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Journal articles on the topic 'Moran model'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Althagafi, Asma, and Mohamed Abdelkader. "Two-Dimensional Moran Model." Symmetry 15, no. 5 (2023): 1046. http://dx.doi.org/10.3390/sym15051046.

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In this paper, we consider a two-dimensional Moran model of random walks consisting of two queues evolving in parallel which can (at each unit of time) either increase by one or reset to 0. We analyze the joint law of their final altitude and prove that the asymptotic distribution of each component is a shifted geometric distribution and we analyze the maximum of these two components, also giving closed forms for the mean and variance.

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2

Dalmau, Joseba. "Convergence of a Moran model to Eigen's quasispecies model." Journal of Theoretical Biology 420 (May 2017): 36–40. http://dx.doi.org/10.1016/j.jtbi.2017.02.035.

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3

Muirhead, Christina A., and John Wakeley. "Modeling Multiallelic Selection Using a Moran Model." Genetics 182, no. 4 (2009): 1141–57. http://dx.doi.org/10.1534/genetics.108.089474.

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4

Donnelly, Peter, and Eliane R. Rodrigues. "Convergence to stationarity in the Moran model." Journal of Applied Probability 37, no. 3 (2000): 705–17. http://dx.doi.org/10.1239/jap/1014842830.

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Consider a population of fixed size consisting of N haploid individuals. Assume that this population evolves according to the two-allele neutral Moran model in mathematical genetics. Denote the two alleles by A1 and A2. Allow mutation from one type to another and let 0 < γ < 1 be the sum of mutation probabilities. All the information about the population is recorded by the Markov chain X = (X(t))t≥0 which counts the number of individuals of type A1. In this paper we study the time taken for the population to ‘reach’ stationarity (in the sense of separation and total variation distances)

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5

Itoh, Yoshiaki, and Hosam M. Mahmoud. "Age statistics in the Moran population model." Statistics & Probability Letters 74, no. 1 (2005): 21–30. http://dx.doi.org/10.1016/j.spl.2005.04.028.

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6

Donnelly, Peter, and Eliane R. Rodrigues. "Convergence to stationarity in the Moran model." Journal of Applied Probability 37, no. 03 (2000): 705–17. http://dx.doi.org/10.1017/s002190020001593x.

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Consider a population of fixed size consisting of N haploid individuals. Assume that this population evolves according to the two-allele neutral Moran model in mathematical genetics. Denote the two alleles by A 1 and A 2. Allow mutation from one type to another and let 0 &lt; γ &lt; 1 be the sum of mutation probabilities. All the information about the population is recorded by the Markov chain X = (X(t)) t≥0 which counts the number of individuals of type A 1. In this paper we study the time taken for the population to ‘reach’ stationarity (in the sense of separation and total variation

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7

Berger, Maxime. "Expansion of error thresholds for the Moran model." Theoretical Population Biology 143 (February 2022): 92–104. http://dx.doi.org/10.1016/j.tpb.2021.12.002.

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8

Karamched, B. R., W. Ott, I. Timofeyev, R. N. Alnahhas, M. R. Bennett, and K. Josić. "Moran model of spatial alignment in microbial colonies." Physica D: Nonlinear Phenomena 395 (August 2019): 1–6. http://dx.doi.org/10.1016/j.physd.2019.02.001.

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9

Kämmerle, K. "Looking forwards and backwards in a bisexual moran model." Journal of Applied Probability 26, no. 4 (1989): 880–85. http://dx.doi.org/10.2307/3214393.

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In this paper a bisexual Moran model is introduced. The population consists of N pairs of individuals. At times t = 1, 2, ·· ·two individuals are born, who ‘choose their parents randomly' and independently of each other. Then one of the pairs is removed and replaced by the two individuals born at that instant.The extinction probability of the descendants of a single pair and the number of ancestors of a whole generation are studied. A limit result for large population sizes has been derived by diffusion approximation methods.

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10

Kämmerle, K. "Looking forwards and backwards in a bisexual moran model." Journal of Applied Probability 26, no. 04 (1989): 880–85. http://dx.doi.org/10.1017/s0021900200027753.

