Spatial Heterogeneity Index Research Articles

Spatial intratumor heterogeneity of programmed death-ligand 1 expression predicts poor prognosis in resected non-small cell lung cancer.

We quantified the pathological spatial intratumor heterogeneity of programmed death-ligand 1 (PD-L1) expression and investigated its relevance to patient outcomes in surgically resected non-small cell lung carcinoma (NSCLC). This study enrolled 239 consecutive surgically resected NSCLC specimens of pathological stage IIA-IIIB. To characterize the spatial intratumor heterogeneity of PD-L1 expression in NSCLC tissues, we developed a mathematical model based on texture image analysis and determined the spatial heterogeneity index of PD-L1 for each tumor. The correlation between the spatial heterogeneity index of PD-L1 values and clinicopathological characteristics, including prognosis, was analyzed. Furthermore, an independent cohort of 70 cases was analyzed for model validation. Clinicopathological analysis showed correlations between high spatial heterogeneity index of PD-L1 values and histological subtype (squamous cell carcinoma; P < .001) and vascular invasion (P = .004). Survival analysis revealed that patients with high spatial heterogeneity index of PD-L1 values presented a significantly worse recurrence-free rate than those with low spatial heterogeneity index of PD-L1 values (5-year recurrence-free survival [RFS] = 26.3% vs 47.1%, P < .005). The impact of spatial heterogeneity index of PD-L1 on cancer survival rates was verified through validation in an independent cohort. Additionally, high spatial heterogeneity index of PD-L1 values were associated with tumor recurrence in squamous cell carcinoma (5-year RFS = 29.2% vs 52.8%, P < .05) and adenocarcinoma (5-year RFS = 19.6% vs 43.0%, P < .01). Moreover, we demonstrated that a high spatial heterogeneity index of PD-L1 value was an independent risk factor for tumor recurrence. We presented an image analysis model to quantify the spatial intratumor heterogeneity of protein expression in tumor tissues. This model demonstrated that the spatial intratumor heterogeneity of PD-L1 expression in surgically resected NSCLC predicts poor patient outcomes.

Early Detection of Coronary Microvascular Dysfunction Using Machine Learning Algorithm Based on Vectorcardiography and Cardiodynamicsgram Features

PurposeAs a main etiology of myocardial ischemia, coronary microvascular dysfunction (CMD) can occur in patients with or without obstructive coronary artery disease. Currently, there is a lack of a non-invasive approach for early detection of CMD. AimWe aim to develop a multilayer perceptron (MLP) algorithm to achieve non-invasive early detection of CMD based on vectorcardiography (VCG) and cardiodynamicsgram (CDG) features. MethodsElectrocardiograms of 82 CMD patients and 107 healthy controls were collected and synthesized into VCGs. The VCGs' ST-T segments were extracted and fed into a deterministic learning algorithm to develop CDGs. Temporal heterogeneity index, spatial heterogeneity index, sample entropy, approximate entropy, and complexity index were extracted from VCGs' ST-T segments and CDGs, entitled as STT- and CDG-based features, respectively. The most effective feature subsets were determined from CDG-based, STT-based, and the combined features (i.e., all features) via the sequential backward selection algorithm as inputs for CDG-, STT-, and CDG-STT-based MLP models optimized with an improved sparrow search algorithm, respectively. Finally, the classification capacity of the corresponding models was evaluated via five-fold cross-validations and tested on a testing dataset to verify the optimal one. ResultsThe CDG-STT-based MLP model had significantly higher evaluated metrics than CDG- and STT-based ones on the validation dataset, with the accuracy, sensitivity, specificity, F1 score, and AUC of 0.904, 0.925, 0.870, 0.870, and 0.897 on the testing dataset respectively. ConclusionsThe MLP model based on VCG and CDG features showed high efficiency in identifying CMD. The CDG-STT-based MLP model may afford a potential computer-aided tool for non-invasive detection of CMD.

