Small-scale Aggregation Research Articles

Invariant Spatial Pattern Across Mediterranean Scrublands in the Iberian Pear (Pyrus bourgaeana).

The spatial distribution pattern of plant species is frequently driven by a combination of biotic and abiotic factors that jointly influence the arrival, establishment, and reproduction of plants. Comparing the spatial distribution of a target plant species in different populations represents a robust approach to identify the underlying mechanisms. We mapped all reproductive individuals of the Iberian pear (Pyrus bourgaeana) in five plots (1.39-8.57 km2) differing in the activity of seed dispersers and vertebrate herbivores in southern Iberian Peninsula. We used Thomas point process models to quantify the consistency in the spatial pattern and the level of spatial aggregation of this mammal-dispersed tree among the five populations. We tested two hypotheses: (i) because the clumped defecation behavior of some dispersers can lead to local tree aggregation, and because denser groups of fruiting trees can limit seed dispersal by attracting frugivores to specific sites, we expected a consistent small-scale aggregation pattern across all populations; and (ii) because ungulates reduce recruitment by preying on seeds and seedlings, we hypothesize that ungulate activity will show negative relationships with tree density and level of aggregation. Our spatial analysis revealed consistent and highly aggregated small-scale patterns of all Iberian pear populations, with one critical scale aggregation, a low density of clusters and high variability in the number of trees per cluster. Ungulate activity and the number of trees per cluster showed a marginally significant negative correlation, suggesting that in areas with higher ungulate activity, trees tend to form less dense clusters. Although several of the underlying processes varied greatly among the five study sites, the Iberian pear showed a relatively consistent spatial pattern with just quantitative nuances throughout the entire region. This result has significant implications for the reproductive success of the species, management strategies, and ultimately the long-term persistence of populations.

TS-STNN: Spatial-temporal neural network based on tree structure for traffic flow prediction

Traffic flow prediction effectively supports the sustainable expansion and operation of modern transport networks, one of the emerging research areas in intelligent transportation systems. Currently, most common traffic flow prediction methods use deep learning spatial–temporal models based on graph convolution theory, which cannot deeply explore the spatial hierarchy and directional information of traffic flow data due to their structural characteristics. To address this problem, a spatial–temporal neural network based on tree structure (TS-STNN) is created to anticipate future traffic flow at a specific time at a target location. The principle of this method is to use the characteristics of the tree structure to construct a plane tree matrix with hierarchical and directional features, which is finally fused into a spatial tree matrix to extract the spatial information. Meanwhile, the temporal correlation of traffic flow data in the traffic network is analyzed by TS-STNN using Gated Recurrent Units (GRUs). By comparing with the existing baseline methods, it is verified that the TS-STNN model has high prediction accuracy in both Random Uniformly Distributed (RND) and Small-Scale Aggregation of Node Distributed (SSAND) scenarios. It is further demonstrated through ablation experiments that the developed tree convolution module greatly impacts the TS-STNN accuracy.

Analysis of the Aggregation Characteristics and Influencing Elements of Urban Catering Points in Small Scale: Methods and Results

Urban catering systems constitute an important subsystem of the complex urban system. They can reveal not only the impact of urban functional structure on the catering but also the behavioral patterns of individual catering points through the exploration of their small-scale aggregation characteristics and influencing elements, thus becoming an essential basis for urban functional planning. In this study, we analyze the aggregation characteristics of catering points in a particular study area using the probabilistic methods, with Beijing catering points as a sample. The analysis revealed a good power-law distribution characteristic of the catering points density at the small scale. Then, an aggregation effect analysis model and an agglomeration effect analysis model were established. Based on this, an empirical analysis of candidate agglomeration kernel elements was conducted. The results showed that the influence of candidate agglomeration kernel elements on catering points exhibited a categorical nature. Additionally, a good power-law attenuation relationship was uncovered between the density and distance of catering points, which ultimately revealed the mechanism of preferential attachment in the competition for catering point site selection. Using the results of the agglomeration analysis, a reasonable explanation was provided for the power-law distribution characteristic of the density of catering points, which achieved an organic connection between micro-analysis and macro-characteristic analysis. These findings could provide a reference for the analysis of aggregation characteristics of other urban commercial formats.

