scholarly journals Non-Homogeneous Markov Set Systems

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 471
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Asymptotic Behavior ◽  
Population Structure ◽  
Confidence Intervals ◽  
Limit Set ◽  
Stroke Patients ◽  
Relative Population ◽  
Set Systems ◽  
Population Structures ◽  
Basic Parameters ◽  
Initial Distributions

A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.

scholarly journals Laws of Large Numbers for Non-Homogeneous Markov Systems

2018 ◽  
Vol 22 (4) ◽  
pp. 1631-1658 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Population Structure ◽  
Law Of Large Numbers ◽  
Mean Square ◽  
Stroke Patients ◽  
University System ◽  
Relative Population ◽  
Laws Of Large Numbers ◽  
Markov Systems ◽  
Large Numbers ◽  
The Law

AbstractIn the present we establish Laws of Large Numbers for Non-Homogeneous Markov Systems and Cyclic Non-homogeneous Markov systems. We start with a theorem, where we establish, that for a NHMS under certain conditions, the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure of memberships in that state. We continue by proving a theorem which provides the conditions under which the mode of covergence is almost surely. We continue by proving under which conditions a Cyclic NHMS is Cesaro strongly ergodic. We then proceed to prove, that for a Cyclic NHMS under certain conditions the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure in the strongly Cesaro sense of memberships in that state. We then proceed to establish a founding Theorem, which provides the conditions under which, the relative population structure asymptotically converges in the strongly Cesaro sense with geometrical rate. This theorem is the basic instrument missing to prove, under what conditions the Law of Large Numbers for a Cycl-NHMS is with almost surely mode of convergence. Finally, we present two applications firstly for geriatric and stroke patients in a hospital and secondly for the population of students in a University system.

Surnames and population structure in the Doctrine of Belén, Altos de Arica, Viceroyalty of Peru (1750–1813)

2021 ◽  
pp. 1-13
Author(s):  
Emma Alfaro ◽  
Xochitl Inostroza ◽  
José E. Dipierri ◽  
Daniela Peña Aguilera ◽  
Jorge Hidalgo ◽  
...  
Keyword(s):  
Population Structure ◽  
Indigenous Population ◽  
Random Mating ◽  
Quantitative Information ◽  
Geographic Space ◽  
Documentary Sources ◽  
Cultural Variables ◽  
The Social ◽  
Population Structures ◽  
And Migration

Abstract The analysis of multiple population structures (biodemographic, genetic and socio-cultural) and their inter-relations contribute to a deeper understanding of population structure and population dynamics. Genetically, the population structure corresponds to the deviation of random mating conditioned by a limited number of ancestors, by restricted migration in the social or geographic space, or by preference for certain consanguineous unions. Through the isonymic method, surname frequency and distribution across the population can supply quantitative information on the structure of a human population, as they constitute universal socio-cultural variables. Using documentary sources to undertake the Doctrine of Belén’s (Altos de Arica, Chile) historical demography reconstruction between 1763 and 1820, this study identified an indigenous population with stable patronymics. The availability of complete marriage, baptism and death records, low rates of migration and the significant percentage of individuals registered and constantly present in this population favoured the application of the isonymic method. The aim of this work was to use given names and surnames recorded in these documentary sources to reconstruct the population structure and migration pattern of the Doctrine of Belén between 1750 and 1813 through the isonymic method. The results of the study were consistent with the ethno-historical data of this ethnic space, where social cohesion was, in multiple ways, related to the regulation of daily life in colonial Andean societies.

scholarly journals Detecting a hierarchical genetic population structure via Multi-InDel markers on the X chromosome

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Guang Yao Fan ◽  
Yi Ye ◽  
Yi Ping Hou
Keyword(s):  
Population Structure ◽  
X Chromosome ◽  
Cost Effective ◽  
Genetic Distances ◽  
Ancestry Informative Marker ◽  
Genetic Population ◽  
Single Nucleotide ◽  
Chinese Populations ◽  
Population Structures ◽  
Biogeographical Ancestry

