Related papers: Two-locus clines on the real line with a step envi…
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on…
We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or…
The fast-slow dynamics of an eco-evolutionary system are studied, where we consider the feedback actions of environmental resources that are classified into those that are self-renewing and those externally supplied. We show although these…
We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…
Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network…
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…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid…
Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve the…
A major problem in evolutionary biology is how species learn and adapt under the constraint of environmental conditions and competition of other species. Models of cyclic dominance provide simplified settings in which such questions can be…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
The topologically protected transport of colloidal particles on top of magnetic patterns of all possible single lattice constant two dimensional magnetic point group symmetries is studied experimentally, theoretically, and with numerical…
We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
We model a spatially detailed, two-sex population dynamics, to study the cost of ecological restoration. We assume that cost is proportional to the number of individuals introduced into a large habitat. We treat dispersal as homogeneous…
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric…