Patterns of macroparasite aggregation in wildlife host populations

Parasitology ◽  
1998 ◽  
Vol 117 (6) ◽  
pp. 597-610 ◽  
Author(s):  
D. J. SHAW ◽  
B. T. GRENFELL ◽  
A. P. DOBSON
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Data Sets ◽  
Frequency Distributions ◽  
System A ◽  
Host Sex ◽  
Host Parasite

Frequency distributions from 49 published wildlife host–macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host–parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

scholarly journals On hypergeometric generalized negative binomial distribution

2002 ◽  
Vol 29 (12) ◽  
pp. 727-736 ◽  
Author(s):  
M. E. Ghitany ◽  
S. A. Al-Awadhi ◽  
S. L. Kalla
Keyword(s):  
Recurrence Relation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Generalized Negative Binomial Distribution ◽  
The Right ◽  
Three Term Recurrence Relation

It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.

scholarly journals DISTRIBUCIÓN ESPACIAL DE Vatiga spp. (HEMIPTERA: TINGIDAE) EN EL CULTIVO DE YUCA

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Antonio De Souza Silva
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Field Data ◽  
Negative Binomial ◽  
Plant Leaves ◽  
Frequency Distributions ◽  
Morisita Index ◽  
Best Fit

<p class="p1"> <strong>RESUMEN</strong></p><p class="p3">El objetivo de este trabajo fue generar informacion acerca de cuál es el modelo de disposición espacial de Vatiga spp. en el cultivo de la yuca. Se realizaron muestreos en dos áreas comerciales de 2500 m<span class="s1">2</span>, divididas en 100 parcelas. Se contaron adultos y de ninfas de Vatiga spp. en las hojas basales y medias de la planta. En total, se realizaron doce muestreos quincenalmente, desde febrero hasta abril de 2014, época de mayor incidencia de esta plaga. De forma general, a través de los índices de dispersión (varianza/media, índice de Morisita y exponente K) y las distribuciones de frecuencia, se observa que la distribución espacial de Vatiga spp. es agregada, es decir, el padrón de distribución Binomial Negativa fue el que resultó de mejor ajuste a los datos obtenidos a campo, con el conteo de los individuos.</p><p class="p1"><strong>ABSTRACT</strong></p><p class="p2">The aim of this study was to generate information about which is the model of spatial distribution of Vatiga spp. in the cassava culture. Sampling was conducted in two commercial areas of 2,500 m<span class="s1">2</span>, divided into 100 plots. Adults and nymphs of Vatiga spp. were counted in the basal and medium plant leaves. In all, twelve samples were taken fortnightly from February to April 2014, when occurs the highest incidence of this pest. Based in the indices of dispersion (variance/mean, Morisita index and K exponent) and the frequency distributions, it was observed that the spatial distribution of Vatiga spp. is aggregate, it means that the standard Negative Binomial distribution was the best fit to the field data obtained, with the counting direction of individuals.</p>

A quantitative approach to parasitism

Parasitology ◽  
1971 ◽  
Vol 62 (2) ◽  
pp. 179-193 ◽  
Author(s):  
H. D. Crofton
Keyword(s):  
Negative Binomial Distribution ◽  
Quantitative Assessment ◽  
Negative Binomial ◽  
Truncated Form ◽  
Great Pleasure ◽  
New Approach ◽  
Frequency Distributions ◽  
Ecological Relationship ◽  
Definition Of ◽  
Host Parasite

The frequency distribution of parasites among hosts is used as the basis of the quantitative assessment of the nature of parasitism. The host–parasite system is regarded as an ecological relationship between populations of two different species of organisms. From the overdispersed frequency distributions exemplified by the Negative Binomial distribution a specially truncated form is derived and shown to fit the data of Hynes & Nicholas (1963). The theoretical consequences are discussed and these form the basis of a definition of parasitism.I am indebted to Professor H. B. N. Hynes who so readily understood my general aims and freely provided detailed information about his work. I also have great pleasure in thanking Professor John H. Whitlock, not only for the original computing facilities which he so generously provided, but also for his many other kindnesses. I am also very grateful to Dr Charles Henderson Jun. for his work on the original computer program and to Dr Mark Westwood for his ingenuity and labours in producing a new approach to the computations.

