Mean Crowding Index Research Articles

Environmental and geographical factors influencing the spread of SARS-CoV-2 over 2 years: a fine-scale spatiotemporal analysis.

Since its emergence in late 2019, the SARS-CoV-2 virus has led to a global health crisis, affecting millions and reshaping societies and economies worldwide. Investigating the determinants of SARS-CoV-2 diffusion and their spatiotemporal dynamics at high spatial resolution is critical for public health and policymaking. This study analyses 194,682 georeferenced SARS-CoV-2 RT-PCR tests from March 2020 and April 2022 in the canton of Vaud, Switzerland. We characterized five distinct pandemic periods using metrics of spatial and temporal clustering like inverse Shannon entropy, the Hoover index, Lloyd's index of mean crowding, and the modified space-time DBSCAN algorithm. We assessed the demographic, socioeconomic, and environmental factors contributing to cluster persistence during each period using eXtreme Gradient Boosting (XGBoost) and SHapley Additive exPlanations (SHAP), to consider non-linear and spatial effects. Our findings reveal important variations in the spatial and temporal clustering of cases. Notably, areas with flatter epidemics had higher total attack rate. Air pollution emerged as a factor showing a consistent positive association with higher cluster persistence, substantiated by both immission models and, to a lesser extent, tropospheric NO2 estimations. Factors including population density, testing rates, and geographical coordinates, also showed important positive associations with higher cluster persistence. The socioeconomic index showed no significant contribution to cluster persistence, suggesting its limited role in the observed dynamics, which warrants further research. Overall, the determinants of cluster persistence remained across the study periods. These findings highlight the need for effective air quality management strategies to mitigate air pollution's adverse impacts on public health, particularly in the context of respiratory viral diseases like COVID-19.

Comparative Spatial Distribution of Sucking Insect-Pest-Complex in Summer and Monsoon Cowpea [Vigna unguiculata (L.) Walp.

Background: Pulse crops are known as an important dietary source of proteins for a major part of the vegetarian population across the globe; especially in India. Legume crops help restoration of soil fertility through symbiotic nitrogen fixation. Spatial distribution is an important aspect as it interprets the interaction between individuals of the species and their habitat. The biological reason of aggregation is highly unpredictable and it depends on behavioural pattern of the insect; therefore, spatial distribution accounts for informative description of organisms. Methods: In order to study the spatial distribution of sucking pests of cowpea, a field trial was laid out during Zaid and Kharif separately at the Instructional Farm of Rajasthan College of Agriculture, Udaipur in 2019 and 2020. Cowpea variety Pusa Komal was cultivated in 6 plots each of 3 m x 3 m with the row to row and plant to plant spacing of 50 cm and 10 cm, respectively. Different distribution pattern were used to determine spatial distribution pattern of species of insect fauna associated with cowpea during the summer and monsoon season. Result: The spatial distribution for most the insect pest complex was contagious during both the respective seasons. All positive IDM (index of clumping) values confirmed the clumping of the pest during the season. The mean crowding index was more than unity, indicated clumped interaction.

Spatiotemporal characteristics and restoration potentiality of seed banks of aquatic plants in Dabokou wetland in Lake Dianchi, southwest China

