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Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a…

We consider populations with time-varying growth rates living in sinks. Each population, when isolated, would become extinct. Dispersal-induced growth (DIG) occurs when the populations are able to persist and grow exponentially when…

Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and…

We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the…

Steady-state thermodynamics (SST) is a relatively newly emerging subfield of physics, which deals with transitions between steady states. In this paper, we find an SST-like structure in population dynamics of organisms that can sense their…

Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under…

We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical…

We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…

The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…

We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…

The degree to which population fluctuations arise from variable adult survival relative to variable recruitment has been debated widely for marine organisms. Disentangling these effects remains challenging because data generally are not…

Perturbation experiments are carried out by contact process and its mean-field version. Here, the mortality rate is increased or decreased suddenly. It is known that the fluctuation enhancement (FE) occurs after the perturbation, where FE…

Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…

Bird migration is an adaptive behavior ultimately aiming at optimizing survival and reproductive success. We propose an optimal switching model to study bird migration, where birds' migration behaviors can be efficiently modeled as…

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…

Changes in the frequency, duration, and severity of climate extremes are forecast to occur under global climate change. The impacts of climate extremes on forest productivity and health are complicated by potential interactions with…

We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…

We study the effect that disturbances in the ecological landscape exert on the spatial distribution of a population that evolves according to the nonlocal FKPP equation. Using both numerical and analytical techniques, we explore the three…

Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…