{"id":{"repo_id":"tu-berlin","oai_identifier":"oai:depositonce.tu-berlin.de:11303/26967"},"canonical_url":"https://search.dev.ndltd.org/etd/tu-berlin/oai:depositonce.tu-berlin.de:11303/26967","repository":{"repo_id":"tu-berlin","name":"Technische Universität Berlin","base_url":"https://api-depositonce.tu-berlin.de/server/oai/request"},"display":{"title":"Dormancy in spatial population models in random environments","abstract":"This thesis introduces spatial models for populations with dormancy in random environments. The models are formulated as continuous-time two-type branching random walks, where individuals switch between active and dormant states. We consider two scenarios: one where the switching rates are influenced by the random environment, and another where they are independent of it. The random environment, which also governs the branching mechanism, is modelled in four specific configurations, each composed of particles: (1) a Bernoulli field of immobile particles, (2) a single moving particle, (3) a Poisson field of moving particles, and (4) a simple symmetric exclusion process. In each case, the environmental particles can act either as catalysts, which accelerate branching, or as traps, which kill individuals. The key distinction between the two types is that dormant individuals are protected from traps but do not participate in migration or reproduction. We quantify the impact of dormancy on population growth and survival by identifying the large-time asymptotics of the expected population size. Our mathematical approach is based on the parabolic Anderson model, analysed via the Feynman-Kac formula. Specifically, we extend the parabolic Anderson model to a two-type random walk to investigate the quantitative role of dormancy.","abstract_html":"This thesis introduces spatial models for populations with dormancy in random environments. The models are formulated as continuous-time two-type branching random walks, where individuals switch between active and dormant states. We consider two scenarios: one where the switching rates are influenced by the random environment, and another where they are independent of it. The random environment, which also governs the branching mechanism, is modelled in four specific configurations, each composed of particles: (1) a Bernoulli field of immobile particles, (2) a single moving particle, (3) a Poisson field of moving particles, and (4) a simple symmetric exclusion process. In each case, the environmental particles can act either as catalysts, which accelerate branching, or as traps, which kill individuals. The key distinction between the two types is that dormant individuals are protected from traps but do not participate in migration or reproduction. We quantify the impact of dormancy on population growth and survival by identifying the large-time asymptotics of the expected population size. Our mathematical approach is based on the parabolic Anderson model, analysed via the Feynman-Kac formula. Specifically, we extend the parabolic Anderson model to a two-type random walk to investigate the quantitative role of dormancy.","abstract_has_math":false,"creators":["Shafigh, Helia"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["König, Wolfgang"],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026","date_published":"2026","updated_at":"2026-07-27T21:28:33Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.14279/depositonce-25801"],"render_values":[{"text":"https://doi.org/10.14279/depositonce-25801","href":"https://doi.org/10.14279/depositonce-25801","code":true}]}]},"links":{"outbound_url":"https://depositonce.tu-berlin.de/handle/11303/26967","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["König, Wolfgang"]},{"key":"dc:creator","label":"Author","values":["Shafigh, Helia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-28T11:32:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-28T11:32:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2026"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://depositonce.tu-berlin.de/handle/11303/26967","https://doi.org/10.14279/depositonce-25801"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis introduces spatial models for populations with dormancy in random environments. The models are formulated as continuous-time two-type branching random walks, where individuals switch between active and dormant states. We consider two scenarios: one where the switching rates are influenced by the random environment, and another where they are independent of it. The random environment, which also governs the branching mechanism, is modelled in four specific configurations, each composed of particles: (1) a Bernoulli field of immobile particles, (2) a single moving particle, (3) a Poisson field of moving particles, and (4) a simple symmetric exclusion process. In each case, the environmental particles can act either as catalysts, which accelerate branching, or as traps, which kill individuals. The key distinction between the two types is that dormant individuals are protected from traps but do not participate in migration or reproduction. We quantify the impact of dormancy on population growth and survival by identifying the large-time asymptotics of the expected population size. Our mathematical approach is based on the parabolic Anderson model, analysed