Objective diagnosis of machine learning method applicability to land comprehensive carrying capacity evaluation: A case study based on integrated RF and DPSIR models

The evaluation of land comprehensive carrying capacity (LCCC) is a popular topic in regional sustainable development and land science research. However, these evaluations are often not objective due to the complexity and nonlinear characteristics of the LCCC evaluation indicators. This study provides a new framework for using machine learning methods to objectively evaluate LCCC. The Driver-Pressure-State-Impact-Response (DPSIR) indicator conceptual framework was used for the spatial visualisation of indicators and was then combined with the random forest (RF) model to optimise the LCCC evaluation. The results showed the following: (1) The accuracy of the integrated RF and DPSIR model was better than that of traditional support vector machine (SVM) and principal component analysis (PCA) methods, indicating that RF model was more suitable for LCCC evaluations. (2) The contribution of the DPSIR indicators after RF optimisation was significantly different from that of the traditional analytic hierarchy process (AHP), the contribution of the influence subsystem (I) (48.7%) was enhanced, while the contribution of the drive subsystem (D) (6.8%) was weakened, demonstrating that after RF optimisation, the DPSIR was more conducive for handling complex nonlinear systems and objectively reflecting indicator contributions. (3) The objective attributes of the DPSIR indicators were optimised through the processing of spatial visualisation models, indicating that RF was suitable for processing evaluations with a multidimensional spatial heterogeneity index system. The LCCC evaluation model can be applied to other carrying capacity case studies and operational processes and provide a scientific method for handling the multidimensional nonlinear evaluation index system and objective evaluation of LCCC.

Determination of intertidal macroalgae community patterns using the power law model.

The spatial heterogeneity of macroalgae in intertidal zones affects the stability of marine ecosystem communities, contributes to the maintenance of coastal biodiversity, and has an essential role in ecosystem and habitat maintenance. We explored the feasibility of applying the power law model to analyze the spatial distribution of macroalgae on Lvhua Island (Zhejiang Province, China) and characterized the intertidal spatial heterogeneity of the macroalgae present. The results showed a strong association between the spatial distribution of macroalgae in the intertidal zone and the power law model (R2 = 0.98). There was a positive association between species occurrence frequency and the spatial heterogeneity index of macroalgae species. The model also indicated there was macroalgal habitat structure at the site as the spatial heterogeneity within the community was greater than that of random distribution. The power law model reported here provides a new method for macroalgae community ecology research and could be broadly utilized to analyze the spatial pattern of macroalgae in intertidal zones.

Reliable Detection of Myocardial Ischemia Using Machine Learning Based on Temporal-Spatial Characteristics of Electrocardiogram and Vectorcardiogram.

Background: Myocardial ischemia is a common early symptom of cardiovascular disease (CVD). Reliable detection of myocardial ischemia using computer-aided analysis of electrocardiograms (ECG) provides an important reference for early diagnosis of CVD. The vectorcardiogram (VCG) could improve the performance of ECG-based myocardial ischemia detection by affording temporal-spatial characteristics related to myocardial ischemia and capturing subtle changes in ST-T segment in continuous cardiac cycles. We aim to investigate if the combination of ECG and VCG could improve the performance of machine learning algorithms in automatic myocardial ischemia detection. Methods: The ST-T segments of 20-second, 12-lead ECGs, and VCGs were extracted from 377 patients with myocardial ischemia and 52 healthy controls. Then, sample entropy (SampEn, of 12 ECG leads and of three VCG leads), spatial heterogeneity index (SHI, of VCG) and temporal heterogeneity index (THI, of VCG) are calculated. Using a grid search, four SampEn and two features are selected as input signal features for ECG-only and VCG-only models based on support vector machine (SVM), respectively. Similarly, three features (S I , THI, and SHI, where S I is the SampEn of lead I) are further selected for the ECG + VCG model. 5-fold cross validation was used to assess the performance of ECG-only, VCG-only, and ECG + VCG models. To fully evaluate the algorithmic generalization ability, the model with the best performance was selected and tested on a third independent dataset of 148 patients with myocardial ischemia and 52 healthy controls. Results: The ECG + VCG model with three features (S I ,THI, and SHI) yields better classifying results than ECG-only and VCG-only models with the average accuracy of 0.903, sensitivity of 0.903, specificity of 0.905, F1 score of 0.942, and AUC of 0.904, which shows better performance with fewer features compared with existing works. On the third independent dataset, the testing showed an AUC of 0.814. Conclusion: The SVM algorithm based on the ECG + VCG model could reliably detect myocardial ischemia, providing a potential tool to assist cardiologists in the early diagnosis of CVD in routine screening during primary care services.