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In this paper a bisexual Moran model is introduced. The population consists of N pairs of individuals. At times t = 1, 2, ·· ·two individuals are born, who ‘choose their parents randomly' and independently of each other. Then one of the pairs is removed and replaced by the two individuals born at that instant. The extinction probability of the descendants of a single pair and the number of ancestors of a whole generation are studied. A limit result for large population sizes has been derived by diffusion approximation methods.

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11

Hössjer, Ola, and Peder A. Tyvand. "A monoecious and diploid Moran model of random mating." Journal of Theoretical Biology 394 (April 2016): 182–96. http://dx.doi.org/10.1016/j.jtbi.2015.12.028.

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12

Donnelly, Peter. "A genealogical approach to variable-population-size models in population genetics." Journal of Applied Probability 23, no. 2 (1986): 283–96. http://dx.doi.org/10.2307/3214173.

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A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

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13

Donnelly, Peter. "A genealogical approach to variable-population-size models in population genetics." Journal of Applied Probability 23, no. 02 (1986): 283–96. http://dx.doi.org/10.1017/s0021900200029600.

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A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

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14

Aguech, Rafik, and Mohamed Abdelkader. "Two-Dimensional Moran Model: Final Altitude and Number of Resets." Mathematics 11, no. 17 (2023): 3774. http://dx.doi.org/10.3390/math11173774.

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In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude Zn. Finally, we analyse the statistical properties of NnX, the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function.

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15

Abdelkader, Mohamed. "Three-Dimensional Moran Walk with Resets." Symmetry 16, no. 9 (2024): 1222. http://dx.doi.org/10.3390/sym16091222.

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In this current paper, we propose to study a three-dimensional Moran model (Xn(1),Xn(2),Xn(3)), where each random walk (Xn(i))∈{1,2,3} increases by one unit or is reset to zero at each unit of time. We analyze the joint law of its final altitude Xn=max(Xn(1),Xn(2),Xn(3)) via the moment generating tools. Furthermore, we show that the limit distribution of each random walk follows a shifted geometric distribution with parameter 1−qi, and we analyze the maximum of these three walks, also giving explicit expressions for the mean and variance.

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16

Clifford, Peter, and Aidan Sudbury. "Looking backwards in time in the Moran model in population genetics." Journal of Applied Probability 22, no. 2 (1985): 437–42. http://dx.doi.org/10.2307/3213786.

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The Moran model in population genetics may also be regarded as an invasion process (or voter model) on the complete n-graph. Tracing lines of ancestry is equivalent to studying the dual process. Using this technique certain results concerning lines of ancestry can be derived very rapidly.

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17

Clifford, Peter, and Aidan Sudbury. "Looking backwards in time in the Moran model in population genetics." Journal of Applied Probability 22, no. 02 (1985): 437–42. http://dx.doi.org/10.1017/s002190020003789x.

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The Moran model in population genetics may also be regarded as an invasion process (or voter model) on the completen-graph. Tracing lines of ancestry is equivalent to studying the dual process. Using this technique certain results concerning lines of ancestry can be derived very rapidly.

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18

Kaveh, Kamran, Alex McAvoy, Krishnendu Chatterjee, and Martin A. Nowak. "The Moran process on 2-chromatic graphs." PLOS Computational Biology 16, no. 11 (2020): e1008402. http://dx.doi.org/10.1371/journal.pcbi.1008402.

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Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph colorin

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19

Li, Bo, Zimeng Yuan, and Zohreh Eskandari. "Dynamics and Bifurcations of a Discrete-Time Moran-Ricker Model with a Time Delay." Mathematics 11, no. 11 (2023): 2446. http://dx.doi.org/10.3390/math11112446.