Abstract Detecting population structure and estimating individual biogeographical ancestry are very important in population genetics studies, biomedical research and forensics. Single-nucleotide polymorphism (SNP) has long been considered to be a primary ancestry-informative marker (AIM), but it is constrained by complex and time-consuming genotyping protocols. Following up on our previous study, we propose that a multi-insertion-deletion polymorphism (Multi-InDel) with multiple haplotypes can be useful in ancestry inference and hierarchical genetic population structures. A validation study for the X chromosome Multi-InDel marker (X-Multi-InDel) as a novel AIM was conducted. Genetic polymorphisms and genetic distances among three Chinese populations and 14 worldwide populations obtained from the 1000 Genomes database were analyzed. A Bayesian clustering method (STRUCTURE) was used to discern the continental origins of Europe, East Asia, and Africa. A minimal panel of ten X-Multi-InDels was verified to be sufficient to distinguish human ancestries from three major continental regions with nearly the same efficiency of the earlier panel with 21 insertion-deletion AIMs. Along with the development of more X-Multi-InDels, an approach using this novel marker has the potential for broad applicability as a cost-effective tool toward more accurate determinations of individual biogeographical ancestry and population stratification.

scholarly journals Evolution and Population Structure of Salmonella enterica Serovar Newport

2010 ◽  
Vol 192 (24) ◽  
pp. 6465-6476 ◽  
Author(s):  
Vartul Sangal ◽  
Heather Harbottle ◽  
Camila J. Mazzoni ◽  
Reiner Helmuth ◽  
Beatriz Guerra ◽  
...  
Keyword(s):  
Population Structure ◽  
North America ◽  
Salmonella Enterica ◽  
Health Concern ◽  
Global Public Health ◽  
Multiple Sequence ◽  
Monophyletic Lineage ◽  
Population Structures ◽  
Paratyphi B ◽  
Multiple Drugs

ABSTRACT Salmonellosis caused by Salmonella enterica serovar Newport is a major global public health concern, particularly because S. Newport isolates that are resistant to multiple drugs (MDR), including third-generation cephalosporins (MDR-AmpC phenotype), have been commonly isolated from food animals. We analyzed 384 S. Newport isolates from various sources by a multilocus sequence typing (MLST) scheme to study the evolution and population structure of the serovar. These were compared to the population structure of S. enterica serovars Enteritidis, Kentucky, Paratyphi B, and Typhimurium. Our S. Newport collection fell into three lineages, Newport-I, Newport-II, and Newport-III, each of which contained multiple sequence types (STs). Newport-I has only a few STs, unlike Newport-II or Newport-III, and has possibly emerged recently. Newport-I is more prevalent among humans in Europe than in North America, whereas Newport-II is preferentially associated with animals. Two STs of Newport-II encompassed all MDR-AmpC isolates, suggesting recent global spread after the acquisition of the bla CMY-2 gene. In contrast, most Newport-III isolates were from humans in North America and were pansusceptible to antibiotics. Newport was intermediate in population structure to the other serovars, which varied from a single monophyletic lineage in S. Enteritidis or S. Typhimurium to four discrete lineages within S. Paratyphi B. Both mutation and homologous recombination are responsible for diversification within each of these lineages, but the relative frequencies differed with the lineage. We conclude that serovars of S. enterica provide a variety of different population structures.

scholarly journals Effect of unfavourable population structure on estimates of heritability, systematic effects and breeding values

2008 ◽  
Vol 51 (6) ◽  
pp. 601-610
Author(s):  
A. P. Kominakis
Keyword(s):  
Population Structure ◽  
Mean Squared Error ◽  
Heritability Estimate ◽  
Breeding Values ◽  
Parameter Estimations ◽  
Squared Error ◽  
Heritability Estimation ◽  
Population Structures ◽  
Systematic Effects ◽  
The Impact

