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Biological applications of the theory of birth-and-death processes

Artem S. Novozhilov, Georgy P. Karev, Eugene V. Koonin
<span title="2006-03-01">2006</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/op7ztx4fhvairowgqifu7dnvsi" style="color: black;">Briefings in Bioinformatics</a> </i> &nbsp;
In this review, we discuss applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics.  ...  Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural and formal framework for modeling a vast variety of biological processes such as population dynamics  ...  A simple introduction to the theory of birth-and-death processes is given in [9] and [8] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/bib/bbk006">doi:10.1093/bib/bbk006</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16761366">pmid:16761366</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/le2awh2puvgzvdk3fofjvskn5q">fatcat:le2awh2puvgzvdk3fofjvskn5q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190307035804/http://pdfs.semanticscholar.org/d0e6/e8eaae784b7d9f7507b443b3ab5d59cd4f30.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d0/e6/d0e6e8eaae784b7d9f7507b443b3ab5d59cd4f30.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/bib/bbk006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Page 364 of Mathematical Reviews Vol. 34, Issue 2 [page]

<span title="">1967</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For a birth-and-death process in a population of finite size with quadratic birth- and death-rates, the author shows how the transition probabilities can be represented in terms of Heun functions. D.  ...  Mode, Charles J. 2096 A multidimensional birth process and its application to some problems in the dynamics of biological populations. Bull. Math. Biophys. 28 (1966), 333-345.  ... 
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Using cell replication data in mathematical modeling in carcinogenesis

C J Portier, A Kopp-Schneider, C D Sherman
<span title="">1993</span> <i title="Environmental Health Perspectives"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3w6amv3ecja7fa3ext35ndpiky" style="color: black;">Environmental Health Perspectives</a> </i> &nbsp;
Recent advances in biology, computing, and mathematics have led to the application of mathematically complicated, mechanistically based models of carcinogenesis to the estimation of risks.  ...  This paper focuses on two aspects of this application, distinguishing between models using available data and the development of new models to keep pace with research developments.  ...  The process currently used is a standard birth-death process, which is common in the area of probability theory (35) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1289/ehp.93101s579">doi:10.1289/ehp.93101s579</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/8013428">pmid:8013428</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC1519438/">pmcid:PMC1519438</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/io54qrzla5extmbm3oaffaw2ja">fatcat:io54qrzla5extmbm3oaffaw2ja</a> </span>
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The First – Passage Time Moment of the GNP Diffusion Process to a Determined Value

Mohammad Zainal, Anwar Alshriaan
<span title="2014-01-28">2014</span> <i title="David Publishing Company"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dqe6tp7qn5cn7ntkbehpn5evvu" style="color: black;">Journal of Statistical Science and Application</a> </i> &nbsp;
For example, McNeil (1970) has derived the distribution of the integral functional = ∫ { ( )} where T x is the first-passage time to the origin in a general birth and death process with ( ) = and g  ...  This increases the applicability of the diffusion process in stochastic modeling in the area of economics. . ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17265/2328-224x/2014.01.002">doi:10.17265/2328-224x/2014.01.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wzyzj5au55cjlda3bzjyxcveia">fatcat:wzyzj5au55cjlda3bzjyxcveia</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190819095719/http://www.davidpublisher.org:80/Public/uploads/Contribute/5567d2f562638.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/58/4d/584d0df85b5fb0b9cdb16f980dd83741f03751a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17265/2328-224x/2014.01.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 34 of Social Forces Vol. 18, Issue 1 [page]

<span title="">1939</span> <i title="Oxford University Press, UK"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_social-forces" style="color: black;">Social Forces </a> </i> &nbsp;
Birth and death are biological processes, but the birth rate and the death rate and trends of fertility and mortality are social phe- nomena.  ...  of his own problems and theories as he comes to them in the course of ex- position.  ... 
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Page 4894 of Mathematical Reviews Vol. , Issue 94h [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Nerman, and this monograph is a sustained application of that theory; as such it is well worth reading.  ...  Independent copies of this process give the birth times of these children’s children, relative to their parent’s birth time, and so on.  ... 
<span class="external-identifiers"> </span>
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On the statistical mechanics of species abundance distributions

Michael G. Bowler, Colleen K. Kelly
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oqkaf3i4szdxhkdjqp4aioyshq" style="color: black;">Theoretical Population Biology</a> </i> &nbsp;
These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates.  ...  They underpin the neutral theory of Hubbell (2001) , the master equation approach of Volkov et al. (2003 Volkov et al. ( , 2005 and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007) ; they  ...  In our treatment (and that of Pueyo, 2006) the prior is dictated by the dynamics of ecological communities and the biological processes of birth and death (second principle; (ii) above).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tpb.2012.05.006">doi:10.1016/j.tpb.2012.05.006</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/22683489">pmid:22683489</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gzqhgoh6sbhrpgxsgxxvb3aat4">fatcat:gzqhgoh6sbhrpgxsgxxvb3aat4</a> </span>
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Page 6546 of Mathematical Reviews Vol. , Issue 90K [page]

<span title="">1990</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
There follow the properties of the Yule process, a simple death process and the simple birth and death process.  ...  To illus- trate, birth and death processes (Chapter 9) have applications to chemical reactions, and branching processes (Chapter 10) have ap- plications in physics but neither of these specific applications  ... 
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Quantum Game Theory [article]

