Gene drives for the extinction of wild metapopulations.

Population-suppressing gene drives may be capable of extinguishing wild populations, with proposed applications in conservation, agriculture, and public health. However, unintended and potentially disastrous consequences of release of drive-engineered individuals are extremely difficult to predict. We propose a model for the dynamics of a sex ratio-biasing drive, and using simulations, we show that failure of the suppression drive is often a natural outcome due to stochastic and spatial effects. We further demonstrate rock-paper-scissors dynamics among wild-type, drive-infected, and extinct populations that can persist for arbitrarily long times. Gene drive-mediated extinction of wild populations entails critical complications that lurk far beyond the reach of laboratory-based studies. Our findings help in addressing these challenges.

Daisy-chain gene drives for the alteration of local populations.

If they are able to spread in wild populations, CRISPR-based gene-drive elements would provide new ways to address ecological problems by altering the traits of wild organisms, but the potential for uncontrolled spread tremendously complicates ethical development and use. Here, we detail a self-exhausting form of CRISPR-based drive system comprising genetic elements arranged in a daisy chain such that each drives the next. "Daisy-drive" systems can locally duplicate any effect achievable by using an equivalent self-propagating drive system, but their capacity to spread is limited by the successive loss of nondriving elements from one end of the chain. Releasing daisy-drive organisms constituting a small fraction of the local wild population can drive a useful genetic element nearly to local fixation for a wide range of fitness parameters without self-propagating spread. We additionally report numerous highly active guide RNA sequences sharing minimal homology that may enable evolutionarily stable daisy drive as well as self-propagating CRISPR-based gene drive. Especially when combined with threshold dependence, daisy drives could simplify decision-making and promote ethical use by enabling local communities to decide whether, when, and how to alter local ecosystems.

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.

Selection for synchronized cell division in simple multicellular organisms.

The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a population model in which there compete simple multicellular organisms that grow by either synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous and asynchronous cell division, and we offer intuition for why these phenotypes are generally not neutral variants of each other.

Evolution of worker policing.

Workers in insect societies are sometimes observed to kill male eggs of other workers, a phenomenon known as worker policing. We perform a mathematical analysis of the evolutionary dynamics of policing. We investigate the selective forces behind policing for both dominant and recessive mutations for different numbers of matings of the queen. The traditional, relatedness-based argument suggests that policing evolves if the queen mates with more than two males, but does not evolve if the queen mates with a single male. We derive precise conditions for the invasion and stability of policing alleles. We find that the relatedness-based argument is not robust with respect to small changes in colony efficiency caused by policing. We also calculate evolutionarily singular strategies and determine when they are evolutionarily stable. We use a population genetics approach that applies to dominant or recessive mutations of any effect size.

Evolution of staying together in the context of diffusible public goods.

We study the coevolution of staying together and cooperation. Staying together means that replicating units do not separate after reproduction, but remain in proximity. For example, following cell division the two daughter cells may not fully separate but stay attached to each other. Repeated cell division thereby can lead to a simple multi-cellular complex. We assume that cooperators generate a diffusible public good, which can be absorbed by any cell in the system. The production of the public good entails a cost, while the absorption leads to a benefit. Defectors produce no public good. Defectors have a selective advantage unless a mechanism for evolution of cooperation is at work. Here we explore the idea that the public good produced by a cooperating cell is absorbed by cells of the same complex with a probability that depends on the size of the complex. Larger complexes are better at absorbing the public goods produced by their own individuals. We derive analytical conditions for the evolution of staying together, thereby studying the coevolution of clustering and cooperation. If cooperators and defectors differ in their intrinsic efficiency to absorb the public good, then we find multiple stable equilibria and the possibility for coexistence between cooperators and defectors. Finally we study the implications of disadvantages that might arise if complexes become too large.

Optimal environmental testing frequency for outbreak surveillance.

Public health surveillance for pathogens presents an optimization problem: we require enough sampling to identify intervention-triggering shifts in pathogen epidemiology, such as new introductions or sudden increases in prevalence, but not so much that costs due to surveillance itself outweigh those from pathogen-associated illness. To determine this optimal sampling frequency, we developed a general mathematical model for the introduction of a new pathogen that, once introduced, increases in prevalence exponentially. Given the relative cost of infection vs. sampling, we derived equations for the expected combined cost per unit time of disease burden and surveillance for a specified sampling frequency, and thus the sampling frequency for which the expected total cost per unit time is lowest.

