Limit theorems for multi-type general branching processes with population dependence
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population density as a measure-valued process and obtain its...
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| creator | Fan, Jie Yen Hamza, Kais Jagers, Peter Klebaner, Fima C |
| description | A general multi-type population model is considered, where individuals live
and reproduce according to their age and type, but also under the influence of
the size and composition of the entire population. We describe the dynamics of
the population density as a measure-valued process and obtain its asymptotics,
as the population grows with the environmental carrying capacity. "Density" in
this paper generally refers to the population size as compared to the carrying
capacity. Thus, a deterministic approximation is given, in the form of a Law of
Large Numbers, as well as a Central Limit Theorem. Migration can also be
incorporated. This general framework is then adapted to model sexual
reproduction, with a special section on serial monogamic mating systems. |
| doi_str_mv | 10.48550/arxiv.1903.04747 |
| format | Article |
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and reproduce according to their age and type, but also under the influence of
the size and composition of the entire population. We describe the dynamics of
the population density as a measure-valued process and obtain its asymptotics,
as the population grows with the environmental carrying capacity. "Density" in
this paper generally refers to the population size as compared to the carrying
capacity. Thus, a deterministic approximation is given, in the form of a Law of
Large Numbers, as well as a Central Limit Theorem. Migration can also be
incorporated. This general framework is then adapted to model sexual
reproduction, with a special section on serial monogamic mating systems.</description><identifier>DOI: 10.48550/arxiv.1903.04747</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2019-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1903.04747$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1903.04747$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Fan, Jie Yen</creatorcontrib><creatorcontrib>Hamza, Kais</creatorcontrib><creatorcontrib>Jagers, Peter</creatorcontrib><creatorcontrib>Klebaner, Fima C</creatorcontrib><title>Limit theorems for multi-type general branching processes with population dependence</title><description>A general multi-type population model is considered, where individuals live
and reproduce according to their age and type, but also under the influence of
the size and composition of the entire population. We describe the dynamics of
the population density as a measure-valued process and obtain its asymptotics,
as the population grows with the environmental carrying capacity. "Density" in
this paper generally refers to the population size as compared to the carrying
capacity. Thus, a deterministic approximation is given, in the form of a Law of
Large Numbers, as well as a Central Limit Theorem. Migration can also be
incorporated. This general framework is then adapted to model sexual
reproduction, with a special section on serial monogamic mating systems.</description><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7tuwyAYQGGWDlXSB-hUXsAuGDB4jKLeJEtdvFsUfmIkGxCQtnn7qmmnsx3pQ-iekpYrIcijzt_-s6UDYS3hkstbNI1-8xXXBWKGrWAXM97Oa_VNvSTAJwiQ9Yo_sg5m8eGEU44GSoGCv3xdcIrpvOrqY8AWEgQLwcAe3Ti9Frj77w5Nz0_T8bUZ31_ejoex0b2UjdPc9pRoSlSnKFM9FU5KYZ3gg-DAGVOaWdPxgVIhBTA6GKCdcoJZrvqO7dDD3_bKmlP2m86X-Zc3X3nsBxNnSss</recordid><startdate>20190312</startdate><enddate>20190312</enddate><creator>Fan, Jie Yen</creator><creator>Hamza, Kais</creator><creator>Jagers, Peter</creator><creator>Klebaner, Fima C</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190312</creationdate><title>Limit theorems for multi-type general branching processes with population dependence</title><author>Fan, Jie Yen ; Hamza, Kais ; Jagers, Peter ; Klebaner, Fima C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-fa4d610a10828138615f775df54954e4338a3dc24911575e319ce128f53d48623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Fan, Jie Yen</creatorcontrib><creatorcontrib>Hamza, Kais</creatorcontrib><creatorcontrib>Jagers, Peter</creatorcontrib><creatorcontrib>Klebaner, Fima C</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Fan, Jie Yen</au><au>Hamza, Kais</au><au>Jagers, Peter</au><au>Klebaner, Fima C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Limit theorems for multi-type general branching processes with population dependence</atitle><date>2019-03-12</date><risdate>2019</risdate><abstract>A general multi-type population model is considered, where individuals live
and reproduce according to their age and type, but also under the influence of
the size and composition of the entire population. We describe the dynamics of
the population density as a measure-valued process and obtain its asymptotics,
as the population grows with the environmental carrying capacity. "Density" in
this paper generally refers to the population size as compared to the carrying
capacity. Thus, a deterministic approximation is given, in the form of a Law of
Large Numbers, as well as a Central Limit Theorem. Migration can also be
incorporated. This general framework is then adapted to model sexual
reproduction, with a special section on serial monogamic mating systems.</abstract><doi>10.48550/arxiv.1903.04747</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Probability |
| title | Limit theorems for multi-type general branching processes with population dependence |
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