eared Grebe colonies in Minnesota were initiated over a span of 11-45 days, with most nests in each colony initiated in < 11 days. In each of six colonies studied, mean nearest-neighbor distance of the earliest nests was greater than that of the complete colony. Nearest-neighbor distance tended to decrease with an increase in emergent vegetation density. Early nests seemed to form the skeleton of a neighborhood, with later nests filling in or establishing other neighborhoods. In five of six colonies, clutch sizes were larger in earlier nests. No significant difference in egg volume between early and late nests was apparent in the two colonies studied. Early nests were more successful than were late nests in two of four colonies; center nests were more successful than were edge nests at only one of four colonies. Most nest destruction in this study was caused by waves generated by high winds; < 2% of nests showed evidence of predation.

The three‐dimensional structure of cumulus clouds over the ocean: 1. Structural analysis

Thermal channel (channel 6, 10.4–12.5 μm) images of five Landsat thematic mapper cumulus scenes over the ocean are examined. These images are thresholded using the standard International Satellite Cloud Climatology Project thermal threshold algorithm. The individual clouds in the cloud fields are segmented to obtain their structural statistics which include size distribution, orientation angle, horizontal aspect ratio, and perimeter‐to‐area (PtA) relationship. It is found that the cloud size distributions exhibit a double power law with the smaller clouds having a smaller absolute exponent. The cloud orientation angles, horizontal aspect ratios, and PtA exponents are found in good agreement with earlier studies. A technique also is developed to recognize individual cells within a cloud so that statistics of cloud cellular structure can be obtained. Cell structural statistics are computed for each cloud. Further examination reveals that unicellular clouds are generally smaller (≤ 1 km) and have smaller PtA exponents, while multicellular clouds are larger (≥ 1 km) and have larger PtA exponents. Cell structural statistics are similar to those of the smaller clouds. Each cell is approximated as a quadric surface using a linear least squares fit. Most cells are found to have the shape of a hyperboloid of one sheet. However, about 15% of the cells are best modeled by a hyperboloid of two sheets. Contrary to intuition, less than 1% of the clouds are found to be ellipsoidal. The number of cells in a cloud is found to increase slightly faster than linearly with increasing cloud size. The mean nearest neighbor distance between cells in a cloud, however, appears to increase linearly with increasing cloud size and to reach a maximum when the cloud effective diameter is about 10 km; then it decreases with increasing cloud size. Sensitivity studies of threshold and lapse rate show that neither has a significant impact upon the results. A goodness‐of‐fit ratio is used to provide a quantitative measure of the individual cloud results. Significantly improved results are obtained after applying a smoothing operator, suggesting that eliminating subresolution scale variations with higher spatial resolution may yield even better shape analyses.