Microscopic lifeforms rarely locomote in an unconfined liquid. Solid boundaries representing biological membranes, other swimmers, or filaments much larger than the swimmer can represent elements of confinement. Due to the long range of hydrodynamic forces at this scale, the boundaries often have a dominant impact on the physics of locomotion. Here we extend previous work on locomotion of a swimmer with a prescribed stroke in confined isotropic fluids to anisotropic fluids, using the model of a nematic liquid crystal. The competition between elasticity, hydrodynamics, and anchoring conditions leads to a complex locomotion problem with unique transport properties. We examine this problem analytically and numerically for a model swimmer near a bounding wall which can itself also be elastic. For strong planar anchoring at a rigid wall, we find that the swimming speed goes to the isotropic Newtonian limit as the swimmer gets close to the wall, although the power required to maintain the swimmer’s speed depends on liquid crystal properties. We also report new findings on the swimming speed due to large-amplitude waveforms in unbounded liquid crystals.
Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a confined liquid crystal”, arXiv, PDF
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march toward fixation or extinction. We describe motion as the swapping of individuals on graphs, and also more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth updating or for any process that combines birth-death and death-birth updating. If the rule is purely birth-death updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and on weighted graphs. In the latter case, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations.
Madison S. Krieger, A. McAvoy and M. A. Nowak, “Effects of motion in structured populations”, Arxiv, PDF
Social networks are an important structural property of evolutionary processes in culture and language. While great strides have been made in modeling the dynamics of discrete linguistic features in reproducing populations, such as individual signs (Nowak et. al. 1999) and grammatical rules (Niyogi 2006), these models haven’t been completely explored on graph structures, and continuous parameters such as those defining vowel formant frequencies or other cultural quantities of interest, such as garment length, are also ill-understood. We discuss a simple model for a reproducing population in which an individual occupies a node on a graph and decides on the value of a single continuous parameter based on the examples received from neighboring nodes. In the context of sound change, this model recapitulates many core results: dispersion of neighboring phonemes in chain shifts (Martinet 1955), the irreversibility of phoneme mergers (Garde 1961) and the uniform expansion of mergers (Herzog 1965). We also compare results of the model to existing studies of sound change in social networks (Labov 2001). These types of events in language evolution are largely “from below”, meaning they are little affected by other meaningful social variables. Time permitting, we will discuss how to expand the model to explore change “from above”, where nodes are decorated with other features to denote membership in different groups, and Sturtevant’s (Sturtevant 1947) conjecture that language change ends when social change ends.
Some of the most critical evolutionary innovations occurred within single-celled prokaryotic organisms in the primitive ocean, such as the development of flagellar motility and the invention of oxidative photosynthesis. Prokaryotes have multiple vectors to exchange genetic material including transduction, transformation and conjugation. Being able to exchange genetic information allows important novel genes to be built up more quickly than if the population were waiting for the proper mutations to arise in a single lineage. However, these methods of genetic exchange require two differing lineages containing subsections of the novel gene to be in close proximity. Here we consider whether the transport properties of the primitive ocean may have accelerated this process. We consider two genetic components which arise via mutation at the same rate within a large background population and afford no selective advantage on their own. Once the pieces are combined via horizontal gene transfer in a single lineage, the selective advantage is immense. We examine the role of different fluid flows and components of complex oceanic flow on the time until the two lineages are united via theory and simulation.
We consider a spatial model of a susceptible-infected-susceptible (SIS) process in which individuals are organized into demes of identical population size. The demes themselves are structured on a spatial lattice. An individual can be in one of three states: susceptible, infected with a drug-resistant strain, or infected with a wild-type strain. Infections spread both within demes and between adjacent demes. Drug treatment enters at the level of demes. Some demes are treated permanently with drug, such that only the resistant strain can infect the individuals inside these demes. The treated demes can be spatially correlated, representing larger structures such as hospitals where drug treatment is employed, or treatment can be spatially uncorrelated. When treated demes are spatially correlated, both the resistant strain and the wild type coexist for timescales many orders of magnitude larger than when drug treatment is not spatially correlated. We analyze and simulate the process in many different parameter regimes and characterize both the initial transients and a quasi-steady state in which both infections exist in similar frequencies and in similar spatial locations for long time periods. We postulate that the magnitude of the extinction time for the drug-resistant strain, which is overall less fit than the wild type, can be approximated by the extinction time for an Ornstein-Uhlenbeck process. These spatial effects may explain the long-term coexistence between wild type infections and drug-resistant strains that has been observed in the United States over the last 70 years.
I wrote an article for Nautilus, appearing in print volume 14 (May/June 2016) and in the online edition. It was republished in issue 49.
An older version that focused less sentimentally on myself and more interestingly on some of the gauge mechanics described in the article can be found here.
We calculate the swimming speed of a swimmer with a prescribed stroke in a liquid crystal solution
and near a wall.
Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a liquid crystal near a wall”, —