以滇池典型生态修复区——大泊口水域为研究对象，研究了富营养化高原湖泊种子库时空特征、种子库与地表覆盖水生植被及水环境的相关关系和恢复潜力.利用高密度样方原位观测与温室控制种子萌发实验相结合，基于2014-2016共3年的长期定位研究，分析湖泊平均种子库密度、分布格局及与覆盖水生植物Sørensen相似性关系，结果显示：年平均种子库形成率在20.35%~34.13%之间，种子库密度2014年为546.67粒/m²，2015年为826粒/m²，2016年为1682粒/m²，眼子菜科的篦齿眼子菜（Potamogeton pectinatus L.）、金鱼藻科的金鱼藻（Ceratophyllum demersum L.）等耐污种属对种子库构成和年增长率贡献较大；垂直方向上种子主要分布于深层底泥（5~30 cm）.随着在时间尺度上的延长，种子库分布更为广泛，且规模越来越大（其中500粒/m²以上规模的分布频率显示增多）.离散系数（V/m）与Lloyd平均拥挤指数（m^*）分析显示主要优势群丛（篦齿眼子菜等）为聚集分布，其余为均匀空间分布格局；种子库与水生植被关系评价指标Sørensen相似性系数（SC）研究显示，滇池大泊口平均SC=（0.3628±0.0265），在湖泊湿地类型和草本群落植被类型属性上处于较低水平，即显示目前植物群落演替过程发生较快，耐污先锋种属在恢复进程上占据优势生态位，而历史优势种和对水环境要求较高的物种却未能规模萌发，一定程度上揭示了高原富营养化湖泊种子库中历史优势植被可恢复性的特征及难点.;Based on long-term dynamics and recent in situ observations across three consecutive years, combined with soil seed samples and greenhouse controlled seedling-emergence methods, this study comprehensively analyzed the scale heterogeneity and spatial-temporal characteristics of seed banks under eutrophic and damaged ecosystems in Dabokou wetland, Lake Dianchi. Seventy-five soil cores were collected from sampling sites within the water area. The sites were systematically distributed using the line-transect method. Investigations were completed a total of 3 times from 2014 to 2016. Species-area relationships were then modeled for pattern detection using seed banks density and characteristics; variance/mean ratio (V/m); and Lloyd's index of mean crowding(m^*). Relationships between seed banks and extant vegetation were also evaluated using Sørensen similarity coefficient(SC). Results showed that the seed density increased significantly accounting for 27.24%. Across the three year period, the mean seed bank densities were:546.67 ind./m², 826 ind./m² and 1682 ind./m², respectively for 2014, 2015 and 2016. Additionally, seven species were detected from seed banks, and most of them were distributed in the deeper bottom sludge as compared to the topsoil(0-5 cm). Over the course of time, there were more and more seed banks dispersal and large-scale density amounting to a distribution frequency of 500 ind./m². The seed pattern of Potamogeton pectinatus L. was aggregated while other extant vegetation was evenly distributed as indicated by aforesaid indices of pattern detection. The mean Sørensen similarity coefficient of Dabokou wetland was 0.3628, a low value for a lake wetland and herbosa-ecosystem. Overall, the succession of aquatic plant communities occurred intensely at Lake Dianchi.

闽南渔场游泳动物优势种种群聚集特性

基于2016年4月和10月闽南渔场渔业资源的专项调查数据，运用相对性重要指数、平均拥挤度指数、聚块指数、Cassie指标、Mrisita指数等方法分析闽南渔场游泳动物优势种组成及其种群聚集特性，比较不同的季节、类群和种类及其相互间的聚集状态，探究种群聚集驱动因子，旨在发现闽南渔场游泳动物优势种种群聚集的特征、内在规律和形成机制。结果表明，闽南渔场游泳动物优势种共17种，其中鱼类6种、虾类3种、蟹类4种、头足类4种；鱼类中六指马鲅（Polydactylus se-xfilis）聚集强度最强，头足类中火枪乌贼（Loligo beka）聚集强度最强；虾类和蟹类中春季以哈氏仿对虾（Parapenaeopsis hardwickii）和拥剑梭子蟹（Portunus gladiator）的聚集强度最强，而秋季以鹰爪虾（Trachypenaeus curvirostris）和日本蟳（Charybdis japonica）的聚集强度最强；鱼类、虾类、蟹类和头足类中春季分别以二长棘犁齿鲷（Evynnis cardinali）、鹰爪虾、三疣梭子蟹（P. trituberculatus）和火枪乌贼的平均拥挤度最高，而秋季分别以带鱼（Trichiurus lepturus）、鹰爪虾、拥剑梭子蟹和杜氏枪乌贼（Loligo duvaucelii）的平均拥挤度最高；闽南渔场游泳动物优势种的平均拥挤度呈现出秋季高于春季，虾类、蟹类种群聚集强度大于鱼类、头足类的特点。;The relative importance index, mean crowding index, patchiness index, Cassie index and Mrisita index were used to analyze the composition and aggregation characteristics of the dominant species of nekton in Minnan Fishing Ground using the special investigation data of fishery resources in Minnan Fishing Ground in April and October 2016. The results showed that there were 17 dominant species of nektons in Minnan Fishing Ground, including 6 species of fish, 3 species of shrimp, 4 species of crab and 4 species of cephalopod. Polydactylus se-xfilis had the strongest aggregation intensity among fishes, and Loligo beka had the strongest aggregation intensity among cephalopods in spring and autumn. Parapenaeopsis hardwickii had the largest aggregation intensity among shrimps, and Portunus gladiator had the largest aggregation intensity among crabs in spring. Trachypenaeus curvirostris had the largest aggregation intensity among shrimps, and Charybdis japonica had the largest aggregation intensity among crabs in autumn. In spring, Evynnis cardinali, Trachypenaeus curvirostris, Portunus trituberculatus, Loligo beka had the highest mean crowding among fishes, shrimps, crabs and cephalopods, respectively. In autumn, Trichiurus lepturus, Trachypenaeus curvirostris, P. gladiator and Loligo duvaucelii had the highest mean crowding among fishes, shrimps, crabs and cephalopods, respectively. The average crowding of main dominant species of nekton in autumn was higher than that in spring, and the aggregation intensity of shrimp and crab was higher than that of fish and cephalopod in the Minnan Fishing Ground.