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This study investigates the dynamics of limited homogeneous populations based on the Moran-Ricker model with time delay. The delay in density dependence caused the preceding generation to consume fewer resources, leading to a decrease in the required resources. Multimodality is evident in the model. Some insect species can be described by the Moran–Ricker model with a time delay. Bifurcations associated with flipping, doubling, and Neimark–Sacker for codimension-one (codim-1) model can be analyzed using bifurcation theory and the normal form method. We also investigate codimension-two (codim-2

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20

Pattni, Karan, Mark Broom, Jan Rychtář, and Lara J. Silvers. "Evolutionary graph theory revisited: when is an evolutionary process equivalent to the Moran process?" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2182 (2015): 20150334. http://dx.doi.org/10.1098/rspa.2015.0334.

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Evolution in finite populations is often modelled using the classical Moran process. Over the last 10 years, this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such population is whether a rare mutant has a higher or lower chance of fixating (the fixation probability) than the Moran probability, i.e. that from the original Moran model, which represents an unstructured population. As evolutionary graph theory has developed, different ways of considering the interactions between individuals through a graph and an associated

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21

Thuraka, Gnana Prakash, L. Sumalatha, and B. Sujatha. "Deep learning model MORAN architecture for text recognition in complex images." i-manager's Journal on Information Technology 13, no. 3 (2024): 10. https://doi.org/10.26634/jit.13.3.21202.

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Recognizing text in images poses significant challenges, particularly in the presence of complex backgrounds. This technology plays a crucial role in assisting visually impaired individuals and interpreting semantic content. This survey explores various techniques developed over the past decade to address text recognition in complex images. It provides an overview and analysis of accumulated works and evaluates the performance of these recognition methods. While image complexity is difficult to quantify, it can be described using parameters such as background details, noise levels, lighting co

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22

Cordero, Fernando. "Common ancestor type distribution: A Moran model and its deterministic limit." Stochastic Processes and their Applications 127, no. 2 (2017): 590–621. http://dx.doi.org/10.1016/j.spa.2016.06.019.

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23

Etheridge, A. M., and R. C. Griffiths. "A coalescent dual process in a Moran model with genic selection." Theoretical Population Biology 75, no. 4 (2009): 320–30. http://dx.doi.org/10.1016/j.tpb.2009.03.004.

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24

Esser, Mareike, Sebastian Probst, and Ellen Baake. "Partitioning, duality, and linkage disequilibria in the Moran model with recombination." Journal of Mathematical Biology 73, no. 1 (2015): 161–97. http://dx.doi.org/10.1007/s00285-015-0936-6.

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25

Coron, Camille, and Yves Le Jan. "Genetic contribution of an advantaged mutant in the biparental Moran model." Ukrains’kyi Matematychnyi Zhurnal 75, no. 11 (2023): 1473–78. http://dx.doi.org/10.3842/umzh.v75i11.7415.

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UDC 519.21 We consider a large population of haploid sexually reproducing individuals. It is assumed that one individual initially carries a very strongly advantageous mutation at a single locus. We study the long-term contribution of this initial individual to the genome of the population.

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26

Huillet, Thierry E. "Fluctuations Analysis of Finite Discrete Birth and Death Chains with Emphasis on Moran Models with Mutations." ISRN Biomathematics 2013 (September 11, 2013): 1–21. http://dx.doi.org/10.1155/2013/939308.

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The Moran model is a discrete-time birth and death Markov chain describing the evolution of the number of type 1 alleles in a haploid population with two alleles whose total size N is preserved during the course of evolution. Bias mechanisms such as mutations or selection can affect its neutral dynamics. For the ergodic Moran model with mutations, we get interested in the fixation probabilities of a mutant, the growth rate of fluctuations, the first hitting time of the equilibrium state starting from state {0}, the first return time to the equilibrium state, and the first hitting time of {N} s

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27

Ariyanto, Tory, Era Yunianto, and Taryadi Taryadi. "Identifikasi Tingkat Pengangguran Terbuka Berdasarkan Kecamatan Di Kabupaten Pekalongan Menggunakan Spatial Model." Jurnal ELTIKOM 5, no. 2 (2021): 65–72. http://dx.doi.org/10.31961/eltikom.v5i2.337.

