scholarly journals On the mechanistic roots of an ecological law: parasite aggregation

2019 ◽  
Author(s):  
Jomar F. Rabajante ◽  
Elizabeth L. Anzia ◽  
Chaitanya S. Gokhale
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Mechanistic Model ◽  
A Priori ◽  
Parasite Ecology ◽  
Mean And Variance ◽  
Parasite Aggregation ◽  
Sampling Procedures ◽  
Host Parasite

AbstractParasite aggregation, a recurring pattern in macroparasite infections, is considered one of the “laws” of parasite ecology. Few hosts have a large number of parasites while most hosts have a low number of parasites. Phenomenological models of host-parasite systems thus use the negative-binomial distribution. However, to infer the mechanisms of aggregation, a mechanistic model that does not make any a priori assumptions is essential. Here we formulate a mechanistic model of parasite aggregation in hosts without assuming a negative-binomial distribution. Our results show that a simple model of parasite accumulation still results in an aggregated pattern, as shown by the derived mean and variance of the parasite distribution. By incorporating the derived statistics in host-parasite interactions, we can predict how aggregation affects the population dynamics of the hosts and parasites through time. Thus, our results can directly be applied to observed data as well as can inform the designing of statistical sampling procedures. Overall, we have shown how a plausible mechanistic process can result in the often observed phenomenon of parasite aggregation occurring in numerous ecological scenarios, thus providing a basis for a “law” of ecology.

The Stability of Weed Seedling Population Models and Parameters in Eastern Nebraska Corn (Zea mays) and Soybean (Glycine max) Fields

Weed Science ◽  
1995 ◽  
Vol 43 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Distribution Model ◽  
Ratio Test ◽  
Weed Species ◽  
Sampling Procedures ◽  
Grass Weed

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is akparameter.kis a nonspatial aggregation parameter related to the variance at a given mean value. Thekparameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of thekparameter across field sites was assessed using the likelihood ratio test There was no stable or commonkvalue across field sites and years for all weed species populations. The lack of stability inkacross field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Becausekis not stable across field sites,kmust be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

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 A mechanistic model for the negative binomial distribution of single-cell mRNA counts

2019 ◽  
Author(s):  
Lisa Amrhein ◽  
Kumar Harsha ◽  
Christiane Fuchs
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Single Cell ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mechanistic Model ◽  
Steady State Probability ◽  
Degradation Models

SummarySeveral tools analyze the outcome of single-cell RNA-seq experiments, and they often assume a probability distribution for the observed sequencing counts. It is an open question of which is the most appropriate discrete distribution, not only in terms of model estimation, but also regarding interpretability, complexity and biological plausibility of inherent assumptions. To address the question of interpretability, we investigate mechanistic transcription and degradation models underlying commonly used discrete probability distributions. Known bottom-up approaches infer steady-state probability distributions such as Poisson or Poisson-beta distributions from different underlying transcription-degradation models. By turning this procedure upside down, we show how to infer a corresponding biological model from a given probability distribution, here the negative binomial distribution. Realistic mechanistic models underlying this distributional assumption are unknown so far. Our results indicate that the negative binomial distribution arises as steady-state distribution from a mechanistic model that produces mRNA molecules in bursts. We empirically show that it provides a convenient trade-off between computational complexity and biological simplicity.Graphical Abstract

Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

2019 ◽  
Vol 53 (5) ◽  
pp. 417-422
Author(s):  
P. De los Ríos ◽  
E. Ibáñez Arancibia
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Rocky Shore ◽  
Negative Binomial ◽  
Null Model ◽  
Easter Island ◽  
Published Data ◽  
Distribution Analysis ◽  
Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

2011 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Y. ARBI ◽  
R. BUDIARTI ◽  
I G. P. PURNABA
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Financial Institution ◽  
Expected Value ◽  
Insurance Companies ◽  
Limited Data ◽  
Loss Distribution Approach ◽  
Potential Loss ◽  
The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

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