Growth models subject to catastrophes and dispersion in varying and random environments

• Grant number: 24/06021-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2024
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Fabio Prates Machado
• Grantee: Lucas Roberto de Lima
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

Population growth models subject to catastrophes and dispersal strategies play a crucial role in understanding population dynamics in the face of adversity and subsequent adaptability. Catastrophes, such as natural disasters or sudden events, can significantly impact population size. On the other hand, dispersal to new areas can facilitate the establishment of new communities, representing an effective survival strategy. The interaction between catastrophes and dispersal strategies influences population persistence and its growth rate.Furthermore, catastrophic events can affect individual behavior across generations, altering birth and growth rates of the new communities formed by survivors. The availability of suitable land for founding new communities may also present random spatial constraints and random available resources. Therefore, we propose implementing these elements in models subject to catastrophes, considering that the generational impact of each catastrophic event will be described by variable and random environments.The main objectives of this project include studying properties such as criticality, extinction, and survival probabilities. Additionally, the project aims to study properties related to the limit behavior of the processes involved, which are typically associated with branching processes.