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While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
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…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of…
Understanding the behavior of particles in a dispersed phase system via population balances holds fundamental importance in studies of particulate sciences across various fields. Particle behavior, however, is sophisticated as a single…
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate \lambda. We…
We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the…
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…