Growth inside a corner: the limiting interface shape.

We investigate the growth of a crystal that is built by depositing cubes inside a corner. The interface of this crystal approaches a deterministic growing limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for basic three-dimensional symmetries, 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.

The Great Oxygenation Event as a consequence of ecological dynamics modulated by planetary change.

The Great Oxygenation Event (GOE), ca. 2.4 billion years ago, transformed life and environments on Earth. Its causes, however, are debated. We mathematically analyze the GOE in terms of ecological dynamics coupled with a changing Earth. Anoxygenic photosynthetic bacteria initially dominate over cyanobacteria, but their success depends on the availability of suitable electron donors that are vulnerable to oxidation. The GOE is triggered when the difference between the influxes of relevant reductants and phosphate falls below a critical value that is an increasing function of the reproductive rate of cyanobacteria. The transition can be either gradual and reversible or sudden and irreversible, depending on sources and sinks of oxygen. Increasing sources and decreasing sinks of oxygen can also trigger the GOE, but this possibility depends strongly on migration of cyanobacteria from privileged sites. Our model links ecological dynamics to planetary change, with geophysical evolution determining the relevant time scales.

Indirect reciprocity with optional games and monitoring of interactions between defectors.

We study evolution of cooperation by indirect reciprocity with optional interactions. There are repeated interactions between two types of players, cooperators and defectors, in a population of finite size. Previously, we considered the scenario where an encounter between a cooperator and a defector results in the defector's identity being revealed with some probability, while an encounter between two defectors does not reveal their identities. Here, we study a generalization of this model: an encounter between a cooperator and a defector results in the defector's identity being revealed with probability QC; an encounter between two defectors results in each of those defectors' identities being revealed independently with probability QD. We find that larger values of QD can significantly increase both the average payoffs for cooperators and, in a dynamical setting, the basin of attraction for cooperation. Moreover, if QC is sufficiently small and QD is sufficiently large, then we find a new behavior over the previous model in which cooperators and defectors can stably coexist. We also study hesitation to cooperate with unknown individuals and defectors refusing interactions with known defectors to preserve their own unknown status.

Primordial sex facilitates the emergence of evolution.

Compartments are ubiquitous throughout biology, and they have very likely played a crucial role at the origin of life. Here we assume that a protocell, which is a compartment enclosing functional components, requires N such components in order to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the timescales polynomially in N By contrast, in the absence of fusion, the worst-case scenario is exponential in N We discuss the implications of this result for the origin of life and other biological processes.

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

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.

Evolutionary dynamics of CRISPR gene drives.

The alteration of wild populations has been discussed as a solution to a number of humanity's most pressing ecological and public health concerns. Enabled by the recent revolution in genome editing, clustered regularly interspaced short palindromic repeats (CRISPR) gene drives-selfish genetic elements that can spread through populations even if they confer no advantage to their host organism-are rapidly emerging as the most promising approach. However, before real-world applications are considered, it is imperative to develop a clear understanding of the outcomes of drive release in nature. Toward this aim, we mathematically study the evolutionary dynamics of CRISPR gene drives. We demonstrate that the emergence of drive-resistant alleles presents a major challenge to previously reported constructs, and we show that an alternative design that selects against resistant alleles could greatly improve evolutionary stability. We discuss all results in the context of CRISPR technology and provide insights that inform the engineering of practical gene drive systems.

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.

Crystal growth inside an octant.

We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After rescaling by the characteristic size, the interface becomes progressively more deterministic in the long-time limit. Utilizing known results for the crystal growth inside a two-dimensional corner, we propose a hyperbolic partial differential equation for the evolution of the limiting shape. This equation is interpreted as a Hamilton-Jacobi equation, which helps in finding an analytical solution. Simulations of the growth process are in excellent agreement with analytical predictions. We then study the evolution of the subleading correction to the volume of the crystal, the asymptotic growth of the variance of the volume of the crystal, and the total number of inner and outer corners. We also show how to generalize the results to arbitrary spatial dimension.

Limiting shapes in two-dimensional Ising ferromagnets.

We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.