{"title":"Collective Evolution Under Catastrophes","authors":"Rinaldo B. Schinazi","doi":"10.1080/00029890.2023.2261828","DOIUrl":null,"url":null,"abstract":"AbstractWe introduce the following discrete time model. Each site of N represents an ecological niche and is assigned a fitness in (0,1). All the sites are updated simultaneously at every discrete time. At any given time the environment may be normal with probability p or a catastrophe may occur with probability 1−p. If the environment is normal the fitness of each site is replaced by the maximum of its current fitness and a random number. If there is a catastrophe the fitness of each site is replaced by a random number. We compute the joint fitness distribution of any finite number of sites at any fixed time. We also show convergence of this system to a stationary distribution. This too is computed explicitly.MSC: 60 ACKNOWLEDGMENTThe author wishes to thank two anonymous referees for their careful reading and thoughtful suggestions.Additional informationNotes on contributorsRinaldo B. SchinaziRINALDO B. SCHINAZI received his Ph.D. in statistics at the University of São Paulo. He has been on the faculty at the University of Colorado at Colorado Springs since 1991. He has been teaching mathematics, writing books in mathematical analysis and probability, and doing research in probability.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2261828","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractWe introduce the following discrete time model. Each site of N represents an ecological niche and is assigned a fitness in (0,1). All the sites are updated simultaneously at every discrete time. At any given time the environment may be normal with probability p or a catastrophe may occur with probability 1−p. If the environment is normal the fitness of each site is replaced by the maximum of its current fitness and a random number. If there is a catastrophe the fitness of each site is replaced by a random number. We compute the joint fitness distribution of any finite number of sites at any fixed time. We also show convergence of this system to a stationary distribution. This too is computed explicitly.MSC: 60 ACKNOWLEDGMENTThe author wishes to thank two anonymous referees for their careful reading and thoughtful suggestions.Additional informationNotes on contributorsRinaldo B. SchinaziRINALDO B. SCHINAZI received his Ph.D. in statistics at the University of São Paulo. He has been on the faculty at the University of Colorado at Colorado Springs since 1991. He has been teaching mathematics, writing books in mathematical analysis and probability, and doing research in probability.
摘要本文介绍了离散时间模型。N的每个位点代表一个生态位，并在(0,1)中分配适应度。所有站点在每个离散时间同时更新。在任何给定时间，环境可能以p的概率正常，也可能以1 - p的概率发生灾难。如果环境正常，则每个位点的适应度由其当前适应度的最大值和一个随机数代替。如果发生突变，每个位点的适合度将被一个随机数代替。我们在任意固定时间计算任意有限个站点的联合适应度分布。我们还证明了该系统收敛于平稳分布。这也是显式计算的。作者希望感谢两位匿名审稿人的仔细阅读和周到的建议。作者简介:aldo B. SCHINAZI在巴西圣保罗大学获得统计学博士学位。自1991年以来，他一直在科罗拉多斯普林斯的科罗拉多大学任教。他一直在教数学，写数学分析和概率论方面的书，做概率论方面的研究。
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