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Unemployment is an economic problem that the central and regional governments must resolve comprehensively and integrated. The open unemployment rate in Pekalongan Regency in the last three years has increased. It is influenced by several factors, one of which is the population growth rate. Likewise, the labor force participation rate has increased. It shows that the increasing availability of the workforce is not accompanied by additional employment and is not proportional to population growth. This study aims to determine the level of open unemployment and labor force participation in the su

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28

BONNEUIL, NOËL. "OPTIMAL CONTROL OF GENETIC DIVERSITY IN THE MORAN MODEL WITH POPULATION GROWTH." Journal of Biological Systems 30, no. 01 (2022): 27–50. http://dx.doi.org/10.1142/s0218339022500012.

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In the Moran model of drift and selection of a mutant allele with population growth, instead of examining the consequences of pre-specified selection and population growth, the coexistence of the wild allele and the mutant allele becomes the maximization of the expected sojourn time in a given set. The process is controlled by the additional mortality of the mutant and by population growth. This makes it possible to retroactively assign fitness values as functions of the constraints, thus guiding a conservation policy or the achievement of a wishful proportion of mutants. This also gives the o

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29

Eldon, Bjarki. "Structured coalescent processes from a modified Moran model with large offspring numbers." Theoretical Population Biology 76, no. 2 (2009): 92–104. http://dx.doi.org/10.1016/j.tpb.2009.05.001.

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30

Aalto, Erkki. "The moran model and validity of the diffusion approximation in population genetics." Journal of Theoretical Biology 140, no. 3 (1989): 317–26. http://dx.doi.org/10.1016/s0022-5193(89)80089-x.

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31

Corujo, Josué. "On the spectrum and ergodicity of a neutral multi-allelic Moran model." Latin American Journal of Probability and Mathematical Statistics 20, no. 1 (2023): 505. http://dx.doi.org/10.30757/alea.v20-18.

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32

Lorio, Jennifer L., Norou Diawara, and Lance A. Waller. "Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic." International Journal of Statistics and Probability 7, no. 2 (2018): 80. http://dx.doi.org/10.5539/ijsp.v7n2p80.

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Moran's Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is c

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33

Permana, Pandu. "Pemodelan Pemodelan Spasial Kasus Balita Laki-Laki Penderita Pneumonia Di Kota Bandung." SATIN - Sains dan Teknologi Informasi 7, no. 2 (2021): 64–72. http://dx.doi.org/10.33372/stn.v7i2.757.

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Pneumonia adalah infeksi saluran pernafasan akut yang mempengaruhi paru-paru. Kasus pneumonia merupakan kasus yang menyebabkan kematian dengan mudah menular terbesar pada anak di seluruh dunia. Teknik pemodelan spasial mampu dalam mengakomodir struktur ketergantungan spasial. Penderita kasus pneumonia di suatu wilayah akan mempengaruhi jumlah penderita yang saling berdekatan/bertetanggaan. Analisis yang dilakukan adalah dengan model regresi linier klasik strategi metode OLS. uji autokorelasi spasial dengan uji Moran I. Memakai matriks pembobot. Lakukan pengambilan nilai autokorelasi spasial da

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34

Lessard, Sabin. "Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models." Journal of Applied Probability 47, no. 3 (2010): 732–51. http://dx.doi.org/10.1239/jap/1285335406.

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Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to

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35

Lessard, Sabin. "Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models." Journal of Applied Probability 47, no. 03 (2010): 732–51. http://dx.doi.org/10.1017/s0021900200007038.

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Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to

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36

Ross, Ciaran. "L' Affaire Molloy-Moran Repensée : Entre La Pensée De La mère et le Nom-du-pére." Samuel Beckett Today / Aujourd'hui 17, no. 1 (2007): 448–63. http://dx.doi.org/10.1163/18757405-017001031.

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Moran's search for Molloy is analysed here by articulating two different psychoanalytic models of interpretation. First the Molloy-Moran relationship is analysed from the post-kleinian perspective of the mother and the role of her thinking. Molloy is read as a destabilising figure of the un-thought which plunges Moran into a gulf that defies thinking and imagining. The second model is Lacanian and shows that the failure of the function of the Name of the Father leaves a void in the chain of signification. This can be seen through Moran's failure to understand the "question of Molloy".

