Domain coarsening and interface kinetics in the Ising model

In this thesis, I investigate in detail two basic problems in nonequilibrium statistical mechanics. First, if a spin system such as a kinetic Ising model or a kinetic Potts model is quenched from supercritical temperature to subcritical temperature, how does the system coarsen, and what complexities arise as the system descends in energy toward one of its equilibrium states? Second, if a kinetic Ising model is evolved from a deterministic initial condition at zero temperature, how do the domain interfaces evolve in time? I first study the nonconserved coarsening of the kinetic spin systems mentioned above. The coarsening of a 2d ferromagnet can be described exactly by an intriguing connection with continuum critical percolation. Furthermore, careful simulations of phase ordering in the 3d Ising model at zero temperature reveal strange nonstatic final states and anomalously slow relaxation modes, which we explain in detail. I find similarly rich phenomena in the zero-temperature evolution of a kinetic Potts model in 2d, where glassy behavior is again manifest. We also find large-scale avalanches in which clusters merge and dramatically expand beyond their original convex hulls at late times in the dynamics. Next, I study the geometrically simpler problem of the evolution of a single corner interface in the Ising model. We extend prior work by investigating the Ising Hamiltonian with longer interaction range. We solve exactly the limiting shapes of the corner interface in 2d for several interaction ranges. In 3d, where analytical treatments are notoriously difficult, we develop novel methods for studying corner interface growth. I conjecture a growth equation for the interface that agrees quite well with simulation data, and I discuss the interface's surprising geometrical features. In the summary, I discuss the broader implications of our findings and offer some thoughts on possible directions for future work

The evolution of queen control over worker reproduction in the social Hymenoptera

Abstract A trademark of eusocial insect species is reproductive division of labor, in which workers forego their own reproduction while the queen produces almost all offspring. The presence of the queen is key for maintaining social harmony, but the specific role of the queen in the evolution of eusociality remains unclear. A long‐discussed scenario is that a queen either behaviorally or chemically sterilizes her workers. However, the demographic and ecological conditions that enable such manipulation are still debated. We study a simple model of evolutionary dynamics based on haplodiploid genetics. Our model is set in the commonly observed case where workers have lost the ability to lay female (diploid) eggs by mating, but retain the ability to lay male (haploid) eggs. We consider a mutation that acts in a queen, causing her to control the reproductive behavior of her workers. Our mathematical analysis yields precise conditions for the evolutionary emergence and stability of queen‐induced worker sterility. These conditions do not depend on the queen's mating frequency. We find that queen control is always established if it increases colony reproductive efficiency, but can evolve even if it decreases colony efficiency. We further derive the conditions under which queen control is evolutionarily stable against invasion by mutant workers who have recovered the ability to lay male eggs

Life cycle synchronization is a viral drug resistance mechanism

Viral infections are one of the major causes of death worldwide, with HIV infection alone resulting in over 1.2 million casualties per year. Antiviral drugs are now being administered for a variety of viral infections, including HIV, hepatitis B and C, and influenza. These therapies target a specific phase of the virus’s life cycle, yet their ultimate success depends on a variety of factors, such as adherence to a prescribed regimen and the emergence of viral drug resistance. The epidemiology and evolution of drug resistance have been extensively characterized, and it is generally assumed that drug resistance arises from mutations that alter the virus’s susceptibility to the direct action of the drug. In this paper, we consider the possibility that a virus population can evolve towards synchronizing its life cycle with the pattern of drug therapy. The periodicity of the drug treatment could then allow for a virus strain whose life cycle length is a multiple of the dosing interval to replicate only when the concentration of the drug is lowest. This process, referred to as “drug tolerance by synchronization”, could allow the virus population to maximize its overall fitness without having to alter drug binding or complete its life cycle in the drug’s presence. We use mathematical models and stochastic simulations to show that life cycle synchronization can indeed be a mechanism of viral drug tolerance. We show that this effect is more likely to occur when the variability in both viral life cycle and drug dose timing are low. More generally, we find that in the presence of periodic drug levels, time-averaged calculations of viral fitness do not accurately predict drug levels needed to eradicate infection, even if there is no synchronization. We derive an analytical expression for viral fitness that is sufficient to explain the drug-pattern-dependent survival of strains with any life cycle length. We discuss the implications of these findings for clinically relevant antiviral strategies

Growth Inside a Corner: The Limiting Interface Shape

We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for the symmetries of the three-dimensional problem, we conjecture a governing equation for the evolution of the interface profile. We solve this equation analytically and find excellent agreement with simulations of the growth process. We also present a generalization to arbitrary spatial dimension.Comment: 4 pages, 2-column revtex4 format. Revised version in response to referee comment

Indirect Reciprocity with Optional Interactions and Private Information

We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright–Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio

The evolution of non-reproductive workers in insect colonies with haplodiploid genetics

Eusociality is a distinct form of biological organization. A key characteristic of advanced eusociality is the presence of non-reproductive workers. Why evolution should produce organisms that sacrifice their own reproductive potential in order to aid others is an important question in evolutionary biology. Here, we provide a detailed analysis of the selective forces that determine the emergence and stability of non-reproductive workers. We study the effects, in situations where the queen of the colony has mated once or several times, of recessive and dominant sterility alleles acting in her offspring. Contrary to widespread belief based on heuristic arguments of genetic relatedness, non-reproductive workers can easily evolve in polyandrous species. The crucial quantity is the functional relationship between a colony’s reproductive rate and the fraction of non-reproductive workers present in that colony. We derive precise conditions for natural selection to favor the evolution of non-reproductive workers. DOI: http://dx.doi.org/10.7554/eLife.08918.00