Do species display characteristic intraspecific levels of patchiness in a given habitat type? The case of intertidal seagrass macrobenthos

Intertidal macrobenthic assemblages associated with monospecific stands of Zostera muelleri, Cymodocea serratula, Halodule uninervis and Halophila ovalis seagrasses are known to display uniform spatial patchiness on the Moreton Bay coast of North Stradbroke Island, Queensland, as do those in Z. capensis in the Knysna estuarine bay, South Africa. Thirty-seven historical datasets of these macrobenthic assemblages were re-analysed to assess variation of local patchiness in each of the 18 most common individual assemblage components at each of these localities in terms of three metrics: overall patchiness (Lloyd's index of patchiness), levels of unoccupancy, and variation in abundance across occupied samples (Lloyd's index of mean crowding). Within-site patchiness was not caused by a restriction of individual species to specific subareas but by variation in their local density, particularly by the extent of unoccupied ‘interstitial’ spaces within patches. Especially in the more uniform Queensland conditions, the more common species occurred relatively widely across the whole locality; individual samples from which a given species was absent never themselves formed patches, the number of such samples conforming to points on truncated normal curves of the frequency of occurrence. Of the 36 species investigated, the two most abundant and widespread both in Queensland and in South Africa displayed significant or near-significant uniformity of levels of local patchiness, whilst five showed significantly uniform mean crowding and ten significantly uniform unoccupancy. This is the first demonstration that some species may display a characteristic level of patchiness in a given habitat type.

Measuring aggregation in parasite populations

Aggregation, a fundamental feature of parasite distributions, has been measured using a variety of indices. We use the definition that parasite-host system A is more aggregated than parasite-host system B if any given proportion of the parasite population is concentrated in a smaller proportion of the host population A than of host population B. This leads to indices based on the Lorenz curve such as the Gini index (Poulin's D), coefficient of variation and the Hoover index, all of which measure departure from a uniform distribution. The Hoover index is particularly useful because it can be interpreted directly in terms of parasites and hosts. An alternative view of aggregation is degree of departure from a Poisson (or random) distribution, as used in the index of dispersion and the negative binomial k. These and Lloyd's mean crowding index are reinterpreted and connected back to Lorenz curves. Aggregation has occasionally been defined as the slope from Taylor's law, although the slope appears unrelated to other indices. The Hoover index may be the method of choice when data points are available, and the coefficient of variation when only variance and mean are given.