Ecological network identification and connectivity robustness evaluation in the Yellow River Basin under a multi-scenario simulation

The deterioration of the environment has been aggravated by the rapid growth of cities and economies, and inter-regional political, economic, scientific, and technological frictions caused by ecological problems are increasing. To safeguard the ecological environment and design healthy urban development, it is crucial to assess the structure and quality of ecological networks (ENs), which serve as links between landscape structure and ecological processes. This paper simulates land use in 2035 under three development scenarios for the Yellow River Basin (YRB), identifying ENs, and assessing the robustness of network connectivity for each scenario. We found that in the ecological protection scenario (ES), forest and water Land expanded the most, increasing by 4.16% and 6.98%, respectively. The ES also produced the most ecological patches (53) and important ecological corridors (141), with the important corridors forming an east–west spatial pattern. In the baseline scenario (BS), important corridors formed a north–south pattern, and in the urban development scenario (US), the important corridors were characterised by small-scale aggregation. The initial connectivity robustness of ENs was 0.5, 0.46, and 0.45 in the ES, BS, and US, respectively. Whether using deliberate or random attack models, the robustness of network connectivity was strongest in the ES. This study provides a theoretical reference for the future planning of eco-friendly development and ecological security patterns in the YRB.

Review of Kerogen’s Geomechanical Properties: Experiments and Molecular Simulation

Measuring the mechanical properties of kerogen, the predominant constituent of organic matter in shale is exceedingly difficult as it constitutes small-scale aggregates interspersed in rocks. Kerogen is characterized by significantly lower stiffness compared to inorganic minerals, thereby the kerogen regions are potential areas for study during, for example, drilling or macroscopic fracture propagation in the course of hydraulic fracturing. For instance, the elastic modulus of kerogen-rich spots is around 10 GPa, while it is about 70 GPa for quartz. Failure of the kerogen nanocantilever beam shows an elastic strain-hardening behavior, indicating a higher energy requirement to propagate a crack. Studies illustrated that the kerogen’s mechanical properties are controlled by maceral composition and are positively correlated to the maturity level. This paper provides a comprehensive review of how the mechanical properties of kerogen are elucidated experimentally and contrast the results with the properties delineated from molecular simulation. In addition, we relate kerogen innate attributes, such as maturity and type, to the physical qualities measured and substantiate why accurate knowledge of the mechanical characteristics is pivotal from a hydraulic fracturing perspective.

Lightweight Detection Algorithm of Kiwifruit Based on Improved YOLOX-S

Considering the high requirements of current kiwifruit picking recognition systems for mobile devices, including the small number of available features for image targets and small-scale aggregation, an enhanced YOLOX-S target detection algorithm for kiwifruit picking robots is proposed in this study. This involved designing a new multi-scale feature integration structure in which, with the aim of providing a small and lightweight model, the feature maps used for detecting large targets in the YOLOX model are eliminated, the feature map of small targets is sampled through the nearest neighbor values, the superficial features are spliced with the final features, the gradient of the SiLU activation function is perturbed, and the loss function at the output is optimized. The experimental results show that, compared with the original YOLOX-S, the enhanced model improved the detection average precision (AP) of kiwifruit images by 6.52%, reduced the number of model parameters by 44.8%, and improved the model detection speed by 63.9%. Hence, with its outstanding effectiveness and relatively light weight, the proposed model is capable of effectively providing data support for the 3D positioning and automated picking of kiwifruit. It may also successfully provide solutions in similar fields related to small target detection.

