Processes governing species richness in communities exposed to temporal environmental stochasticity: A review and synthesis of modelling approaches.

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks.

Quantifying invasibility.

Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases.

How temporal environmental stochasticity affects species richness: Destabilization, neutralization and the storage effect.

Temporal environmental stochasticity (TES), along with the variations of demographic rates associated with it, is ubiquitous in nature. Here we study the effect of TES on the species richness of diverse communities. In such communities the biodiversity at equilibrium reflects the balance between the rate at which new types are added (via migration, mutation or speciation) and the rate of extinction.

Taming the diffusion approximation through a controlling-factor WKB method.

The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. The DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign.

Invasion growth rate and its relevance to persistence: a response to Technical Comment by Ellner et al.

Ellner et al. (2020) state that identifying the mechanisms producing positive invasion growth rates (IGR) is useful in characterising species persistence. We agree about the importance of the sign of IGR as a binary indicator of persistence, but question whether its magnitude provides much information once the sign is given.

Mean growth rate when rare is not a reliable metric for persistence of species.

The coexistence of many species within ecological communities poses a long-standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, , is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population.

Optimal motion of triangular magnetocapillary swimmers.

A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two, and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field.

Effect of body deformability on microswimming.

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we run immersed-boundary-lattice-Boltzmann simulations of a microswimmer composed of deformable beads connected with springs. We find that the same deformations in the beads can result in different effects on the swimming velocity, namely an enhancement or a reduction, depending on the other parameters. To understand this we determine analytically the velocity of the swimmer, starting from the forces driving the motion and assuming that the deformations in the beads are known as functions of time and are much smaller than the beads themselves.

Lattice Boltzmann simulations of the bead-spring microswimmer with a responsive stroke-from an individual to swarms.

Propulsion at low Reynolds numbers is often studied by defining artificial microswimmers which exhibit a particular stroke. The disadvantage of such an approach is that the stroke does not adjust to the environment, in particular the fluid flow, which can diminish the effect of hydrodynamic interactions. To overcome this limitation, we simulate a microswimmer consisting of three beads connected by springs and dampers, using the self-developed waLBerla and [Formula: see text] framework based on the lattice Boltzmann method and the discrete element method.

Forces and shapes as determinants of micro-swimming: effect on synchronisation and the utilisation of drag.

In this analytical study we demonstrate the richness of behaviour exhibited by bead-spring micro-swimmers, both in terms of known yet not fully explained effects such as synchronisation, and hitherto undiscovered phenomena such as the existence of two transport regimes where the swimmer shape has fundamentally different effects on the velocity. For this purpose we employ a micro-swimmer model composed of three arbitrarily-shaped rigid beads connected linearly by two springs. By analysing this swimmer in terms of the forces on the different beads, we determine the optimal kinematic parameters for sinusoidal driving, and also explain the pusher/puller nature of the swimmer.