Spatial distribution of cabbage aphid, Brevicoryne brassicae (L.) and its parasitoid,Diaeretiella rapae (Mc Intosh) under sub-temperate conditions of Himachal Pradesh, India

Cabbage aphid, Brevicoryne brassicae (L) (Aphididae: Hemiptera) is one of the most serious pest of cauliflower throughout the world. Knowledge of spatial distribution is important for developing an effective sampling plan and ultimately for IPM strategies for a given pest. In the present study spatial distribution of B. brassicae and its parasitoid, Diaeretiella rapae (Mc lntosh) (Braconidae: Hymenoptera) was studied on cauliflower ( Brassica oleracea var botrytis ) under sub-temperate conditions of India during 2017. Both B. brassicae and D. rapae assumed activity in the fourth week of January and remained active till May end with peak activity during fourth week of March, 2017. Dispersion indices like variance to mean ratio (Iƒ 2 /X), David-Moore index (IDM = Iƒ 2 /X-1), mean crowding (X*), Lloyd’s mean crowding index (X*/X) and ‘k’ of negative binomial indicated that both the aphid and the parasitoid followed negative binomial distribution throughout the cropping season, Taylor’s power equation was Iƒ 2 = 1.7013X0.5314 for B. brassicae and Iƒ 2 = 2.2057X1.4467 for D. rapae , while Iwao’s patchiness regression equation was X*= 32.0099+1.7947X and X*= -2.0678+2.2746X for B. brassicae and D. rapae , respectively. Optimum number of samples required varied with the mean density and the desired precision level for both the aphid and the parasitoid.

Incidence of the fall armyworm Spodoptera Frugiperda (J.E. Smith) at Udaipur in Maize

The fall armyworm, Spodoptera frugiperda (J.E. Smith) incidence on maize during the monsoon season was confirmed at Udaipur, and its infestation was 19±3.35 to 20±5.59 plants/100 m2. The spatial distribution pattern of the larvae was uniform or close to random, rather than aggregated. The mean crowding index ranged from 9.63 to 25.27 and the Lloyd's index was close to 1.0.

Relation of Blood Group, Crowding Index and Family History of Dyspepsia with Helicobacter pylori Infection

Background: Dyspepsia is a common problem that frequently associated with gastritis. The risk of acquiring Helicobacter pylori is related with living conditions and the family's socioeconomic status. Thus, a relation between the H. pylori infection and group O blooded individuals was discovered. Currently, no published data available regarding the association of blood group, crowding index and family history of dyspepsia with H. pylori infection in Kurdistan region. So this study aims to assess the blood group, crowding index and family history of dyspepsia among patients with H. pylori infection.Patients and Methodology: Exactly One hundred dyspeptic patients with anti H. pylori Immunoglobulin G (IgG) positive underwent gastroscopy and 75 apparently healthy individuals with no dyspepsia and negative H. pylori IgG antibodies (escorts of patients) using Enzyme-Linked Immuno Sorbent Assay tests (NovaLisa, NovaTec). The samples were collected from Kurdistan Teaching Center for Gastroenterology & Hepatology and Ali Kamal Consultation Clinic in Sulaimani city form December 2012 to March 2014. ABO Blood groups were determined using standardized hemagglutination methods.Results: About 48% of the patients complained of dyspepsia between 1 to 5 years. A significant correlation was found between duration of dyspepsia and the titer of anti H. pylori IgG. The maximum level was found among patients with longer duration (5-15years) of dyspepsia. The most common presentation was epigastric pain (78%) followed by decreasing appetite (39%) and GI bleeding (26%). The most common OGD finding in patients was antral gastritis (59%) followed by duodenal ulcer (21%). Most of the patients had either blood group O (44%) or A (30%) than controls (17.3%, 20%). There was statistically significant (p<0.01), OR = 3.5 (1.3 – 5.2) relation between blood group and H. pylori infection. The majority (70%) of patients had positive family history of dyspepsia than controls (17.3%), with OR=10.5 (2.9 – 37.3). There was significant relation between crowding index and H. pylori infection. The mean crowding index among patients and controls were (4.4 ± 2.3), (2.1 ± 0.9) respectively, with OR= 3.0 (1.9 - 4.9). No significant difference was found between patients and control group regarding age, gender, and marital status.Conclusions: We realized that there was significant association between H. pylori infection and family history of dyspepsia, crowding index and ABO blood group.