Spatial Distribution and Species Association of Dominant Tree Species in Huangguan Plot of Qinling Mountains, China

The spatial distribution pattern and population structure of trees are shaped by multiple processes, such as species characteristics, environmental factors, and intraspecific and interspecific interactions. Studying the spatial distribution patterns of species, species associations, and their relationships with environmental factors is conducive to uncovering the mechanisms of biodiversity maintenance and exploring the underlying ecological processes of community stability and succession. This study was conducted in a 25-ha Qinling Huangguan forest (warm-temperate, deciduous, broad-leaved) dynamic monitoring plot. We used univariate and bivariate g(r) functions of the point pattern analysis method to evaluate the spatial distribution patterns of dominant tree species within the community, and the intra- and interspecific associations among different life-history stages. Complete spatial randomness and heterogeneous Poisson were used to reveal the potential process of community construction. We also used Berman’s test to determine the effect of three topographic variables on the distribution of dominant species. The results indicated that all dominant species in this community showed small-scale aggregation distribution. When we excluded the influence of environmental heterogeneity, the degree of aggregation distribution of each dominant species tended to decrease, and the trees mainly showed random or uniform distribution. This showed that environmental heterogeneity significantly affects the spatial distribution of tree species. Dominant species mainly showed positive associations with one another among different life-history stages, while negative associations prevailed among different tree species. Furthermore, we found that the associations between species were characterized by interspecific competition. Berman’s test results under the assumption of complete spatial randomness showed that the distribution of each dominant species was mainly affected by slope and convexity.

Community structure of benthic megafauna on a seamount with cobalt-rich ferromanganese crusts in the northwestern Pacific Ocean

Increasing threats to seamount ecosystems potentially from fishing and seabed mining are creating an urgent demand for research on megafauna to inform conservation and management. We surveyed the community structure of benthic megafauna on the Weijia Seamount, which is covered by cobalt-rich ferromanganese crusts, in the northwestern Pacific Ocean. A multidisciplinary dataset was generated from video recordings taken by a human occupied vehicle (HOV) and remotely operated vehicle (ROV) along transects and bathymetry-derived environmental variables. The spatial variation of community structure and its environmental and spatial factors impacting the community were then explored. A total of 2779 individuals of the megabenthos (from depths of 1533–2763 m, covering 24.4 km in distance and with a maximum of 109 individuals per 100 m by linear observation), was counted and classified into 76 morphospecies, which was dominated by crinoids, ophiuroids, hexactinellids and octocorals. Moderately abundant and diverse megafauna, high beta diversity and distinct assemblages were present in the Weijia Seamount, suggesting a highly patchy pattern within a single seamount. Six clusters of megafauna were revealed, with significant differences in species composition and biodiversity. The results of statistical analyses showed that the megafaunal community was impacted by at least eight environmental variables (latitude, depth, slope, curvature, rugosity, bathymetric position index, topography type, and substrate type), and excluding aspect. Among these variables, the topography and substrate types played key roles in the occurrence of small-scale aggregations of hexactinellids; depth-related variables were key factors, but no gradual depth-related change in terms of abundance, richness or species turnover was observed. This case study on the megabenthic community of the Weijia Seamount can serve as an environmental baseline, providing a reference status for seamount conservation and management.

Aggregation patterns of two corallivorous snails and consequences for coral dynamics

Spatial heterogeneity plays an important role in consumer–resource interactions. It arises from variability in the underlying distribution of the resource and/or the consumer, as well as the habitat in which the consumer–resource interaction occurs. In some cases, the resource is the habitat, especially when the habitat is biogenic (e.g., kelp, corals, seagrasses). In these systems, the resulting dynamics can be particularly rich because the consumer–resource interactions are coupled with changes in the habitat (i.e., resource) that are due to the consumer–resource interaction. In Moorea, French Polynesia, two corallivorous snails, Coralliophila violacea and Drupella cornus, feed and live on massive Porites corals. Here, I (1) document the spatial patterns of the snails among sites, within sites, and on corals; (2) examine the drivers of small-scale aggregations by testing the attraction of the snails to chemical cues coming from conspecifics and corals; (3) test the effects of aggregations of snails on coral growth by manipulating snail density. The distributions of both snails were highly heterogeneous among sites across the island, and both species were spatially aggregated both among and within corals. The source of chemical attraction that caused the small-scale clustering differed between the two snails. D. cornus was attracted to conspecifics and to corals damaged by conspecifics, whereas C. violacea was attracted to damaged corals (regardless of the cause). Increasing snail density caused a linear decline in coral growth that was similar for the two snail species. The combination of the clustered spatial pattern of both snail species and their negative effects on coral growth could lead to important feedbacks in which high densities of snails reduce coral cover in localized areas and create spatial dynamics that affect the spatial distributions of both corals and snails across the reef.

