Mathematical models of seasonally migrating populations

J. Donohue
{"title":"Mathematical models of seasonally migrating populations","authors":"J. Donohue","doi":"10.33232/bims.0076.27.28","DOIUrl":null,"url":null,"abstract":"This is an abstract of the PhD thesis Mathematical models of seasonally migrating populations written by J. Donohue under the supervision of Dr. P. T. Piiroinen at the School of Mathematics, Statistics, and Applied Mathematics, National University of Ireland, Galway and submitted in September 2015. The phenomenon of seasonal migration has attracted a wealth of attention from biologists. However, the dynamics of migratory populations have been little considered. In this thesis, we use differential equations to model the variation in abundance of seasonally migrating populations. Our contribution to the field begins with a representation of seasonal breeding. We use piecewise-smooth differential equations to model the variation in the size of a population that has a short interval each year during which successful reproduction is possible. We first consider a one-species model which illustrates the dynamics of a population of specialist feeders over the course of a single breeding season and use it to examine how reproductive success depends on the population’s distribution of breeding dates. We then introduce time-dependent switches to extend the model to a broader class of species. This allows us to consider the effect of climate change on populations that annually travel long distances. We then shift focus to consider interactions between migrants and species at higher levels in the food web. Predatory pressure influences almost all populations to some extent. Here, however, interactions may occur for just a brief period each year before the populations involved become spatially separated. The range of a migrating population may overlap with that of a population of predators for a","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Irish Mathematical Society Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33232/bims.0076.27.28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

This is an abstract of the PhD thesis Mathematical models of seasonally migrating populations written by J. Donohue under the supervision of Dr. P. T. Piiroinen at the School of Mathematics, Statistics, and Applied Mathematics, National University of Ireland, Galway and submitted in September 2015. The phenomenon of seasonal migration has attracted a wealth of attention from biologists. However, the dynamics of migratory populations have been little considered. In this thesis, we use differential equations to model the variation in abundance of seasonally migrating populations. Our contribution to the field begins with a representation of seasonal breeding. We use piecewise-smooth differential equations to model the variation in the size of a population that has a short interval each year during which successful reproduction is possible. We first consider a one-species model which illustrates the dynamics of a population of specialist feeders over the course of a single breeding season and use it to examine how reproductive success depends on the population’s distribution of breeding dates. We then introduce time-dependent switches to extend the model to a broader class of species. This allows us to consider the effect of climate change on populations that annually travel long distances. We then shift focus to consider interactions between migrants and species at higher levels in the food web. Predatory pressure influences almost all populations to some extent. Here, however, interactions may occur for just a brief period each year before the populations involved become spatially separated. The range of a migrating population may overlap with that of a population of predators for a
季节性迁徙人口的数学模型
本文是J. Donohue在高威爱尔兰国立大学数学、统计与应用数学学院p.t. Piiroinen博士指导下于2015年9月提交的博士论文《季节性迁移人口的数学模型》的摘要。季节性迁徙现象引起了生物学家的广泛关注。然而,很少考虑到迁徙人口的动态。在本文中,我们使用微分方程来模拟季节性迁徙种群丰度的变化。我们对该领域的贡献始于季节性育种的表现。我们使用分段平滑微分方程来模拟一个种群的大小变化,这个种群每年有一个很短的间隔,在这段时间里,成功的繁殖是可能的。我们首先考虑一个单物种模型,该模型说明了在单个繁殖季节中专业喂食者群体的动态,并用它来研究繁殖成功如何依赖于种群繁殖日期的分布。然后,我们引入时间相关开关,将模型扩展到更广泛的物种类别。这使我们能够考虑气候变化对每年长途旅行的人口的影响。然后,我们将重点转移到考虑迁徙者和食物网中更高层次物种之间的相互作用。捕食压力在某种程度上影响着几乎所有的种群。然而,在这里,相互作用可能每年只发生很短的一段时间,然后相关的种群就会在空间上分开。在一段时间内,迁徙种群的活动范围可能与捕食种群的活动范围重叠
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信