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37

Kopfová, Lenka, and Josef Tkadlec. "Colonization times in Moran process on graphs." PLOS Computational Biology 21, no. 5 (2025): e1012868. https://doi.org/10.1371/journal.pcbi.1012868.

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Moran Birth-death process is a standard stochastic process that is used to model natural selection in spatially structured populations. A newly occurring mutation that invades a population of residents can either fixate on the whole population or it can go extinct due to random drift. The duration of the process depends not only on the total population size n, but also on the spatial structure of the population. In this work, we consider the Moran process with a single type of individuals who invade and colonize an otherwise empty environment. Mathematically, this corresponds to the setting wh

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38

Hadisov, Magomed-Ramzan Buvaysarovich, and Nadezhda Vladimirovna Nasukhanova. "CONSTRUCTION OF AN ECONOMETRIC MODEL OF SPATIAL AUTOCORRELATION." Scientific Review: Theory and Practice 14, no. 8 (2024): 1542–48. http://dx.doi.org/10.35679/2226-0226-2024-14-8-1542-1548.

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The article analyzes panel data using statistical indicators for the period 2014-2022 for 85 subjects of the Russian Federation, and a spatial autocorrelation table is constructed. The authors aim their research to analyze and build a spatial model of endogenous growth, characterized by an assessment of the impact of research and development costs and the number of researchers under the age of 39, their flows, on GRP per capita. To build a spatial model, linearization was carried out by logarithm of the studied indicators, as well as statistical software packages (MS Excel, Gretl, STATA) were

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39

Rothschild, Jeremy, Tianyi Ma, Joshua N. Milstein, and Anton Zilman. "Spatial exclusion leads to “tug-of-war” ecological dynamics between competing species within microchannels." PLOS Computational Biology 19, no. 12 (2023): e1010868. http://dx.doi.org/10.1371/journal.pcbi.1010868.

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Competition is ubiquitous in microbial communities, shaping both their spatial and temporal structure and composition. Classical minimal models of competition, such as the Moran model, have been employed in ecology and evolutionary biology to understand the role of fixation and invasion in the maintenance of population diversity. Informed by recent experimental studies of cellular competition in confined spaces, we extend the Moran model to incorporate mechanical interactions between cells that divide within the limited space of a one-dimensional open microchannel. The model characterizes the

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40

Oyamakin, S. Oluwafemi, Angela U. Chukwu, Wale-Orojo Oluwaseun A, and Ogunjobi E. O. "Allele Based Inference on Evolution and Extinction; A Genetic Drift Approach." Journal of Cancer Genetics and Biomarkers 1, no. 4 (2019): 1–15. http://dx.doi.org/10.14302/issn.2572-3030.jcgb-19-2597.

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In other to present a series of stochastic models from population dynamics capable of describing rudimentary aspects of genetic evolution, we studied two-allele Wright–Fisher and the Moran models for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size “simplest form, selection, and random mutation”. Principal results were presented in qualitative terms, illustrated by Monte Carlo simulations from R and http://www.radford.edu/~rsheehy/Gen_flash/popgen. Moran and the Wright-Fisher Models exhibited the same fixation prob

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41

Zulheri, Evan Ilham, Yudiantri Asdi, and Hazmira Yozza. "MODEL REGRESI SPASIAL LAG PADA KASUS PENYAKIT DEMAM BERDARAH DENGUE (DBD) DI SUMATRA UTARA TAHUN 2016." Jurnal Matematika UNAND 8, no. 2 (2019): 59. http://dx.doi.org/10.25077/jmu.8.2.59-66.2019.