Quantification of clot spatial heterogeneity and its impact on thrombectomy

BackgroundCompositional and structural features of retrieved clots by thrombectomy can provide insight into improving the endovascular treatment of ischemic stroke. Currently, histological analysis is limited to quantification of compositions and...

Multivariate geotechnical zonation of seismic site effects with clustering-blended model for a city area, South Korea

The site classification system in the seismic design code and its dependent zonation should be guaranteed to represent the local spatial uncertainty of subsurface features, but have been uniformly used based on the site response parameters. Spatial interpolation-based zonation is only practically feasible if there are clear-cut stochastic/spatial correlations in geotechnical/geophysical measurements. The geology and terrain features can be substituted as an influential proxy for site amplification. To develop cluster-oriented zonation considering the spatial heterogeneity of the different site response parameters focusing on an uninvestigated area, this study proposes a new approach for multivariate site classification blended with geographic information system (GIS)-based spatial clustering and machine learning (ML)-based clustering ensemble technologies. GIS-based clustering characterizes a hot spot cluster with statistical and spatial correlation values of the site response parameters and defines the relative weight using the Gi∗Z-score as the index of spatial heterogeneity. ML-based clustering ensembles aim to combine the clustering model in terms of consistency and performance, and are designed for optimization through a consensus function by comparing the fitness with the site classification system to obtain better results than individual clustering algorithms. The novelty of the proposed workflow is the stepwise improvement of the proposed models compared with the zonation phases and practical methods.

Label-Free Quantitative Phase Imaging Reveals Spatial Heterogeneity of Extracellular Vesicles in Select Colon Disorders

Three-dimensional (3D) imaging and quantitative analysis of extracellular vesicles (EVs) remain largely unexplored, mainly because of limitations in detection techniques. In this study, EVs from patients diagnosed with colorectal cancer (CRC) and ulcerative colitis were examined. To investigate the spatial heterogeneity and 3D refractive index (RI) distribution of single EVs, a label-free digital holographic tomography technique was used at a submicrometer spatial resolution. The presented image-processing algorithms were used in quantitative analysis with digital staining and 3D visualization, the determination of the EV size distribution and extraction of fractions with different RIs. Reconstructed 3D RI distributions revealed variations in the spatial heterogeneity of EVs related to tissue specificity, such as CRC, normal colonic mucosa, and ulcerative colitis, as well as the isolation procedures used. The RI values of EVs isolated from solid tissues of frozen CRC samples were also dependent on the tumor grade and cancer cell proliferation. The simultaneous examination of cell culture models confirmed the association of the RI of EVs with the tumor grade. 3D-RI data analysis generates new perspectives with the optical, contact-free, label-free examination of the individual EVs. Depending on the specific tissue and isolation method, EVs exhibit significant spatial heterogeneity. The optical parameters of single EVs enabled their classification into two unique subgroups with different RI values.