scholarly journals Spatial Pattern of Strawberry Powdery Mildew (Podosphaera aphanis) and Airborne Inoculum

Plant Disease ◽  
2014 ◽  
Vol 98 (1) ◽  
pp. 43-54 ◽  
Author(s):  
H. Van der Heyden ◽  
M. Lefebvre ◽  
L. Roberge ◽  
L. Brodeur ◽  
O. Carisse
Keyword(s):  
Powdery Mildew ◽  
Power Law ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Disease Incidence ◽  
Data Sets ◽  
Incidence Data ◽  
Airborne Inoculum ◽  
The Relationship

The relationship between strawberry powdery mildew and airborne conidium concentration (ACC) of Podosphaera aphanis was studied using data collected from 2006 to 2009 in 15 fields, and spatial pattern was described using 2 years of airborne inoculum and disease incidence data collected in fields planted with the June-bearing strawberry (Fragaria × ananassa) cultivar Jewel. Disease incidence, expressed as the proportion of diseased leaflets, and ACC were monitored in fields divided into 3 × 8 grids containing 24 100 m2 quadrats. Variance-to-mean ratio, index of dispersion, negative binomial distribution, Poisson distribution, and binomial and beta-binomial distributions were used to characterize the level of spatial heterogeneity. The relationship between percent leaf area diseased and daily ACC was linear, while the relationship between ACC and disease incidence followed an exponential growth curve. The V/M ratios were significantly greater than 1 for 100 and 96% of the sampling dates for ACC sampled at 0.35 m from the ground (ACC0.35m) and for ACC sampled at 1.0 m from the ground (ACC1.0m), respectively. For disease incidence, the index of dispersion D was significantly greater than 1 for 79% of the sampling dates. The negative binomial distribution fitted 86% of the data sets for both ACC1.0m and ACC0.35m. For disease incidence data, the beta-binomial distribution provided a good fit of 75% of the data sets. Taylor's power law indicated that, for ACC at both sampling heights, heterogeneity increased with increasing mean ACC, whereas the binary form of the power law suggested that heterogeneity was not dependent on the mean for disease incidence. When the spatial location of each sampling location was taken into account, Spatial Analysis by Distance Indices showed low aggregation indices for both ACCs and disease incidence, and weak association between ACC and disease incidence. Based on these analyses, it was found that the distribution of strawberry powdery mildew was weakly aggregated. Although a higher level of heterogeneity was observed for airborne inoculum, the heterogeneity was low with no distinct foci, suggesting that epidemics are induced by well-distributed inoculum. This low level of heterogeneity allows mean airborne inoculum concentration to be estimated using only one sampler per field with an overall accuracy of at least 0.841. The results obtained in this study could be used to develop a sampling scheme that will improve strawberry powdery mildew risk estimation.

On the empty cells of Poisson histograms

1993 ◽  
Vol 30 (03) ◽  
pp. 561-574
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Cell Size ◽  
Poisson Distribution ◽  
Finite Groups ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Almost Sure Convergence ◽  
Unit Cell Size ◽  
Independent Observations

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (μ) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown that the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when μ is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed.

scholarly journals Negative Binomial Distribution to Explain the Domestic Fire Incidence in Nepal

2021 ◽  
pp. 51-66
Author(s):  
Arun Kumar Yadav ◽  
Santosh Kumar Shah
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Information Criteria ◽  
Descriptive Statistics ◽  
Probability Models ◽  
Ecological Regions ◽  
The Hill ◽  
Fire Incidence