Does size matter? Ontogenetic responses of an Andean shrub to conspecific density-dependence

Dispersal, population spatial structure and intraspecific density-dependent processes are critical determinants of plant population dynamics. However, we lack empirical data on how the interplay between these factors changes across the plant species life cycle, particularly for long-lived plants. This is in great part due to the difficulty in implementing experimental approaches to discriminate the relative effects of these factors. Here, we studied the spatial pattern of adults and recruits of the Andean shrub Croton wagneri Müll. Arg. (Euphorbiaceae) and assessed the role of dispersal, population spatial structure and intraspecific interactions on individual plant performance. For this purpose, we developed a spatially explicit approach in which plant spatial position is combined with vegetative and reproductive attributes. The spatial pattern of C. wagneri showed small-scale aggregation. This is consistent with the species' short-distance seed dispersal. The spatial pattern of recruits was dependent on the spatial pattern of adults, signifying a high relevance of adult-recruit interactions in the spatial pattern creation. However, once established, recruits seemed to be subjected to self-thinning (i.e., negative density dependence). Finally, a positive density-dependent effect of the conspecific neighbourhood was found on adult reproductive performance, while plant growth was affected by intraspecific competition. Overall, dispersal, population spatial structure and intra-specific interactions combine to influence vegetative and reproductive performance of the species. We also found that plant interaction at the intraspecific level can be a composite of facilitative and competitive effects that combine in complex ways to influence population spatial structure and individual plant performance. Furthermore, such effects did not always leave a spatial signature, which highlights the importance of complementing plant position with quantitative fitness attributes in spatial pattern analysis in plant ecology.

Role of density in aggregation patterns and synchronization of spawning in the hermaphroditic scallop Pecten fumatus

In broadcast spawners, low densities and poor spawning synchronization can reduce fertilization success. In wild populations, individuals in close proximity tend to spawn more synchronously than those further apart, sug- gesting that low spawner densities may reduce gamete pro- duction by lessening the efficacy of pheromone signalling. This study assessed the role of adult density in aggregation patterns and spawning synchronization in a semi-sessile, hermaphroditic scallop, Pecten fumatus. The study was carried out in Great Bay, Tasmania, Australia (147.335 W, 43.220 S) in 2010-2012 by assessing (1) the relationship between density, small-scale aggregation patterns and near- est neighbour distance (NND), (2) the temporal pattern of spawning synchronization, and (3) the effect of site density and conspecific proximity on the probability of spawn- ing. Densities observed in the field ranged from 1.455 to 0.021 ind m −2 . Sites with lower densities had less small- scale aggregation and greater NNDs. Patterns of small- scale aggregation and NNDs in P. fumatus were compara- ble to those observed in a gonochoristic species. Spawning synchronization was highly variable, ranging between 3.5

Spatiotemporal Characterization of Sclerotinia Crown Rot Epidemics in Pyrethrum.