Presence frequency of plant species can predict spatial patterns of the species in small patches on the Qinghai-Tibetan Plateau

Patchiness is an important feature in grassland ecosystems, but the distribution pattern of plant species in small patches on the Qinghai-Tibetan Plateau (QTP) is largely unknown. We questioned: (1) whether the power law can be applied to determine the spatial pattern of plant species in small patches; and (2) how species frequency (dominant, companion and rare) affects the spatial heterogeneity of small patches on the QTP? The power law was used to examine the spatial pattern of plant species and examine the relationship between the plant species presence frequency and spatial pattern in three types of small patches (Cyperaceae, Polygonaceae and Compositae), each with three spatial extents according to the size of the area (scale 1: 0.6–0.9 m2, scale 2: 3.0–3.8 m2 and scale 3: 6.5–8.8 m2) on the QTP. Plant species in patches showed an aggregated distribution and the spatial heterogeneity index differed among species. The spatial heterogeneities of Cyperaceae and Polygonaceae patches were influenced strongly by dominant and companion plant species, while the Compositae patch was influenced by dominant and rare species. The Compositae patches exhibited a lower species diversity and higher spatial heterogeneity index than the other patches, and the extensive distribution of Compositae community can be linked to degradation processes in the alpine meadow. We concluded that the spatial pattern of plant species and the heterogeneity index for small patches could be determined by the species presence frequency on the QTP.

In Vivo Quantification of Regional Circumferential Green Strain in the Thoracic and Abdominal Aorta by Two-Dimensional Spiral Cine DENSE MRI

Regional tissue mechanics play a fundamental role in the patient-specific function and remodeling of the cardiovascular system. Nevertheless, regional in vivo assessments of aortic kinematics remain lacking due to the challenge of imaging the thin aortic wall. Herein, we present a novel application of displacement encoding with stimulated echoes (DENSE) magnetic resonance imaging (MRI) to quantify the regional displacement and circumferential Green strain of the thoracic and abdominal aorta. Two-dimensional (2D) spiral cine DENSE and steady-state free procession (SSFP) cine images were acquired at 3T at either the infrarenal abdominal aorta (IAA), descending thoracic aorta (DTA), or distal aortic arch (DAA) in a pilot study of six healthy volunteers (22-59 y.o., 4 females). DENSE data were processed with multiple custom noise reduction techniques including time-smoothing, displacement vector smoothing, sectorized spatial smoothing, and reference point averaging to calculate circumferential Green strain across 16 equispaced sectors around the aorta. Each volunteer was scanned twice to evaluate interstudy repeatability. Circumferential Green strain was heterogeneously distributed in all volunteers and locations. The mean spatial heterogeneity index (standard deviation of all sector values divided by the mean strain) was 0.37 in the IAA, 0.28 in the DTA, and 0.59 in the DAA. Mean (homogenized) peak strain by DENSE for each cross section was consistent with the homogenized linearized strain estimated from SSFP cine. The mean difference in peak strain across all sectors following repeat imaging was -0.1±2.3%, with a mean absolute difference of 1.7%. Aortic cine DENSE MRI is a viable noninvasive technique for quantifying heterogeneous regional aortic wall strain and has significant potential to improve patient-specific clinical assessments of numerous aortopathies, as well as to provide the lacking spatiotemporal data required to refine patient-specific computational models of aortic growth and remodeling.

Population spatial patterns of grassland plant communities in different slope aspects in the loess hilly area, China.

We investigated the species composition and diversity of four grassland communities with different slope aspects in the loess hilly area of China. The power law was used to analyze spatial heterogeneity of the community and spatial pattern of the population. The results showed that Artemisia sacrorum was the dominant species and occurred in each site. Other species had different status and contributed differently to the spatial pattern of communities. Moreover, the spatial patterns of communities responded differently to various slope aspects, with the degree of aggregation ranked as sunny > half-sunny > half-shady > shady. The spatial heterogeneity index of community was positively correlated with the Simpson diversity index, but was negatively correlated with Margalef richness, Shannon diversity and Pielou evenness. The relative spatial heterogeneity index of the dominant species (A. sacrorum), sub-dominant species (Lespedeza dahurica and Stipa bungeana), and a few associated species (Artemisia scoparia, Melica scabrosa) were larger than that of the community, which resulted in cluster distribution. However, the relative spatial heterogeneity index of most associated species (Phragmites communis, Sonchus arvensis, and Bothriochloa flaccidum) showed the similar trends with the distribution of the community. In contrast, the relative spatial heterogeneity index of Cephalanoplos segetum, Gueldenstaedtia multiflora and Artemisia giraldii was lower than that of the community. These differences reduced the aggregation degree of the community. In summary, the aggregation degree of community was determined by dominant species, sub-dominant species and occasional species. Specifically, the dominant species, sub-dominant species and some associated species could promote the aggregation of the community, but occasional species would reduce the cluster distribution.

