The khmer package is a freely available software library for working efficiently with fixed length DNA words, or k-mers. khmer provides implementations of a probabilistic k-mer counting data structure, a compressible De Bruijn graph representation, De Bruijn graph partitioning, and digital normalization. khmer is implemented in C++ and Python, and is freely available under the BSD license at  https://github.com/dib-lab/khmer/.

It is not immediately clear how costly behavior that benefits others evolves by natural selection. By saving on inherent costs, individuals that do not contribute socially have a selective advantage over altruists if both types receive equal benefits. Restrained consumption of a common resource is a form of altruism. The cost of this kind of prudent behavior is that restrained individuals give up resources to less-restrained individuals. The benefit of restraint is that better resource management may prolong the persistence of the group. One way to dodge the problem of defection is for altruists to interact disproportionately with other altruists. With limited dispersal, restrained individuals persist because of interaction with like types, whereas it is the unrestrained individuals that must face the negative long-term consequences of their rapacity. Here, we study the evolution of restraint in a community of three competitors exhibiting a nontransitive (rock-paper-scissors) relationship. The nontransitivity ensures a form of negative feedback, whereby improvement in growth of one competitor has the counterintuitive consequence of lowering the density of that improved player. This negative feedback generates detrimental long-term consequences for unrestrained growth. Using both computer simulations and evolution experiments with a nontransitive community of Escherichia coli, we find that restrained growth can evolve under conditions of limited dispersal in which negative feedback is present. This research, thus, highlights a set of ecological conditions sufficient for the evolution of one form of altruism.survival of the weakest | experimental evolution | positive assortment | ecological feedback | bacteriocin Wisely and slow; they stumble that run fast. William ShakespeareT he conflict between individual and group interests is a common element in many social dilemmas. Consider the rate at which an organism consumes shared resources. Prudent use of common resources promotes the longevity or fecundity of the group; however, any individual that exhibits restraint suffers in competition with those using resources rapidly. Rapacity is selectively favored and the displacement of prudent types by their unrestrained contemporaries occurs despite harmful consequences for the group (1, 2). Restraint in the use of common resources is a form of altruism: behavior that is self-sacrificial and prosocial. Like other types of altruistic behavior, restraint faces a fundamental problem of subversion (3, 4). How can restrained types persist in the midst of would-be cheaters-individuals that have a competitive edge because they are unrestrained? In this article, we address this question directly by outlining ecological conditions sufficient to favor the evolution of restraint.One ingredient found in most explanations for the evolution of altruism, and thus relevant to the evolution of restraint, is positive assortment. Altruism stands a better chance when altruistic individuals disproportionately help those possessing the genes f...

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50 000 generations were better described by a power-law model than by a hyperbolic model. According to the power-law model, the rate of fitness gain declines over time but fitness has no upper limit, whereas the hyperbolic model implies a hard limit. Here, we examine whether the previously estimated power-law model predicts the fitness trajectory for an additional 10 000 generations. To that end, we conducted more than 1100 new competitive fitness assays. Consistent with the previous study, the power-law model fits the new data better than the hyperbolic model. We also analysed the variability in fitness among populations, finding subtle, but significant, heterogeneity in mean fitness. Some, but not all, of this variation reflects differences in mutation rate that evolved over time. Taken together, our results imply that both adaptation and divergence can continue indefinitely—or at least for a long time—even in a constant environment.

In the context of Wright's adaptive landscape, genetic epistasis can yield a multipeaked or "rugged" topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to fix rapidly on one, which may not be the highest peak. In a spatially structured population, on the other hand, beneficial mutations take longer to spread. This slowdown allows distant parts of the population to explore the landscape semiindependently. Such a population can simultaneously discover multiple peaks, and the genotype at the highest discovered peak is expected to dominate eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the fable of the tortoise and the hare, the structured population (tortoise) starts relatively slow but eventually surpasses the unstructured population (hare) in average fitness. In contrast, on singlepeak landscapes that lack epistasis, all uphill paths converge. Given such "smooth" topography, breadth of search is devalued and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the tortoise-hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a tortoise-hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright's shifting balance process.adaptive landscape | experimental evolution | NK model | landscape topography | spatial structure

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50 000 generations were better described by a power-law model than by a hyperbolic model. According to the power-law model, the rate of fitness gain declines over time but fitness has no upper limit, whereas the hyperbolic model implies a hard limit. Here, we examine whether the previously estimated power-law model predicts the fitness trajectory for an additional 10 000 generations. To that end, we conducted more than 1100 new competitive fitness assays. Consistent with the previous study, the power-law model fits the new data better than the hyperbolic model. We also analysed the variability in fitness among populations, finding subtle, but significant, heterogeneity in mean fitness. Some, but not all, of this variation reflects differences in mutation rate that evolved over time. Taken together, our results imply that both adaptation and divergence can continue indefinitely-or at least for a long time-even in a constant environment.