Abstract. Empirical estimations of heritability, systematic effects and predictions of sires’ breeding values (BVs) were obtained under various population structures for simulated populations consisted of n = 400 animals in 5 herds for a trait of medium heritability (h2 = 0.30). An infinitesimal additive genetic animal model was assumed while simulating data. Population structure was varied to allow for good and poor connectedness across herds and (non)random association between the genetic and the environmental effects. The impact of the various population structures on the parameter estimation(s) was assessed using Mean Squared Error (MSE) and Pearson’s correlations. Allowing sires to have progenies in more than one herd (good herd connectedness) and random use of sires across herds generally resulted in good parameter estimations. Poor connectedness significantly affected herd effects estimation and BV prediction but not heritability estimation as long as random usage of sires across environments was guaranteed. Selective use of the best sires in the best herds along with poor connectedness resulted in poorest estimations of all parameters examined. In the latter case, heritability was seriously underestimated (h2 = 0.06) while highest error, lowest accuracies for the BVs and a remarkable underestimation of the genetic gain were observed. Use of reference sires on a natural mating basis to create genetic links between herds has served a good solution for both heritability and BVs estimation under unfavorable structure. Mating 0.25 of the herd ewes with reference sires resulted in a heritability estimate close to the simulated one. Significantly better estimates of systematic effects and BVs were, however, obtained when 0.5 of the herd ewes were mated by reference sires.

scholarly journals Ordering structured populations in multiplayer cooperation games

2015 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Multiplayer Games ◽  
Spatial Games ◽  
Population Structures ◽  
Single Structure ◽  
Containment Order ◽  
Update Rules

AbstractSpatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure 𝒮1 is greater than population structure 𝒮2 in the containment or the volume order, then 𝒮1 can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.

scholarly journals Genetic Diversity in the mtDNA control region and population structure of Chrysichthys nigrodigitatus from selected Nigerian rivers: Implications for conservation and aquaculture

2016 ◽  
Vol 24 (2) ◽  
pp. 85-97 ◽  
Author(s):  
Sylvanus A. Nwafili ◽  
Tian-Xiang Gao
Keyword(s):  
Genetic Diversity ◽  
Population Structure ◽  
Control Region ◽  
Haplotype Diversity ◽  
Population Expansion ◽  
Mitochondrial Control Region ◽  
Recent Population Expansion ◽  
Base Pair Fragment ◽  
Population Structures ◽  
High Level

Abstract The genetic diversity and population structure of Chrysichthys nigrodigitatus were evaluated using a 443 base pair fragment of the mitochondrial control region. Among the eight populations collected comprising 129 individuals, a total of 89 polymorphic sites defined 57 distinct haplotypes. The mean haplotype diversity and nucleotide diversity of the eight populations were 0.966±0.006 and 0.0359±0.004, respectively. Analysis of molecular variance showed significant genetic differentiation among the eight populations (FST =0.34; P < 0.01). The present results revealed that C. nigrodigitatus populations had a high level of genetic diversity and distinct population structures. We report the existence of two monophyletic matrilineal lineages with mean genetic distance of 10.5% between them. Non-significant negative Tajima’s D and Fu’s Fs for more than half the populations suggests that the wild populations of C. nigrodigitatus underwent a recent population expansion, although a weak one since the late Pleistocene.

The non-homogeneous Markov system in a stochastic environment

1993 ◽  
Vol 30 (02) ◽  
pp. 285-301 ◽  
Author(s):  
N. Tsantas ◽  
P.-C. G. Vassiliou
Keyword(s):  
Population Structure ◽  
Stochastic Environment ◽  
Input Process ◽  
Relative State ◽  
Markov System ◽  
Basic Parameters ◽  
Manpower System ◽  
Relative Structure ◽  
First Time