via the Feynman-Kac formula. Specifically, we extend the parabolic Anderson model to a two-type random walk to investigate the quantitative role of dormancy.","In dieser Arbeit werden räumliche Modelle für Populationen mit Dormanz in zufälligen Umgebungen vorgestellt. Die Modelle werden als kontinuierliche Zwei-Typ-Verzweigungsirrfahrten formuliert, bei denen Individuen zwischen einem aktiven und dormanten Zustand wechseln können. Wir betrachten zwei Szenarien: eines, bei dem die Wechselraten von der zufälligen Umgebung beeinflusst werden, und ein weiteres, bei dem sie unabhängig von dieser sind. Die zufällige Umgebung, die auch den Verzweigungsmechanismus bestimmt, wird in vier spezifischen Konfigurationen modelliert, die jeweils aus Partikeln bestehen: (1) ein Bernoulli-Feld unbeweglicher Partikel, (2) ein einzelnes sich bewegendes Partikel, (3) ein Poisson-Feld sich bewegender Partikel und (4) ein einfacher symmetrischer Ausschluss-Prozess. In jedem Fall können die Partikel der Umgebung entweder als Katalysatoren wirken, die die Verzweigung vorantreiben, oder als Fallen, welche die Individuen töten. Der entscheidende Unterschied zwischen den beiden Individuentypen besteht darin, dass dormante Individuen vor Fallen geschützt sind, jedoch nicht an Migration oder Verzweigung teilnehmen. Wir quantifizieren den Einfluss der Dormanz auf das Wachstum bzw. das Überleben der Population, indem wir die Asymptotik der erwarteten Populationsgröße auf lange Sicht identifizieren. Unser mathematischer Ansatz basiert auf dem parabolischen Anderson-Modell und der Feynman-Kac-Formel. Konkret wird das parabolische Anderson-Modell zu einer Zwei-Typ-Irrfahrt erweitert, anhand derer die quantitative Rolle der Dormanz untersucht wird."]},{"key":"dc:title","label":"Title","values":["Dormancy in spatial population models in random environments"]}]}],"canonical_facts":{"dc:contributor.advisor":["König, Wolfgang"],"dc:creator":["Shafigh, Helia"],"dc:date.accessioned":["2026-04-28T11:32:45Z"],"dc:date.available":["2026-04-28T11:32:45Z"],"dc:date.issued":["2026"],"dc:description.abstract":["This thesis introduces spatial models for populations with dormancy in random environments. The models are formulated as continuous-time two-type branching random walks, where individuals switch between active and dormant states. We consider two scenarios: one where the switching rates are influenced by the random environment, and another where they are independent of it. The random environment, which also governs the branching mechanism, is modelled in four specific configurations, each composed of particles: (1) a Bernoulli field of immobile particles, (2) a single moving particle, (3) a Poisson field of moving particles, and (4) a simple symmetric exclusion process. In each case, the environmental particles can act either as catalysts, which accelerate branching, or as traps, which kill individuals. The key distinction between the two types is that dormant individuals are protected from traps but do not participate in migration or reproduction. We quantify the impact of dormancy on population growth and survival by identifying the large-time asymptotics of the expected population size. Our mathematical approach is based on the parabolic Anderson model, analysed via the Feynman-Kac formula. Specifically, we extend the parabolic Anderson model to a two-type random walk to investigate the quantitative role of dormancy.","In dieser Arbeit werden räumliche Modelle für Populationen mit Dormanz in zufälligen Umgebungen vorgestellt. Die Modelle werden als kontinuierliche Zwei-Typ-Verzweigungsirrfahrten formuliert, bei denen Individuen zwischen einem aktiven und dormanten Zustand wechseln können. Wir betrachten zwei Szenarien: eines, bei dem die Wechselraten von der zufälligen Umgebung beeinflusst werden, und ein weiteres, bei dem sie unabhängig von dieser sind. Die zufällige Umgebung, die auch den Verzweigungsmechanismus bestimmt, wird in vier spezifischen Konfigurationen modelliert, die jeweils aus Partikeln bestehen: (1) ein Bernoulli-Feld unbeweglicher Partikel, (2) ein einzelnes sich bewegendes Partikel, (3) ein Poisson-Feld sich bewegender Partikel und (4) ein einfacher symmetrischer Ausschluss-Prozess. In jedem Fall können die Partikel der Umgebung entweder als Katalysatoren wirken, die die Verzweigung vorantreiben, oder als Fallen, welche die Individuen töten. Der entscheidende Unterschied zwischen den beiden Individuentypen besteht darin, dass dormante Individuen vor Fallen geschützt sind, jedoch nicht an Migration oder Verzweigung teilnehmen. Wir quantifizieren den Einfluss der Dormanz auf das Wachstum bzw. das Überleben der Population, indem wir die Asymptotik der erwarteten Populationsgröße auf lange Sicht identifizieren. Unser mathematischer Ansatz basiert auf dem parabolischen Anderson-Modell und der Feynman-Kac-Formel. Konkret wird das parabolische Anderson-Modell zu einer Zwei-Typ-Irrfahrt erweitert, anhand derer die quantitative Rolle der Dormanz untersucht wird."],"dc:identifier.uri":["https://depositonce.tu-berlin.de/handle/11303/26967","https://doi.org/10.14279/depositonce-25801"],"dc:language.iso":["en"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:title":["Dormancy in spatial population models in random environments"],"dc:type":["Doctoral Thesis"]},"updated_at":"2026-07-27T21:28:33Z"}