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Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
The day-night cycle drives the largest biomass migration on Earth: the diel vertical migration (DVM) of aquatic organisms. Here, we present a three-dimensional agent-based model that incorporates photokinesis, gyrotaxis, and stochastic…
The emergence of eusocial species is both very rare in evolutionary history and results in remarkably successful species. By inverting an agent based model, agent rules are discovered that display behaviors characteristic of eusocial…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…
We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time moving in the enclosure (such as a lake or slough). We start…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
In the natural world, life has found innumerable ways to survive and often thrive. Between and even within species, each individual is in some manner unique, and this diversity lends adaptability and robustness to life. In this work, we aim…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
The vertical distribution of phytoplankton is of fundamental importance for the dynamics and structure of aquatic communities. Here, using an advection-reaction-diffusion model, we investigate the distribution and competition of…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
Dye experimentation is a widely used method in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid. This technique is particularly useful in biomedical diagnostic applications ranging…
In this article, we propose a traffic rule inspired from nature, that facilitates an elite agent to move efficiently through a crowd of inert agents. When an object swims in a fluid medium or an intruder is forced through granular matter,…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…
We derive from first principles a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of…