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Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should…
Organisms are composed of multiple chemical elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can severely restrict organismal and population growth. However, many trophic interaction models only…
We design a stochastic individual-based model structured in energy, for single species consuming an external resource, where populations are characterized by a typical energy at birth in $\mathbb{R}^{*}_{+}$. The resource is maintained at a…
We develop a stochastic, individual-based model for food web simulation which in the large-population limit reduces to the well-studied Webworld model, which has been used to successfully construct model food webs with several realistic…
We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem…
We analyze plankton-nutrient food chain models composed of phytoplankton, herbivorous zooplankton and a limiting nutrient. These models have played a key role in understanding the dynamics of plankton in the oceanic layer. Given the strong…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
Statistical averaging and asynchronous population dynamics as portfolio mechanisms are considered as the most important processes with which biodiversity contributes to ecosystem stability. However, portfolio theories usually regard…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
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…
The eco-evolutionary dynamics of species are fundamentally linked to the energetic constraints of its constituent individuals. Of particular importance is the interplay between reproduction and the dynamics of starvation and recovery. To…
Evolutionary dynamics are shaped by a variety of fundamental, generic drivers, including spatial structure, ecology, and selection pressure. These drivers impact the trajectory of evolution, and have been hypothesized to influence…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that…
Ecosystems, which are intricate amalgams of biological communities and their surrounding environments, continually evolve under the influence of their myriad interactions. The world is currently facing intensifying environmental…