We introduce and define for the first time the concept of a non-homogeneous Markov system in a stochastic environment (S-NHMS). The problem of finding the expected population structure in an S-NHMS is studied, and important properties among the basic parameters of the S-NHMS are established. Moreover, we study the problem of maintaining the relative sizes of the states in a stochastic environment applying control in the input process. Among other things, we provide the probability of maintaining any vector of relative state sizes. Also strategies for attaining in an optimal way a desired relative structure are designed, with the use of a given algorithm. Finally, an illustration is provided of the present results in a manpower system.

scholarly journals Coevolutionary fine-tuning: evidence for genetic tracking between a specialist wasp parasitoid and its aphid host in a dual metapopulation interaction

2011 ◽  
Vol 102 (2) ◽  
pp. 149-155 ◽  
Author(s):  
F.N. Nyabuga ◽  
H.D. Loxdale ◽  
D.G. Heckel ◽  
W.W. Weisser
Keyword(s):  
Population Structure ◽  
Life Histories ◽  
Mantel Test ◽  
Fine Tuning ◽  
Red Queen Hypothesis ◽  
Shared Allele ◽  
Metapopulation Structure ◽  
Population Structures ◽  
Associated Species ◽  
Aphid Host

AbstractIn the interaction between two ecologically-associated species, the population structure of one species may affect the population structure of the other. Here, we examine the population structures of the aphidMetopeurum fuscoviride, a specialist on tansyTanacetum vulgare, and its specialist primary hymenopterous parasitoidLysiphlebus hirticornis, both of which are characterized by multivoltine life histories and a classic metapopulation structure. Samples of the aphid host and the parasitoid were collected from eight sites in and around Jena, Germany, where both insect species co-occur, and then were genotyped using suites of polymorphic microsatellite markers. The host aphid was greatly differentiated in terms of its spatial population genetic patterning, while the parasitoid was, in comparison, only moderately differentiated. There was a positive Mantel test correlation between pairwise shared allele distance (DAS) of the host and parasitoid, i.e. if host subpopulation samples were more similar between two particular sites, so were the parasitoid subpopulation samples. We argue that while the differences in the levels of genetic differentiation are due to the differences in the biology of the species, the correlations between host and parasitoid are indicative of dependence of the parasitoid population structure on that of its aphid host. The parasitoid is genetically tracking behind the aphid host, as can be expected in a classic metapopulation structure where host persistence depends on a delay between host and parasitoid colonization of the patch. The results may also have relevance to the Red Queen hypothesis, whereupon in the ‘arms race’ between parasitoid and its host, the latter ‘attempts’ to evolve away from the former.

scholarly journals Accounting for spatial complexities in the calculation of biological reference points: effects of misdiagnosing population structure for stock status indicators

2017 ◽  
Vol 74 (11) ◽  
pp. 1878-1894 ◽  
Author(s):  
Daniel R. Goethel ◽  
Aaron M. Berger
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Reference Points ◽  
Stock Status ◽  
Spatial Population ◽  
Management Procedures ◽  
Population Structures ◽  
Explicit Simulation ◽  
The One ◽  
Source Sink

Misidentifying spatial population structure may result in harvest levels that are unable to achieve management goals. We developed a spatially explicit simulation model to determine how biological reference points differ among common population structures and to investigate the performance of management quantities that were calculated assuming incorrect spatial population dynamics. Simulated reference points were compared across a range of population structures and connectivity scenarios demonstrating the influence of spatial assumptions on management benchmarks. Simulations also illustrated that applying a harvest level based on misdiagnosed spatial structure leads to biased stock status indicators, overharvesting, or foregone yield. Across the scenarios examined, incorrectly specifying the connectivity dynamics (particularly misdiagnosing source–sink dynamics) was often more detrimental than ignoring spatial structure altogether. However, when the true dynamics exhibited spatial structure, incorrectly assuming panmictic structure resulted in severe depletion if harvesting concentrated on more productive population units (instead of being homogeneously distributed). Incorporating spatially generalized operating models, such as the one developed here, into management strategy evaluations will help develop management procedures that are more robust to spatial complexities.

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