The evolution of complex gene regulation by low specificity binding sites

Transcription factor binding sites vary in their specificity, both within and between species. Binding specificity has a strong impact on the evolution of gene expression, because it determines how easily regulatory interactions are gained and lost. Nevertheless, we have a relatively poor understanding of what evolutionary forces determine the specificity of binding sites. Here we address this question by studying regulatory modules composed of multiple binding sites. Using a population-genetic model, we show that more complex regulatory modules, composed of a greater number of binding sites, must employ binding sites that are individually less specific, compared to less complex regulatory modules. This effect is extremely general, and it hold regardless of the regulatory logic of a module. We attribute this phenomenon to the inability of stabilising selection to maintain highly specific sites in large regulatory modules. Our analysis helps to explain broad empirical trends in the yeast regulatory network: those genes with a greater number of transcriptional regulators feature by less specific binding sites, and there is less variance in their specificity, compared to genes with fewer regulators. Likewise, our results also help to explain the well-known trend towards lower specificity in the transcription factor binding sites of higher eukaryotes, which perform complex regulatory tasks, compared to prokaryotes

The collapse of cooperation in evolving games

Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner's Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as a robust outcome in evolving populations. Here we extend evolutionary game theory by allowing players' strategies as well as their payoffs to evolve in response to selection on heritable mutations. In nature, many organisms engage in mutually beneficial interactions, and individuals may seek to change the ratio of risk to reward for cooperation by altering the resources they commit to cooperative interactions. To study this, we construct a general framework for the co-evolution of strategies and payoffs in arbitrary iterated games. We show that, as payoffs evolve, a trade-off between the benefits and costs of cooperation precipitates a dramatic loss of cooperation under the Iterated Prisoner's Dilemma; and eventually to evolution away from the Prisoner's Dilemma altogether. The collapse of cooperation is so extreme that the average payoff in a population may decline, even as the potential payoff for mutual cooperation increases. Our work offers a new perspective on the Prisoner's Dilemma and its predictions for cooperation in natural populations; and it provides a general framework to understand the co-evolution of strategies and payoffs in iterated interactions.Comment: 33 pages, 13 figure

Small games and long memories promote cooperation

Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists in particular the question is often how such behaviors can arise \textit{de novo} in a simple evolving system. How can group behaviors such as collective action, or decision making that accounts for memories of past experience, emerge and persist? Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. To study this problem we construct a coordinate system for memory-$m$ strategies in iterated $n$-player games that permits us to characterize all the cooperative strategies that resist invasion by any mutant strategy, and thus stabilize cooperative behavior. We show that while larger games inevitably make cooperation harder to evolve, there nevertheless always exists a positive volume of strategies that stabilize cooperation provided the population size is large enough. We also show that, when games are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. Finally we explore the co-evolution of behavior and memory capacity, and we find that longer-memory strategies tend to evolve in small games, which in turn drives the evolution of cooperation even when the benefits for cooperation are low

Identifying Signatures of Selection in Genetic Time Series

Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard $\chi^2$-based likelihood ratio test was previously proposed to address this problem. Here we show that the $\chi^2$ test of selection substantially underestimates the probability of Type I error, leading to more false positives than indicated by its $P$-value, especially at stringent $P$-values. We introduce two methods to correct this bias. The empirical likelihood ratio test (ELRT) rejects neutrality when the likelihood ratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of co-segregating linked loci.Comment: 24 pages, 6 figures, 4 tables, 7 supplementary figures and table