Features of the Left Ventricular Functional Geometry in Patients with Myocardial Diseases with Varying Degrees of Systolic Dysfunction.

We revealed some features of the left ventricular functional geometry in patients with myocardial diseases with different degrees of left ventricular systolic dysfunction. A negative correlation was found between the spatio-temporal heterogeneity of the kinetics of the left ventricular wall during systole and ejection fraction in normal heart and in systolic dysfunction. The differences in the quantitative characteristics of the functional geometry between patients and normal subjects and between different groups of patients depended on the severityof left-ventricular systolic dysfunction. In particular, spatial heterogeneity index that characterizes heterogeneity of systolic movement of the wall segments and end-systolic Fourier shape-power index characterizing complexity of the left ventricle shape during systole differed significantly in the examined groups of patients and have the greatest diagnostic power.

Analyzing the spatial heterogeneity of number of plant individuals in grassland community by using power law model

Spatial pattern of grassland community affects ecological processes, and the number of plant individuals is important to evaluate community dynamics as the fundamental ecological parameter of plant species, but so far few studies have dealt with spatial pattern of the number of plant individuals in grassland community. The research we present here explores whether the power law model can be used to evaluate spatial heterogeneity of the number of plant individuals of species in grassland community. As reference data, surveys of individuals were conducted on a natural grassland and a weed community, following random sampling method using 100 0.5 m×0.5m quadrats. We recorded the number of plant individuals of each species occurring in each quadrat. Our results show that (1) the power law model fits well to the spatial pattern of number of plant individuals, (2) the power law model can be applied to evaluate the spatial pattern of number of plant individuals in grassland community, and (3) spatial heterogeneity index value (δ) was positively associated with the average number of plant individuals (m) of species. Our research provides a new application of the power law model to study spatial heterogeneity of grassland community.

High Resolution Strain Analysis Comparing Aorta and Abdominal Aortic Aneurysm with Real Time Three Dimensional Speckle Tracking Ultrasound

Ultrasound measurement of aortic diameter for aneurysm screening allows supervision of aneurysm growth. Additional biomechanical analysis of wall motion and aneurysm deformation can supply information about individual elastic properties and the pathological state of the aortic wall. Local aortic wall motion was analyzed through imaged aortic segments according to age and pathology. Sixty-five patients were examined with a commercial four dimensional ultrasound system (4D-US). Three groups were defined: patients with normal aortic diameter and younger than 60 years of age (n = 21); those with normal aortic diameter and older than 60 years of age (n = 25); and those with infrarenal aortic aneurysm (n = 19). A diastolic reference shape of aortic wall segments was obtained and local and temporally resolved wall strain was determined. Indices characterizing the resulting wall strain distribution were determined. The analysis of biomechanical properties displayed increasing heterogeneous and dyssynchronous circumferential strain with increasing patient age. Young patients exhibited higher mean strain amplitude. The distribution of the spatial heterogeneity index and local strain ratio was inversely proportional to age. The maximum local strain amplitude was significantly higher in the young (0.26 ± 0.17) compared with the old (0.16 ± 0.07) or aneurysmal aorta (0.16 ± 0.10). Temporal dyssynchrony significantly differed between young (0.13 ± 0.10) and old (aneurysmal 0.31 ± 0.04, non-aneurysmal 0.29 ± 0.05), regardless of aortic diameter. The spatial heterogeneity index and local strain ratio differentiate non-aneurysmal and aneurysmal aorta, regardless of age. 4D-US strain imaging enables description of individual wall motion (kinematics) of the infrarenal aorta with high spatial and temporal resolution. Functional differences between young, old, and aneurysmal aorta can be described by mean (circumferential) strain amplitude, the spatial heterogeneity index, and the local strain ratio. Further investigation is required to refine this new perspective of patient individualized characterization of the pathological AAA wall and eventually to rupture risk stratification.