Sclerotinia crown rot, caused by Sclerotinia minor and S. sclerotiorum, is a disease of pyrethrum in Australia that may cause substantial decline in plant density. The spatiotemporal characteristics of the disease were quantified in 14 fields during three growing seasons. Fitting the binary power law to disease incidence provided slope (b = 1.063) and intercept (ln(Ap) = 0.669) estimates significantly (P ≤ 0.0001) greater than 1 and 0, respectively, indicating spatial aggregation at the sampling unit scale that was dependent upon disease incidence. Covariate analyses indicated that application of fungicides did not significantly influence these estimates. Spatial autocorrelation and spatial analysis by distance indices indicated that spatial aggregation above the sampling unit scale was limited to 20 and 17% of transects analyzed, respectively. The range of significant aggregation was limited primarily to neighboring sampling units only. Simple temporal disease models failed to adequately describe disease progress, due to a decline in disease incidence in spring. The relationships between disease incidence at the scales of individual plants within quadrats and quadrats within a field was modeled using four predictors of sample size. The choice of the specific incidence-incidence relationship influenced the classification of disease incidence as greater than or less than 2% of plants, a provisional commercial threshold for fungicide application. Together, these studies indicated that epidemics of Sclerotinia crown rot were dominated by small-scale aggregation of disease. Larger scale patterns of diseased plants, when present, were associated with severe disease outbreaks. The spatial and temporal analyses were suggestive of disease epidemics being associated with localized primary inoculum and other factors that favor disease development at a small scale.

How does length of alkyl hydrocarbon chains on zwitterion functionalised multiwalled carbon nanotubes influence dispersion of carbon nanotubes?

Zwitterion functionalisation is carried out to alter surface properties and hence disperability of carbon nanotubes by attaching short and long alkyl hydrocarbon chains onto the nanotubes. Long chain attachment results in long term stabilisation of the carbon nanotubes in toluene, whereas short chain simply enhances their dispersion. Small angle light scattering is used to measure the dispersion of the carbon nanotubes suspended in toluene. Analysis of these data elucidates the mechanism by which the functionalisation assists in the dispersion and ultimately leads to the long term stabilisation of the nanotubes in toluene. Functionalised and untreated nanotubes exhibit hierarchical morphology consisting of small scale aggregates (bundles) that form fractal agglomerates. The bundles consist of multiple tubes possibly aggregated side by side. The bundle morphology and agglomeration of the bundles are quite dependent on functionalisation. In the case of long solubilising chain attachment, the small scale aggregates are broken up into smaller sizes, and no agglomeration is observed over months, whereas the short chain nanotubes agglomerate and eventually precipitate out of solution in several days. For untreated tubes, large agglomerates appear immediately after cessation of sonication. Functionalisation leads to the long term stabilisation of the nanotubes, not only by inhibiting agglomeration but also by breaking up the side by side bundles.

Grassland management influences spatial patterns of soil microbial communities

Soil micro-organisms play a vital role in grassland ecosystem functioning but little is known about the effects of grassland management on spatial patterns of soil microbial communities. We compared plant species composition with terminal restriction fragment length polymorphism (T-RFLP) fingerprints of soil bacterial and fungal communities in unimproved, restored and improved wet grasslands. We assessed community composition of soil micro-organisms at distances ranging from 0.01 m to 100 m and determined taxa–area relationships from field- to landscape level. We show that land management type influenced bacterial but not fungal community composition. However, extensive grassland management to restore aboveground diversity affected spatial patterns of soil fungi. We found distinct distance–decay and small-scale aggregation of fungal populations in extensively managed grasslands restored from former arable use. There were no clear spatial patterns in bacterial communities at the field-scale. However, at the landscape level there was a moderate increase in bacterial taxa and a strong increase in fungal taxa with the number of sites sampled. Our results suggest that grassland management affects soil microbial communities at multiple scales; the observed small-scale variation may facilitate plant species coexistence and should be taken into account in field studies of soil microbial communities.

Analysing small-scale aggregation in animal visits in space and time: the ST-BBD method

Movement behaviour plays an important role in many ecological interactions. As animals move through the environment, they generate movement patterns, which are a combined result of landscape characteristics and species-specific behaviour. Measuring these ranging patterns is being facilitated by technological advances in collection methods, such as GPS collars, that are capturing movement on finer spatial and temporal scales. We propose the use of a novel spatiotemporal analytical framework (ST-BBD), based on the beta-binomial distribution (BBD) model, to measure small-scale aggregation in animal movement data sets, including two simulated and three collected primate data sets. We use this approach to distinguish different habitat uses of three primate species (red colobus, Procolobus rufomitratus, black howler, Alouatta pigra, and spider monkey, Ateles geoffroyi) and quantify their specific use of the landscape in space and in time, using a parameter of the BBD that measures the variation in sites visited on a landscape. We found that estimates of aggregation in habitat use were higher in the frugivorous spider monkey, compared to the more folivorous howler monkey, and that in the red colobus, aggregation in site visits was dependent on group size and food availability. Applications of this framework to animal movement data could be useful in understanding ecological systems where habitat use is an important factor, such as the relationships between hosts and parasites, or parent plants and seed dispersers.

