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Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
One of the most challenging problems in microbiology is to understand how a small fraction of microbes that resists killing by antibiotics can emerge in a population of genetically identical cells, the phenomenon known as persistence or…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Ecological interactions among phytoplankton occur in a moving fluid environment. Oceanic flows can modulate the competition and coexistence between phytoplankton populations, which in turn can affect ecosystem function and biogeochemical…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement. These observations are of a link between two a priori…
We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of…
Key traits of unicellular species, like cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of…
During the early-stages of embryo development, morphogenesis--- the emergence of shape and form in living organisms--- is almost exclusively associated with monolayers of tightly bound epithelial cells. To understand how such tissues change…
Conventional discrete-to-continuum approaches have seen their limitation in describing the collective behaviour of the multi-polar configurations of dislocations, which are widely observed in crystalline materials. The reason is that…
An extension of the Truscott-Brindley model (Bull. Math. Biol. {\bf 56}, 981 (1994)) is derived to account for the effect of demographic fluctuations. In the presence of seasonal forcing, and sufficiently shallow water conditions, the…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to…
We demonstrate that the chaotic nature of N-body systems can lead to macroscopic variations in the evolution of collisionless simulations containing rotationally supported discs. The unavoidable stochasticity that afflicts all simulations…
Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief…
Many biological populations exhibit diversity in their strategy for survival and reproduction in a given environment, and microbes are an example. We explore the fate of different strategies under sustained environmental change by…