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.