Theoretical ecologists have long sought to understand how the persistence of populations
depends on biotic and abiotic factors. Classical work showed that demographic stochasticity …

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 …

We investigate the phenomenon of extinction of a long-lived self-regulating stochastic
population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of …

This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …

The dynamics of a local community of competing species with weak immigration from a static
regional pool is studied. Implementing the generalized competitive Lotka-Volterra model …

Noise plays a fundamental role in a wide variety of physical and biological dynamical
systems. It can arise from an external forcing or due to random dynamics internal to the …

We study the evolution of aggregates triggered by collisions with monomers that either lead
to the attachment of monomers or the break-up of aggregates into constituting monomers …

The coexistence of many species within ecological communities poses a long‐standing
theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this …

Applications of first passage times in stochastic processes arise across a wide range of
length and time scales in biological settings. After an initial technical overview, we survey …

There are conflicting reports in the literature regarding the finite-size scaling of the
Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various …