Solving the Fisher-Wright and coalescence problems with a discrete Markov chain analysis

We develop a new, self-contained proof that the expected number of generations required for gene allele fixation or extinction in a population of size n is O(n) under general assumptions. The proof relies on a discrete Markov chain analysis. We further develop an algorithm to compute expected fixation or extinction time to any desired precision. Our proofs establish O(nH(p)) as the expected time for gene allele fixation or extinction for the Fisher-Wright problem, where the gene occurs with initial frequency p and H(p) is the entropy function. Under a weaker hypothesis on the variance, the expected time is O(n(p(1-p))1/2) for fixation or extinction. Thus, the expected-time bound of O(n) for fixation or extinction holds in a wide range of situations. In the multi-allele case, the expected time for allele fixation or extinction in a population of size n with n distinct alleles is shown to be O(n). From this, a new proof is given of a coalescence theorem about the mean time to the most recent common ancestor (MRCA), which applies to a broad range of reproduction models satisfying our mean and weak variation conditions.

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Structural Changes in Basmati Rice Exports from India: A Markov Chain Analysis

Economic Affairs ◽

10.46852/0424-2513.2.2021.8 ◽

2021 ◽

Vol 66 (2) ◽

Author(s):

Shailza S

Keyword(s):

Markov Chain ◽

United Arab Emirates ◽

Structural Changes ◽

The United States ◽

Basmati Rice ◽

Steady Increase ◽

Annual Growth Rate ◽

Markov Chain Analysis ◽

Chain Analysis ◽

Wide Range

Basmati rice is considered a “strategic“ agricultural export commodity from India and has consequently remained subject to a wide range of government interventions. Basmati rice is exported from India to many countries, especially to the Gulf and European countries. A steady increase in Bbasmati rice production, availability of buffer stocks, and growing demand for basmati rice in the international market made India a vital rice exporting country of the world. The present study explored the structural changes in basmati rice exports from India from 1991 to 2020. The stability in the importing partners of basmati rice from India was analyzed using first-order Markov chain analysis. The compound annual growth rate for the export quantity of basmati rice varied from 5.74 to 12.65 percent per annum. In contrast, the export value of basmati rice ranged between 4.40 to 21.06 percent per annum during the three selected decades. Further, the basmati rice export value showed higher instability than export quantity. Saudi Arabia, Iran, and the United Arab Emirates served to be the stable importers. In contrast, the United States and the United Kingdom served as the most unstable markets for Indian basmati rice according to the transitional probability matrix. Therefore, to reduce variability in exports of basmati rice, India should maintain long-term stable trading partners further to increase the export earnings.

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How Mutation and Selection Solve Long-Path Problems in Polynomial Expected Time

Evolutionary Computation ◽

10.1162/evco.1996.4.2.195 ◽

1996 ◽

Vol 4 (2) ◽

pp. 195-205 ◽

Cited By ~ 53

Author(s):

Günter Rudolph

Keyword(s):

Markov Chain ◽

Markov Chain Analysis ◽

Expected Time ◽

Bounded Number ◽

Chain Analysis ◽

Elitist Selection ◽

Mutation And Selection

It is shown by means of Markov chain analysis that unimodal binary long-path problems can be solved by mutation and elitist selection in a polynomially bounded number of trials on average.

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The Ancestry of a Sample of Sequences Subject to Recombination

Genetics ◽

10.1093/genetics/151.3.1217 ◽

1999 ◽

Vol 151 (3) ◽

pp. 1217-1228 ◽

Cited By ~ 1

Author(s):

Carsten Wiuf ◽

Jotun Hein

Keyword(s):

Genetic Distance ◽

Population Size ◽

Upper Bound ◽

Recombination Rate ◽

Common Ancestor ◽

Recent Common Ancestor ◽

Sequence Length ◽

Most Recent Common Ancestor ◽

The Mean ◽

Mean Time

Abstract In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is ≈log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.

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Genome Sequence Analysis of First Ross River Virus Isolate from Papua New Guinea Indicates Long-Term, Local Evolution

Viruses ◽

10.3390/v13030482 ◽

2021 ◽

Vol 13 (3) ◽

pp. 482

Author(s):

Alice Michie ◽

John S. Mackenzie ◽

David W. Smith ◽

Allison Imrie

Keyword(s):

Papua New Guinea ◽

Large Scale ◽

Solomon Islands ◽

Febrile Illness ◽

New Guinea ◽

Recent Common Ancestor ◽

Ross River Virus ◽

Most Recent Common Ancestor ◽

Mean Time

Ross River virus (RRV) is the most medically significant mosquito-borne virus of Australia, in terms of human morbidity. RRV cases, characterised by febrile illness and potentially persistent arthralgia, have been reported from all Australian states and territories. RRV was the cause of a large-scale epidemic of multiple Pacific Island countries and territories (PICTs) from 1979 to 1980, involving at least 50,000 cases. Historical evidence of RRV seropositivity beyond Australia, in populations of Papua New Guinea (PNG), Indonesia and the Solomon Islands, has been documented. We describe the genomic characterisation and timescale analysis of the first isolate of RRV to be sampled from PNG to date. Our analysis indicates that RRV has evolved locally within PNG, independent of Australian lineages, over an approximate 40 year period. The mean time to most recent common ancestor (tMRCA) of the unique PNG clade coincides with the initiation of the PICTs epidemic in mid-1979. This may indicate that an ancestral variant of the PNG clade was seeded into the region during the epidemic, a period of high RRV transmission. Further epidemiological and molecular-based surveillance is required in PNG to better understand the molecular epidemiology of RRV in the general Australasian region.

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On-Bark Behavior of Dendroctonus frontalis: A Markov Chain Analysis

Journal of Insect Behavior ◽

10.1023/b:joir.0000031531.07035.10 ◽

2004 ◽

Vol 17 (3) ◽

pp. 281-301 ◽

Cited By ~ 3

Author(s):

J. Bishir ◽

J. H. Roberds ◽

B. L. Strom

Keyword(s):

Markov Chain ◽

Dendroctonus Frontalis ◽

Markov Chain Analysis ◽

Chain Analysis

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Assessing Changes in Soil Erosion Rates: A Markov Chain Analysis

Journal of Agricultural and Applied Economics ◽

10.1017/s1074070800008877 ◽

1999 ◽

Vol 31 (3) ◽

pp. 611-622 ◽

Cited By ~ 3

Author(s):

Rhonda Skaggs ◽

Soumen Ghosh

Keyword(s):

Markov Chain ◽

Soil Erosion ◽

Great Plains ◽

Markov Chain Analysis ◽

Conservation Policies ◽

Erosion Rates ◽

National Resources Inventory ◽

Long Run ◽

Chain Analysis ◽

Soil Erosion Rates

AbstractMarkov chain analysis (one-step and long-run) is applied to the National Resources Inventory (NRI) database to evaluate changes in wind-based soil erosion rates over time. The research compares changes in soil erosion rates between NRI sample sites with and without applied conservation practices for a random sample of Great Plains counties. No significant differences between sites are found for half of the counties evaluated. The effectiveness and efficiency of conservation policies are thus questioned in light of these research results.

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