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Regresi spasial adalah regresi yang melibatkan pengaruh spasial. Regresi spasial lag adalah suatu pendekatan pada analisis regresi spasial. Pada penelitian ini model regresi spasial lag digunakan untuk memodelkan data penyakit demam berdarah dengue (DBD) di provinsi Sumatra Utara. Pemodelan ini didahului oleh pengujian autokorelasi spasial dengan uji moran I. Diperoleh bahwa terjadi autokorelasi pada data penyakit demam berdarah dengue (DBD) di provinsi Sumatra Utara dan didapatkan model sebagai berikut:y = −412, 053 + 0, 246971Wy + 7, 91774x2 + 2, 59216x3 + 3, 23628x4.Pada model dapat dijelas

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42

Huillet, Thierry, and Martin Möhle. "On the extended Moran model and its relation to coalescents with multiple collisions." Theoretical Population Biology 87 (August 2013): 5–14. http://dx.doi.org/10.1016/j.tpb.2011.09.004.

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43

Schinazi, Rinaldo B. "The waiting time for a second mutation: An alternative to the Moran model." Physica A: Statistical Mechanics and its Applications 401 (May 2014): 224–27. http://dx.doi.org/10.1016/j.physa.2014.01.031.

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44

Watkins, Joseph C. "Convergence time to the Ewens sampling formula in the infinite alleles Moran model." Journal of Mathematical Biology 60, no. 2 (2009): 189–206. http://dx.doi.org/10.1007/s00285-009-0255-x.

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45

Shen, Tao, Zheng Liu, and Kejin Li. "Underwriting Risk Prediction Based on Moran Process and Fourier Fitting." Transactions on Computer Science and Intelligent Systems Research 5 (August 12, 2024): 1345–53. http://dx.doi.org/10.62051/c4m43m85.

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Extreme-weather events are becoming a crisis for property owners and insurers, which has drawn widespread attention. For insurance companies, predicting regional losses from Extreme-weather events and studying the participation decisions of insurers can inform insurance strategies. This paper primarily focuses on the impact of extreme-weather events on insurance behavior, based on ten years of extreme-weather data of Michigan, we use Fourier fitting to predict the frequency of extreme-weather events in the subsequent year. Next, to measure underwriting risk, this paper considers economic losse

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46

Luo, Qing, Daniel A. Griffith, and Huayi Wu. "On the Statistical Distribution of the Nonzero Spatial Autocorrelation Parameter in a Simultaneous Autoregressive Model." ISPRS International Journal of Geo-Information 7, no. 12 (2018): 476. http://dx.doi.org/10.3390/ijgi7120476.

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This paper focuses on the spatial autocorrelation parameter ρ of the simultaneous autoregressive model, and furnishes its sampling distribution for nonzero values, for two regular square (rook and queen) tessellations as well as a hexagonal case with rook connectivity, using Monte Carlo simulation experiments with a large sample size. The regular square lattice directly relates to increasingly used, remotely sensed images, whereas the regular hexagonal configuration is frequently used in sampling and aggregation situations. Results suggest an asymptotic normal distribution for estimated ρ. Mor

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Voorhees, Burton. "Birth–death fixation probabilities for structured populations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2153 (2013): 20120248. http://dx.doi.org/10.1098/rspa.2012.0248.

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This paper presents an adaptation of the Moran birth–death model of evolutionary processes on graphs. The present model makes use of the full population state space consisting of 2 N binary-valued vectors, and a Markov process on this space with a transition matrix defined by the edge weight matrix for any given graph. While the general case involves solution of 2 N – 2 linear equations, symmetry considerations substantially reduce this for graphs with large automorphism groups, and a number of simple examples are considered. A parameter called graph determinacy is introduced, measuring the ex

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Vogl, Claus, and Lynette Caitlin Mikula. "A nearly-neutral biallelic Moran model with biased mutation and linear and quadratic selection." Theoretical Population Biology 139 (June 2021): 1–17. http://dx.doi.org/10.1016/j.tpb.2021.03.003.

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Huillet, Thierry. "Siegmund duality with applications to the neutral Moran model conditioned on never being absorbed." Journal of Physics A: Mathematical and Theoretical 43, no. 37 (2010): 375001. http://dx.doi.org/10.1088/1751-8113/43/37/375001.

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Cerf, Raphaël, and Joseba Dalmau. "The distribution of the quasispecies for a Moran model on the sharp peak landscape." Stochastic Processes and their Applications 126, no. 6 (2016): 1681–709. http://dx.doi.org/10.1016/j.spa.2015.12.002.

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