Distribution patterns of Juglans cathayensis populations at different slope aspects in Tianshan valley in Xinjiang, China

Eight 4000 m2 plots were set up at eight sites distributed on sunny and shady slopes of four valleys, and adjacent lattice method was used to survey Juglans cathayensis populations. At different scales, aggregation intensity index such as variance/mean ration and deviation index (Cx), negative binomial parameter (K), clumping index (I), mean crowding index (m*), patchiness index (PAI) and aggregation index (Ca) were used to analyze distribution patterns of populations. With the increase of surveying scales, the distribution patterns changed from cluster to random. Populations presented a clustered distribution when the scale was 25 m2. Aggregation intensity had great differences among different plots, and the maximum one located on west shady slope and the minimum one did on south shady slope. However, populations presented a random distribution when the scale was 50-400 m2. When scale was 25 m2, saplings, young and mature trees showed a clustered distribution. Aggregation intensity of mature trees was the maximum one and that of saplings was the minimum one. When the scale was 200-400 m2, saplings, young and mature trees showed random distribution. The pattern size of J. cathayensis populations was 25 m2 and pattern intensity was 2.49-9.38 m2. The pattern intensity of young trees was the largest and that of mature trees was the least in population components. In a word, when sampling scale was close to population patch size, a reliable conclusion usually could be obtained by using adaptive determination method and multi-index comprehensive decision.

Spatial heterogeneity in simple deterministic SIR models assessed ecologically

Patchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity. doi:10.1017/S1446181113000035

SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

Quantitative Evaluation of the Uniformity of Abrasive Distribution Based on Image Processing

In precision machining, the uniformity degree of abrasive distribution affects significantly the surface quality. To quantitatively evaluate the uniformity of abrasive distribution, in this paper digital image processing technology was employed to segment the working face images of impregnated diamond tools; mean crowding index was used to classify the pattern of abrasive distribution; fractal dimension determined by gyration radius method was applied to characterize the bulk uniformity of abrasive distribution on face plane; the coefficient of variation of Voronoi cell areas was adopted to describe the local distribution feature of abrasive grits. The results show that mean crowding index, fractal dimension and CV of Voronoi cell areas can characterize the uniformity of abrasive distribution from different points of view, and can be used to quantitatively evaluate the uniformity of abrasive distribution.

QUANTIFYING SPATIAL PATTERN WITH EVENNESS INDICES

Quantifying the spatial distributions of organisms in simple and meaningful ways is important for understanding the ecology and habitat needs of species subject to anthropogenic disturbances. Most multi‐species conservation and management programs do not yet account for the variation of space‐use patterns exhibited by species preferring the same habitat type. To measure species' space‐use patterns as a step toward determining habitat needs, we suggest using evenness indices. Although commonly used in characterizing communities (i.e., as a measure of species diversity), these indices are suitable for characterizing many other ecological patterns, including patterns of site use by individuals.We investigate the statistical properties of five indices (Camargo's index of evenness, E′; Simpson's index of evenness, E1/D^; Lloyd's index of mean crowding, J; Smith‐Wilson index Evar; and Dispersion index, DL, a variant of the Shannon diversity index) to evaluate their utility for quantifying broad‐scale spatial patterns of migratory shorebirds. We use a Monte Carlo simulation approach to compare these indices for their (1) ability to characterize a wide range of spatial patterns (from even to patchy); (2) ability to discriminate among distributions; and (3) robustness to incomplete sampling. In addition, we compare the ability of these indices to characterize spatial dispersion for four species of shorebirds migrating through the United States: Killdeer (Charadrius vociferus), Semipalmated Plover (C. semipalmatus), Sanderling (Calidris alba), and Red Knot (C. canutus).Overall, we recommend Camargo, Simpson, and Lloyd indices for quantifying spatial dispersion. All three indices gave precise and unbiased estimates once 35 or more sites (3.5% of 1000 simulated sites) were sampled randomly, regardless of the degree of patchiness. Nonrandom sampling resulted in biased estimates until a much greater proportion of sites (at least 30–50%) were sampled, highlighting the importance of site selection in sampling programs. Our analysis of shorebird spatial patterns revealed that evenness indices discriminate well among the species we considered, ranking Killdeer as most dispersed and Red Knot as most aggregated. Our results agree with earlier (independent) assessments of these species' migration strategies and illustrate how simple univariate metrics may be useful tools for characterizing complex spatial patterns.

