[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-157006-105":59,"doc-detail-157006-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","evolution-and-mass-extinctions-as-lognormal-stochastic-processes","Evolution and mass extinctions as lognormal stochastic processes","","Evolution and mass extinctions are modeled as lognormal stochastic processes within a unified statistical framework termed Evo-SETI. The approach uses geometric Brownian motion to represent the stochastic increase of species, b-lognormals aligned to the GBM mean curve via the Peak-Locus theorem, and Shannon entropy as a measure of progress and reduced chaos. The model connects to SETI through a statistical Drake equation, links to the molecular clock via entropy growth, and extends to alternative extinction and recovery forms and other Darwinian evolution constructions.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/evolution-and-mass-extinctions-as-lognormal-stochastic-processes/157006/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/evolution-and-mass-extinctions-as-lognormal-stochastic-processes/157006.png","ImageObject",300,407,{"name":92,"@type":93},"Sage","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-08-29",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is Evo-SETI in the model presented?","Question",{"text":113,"@type":114},"Evo-SETI is a unified statistical picture that combines Darwinian Evolution, human history, and the search for extra-terrestrial intelligence (SETI) using lognormal stochastic processes and b-lognormals.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which mathematical tools are central to the framework?",{"text":118,"@type":114},"The framework uses geometric Brownian motion to model evolution over time, b-lognormals whose peak is forced onto the GBM exponential mean curve, and Shannon entropy to quantify progress and decreasing chaos.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the model connect molecular evolution with the molecular clock?",{"text":122,"@type":114},"It identifies the growth rate of entropy in the Evo-SETI model with the linear growth behavior implied by Kimura’s Neutral Theory, matching the molecular clock since the origin of life.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},157006,1787971120,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":31,"preview_page_count":4},687197207057,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","International Journal of Astrobiology 13 (4): 290–309 (2014) doi:10 . 1017/S147355041400010X  \n© Cambridge University Press 2014 . The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence [http://creativecommons.org/licenses/by/3.0/](http://creativecommons.org/licenses/by/3.0/) .  \nEvolution and mass extinctions as lognormal stochastic processes  \nClaudio Maccone  \nInternational Academy of Astronautics (IAA), IAA SETI Permanent Committee, Istituto Nazionale di Astrofisica (INAF), Via Martorelli, 43 – Torino (Turin) 10155, Italy  \ne-mail: [clmaccon@libero.it and claudio.maccone@iaamail.org](clmaccon@libero.it and claudio.maccone@iaamail.org)  \nAbstract: In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are:  \n(1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3 . 5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.  \n(2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem) . In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics.  \n(3) The (Shannon) entropy of such b-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.  \n(4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics) .  \n(5) But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the‘constant rate of Evolution atthe molecular level’ as shown by Kimura’s Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life.  \n(6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms.  \n(7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time.  \nIn conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with","cbCaihEISs0NNZjC","https://ap.wps.com/l/cbCaihEISs0NNZjC","pdf",744763,"English","# Abstract\n# Introduction: mathematics and science\n## Evo-SETI and unified statistical modeling\n## Mathematical tools: GBM, b-lognormals, and entropy\n## Links to SETI and the statistical Drake equation\n## Molecular clock connection\n## Applications: mass extinctions and Darwinian evolution models\n# Conclusion","[{\"question\":\"What is Evo-SETI in the model presented?\",\"answer\":\"Evo-SETI is a unified statistical picture that combines Darwinian Evolution, human history, and the search for extra-terrestrial intelligence (SETI) using lognormal stochastic processes and b-lognormals.\"},{\"question\":\"Which mathematical tools are central to the framework?\",\"answer\":\"The framework uses geometric Brownian motion to model evolution over time, b-lognormals whose peak is forced onto the GBM exponential mean curve, and Shannon entropy to quantify progress and decreasing chaos.\"},{\"question\":\"How does the model connect molecular evolution with the molecular clock?\",\"answer\":\"It identifies the growth rate of entropy in the Evo-SETI model with the linear growth behavior implied by Kimura’s Neutral Theory, matching the molecular clock since the origin of life.\"}]","Evolution and mass extinctions as lognormal stochastic processes | PDF"]