Comparative power law analysis for the spatial heterogeneity scaling of the hot‐spring microbiomes

2019 ◽  
Author(s):  
Lianwei Li ◽  
Zhanshan (Sam) Ma
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Hot Spring

scholarly journals Spatial Heterogeneity of the Incidence of Powdery Mildew on Hop Cones

Plant Disease ◽  
2006 ◽  
Vol 90 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
David H. Gent ◽  
Walter F. Mahaffee ◽  
William W. Turechek
Keyword(s):  
Powdery Mildew ◽  
Spatial Heterogeneity ◽  
Power Law ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Disease Assessment ◽  
Cluster Sampling ◽  
Data Sets ◽  
Ratio Test ◽  
Frequency Distributions

The spatial heterogeneity of the incidence of hop cones with powdery mildew (Podosphaera macularis) was characterized from transect surveys of 41 commercial hop yards in Oregon and Washington from 2000 to 2005. The proportion of sampled cones with powdery mildew ( p) was recorded for each of 221 transects, where N = 60 sampling units of n = 25 cones assessed in each transect according to a cluster sampling strategy. Disease incidence ranged from 0 to 0.92 among all yards and dates. The binomial and beta-binomial frequency distributions were fit to the N sampling units in a transect using maximum likelihood. The estimation procedure converged for 74% of the data sets where p > 0, and a loglikelihood ratio test indicated that the beta-binomial distribution provided a better fit to the data than the binomial distribution for 46% of the data sets, indicating an aggregated pattern of disease. Similarly, the C(α) test indicated that 54% could be described by the beta-binomial distribution. The heterogeneity parameter of the beta-binomial distribution, θ, a measure of variation among sampling units, ranged from 0.01 to 0.20, with a mean of 0.037 and a median of 0.015. Estimates of the index of dispersion ranged from 0.79 to 7.78, with a mean of 1.81 and a median of 1.37, and were significantly greater than 1 for 54% of the data sets. The binary power law provided an excellent fit to the data, with slope and intercept parameters significantly greater than 1, which indicated that heterogeneity varied systematically with the incidence of infected cones. A covariance analysis indicated that the geographic location (region) of the yards and the type of hop cultivar had little effect on heterogeneity; however, the year of sampling significantly influenced the intercept and slope parameters of the binary power law. Significant spatial autocorrelation was detected in only 11% of the data sets, with estimates of first-order autocorrelation, r1, ranging from -0.30 to 0.70, with a mean of 0.06 and a median of 0.04; however, correlation was detected in only 20 and 16% of the data sets by median and ordinary runs analysis, respectively. Together, these analyses suggest that the incidence of powdery mildew on cones was slightly aggregated among plants, but patterns of aggregation larger than the sampling unit were rare (20% or less of data sets). Knowledge of the heterogeneity of diseased cones was used to construct fixed sampling curves to precisely estimate the incidence of powdery mildew on cones at varying disease intensities. Use of the sampling curves developed in this research should help to improve sampling methods for disease assessment and management decisions.

scholarly journals Spatial heterogeneity and variability of a large-scale vegetation community using a power-law model

2005 ◽  
Vol 10 (4) ◽  
pp. 469-477 ◽  
Author(s):  
Zhiyuan Song ◽  
Darning Huang ◽  
Masae Shiyomi ◽  
Yusheng Wang ◽  
Shiqeo Takahashi ◽  
...  
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Large Scale ◽  
Power Law Model ◽  
Vegetation Community

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

2016 ◽  
Vol 320 ◽  
pp. 316-321 ◽  
Author(s):  
Qingqing Guan ◽  
Jun Chen ◽  
Zhicheng Wei ◽  
Yuxia Wang ◽  
Masae Shiyomi ◽  
...  
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Power Law Model ◽  
Grassland Community

Spatial heterogeneity in a grassland community: Use of power law

2001 ◽  
Vol 16 (3) ◽  
pp. 487-495 ◽  
Author(s):  
Masae Shiyomi ◽  
Shigeo Takahashi ◽  
Jin Yoshimura ◽  
Taisuke Yasuda ◽  
Michio Tsutsumi ◽  
...  
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Grassland Community

scholarly journals Heterogeneity–disease relationship in the human microbiome-associated diseases

2020 ◽  
Vol 96 (7) ◽  
Author(s):  
Zhanshan (Sam) Ma
Keyword(s):  
Spatial Distribution ◽  
Spatial Heterogeneity ◽  
Power Law ◽  
Human Microbiome ◽  
Deep Understanding ◽  
High Profile ◽  
General Methodology ◽  
Associated Diseases ◽  
Microbiome Research

ABSTRACT Space is a critical and also challenging frontier in human microbiome research. It has been found that lack of consideration of scales beyond individual and ignoring of microbe dispersal are two crucial roadblocks in preventing deep understanding of the spatial heterogeneity of human microbiome. Assessing and interpreting the heterogeneity and dispersal in microbiomes explicitly are particularly challenging, but implicit approaches such as Taylor's power law (TPL) can be rather effective. Based on TPL, which achieved a rare status of ecological laws, we introduce a general methodology for characterizing the spatial heterogeneity of microbiome (i.e. characterization of microbial spatial distribution) and further apply it for investigating the heterogeneity–disease relationship (HDR) via analyzing a big dataset of 26 MAD (microbiome-associated disease) studies covering nearly all high-profile MADs including obesity, diabetes and gout. It was found that in majority of the MAD cases, the microbiome was sufficiently resilient to endure the disease disturbances. Specifically, in ∼10–16% cases, disease effects were significant—the healthy and diseased cohorts exhibited statistically significant differences in the TPL heterogeneity parameters. We further compared HDR with classic diversity–disease relationship (DDR) and explained their mechanistic differences. Both HDR and DDR cross-verified remarkable resilience of the human microbiomes against MADs.

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

Weed Science ◽  
2009 ◽  
Vol 57 (3) ◽  
pp. 248-255 ◽  
Author(s):  
Xin-Ming Xie ◽  
You-Zhi Jian ◽  
Xiao-Na Wen
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Temporal Dynamics ◽  
Line Transect ◽  
Frequency Of Occurrence ◽  
Power Law Model ◽  
Seashore Paspalum ◽  
Frequency Distributions ◽  
Weed Communities ◽  
Spatial And Temporal Dynamics

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) > May (5.6775) > September (5.6631) > March (5.5727) > January (5.1742) > 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.

scholarly journals Airborne Pathogens in a Heterogeneous World: Superspreading & Mitigation

2020 ◽  
Author(s):  
Julius B. Kirkegaard ◽  
Joachim Mathiesen ◽  
Kim Sneppen
Keyword(s):  
University Students ◽  
Spatial Heterogeneity ◽  
Short Duration ◽  
Power Law ◽  
Solvable Model ◽  
Pathogen Transmission ◽  
Single Individual ◽  
Tracking Data ◽  
Extreme Statistics ◽  
Social Events

Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We find that diseases that have a short duration of high infectiousness can give extreme statistics such as 20 % infecting more than 80 %, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation efforts applied to our model. We find that the effect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity.

scholarly journals Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence

2018 ◽  
Vol 108 (6) ◽  
pp. 656-680 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes ◽  
W. Bucker Moraes ◽  
X.-M. Xu ◽  
W. W. Turechek
Keyword(s):  
Spatial Heterogeneity ◽  
Power Law ◽  
Disease Incidence ◽  
Plant Diseases ◽  
Stochastic Simulations ◽  
Sampling Unit ◽  
Small Scale ◽  
Parameter Estimates ◽  
Quarter Century ◽  
Wide Range

Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor’s power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

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