Spatial pattern analysis of seeds of an arable soil seed bank and its relationship with above-ground vegetation in an arid region

The composition and spatial pattern of weeds was analysed in an arable-soil seed bank after the harvest of wheat. Four hundred cores were collected from a 10×10 m grid in April 1999. Three indices of pattern detection (variance/mean ratio, Lloyd's index of mean crowding, and Morisita's index of aggregation) and Moran's I statistic of spatial autocorrelation were computed. The above-ground vegetation of the corresponding area was sampled by 100 randomly placed quadrats in March and September 1999 and variance/mean ratio of all the species was calculated. The seed bank of the field was dominated by annuals including Convovulus arvensis, Amaranthus viridis, Anagallis arvensis, Chenopodium album and Conyza canadensis. In all 27 species were recorded from the seed bank. For most of the species with a mean higher than 0.05 per core, the seed pattern (with two exceptions) was aggregated as indicated by various indices of pattern detection. Among the common species, only Amaranthus viridis exhibited a random pattern. Aggregated pattern of seeds was generally due to seeds settling in the neighbourhood of the mother plant and the clumped distribution of plant species in the overlying vegetation. Suggestions have been made regarding the improvement of the precision of the soil seed bank sample, in view of the aggregated distribution of seeds in soil. Seed bank showed considerable qualitative similarity with the above-ground vegetation, which is presumably the consequence of recurrent disturbances in the arable field.

Spatial distribution of red palm weevil Rhynchophorus ferrugineus Oliv. (Coleoptera: Curculionidae) in coconut plantations

The spatial distribution of red palm weevil, Rhynchophorus ferrugineus Oliv. in coconut plantations was studied by applying a series of statistical tests. Population dispersion parameters and also different dispersion indices were calculated for monthly weevil counts obtained through 40 pheromone (Ferrolure+) trap captures, between August, 1999 and July, 2000. The dispersion parameters, viz. mean–variance test, clumping parameter ( K) and statistic t tests revealed that red palm weevil population followed the negative binomial distribution pattern and was highly aggregated or clumped. Further, the different dispersion indices, viz. variance to mean ratio, Cole's index, David and Moore's index, ‘ K’ of negative binomial and Lloyd's index of mean crowding went on to confirm the aggregated or contagious distribution pattern of red palm weevil. Due to the clumped nature of palm weevil population, these results emphasize the need of adopting preventive management practices in and around plantations infested by red palm weevil.

Experimental analysis of factors influencing the aggregating behaviour of the green sea urchin Strongylocentrotus droebachiensis (Müller)

The aggregating behaviour of the green sea urchin Strongylocentrotus droebachiensis was investigated in a multifactorial laboratory experiment. The null hypothesis of a random pattern of aggregation was rejected prior to analyses of treatment effects and patterns of aggregation were quantified using three indices of aggregation: the mean aggregation size, the index of mean crowding and the index of patchiness. Sea urchin density and body size were the two most important determinants of spatial pattern. Sea urchins, irrespective of size, had a regular pattern of aggregation at low density, a nearly random pattern at medium density and a clumped pattern at high density. Large urchins were consistently more aggregated than small urchins, even though urchin size was involved in several interactions with other experimental factors. Averaged over all densities, large urchins had a clumped, while small urchins had a regular pattern of aggregation. The presence of decapod predators had no detectable effect on the aggregation behaviour of S. droebachiensis. Significant predator effects were entirely due to the presence of wolffish, which reduced the size of sea urchin aggregations both by eliciting behavioural responses, and by decreasing the population density of the urchins. Additional spatial heterogeneity, in the form of claypipe refuges, also made the urchins less aggregated. Prefeeding, food and season had minor effects on the aggregating behaviour of S. droebachiensis.