Multi‐scale marine biodiversity patterns inferred efficiently from habitat image processing

Cost-effective proxies of biodiversity and species abundance, applicable across a range of spatial scales, are needed for setting conservation priorities and planning action. We outline a rapid, efficient, and low-cost measure of spectral signal from digital habitat images that, being an effective proxy for habitat complexity, correlates with species diversity and requires little image processing or interpretation. We validated this method for coral reefs of the Great Barrier Reef (GBR), Australia, across a range of spatial scales (1 m to 10 km), using digital photographs of benthic communities at the transect scale and high-resolution Landsat satellite images at the reef scale. We calculated an index of image-derived spatial heterogeneity, the mean information gain (MIG), for each scale and related it to univariate (species richness and total abundance summed across species) and multivariate (species abundance matrix) measures of fish community structure, using two techniques that account for the hierarchical structure of the data: hierarchical (mixed-effect) linear models and distance-based partial redundancy analysis. Over the length and breadth of the GBR, MIG alone explained up to 29% of deviance in fish species richness, 33% in total fish abundance, and 25% in fish community structure at multiple scales, thus demonstrating the possibility of easily and rapidly exploiting spatial information contained in digital images to complement existing methods for inferring diversity and abundance patterns among fish communities. Thus, the spectral signal of unprocessed remotely sensed images provides an efficient and low-cost way to optimize the design of surveys used in conservation planning. In data-sparse situations, this simple approach also offers a viable method for rapid assessment of potential local biodiversity, particularly where there is little local capacity in terms of skills or resources for mounting in-depth biodiversity surveys.

Parsimonious classification of binary lacunarity data computed from food surface images using kernel principal component analysis and artificial neural networks

Lacunarity is about quantifying the degree of spatial heterogeneity in the visual texture of imagery through the identification of the relationships between patterns and their spatial configurations in a two-dimensional setting. The computed lacunarity data can designate a mathematical index of spatial heterogeneity, therefore the corresponding feature vectors should possess the necessary inter-class statistical properties that would enable them to be used for pattern recognition purposes. The objectives of this study is to construct a supervised parsimonious classification model of binary lacunarity data–computed by Valous et al. (2009)–from pork ham slice surface images, with the aid of kernel principal component analysis (KPCA) and artificial neural networks (ANNs), using a portion of informative salient features. At first, the dimension of the initial space (510 features) was reduced by 90% in order to avoid any noise effects in the subsequent classification. Then, using KPCA, the first nineteen kernel principal components (99.04% of total variance) were extracted from the reduced feature space, and were used as input in the ANN. An adaptive feedforward multilayer perceptron (MLP) classifier was employed to obtain a suitable mapping from the input dataset. The correct classification percentages for the training, test and validation sets were 86.7%, 86.7%, and 85.0%, respectively. The results confirm that the classification performance was satisfactory. The binary lacunarity spatial metric captured relevant information that provided a good level of differentiation among pork ham slice images.

Defects in myoglobin oxygenation in K ATP-deficient mouse hearts under normal and stress conditions characterized by near infrared spectroscopy and imaging