Michael Lassig
<span title="2002-06-06">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The implications of this theory for biological systems are discussed in detail.  ...  In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection.  ...  ACKNOWLEDGMENTS It is a pleasure to thank Peter Hammerstein and Antony Zee for inspiring discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cond-mat/0206093v1">arXiv:cond-mat/0206093v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z7ju5wntbbatpmbzae72rhj6s4">fatcat:z7ju5wntbbatpmbzae72rhj6s4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-cond-mat0206093/cond-mat0206093.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/76/35/763570a43160c703fa6b06be92483415e4c8e362.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cond-mat/0206093v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The aging process: major risk factor for disease and death

D. Harman
<span title="1991-06-15">1991</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
Many theories have been advanced to account for the aging process. The free radical theory of aging is discussed briefly.  ...  The inborn aging process is now the major risk factor for disease and death after around age 28 in the developed countries and limits average life expectancy at birth to approximately 85 years.  ...  The free radical theory of aging (23, (28) (29) (30) shows promise of application today.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1073/pnas.88.12.5360">doi:10.1073/pnas.88.12.5360</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/2052612">pmid:2052612</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC51872/">pmcid:PMC51872</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/33f5aes2mvfhtfcnw2ptygixji">fatcat:33f5aes2mvfhtfcnw2ptygixji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200226061932/https://www.pnas.org/content/pnas/88/12/5360.full.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/c2/c2c23aff615e58c03bf933adb7b303126b41a111.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1073/pnas.88.12.5360"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC51872" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Towards a mechanistic foundation of evolutionary theory

Michael Doebeli, Yaroslav Ispolatov, Burt Simon
<span title="2017-02-15">2017</span> <i title="eLife Sciences Publications, Ltd"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/en4qj5ijrbf5djxx7p5zzpjyoq" style="color: black;">eLife</a> </i> &nbsp;
Instead, we propose that evolutionary birth-death processes, in which individuals give birth and die at ever-changing rates, should be the basis of evolutionary theory, because such processes capture the  ...  In evolutionary birth-death processes, fitness is at best a derived quantity, and owing to the potential complexity of such processes, there is no guarantee that there is a simple scalar, such as fitness  ...  approximations can describe the same evolutionary birth-death process, and the 258 question then becomes which one of these approximations is biologically most relevant.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7554/elife.23804">doi:10.7554/elife.23804</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/28198700">pmid:28198700</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC5333952/">pmcid:PMC5333952</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gy6gdhbla5hmtmiy7umlhyl3uu">fatcat:gy6gdhbla5hmtmiy7umlhyl3uu</a> </span>
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An inclusive fitness analysis of altruism on a cyclical network

A. GRAFEN
<span title="">2007</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnsw3nl5bvayvkxur22vrrmlju" style="color: black;">Journal of Evolutionary Biology</a> </i> &nbsp;
A recent model studies the evolution of cooperation on a network, and concludes with a result connecting the benefits and costs of interactions and the number of neighbours.  ...  This brings the result within a biologically familiar framework.  ...  , and for sight of the MSS by Taylor et al. (2007a) and Taylor et al. (2007b) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/j.1420-9101.2007.01413.x">doi:10.1111/j.1420-9101.2007.01413.x</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/17956390">pmid:17956390</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gta2biz62nb5pg3jc27k26unym">fatcat:gta2biz62nb5pg3jc27k26unym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080221170320/http://www.stanford.edu/~lehmann/MsKinGraphGrafen.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c6/b7/c6b7d994b9f02c0d34b973f2b77a3121783618cb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/j.1420-9101.2007.01413.x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Stirring does not make populations well mixed

Francisco Herrerías-Azcué, Vicente Pérez-Muñuzuri, Tobias Galla
<span title="2018-03-06">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnqhc2x2aneavcd3gx5h7mswhm" style="color: black;">Scientific Reports</a> </i> &nbsp;
This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local.  ...  In most cases, these models do not predict fixation probabilities in groups of individuals mixed by flows. We propose an analytical description in the fast-flow limit.  ...  VPM acknowledges support by Ministerio de Economía y Competitividad and Xunta de Galicia (MAT2015-71119-R, GPC2015/014), contributions by COST Action MP1305 and CRETUS Strategic Partnership (AGRUP2015/  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/s41598-018-22062-w">doi:10.1038/s41598-018-22062-w</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/29511246">pmid:29511246</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC5840425/">pmcid:PMC5840425</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gtzodowxznekxhpqmo2mrdegt4">fatcat:gtzodowxznekxhpqmo2mrdegt4</a> </span>
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The general theory of species abundance distributions [article]

Michael G. Bowler, Colleen K. Kelly
<span title="2011-05-09">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These principles are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates.  ...  We thus unify the neutral theory of Hubbell [1], the master equation approach of Volkov et al [2, 3] and a recent attempt at deploying statistical mechanics to deal with this problem, the idiosyncratic  ...  the very biological processes of individuals giving birth and dying.  ... 
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Page 5300 of Mathematical Reviews Vol. , Issue 85k [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
design Amherst, Mass., 1981 Anniversary: Birth of al-Khwarizmi, Muhammad ibn Misa Birth of Maxwell, James Clerk ...... ae Death of Euler, Leonhard Asymptotic methods for investigating stochastic systems  ...  , 4th Quadratic forms and Hermitian K-theory *11001 Random walks and their applications in the physical and biological sciences *82002 Relativity Consensus Controllable dynamic systems with continuous-discrete  ... 
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