Intra-specific competition (crowding) of giant sequoias ( Sequoiadendron giganteum)

Information on the size and location of 1916 giant sequoias ( Sequoiadendron giganteum (Lindl.) Buchholz) in Muir Grove, Sequoia National Park, in the southern Sierra Nevada of California was used to assess intra-specific crowding. Study objectives were to: (1) determine which parameters associated with intra-specific competition (i.e. size and distance to nearest neighbor, crowding/root system area overlap, or number of neighbors) might be important in spatial pattern development, growth, and survivorship of established giant sequoias; (2) quantify the level of intra-specific crowding of different sized live sequoias based on a model of estimated overlapping root system areas (i.e. an index of relative crowding); (3) compare the level of intra-specific crowding of similarly sized live and dead giant sequoias (less than 30 cm diameter at breast height (dbh) at the time of inventory (1969). Mean distances to the nearest live giant sequoia neighbor were not significantly different (at α = 0.05) for live and dead sequoias in similar size classes. A zone of influence competition model (i.e. index of crowding) based on horizontal overlap of estimated root system areas was developed for 1753 live sequoias. The model, based only on the spatial arrangement of live sequoias, was then tested on dead sequoias of less than 30 cm dbh ( n = 163 trees; also recorded in 1969). The dead sequoias had a significantly higher crowding index than 561 live trees of similar diameter. Results showed that dead sequoias of less than 16.6 cm dbh had a significantly greater mean number of live neighbors and mean crowding index than live sequoias of similar size. Intra-specific crowding may be an important mechanism in determining the spatial distribution of sequoias in old-growth forests.

Effects of Host Plant on the Between-Plant Spatial Distribution of the Russian Wheat Aphid (Homoptera: Aphididae

The spatial distribution of the Russian wheat aphid, Diuraphis noxia (Mordvilko), on ‘Stephens’ wheat and ‘Border’ oats was evaluated using geostatistics. Geostatistics uses spatial variation to determine the degree and type of spatial dependence of spatially related data. These analyses revealed unique spatial distributions of Russian wheat aphids on wheat and oats, which varied as the population developed and dispersed among the plants. On ‘Stephens’ wheat, Russian wheat aphid dispersal from the release site was delayed, and when aphids dispersed, they moved a greater distance than those on ‘Border’ oats. When placed on ‘Border’ oats, Russian wheat aphids dispersed within 3 d of the initial infestation and continued to disperse throughout the 21-d sampling period. The Russian wheat aphid distributions estimated by negative binomial K, Lloyd’s mean crowding index, Iwao’s patchiness regression, and Taylors’ power law were compared with the geostatistical analysis and found to have a similar interpretation of distribution only 50-80% of the time under the laboratory conditions of this research. These differences reveal the limited value of these dispersion indices for evaluating spatial distribution.

Changes in growth of plaice Pleuronectes platessa L. and sole Solea solea (L.) in the North Sea

The changes in growth of plaice and sole between 1957 and 1988, as estimated from samples of the commercial fishery and pre-recruit surveys, were analysed in order to study possible density dependent effects. Indices of potentially competitive biomasses of plaice and sole, based on Lloyd's index of mean crowding, were estimated from the average spatial distribution of various age groups during the summer growing period and from the population age structure as estimated by virtual population analysis. Growth of all age groups of sole increased in the 1960s and was stable in the 1970s and 1980s. In plaice only age groups 1 to 3 showed a similar increase in the 1960s, whereas the growth of 1-year-old plaice tended to decrease in the 1980s. Growth did not show a negative correlation with mean crowding, except in age group 1 of plaice and in age group 3+ of sole. It is concluded that these negative correlations do not provide unequivocal evidence for density dependent growth in plaice and sole, since they could equally well be caused by parallel but unrelated trends in time of one or more other factors. The simultaneous increase in growth in the 1960s of age groups of sole and plaice in the southern North Sea, and the absence of such an increase in age groups in the central North Sea, suggests that food availability must have increased in the Southern North Sea. This inference is supported by several macrobenthos studies. Whether the reduced growth of 1-group plaice in the 1980s, when recruitment was well above the average level, is caused by density dependent growth or to a reduced food availability remains an open question.