Treatment with antibiotics is one of the most extreme perturbations to the human microbiome. Even standard courses of antibiotics dramatically reduce the microbiome’s diversity and can cause transitions to dysbiotic states. Conceptually, this is often described as a ‘stability landscape’: the microbiome sits in a landscape with multiple stable equilibria, and sufficiently strong perturbations can shift the microbiome from its normal equilibrium to another state. However, this picture is only qualitative and has not been incorporated in previous mathematical models of the effects of antibiotics. Here, we outline a simple quantitative model based on the stability landscape concept and demonstrate its success on real data. Our analytical impulse-response model has minimal assumptions with three parameters. We fit this model in a Bayesian framework to data from a previous study of the year-long effects of short courses of four common antibiotics on the gut and oral microbiomes, allowing us to compare parameters between antibiotics and microbiomes, and further validate our model using data from another study looking at the impact of a combination of last-resort antibiotics on the gut microbiome. Using Bayesian model selection we find support for a long-term transition to an alternative microbiome state after courses of certain antibiotics in both the gut and oral microbiomes. Quantitative stability landscape frameworks are an exciting avenue for future microbiome modelling.

10Even short courses of antibiotics are known to reduce gut microbiome diversity. However, there has been 11 limited mathematical modelling of the associated dynamical time-response. Here, we take inspiration from a 12 'stability landscape' schematic and develop an impulse-response model of antibiotic perturbation. We fit this 13 model to previously published data where individuals took a ten-day course of antibiotics (clindamycin or 14 ciprofloxacin) and were sampled up to a year afterwards. By fitting an extended model allowing for a 15 transition to an alternative stable state, we find support for a long-term transition to an alternative community 16 state one year after taking antibiotics. This implies that a single treatment of antibiotics not only reduces the 17 diversity of the gut flora for up to a year but also alters its composition, possibly indefinitely. Our results 18provide quantitative support for a conceptual picture of the gut microbiome and demonstrate that simple 19 models can provide biological insight.

Humans possess a rich repertoire of abstract concepts about which they can often judge their confidence. These judgements help guide behaviour, but the mechanisms underlying them are still poorly understood. Here, we examine the evolution of people's sense of confidence as they engage in probabilistic concept learning. Participants learned a continuous function of four continuous features, reporting their predictions and confidence about these predictions. Participants indeed had insight into their uncertainties: confidence was correlated with the accuracy of predictions, increasing as learning progressed. There were substantial individual differences. In contrast to many classical models that try to explain only the predictions, we formalized human function learning in Bayesian terms as Gaussian process inference. This model generates posterior distributions, allowing us to link predictions and confidence judgements. Gaussian process inference well matched participants' predictions, and also the confidence judgements of metacognitively competent participants. Our results show that human confidence judgements during learning are tied to uncertainty, suggesting that concept learning is fundamentally probabilistic.

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