Indirect reciprocity is a key mechanism for large-scale cooperation. This mechanism captures the insight that in part, people help others to build and maintain a good reputation. To enable such cooperation, appropriate social norms are essential. They specify how individuals should act based on each others' reputations, and how reputations are updated in response to individual actions. Although previous work has identified several norms that sustain cooperation, a complete analytical characterization of all evolutionarily stable norms remains lacking, especially when assessments or actions are noisy. In this study, we provide such a characterization for the public assessment regime. This characterization reproduces known results, such as the leading eight norms, but it extends to more general cases, allowing for various types of errors and additional actions including costly punishment. We also identify norms that impose a fixed payoff on any mutant strategy, analogous to the zero-determinant strategies in direct reciprocity. These results offer a rigorous foundation for understanding the evolution of cooperation through indirect reciprocity and the critical role of social norms.

Researchers have explored the performance of Iterated Prisoner's Dilemma strategies for decades, from the celebrated performance of Tit for Tat to the introduction of the zero-determinant strategies and the use of sophisticated learning structures such as neural networks. Many new strategies have been introduced and tested in a variety of tournaments and population dynamics. Typical results in the literature, however, rely on performance against a small number of somewhat arbitrarily selected strategies, casting doubt on the generalizability of conclusions. In this work, we analyze a large collection of 195 strategies in thousands of computer tournaments, present the top performing strategies across multiple tournament types, and distill their salient features. The results show that there is not yet a single strategy that performs well in diverse Iterated Prisoner's Dilemma scenarios, nevertheless there are several properties that heavily influence the best performing strategies. This refines the properties described by Axelrod in light of recent and more diverse opponent populations to: be nice, be provocable and generous, be a little envious, be clever, and adapt to the environment. More precisely, we find that strategies perform best when their probability of cooperation matches the total tournament population's aggregate cooperation probabilities. The features of high performing strategies help cast some light on why strategies such as Tit For Tat performed historically well in tournaments and why zero-determinant strategies typically do not fare well in tournament settings.

SUMMARY: For model species, single-cell RNA-based cell atlases are available. A good cell atlas includes all major stages in a species' ontogeny, and soon, they will be standard even for nonmodel species. Here, we propose a Python package called oggmap, which allows for the easy extraction of an orthomap (gene ages per orthogroup) for any given query species from OrthoFinder and other gene family data resources, like homologous groups from eggNOG or PLAZA. oggmap provides extracted gene ages for more than thousand eukaryotic species which can be further used to calculate gene age-weighted expression data from scRNA sequencing objects using the Python Scanpy toolkit. Not limited to one transcriptome evolutionary index, oggmap can visualize the individual gene category (e.g. age class, nucleotide diversity bin) and their corresponding expression profiles to investigate scRNA-based cell type assignments in an evolutionary context. AVAILABILITY AND IMPLEMENTATION: oggmap source code is available at https://github.com/kullrich/oggmap, documentation is available at https://oggmap.readthedocs.io/en/latest/. oggmap can be installed via PyPi or directly used via a docker container.