Effects of Zoospore Aggregation and Substrate Rugosity on Kelp Recruitment Success.

Successful kelp recruitment is important for kelp population persistence and associated kelp forest communities. The proximity of settled kelp zoospores is a known requirement for successful kelp recruitment and proximity can be increased as zoospores aggregate. Substrate rugosity can also be an important factor affecting macroalgal settlement and recruitment in wave-swept areas, and may affect kelp recruitment by aggregating zoospores. In this study, kelp zoospores were cultured at different levels of small-scale aggregation and kelp recruitment was quantified. Sporophyte production significantly increased as zoospores became more aggregated indicating that processes that aggregate kelp zoospores have the potential to enhance kelp recruitment. A 13-month field experiment demonstrated differential kelp recruitment onto settlement plates that mimicked surface rugosities of two common rock types within Stillwater Cove, Carmel Bay in central California (Carmelo Formation sandstone and Santa Lucia granodiorite). Significantly more kelp recruited to molds mimicking granodiorite over the yearlong study (granodiorite=2.7 recruits±SE 0.50, sandstone= 1.2 recruits±SE 0.51). There was a significant difference in recruitment between seasons and this variability was due to the fact that spring had the highest average number of kelp recruits per mold. However, the interaction between substrate and season was not significant. This study emphasizes the importance of kelp zoospore aggregation on kelp recruitment and demonstrates that small-scale rugosity affects kelp recruitment.

The effects of back-reaction on turbulence modulation in shear flows: a new exact regularized point-particle method

Particles advected by turbulent flows spread non uniformly and form small scale aggregates known as clusters where their local concentration is much higher than it is in nearby rarefaction regions. Recently it has been shown that the addition of a mean flow, through its large scale anisotropy, induces a preferential orientation of the clusters whose directionality can even increase in the smallest scales. Such finding opens new issues in presence of large mass loads, when the momentum exchange between the two phases becomes significant and the back-reaction of the particles on the carrier flow cannot be neglected. These aspects are addressed by direct numerical simulations data of particle laden homogeneous shear flows in the two-way coupling regime. Particles with Stokes number of order one induce an energy depletion of the classical inertial scales and the amplitude increase of the smallest ones where the particle back-reaction pumps energy into the turbulent eddies. We find that increased mass loads results in a broadening of the energy co-spectrum extending the range of scales driven by anisotropic production mechanisms. Such results are obtained in the context of the classical "particle in cell" method. To go beyond this approach we propose a new methodology to model particle laden two phase flows. The method is based on the exact unsteady Stokes solution around a point-particle and is intended to provide a physically consistent picture of the momentum exchange between the carrier and disperse phase.

