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Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
This paper deals with an impulsive degenerate logistic model, where pulses are introduced for modeling interventions or disturbances, and degenerate logistic term may describe refugees or protections zones for the species. Firstly, the…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
We study a system of PDEs modeling the population dynamics of two competitive species whose spatial movements are governed by both diffusion and mutually repulsive chemotaxis effects. We prove that solutions to this system are globally…
When confronted with an undesired cell population, such as bacterial infections or tumors, we seek the most effective treatment, designed to eliminate the population as rapidly as possible. A common practice is to monitor the cells…
The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied,…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
This study focuses on optimizing species release $S_2$ to control species population $S_1$ through impulsive release strategies. We investigate the conditions required to remove species $S_1$, which is equivalent to the establishment of…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different…
We consider the dynamics of spatially-distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the…
We investigate the phenomenology emerging from a 2-species dynamics under the scenario of a quasi-neutral competition within a metapopulation framework. We employ stochastic and deterministic approaches, namely spatially-constrained…
We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than…