Background: Fire disaster is one of the most destructive disasters. According to global dataset of Sendai Framework, domestic fire incidence was 9.9% up to 2019. In Nepal, 62% fire incidence was reported during 2017 and 2018. However, many studies have been conducted on fire incidence, few of them are based on domestic fire incidence. Objective: To find the descriptive statistics of fire occurrences and fire fatalities, and to identify the probability distributions that best fit the data of fire occurrences observed in three ecological regions as well as overall in Nepal. Material and Methods: The data of fire incidences from May 2011 to April 2021 were retrieved from Nepal Disaster Risk Reduction Portal, Government of Nepal. At first, a statistical software "Mathwave EasyFit" of 30 days trial version was used to identify the candidate probability models. Further, the best probability model was determined after testing the goodness of fit of the candidate models by using graphical tools-histogram and theoretical densities, empirical and theoretical CDFs, Q-Q plot and P-P plot; and mathematical tools-maximum likelihood, Akaike Information Criteria and Bayesian Information Criteria by using the package “fitdistrplus” of software R version 4.1.1. Results: On an average, 135 fire incidences per month were occurred in Nepal. However, the Terai faced the highest monthly fire incidences compared to the Hill and the Mountain, it has less fatality per 100 fire incidence followed by the Hill and the Mountain. Descriptive statistics reveals that fire occurrences are moderate during November to February and high in March and April. The fire incidences were reported high during spring and winter and low during summer and autumn season which reveals that fire incidence might be related with the precipitation and temperature. The sample data was run in "Mathwave EasyFit" software which suggested Poisson, geometric and negative binomial distribution as candidate probability models. The goodness of fit of these models were further tested by graphical as well as mathematical tools where negative binomial distribution was found to be best among the candidate models for the data set. Conclusion: Incidence of fire disasters varies by ecological regions as well as by seasons. It is low in the Mountain region and during Monsoon/rainy season. Negative binomial distribution fits the best to monthly data of fire incidence in Nepal.

Modeling earthquake numbers by Negative Binomial Hidden Markov models

2020 ◽  
Author(s):  
Katerina Orfanogiannaki ◽  
Dimitris Karlis
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Time Window ◽  
Hidden Markov ◽  
Maximum Likelihood Estimates ◽  
Ongoing Research ◽  
Real Earthquake ◽  
Earthquake Data

&lt;p&gt;Modeling seismicity data is challenging and it remains a subject of ongoing research. Assumptions about the distribution of earthquake numbers play an important role in seismic hazard and risk analysis. The most common distribution that has been widely used in modeling earthquake numbers is the Poisson distribution because of its simplicity and easy to use. However, the heterogeneity in earthquake data and temporal dependencies that are often present in many real earthquake sequences make the use of the Poisson distribution inadequate. So, we propose the use of a Hidden Markov model (HMM) with state-specific Negative Binomial distributions in which some states are allowed to approach the Poisson distribution. A HMM is a generalization of a mixture model where the different unobservable (hidden) states are related through a Markov process rather than being independent of each other. We parameterize the Negative Binomial distribution in terms of the mean and dispersion (clustering) parameter. Maximum likelihood estimates of the models&amp;#8217; parameters are obtained through an Expectation-Maximization algorithm (EM-algorithm).&lt;/p&gt;&lt;p&gt;We apply the model to real earthquake data. We have selected the area of Killini Western Greece to test the proposed hypothesis. The area of Killini has been selected based on the fact that in a time window of 17 years three clusters of seismicity associated with strong mainshocks are included in the catalog. Application of the model to the data resulted in three states, representing different levels of seismicity (low, medium, high). The state that corresponds to the low seismicity level approaches the Poisson distribution while the other two states (medium and high) are following the Negative Binomial distribution. This result complies with the nature of the data. The variation within each state that is introduced to the model by the Negative Binomial distribution is greater in the states of medium and high seismicity.&amp;#160;&lt;/p&gt;

On the empty cells of Poisson histograms

1993 ◽  
Vol 30 (3) ◽  
pp. 561-574
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Cell Size ◽  
Poisson Distribution ◽  
Finite Groups ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Empirical Bayes ◽  
Negative Binomial ◽  
Almost Sure Convergence ◽  
Unit Cell Size ◽  
Independent Observations

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (μ) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown that the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when μ is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed.

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