Comments Regarding the Binary Power Law for Heterogeneity of Disease Incidence

The binary power law (BPL) has been successfully used to characterize heterogeneity (overdispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial distribution over the range of incidence values, and the estimated scale (?) and slope (b) parameters provide information on the characteristics of aggregation. When b = 1, the interpretation is that the degree of aggregation remains constant over the range of incidence values observed; otherwise, aggregation is variable. In two articles published in this journal in 2009, Gosme and Lucas used their stochastic simulation model, Cascade, to show a multiphasic (split-line) relationship of the variances, with straight-line (linear) relationships on a log-log scale within each phase. In particular, they showed a strong break point in the lines at very low incidence, with b considerably >1 in the first line segment (corresponding to a range of incidence values usually not observed in the field), and b being ?1 in the next segment (corresponding to the range of incidence values usually observed). We evaluated their findings by utilizing a general spatially explicit stochastic simulator developed by Xu and Ridout in 1998, with a wide range of median dispersal distances for the contact distribution and number of plants in the sampling units (quadrats), and through an assessment of published BPL results. The simulation results showed that the split-line phenomenon can occur, with a break point at incidence values of ?0.01; however, the split is most obvious for short median dispersal distances and large quadrat sizes. However, values of b in the second phase were almost always >1, and only approached 1 with extremely short median dispersal distances and small quadrat sizes. An appraisal of published results showed no evidence of multiple phases (although the minimum incidence may generally be too high to observe the break), and estimates of b were almost always >1. Thus, it appears that the results from the Cascade simulation model represent a special epidemiological case, corresponding primarily to a roughly nearest-neighbor population-dynamic process. Implications of a multiphasic BPL property may be important and are discussed.

Spatial heterogeneity, incidence-incidence and incidence-lesion density relationship of apple scab (Venturia inaequalis) in managed orchards

The spatial pattern of apple scab was characterized using 10 years of disease incidence and lesion density data collected in managed orchards located in Quebec, Canada. Distributional analyses indicated that scab incidence was better characterized by the beta-binomial than the binomial distribution in 53 and 65% of the data sets at the leaf and shoot scales, respectively. Median values of the beta-binomial parameter θ, a measure of small-scale aggregation, were near 0 (0.003 and 0.028) at both sampling scales, indicating that disease incidence was close to being randomly distributed (low degree of aggregation). For lesion density, the negative binomial distribution fitted the data better than the Poisson distribution in 86% of the data sets at the leaf scale. The median value of the index of dispersion k was 0.068, indicating that aggregation was present. For all apple scab measurements, the power law models provided a good fit to the data. The estimated slope and intercept parameters were significantly greater than 1 and 0, respectively, suggesting that spatial heterogeneity changed systematically with disease incidence. Results of a covariance analysis showed that spatial heterogeneity of scab incidence at both scales and lesion density was not dependent upon shoot type but that spatial heterogeneity of scab incidence and lesion density at the leaf scale was influenced by the sampling period. A hierarchical analysis showed that scab incidence at the tree scale increased as a saturation-type curve with respect to incidence at the leaf or shoot scales. A similar relationship was observed for incidences at the shoot and leaf scales. An effective sample size model based on the binary power law parameters (Madden and Hughes, Phytopathology 89:770–781, 1999) gave the best fit to the leaf and shoot data, respectively. The incidence-lesion density relationship at both scales was well described by a complementary log-log (CLL) and log transformation model $$ \left( {R_{{adj}}^2 = 0.97\,and\,R_{{adj}}^2 = 0.94} \right) $$ , however, the models tended to underestimate lesion density. The information of the spatial relations of apple scab within and between hierarchical scales acquired from this study can be used in developing and evaluating practical disease management strategies and to improve apple scab assessments for fungicide or cultivar susceptibility trials.

Effect of Post Production Processing on Dispersion of Carbon Nanofibers in Water

Dispersion of carbon nanofibers subjected to post production processing, heat treatment (HT) and pyrolytical stripping (PS), is investigated in aqueous suspension using small-angle light scattering. Both samples exhibit a hierarchical morphology consisting of small-scale aggregates and large-scale fractal agglomerates that precipitate rapidly. Although small-scale objects are formed by side-by-side aggregation of the nanofibers in both cases, the determination of the size distribution by assuming a tube model indicates that the PS sample is much less aggregated because of the presence of chemical vapor deposition layer. For HT fibers, the size of large agglomerates remains nearly unchanged during the precipitation process. For PS fibers, large agglomerates precipitate with time, leaving small entities in suspension, which never agglomerate. The HT nanofibers show greater degree of aggregation and agglomeration due to their highly ordered graphite nature. The carbon nanofiber structure significantly influences the dispersion of carbon nanofibers. These findings have significant implications for potential applications of carbon nanofibers in the fields of nanocomposites and biomedical nanostructures.