Background Disruption of ATP-sensitive potassium (K ATP) channel activity results in the development of dilated cardiomyopathy in response to different forms of stress, likely due to the underlying metabolic defects. To further understand the role of Kir6.2-containing channels in the development of cardiac disease, we analysed the left ventricular (LV) wall oxygenation and the physiologic responses induced by acute stress in non-dilated Kir6.2 −/− hearts. Methods Control (C57BL6) and Kir6.2 −/− mouse hearts were perfused in constant flow Langendorff mode with Krebs–Henseleit buffer. Myocardial oxygenation was evaluated using a newly developed technique, near infrared spectroscopic imaging (NIRSI) of the myoglobin (Mb) oxygen saturation parameter (OSP, ratio of oxy- to total Mb). Results 2,4-dinitrophenol (DNP, 50-µM) and isoproterenol (0.1-µM) failed to produce a transient vasodilatory response and caused a significant diastolic pressure increase in Kir6.2 −/− hearts. DNP strongly suppressed contractile function in both groups and induced severe mean OSP decreases in Kir6.2 −/− hearts. Isoproterenol-induced decreases in OSP were similar despite the lack of contractile function stimulation in the Kir6.2 −/− group. The index of OSP spatial heterogeneity (relative dispersion, RD) was lower by 15% in the Kir6.2 −/− group at the baseline conditions. Recovery after stress caused reduction of RD values by 20% (DNP) and 8% (isoproterenol) in controls; however, these values did not change in the Kir6.2 −/− group. Conclusions 1) NIRSI can be used to analyse 2-D dynamics of LV oxygenation in rodent models of cardiomyopathy; 2) Kir6.2-containing K ATP channels play an important role in maintaining myocardial oxygenation balance under acute stress conditions and in post-stress recovery.

Spatial and Temporal Dynamics of the Weed Community in a Seashore Paspalum Turf

The temporal dynamics of spatial heterogeneity was studied for the weed communities in a seashore paspalum turf with the use of a power-law model. Surveys were conducted in January, March, May, July, September, and November in 2007. In every survey, we set 100 quadrats (50 by 50 cm) referred to as L quadrats on a 50-m line transect at the same position in the turf. Each L quadrat was then divided into four S quadrats (25 by 25 cm) and all plant species occurring in each of these S quadrats were identified and recorded. These data were summarized into frequency distributions and the percentage of S quadrats containing a given species, and the variance of each species was estimated. The power law was used to evaluate the spatial heterogeneity (δ) and frequency of occurrence (p) for each species in the weed communities in six survey months. The results showed that weeds emerged more frequently in the summer–spring season than in winter–autumn, and the spatial heterogeneity was much higher in summer–spring than winter–autumn, especially in summer. The Shannon–Wiener diversity indexes (H') from large to small were July (5.9202) &gt; May (5.6775) &gt; September (5.6631) &gt; March (5.5727) &gt; January (5.1742) &gt; November (4.9668). Likewise, the spatial heterogeneity index (δc) of the whole community was also different in different months. The biggest δc (0.2790) was in July, and the smallest (0.1811) in November. Meanwhile, manilagrass had a high p (= 1.0), indicating that it occurred in all S quadrats in every weed community of every month. However, the turfgrass, seashore paspalum, only emerged in March, May, July, and November, and possessed a low p, indicating the seashore paspalum turf has been naturally replaced by manilagrass.

Why apply ecological laws to epidemiology?

Using ecological laws, or rules, is a useful strategy for epidemiological observations. The application of Taylor's power law to epidemiology and evolutionary ecology of parasites is exemplified here. Taylor's power law takes the form of s2=amb, where s2 is the variance in population abundance, m is the mean abundance of the population, a represents a constant parameter and b represents an index of spatial heterogeneity. Although Taylor's power law reflects the aggregation of parasite (or pathogen) individuals among host population, the values of b could reflect regulation processes in host-parasite systems. Illustrations are given showing how b value is linked to various epidemiological situations: pathogen emergence, the impact of vaccination or the level of host immune defence.

Frequency distribution models for spatial patterns of vegetation abundance

In a plant community, measurements of the number of plant individuals, the number of binary occurrences, plant cover, and biomass per unit area have frequently been used to explain species composition and spatial variation. Studies have shown that frequency distribution can be expressed in several ways: the number of individuals can be expressed using the negative binomial distribution, the number of binary occurrences can be expressed using the beta-binomial distribution, plant cover can be expressed by the beta distribution, and biomass by the gamma distribution. In this study, we have mathematically clarified the relationships between these distributions and their biological relevance. We have also defined a spatial heterogeneity index for each of the above four methods of measurement. For each of these four distribution patterns, several-fitted examples of plant populations or communities, obtained from grassland surveys, are provided.