Statistical Properties of a DNA Sample Under the Finite-Sites Model

Genetics ◽  
1996 ◽  
Vol 144 (4) ◽  
pp. 1941-1950 ◽  
Author(s):  
Ziheng Yang
Keyword(s):  
Process Model ◽  
Random Mating ◽  
Major Effect ◽  
Statistical Properties ◽  
Parameter Estimates ◽  
Rate Variation ◽  
Markov Process Model ◽  
D Loop ◽  
Infinite Sites Model ◽  
Segregating Sites

Statistical properties of a DNA sample from a random-mating population of constant size are studied under the finite-sites model. It is assumed that there is no migration and no recombination occurs within the locus. A Markov process model is used for nucleotide substitution, allowing for multiple substitutions at a single site. The evolutionary rates among sites are treated as either constant or variable. The general likelihood calculation using numerical integration involves intensive computation and is feasible for three or four sequences only; it may be used for validating approximate algorithms. Methods are developed to approximate the probability distribution of the number of segregating sites in a random sample of n sequences, with either constant or variable substitution rates across sites. Calculations using parameter estimates obtained for human D-loop mitochondrial DNAs show that among-site rate variation has a major effect on the distribution of the number of segregating sites; the distribution under the finite-sites model with variable rates among sites is quite different from that under the infinite-sites model.

Markov Process Model Forecasting of Quarterly Accounting Earnings Per Share

2011 ◽  
Vol 3 (6) ◽  
pp. 99-103
Author(s):  
M. P. Rajakumar M. P. Rajakumar ◽  
◽  
Dr. V. Shanthi Dr. V. Shanthi
Keyword(s):  
Markov Process ◽  
Process Model ◽  
Accounting Earnings ◽  
Earnings Per Share ◽  
Markov Process Model

scholarly journals Empirical Model With Excellent Statistical Properties for Describing Temperature-Dependent Developmental Rates of Insects and Mites

2017 ◽  
Vol 110 (3) ◽  
pp. 302-309 ◽  
Author(s):  
David A. Ratkowsky ◽  
Gadi V. P. Reddy
Keyword(s):  
Nonlinear Regression ◽  
Empirical Model ◽  
Minimum Variance ◽  
Statistical Properties ◽  
Parameter Estimates ◽  
Regression Equations ◽  
Temperature Dependent ◽  
Temperature Range ◽  
Least Squares Estimators ◽  
Development Rates

Abstract Previous empirical models for describing the temperature-dependent development rates for insects include the Briére, Lactin, Beta, and Ratkowsky models. Another nonlinear regression model, not previously considered in population entomology, is the Lobry–Rosso–Flandrois model, the shape of which is very close to that of the Ratkowsky model in the suboptimal temperature range, but which has the added advantage that all four of its parameters have biological meaning. A consequence of this is that initial parameter estimates, needed for solving the nonlinear regression equations, are very easy to obtain. In addition, the model has excellent statistical properties, with the estimators of the parameters being “close-to-linear,” which means that the least squares estimators are close to being unbiased, normally distributed, minimum variance estimators. The model describes the pooled development rates very well throughout the entire biokinetic temperature range and deserves to become the empirical model of general use in this area.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals Age and growth rate variation influence the functional relationship between somatic and otolith size

2017 ◽  
Vol 74 (5) ◽  
pp. 680-692 ◽  
Author(s):  
Eloïse C. Ashworth ◽  
Norman G. Hall ◽  
S. Alex Hesp ◽  
Peter G. Coulson ◽  
Ian C. Potter
Keyword(s):  
Growth Rate ◽  
Age And Growth ◽  
Growth Effect ◽  
Parameter Estimates ◽  
Rate Variation ◽  
Fish Length ◽  
Correlated Errors ◽  
Otolith Growth ◽  
Positive Dependence ◽  
Otolith Size

Curves describing the length–otolith size relationships for juveniles and adults of six fish species with widely differing biological characteristics were fitted simultaneously to fish length and otolith size at age, assuming that deviations from those curves are correlated rather than independent. The trajectories of the somatic and otolith growth curves throughout life, which reflect changing ratios of somatic to otolith growth rates, varied markedly among species and resulted in differing trends in the relationships formed between fish and otolith size. Correlations between deviations from predicted values were always positive. Dependence of length on otolith growth rate (i.e., “growth effect”) and “correlated errors in variables” introduce bias into parameter estimates obtained from regressions describing the allometric relationships between fish lengths and otolith sizes. The approach taken in this study to describe somatic and otolith growth accounted for both of these effects and that of age to produce more reliable determinations of the length–otolith size relationships used for back-calculation and assumed when drawing inferences from sclerochronological studies.

scholarly journals Mapping species richness using opportunistic samples: a case study on ground-floor bryophyte species richness in the Belgian province of Limburg

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Thomas Neyens ◽  
Peter J. Diggle ◽  
Christel Faes ◽  
Natalie Beenaerts ◽  
Tom Artois ◽  
...  
Keyword(s):  
Species Richness ◽  
Process Model ◽  
Cost Effective ◽  
Sampling Bias ◽  
Parameter Estimates ◽  
Multiple Sources ◽  
Ground Floor ◽  
Sampling Process ◽  
Ecological Predictors ◽  
Geostatistical Models

AbstractIn species richness studies, citizen-science surveys where participants make individual decisions regarding sampling strategies provide a cost-effective approach to collect a large amount of data. However, it is unclear to what extent the bias inherent to opportunistically collected samples may invalidate our inferences. Here, we compare spatial predictions of forest ground-floor bryophyte species richness in Limburg (Belgium), based on crowd- and expert-sourced data, where the latter are collected by adhering to a rigorous geographical randomisation and data collection protocol. We develop a log-Gaussian Cox process model to analyse the opportunistic sampling process of the crowd-sourced data and assess its sampling bias. We then fit two geostatistical Poisson models to both data-sets and compare the parameter estimates and species richness predictions. We find that the citizens had a higher propensity for locations that were close to their homes and environmentally more valuable. The estimated effects of ecological predictors and spatial species richness predictions differ strongly between the two geostatistical models. Unknown inconsistencies in the sampling process, such as unreported observer’s effort, and the lack of a hypothesis-driven study protocol can lead to the occurrence of multiple sources of sampling bias, making it difficult, if not impossible, to provide reliable inferences.

scholarly journals Inferring the Demographic History of Inbred Species from Genome-Wide SNP Frequency Data

2020 ◽  
Vol 37 (7) ◽  
pp. 2124-2136
Author(s):  
Paul D Blischak ◽  
Michael S Barker ◽  
Ryan N Gutenkunst
Keyword(s):  
Puma Concolor ◽  
Demographic History ◽  
Random Mating ◽  
Simulated Data ◽  
Conservation Agriculture ◽  
Model Fit ◽  
Parameter Estimates ◽  
History Of ◽  
Demographic Inference ◽  
Inbred Populations

Abstract Demographic inference using the site frequency spectrum (SFS) is a common way to understand historical events affecting genetic variation. However, most methods for estimating demography from the SFS assume random mating within populations, precluding these types of analyses in inbred populations. To address this issue, we developed a model for the expected SFS that includes inbreeding by parameterizing individual genotypes using beta-binomial distributions. We then take the convolution of these genotype probabilities to calculate the expected frequency of biallelic variants in the population. Using simulations, we evaluated the model’s ability to coestimate demography and inbreeding using one- and two-population models across a range of inbreeding levels. We also applied our method to two empirical examples, American pumas (Puma concolor) and domesticated cabbage (Brassica oleracea var. capitata), inferring models both with and without inbreeding to compare parameter estimates and model fit. Our simulations showed that we are able to accurately coestimate demographic parameters and inbreeding even for highly inbred populations (F = 0.9). In contrast, failing to include inbreeding generally resulted in inaccurate parameter estimates in simulated data and led to poor model fit in our empirical analyses. These results show that inbreeding can have a strong effect on demographic inference, a pattern that was especially noticeable for parameters involving changes in population size. Given the importance of these estimates for informing practices in conservation, agriculture, and elsewhere, our method provides an important advancement for accurately estimating the demographic histories of these species.

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