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Since its introduction, the reward prediction error theory of dopamine has explained a wealth of empirical phenomena, providing a unifying framework for understanding the representation of reward and value in the brain(1-3). According to the now canonical theory, reward predictions are represented as a single scalar quantity, which supports learning about the expectation, or mean, of stochastic outcomes. Here we propose an account of dopamine-based reinforcement learning inspired by recent artificial intelligence research on distributional reinforcement learning(4-6). We hypothesized that the brain represents possible future rewards not as a single mean, but instead as a probability distribution, effectively representing multiple future outcomes simultaneously and in parallel. This idea implies a set of empirical predictions, which we tested using single-unit recordings from mouse ventral tegmental area. Our findings provide strong evidence for a neural realization of distributional reinforcement learning.

Analyses of single-cell recordings from mouse ventral tegmental area are consistent with a model of reinforcement learning in which the brain represents possible future rewards not as a single mean of stochastic outcomes, as in the canonical model, but instead as a probability distribution.

Levels of gene expression underpin organismal phenotypes(1,2), but the nature of selection that acts on gene expression and its role in adaptive evolution remain unknown(1,2). Here we assayed gene expression in rice (Oryza sativa)(3), and used phenotypic selection analysis to estimate the type and strength of selection on the levels of more than 15,000 transcripts(4,5). Variation in most transcripts appears (nearly) neutral or under very weak stabilizing selection in wet paddy conditions (with median standardized selection differentials near zero), but selection is stronger under drought conditions. Overall, more transcripts are conditionally neutral (2.83%) than are antagonistically pleiotropic(6) (0.04%), and transcripts that display lower levels of expression and stochastic noise(7-9) and higher levels of plasticity(9) are under stronger selection. Selection strength was further weakly negatively associated with levels of cis-regulation and network connectivity(9). Our multivariate analysis suggests that selection acts on the expression of photosynthesis genes(4,5), but that the efficacy of selection is genetically constrained under drought conditions(10). Drought selected for earlier flowering(11,12) and a higher expression of OsMADS18 (Os07g0605200), which encodes a MADS-box transcription factor and is a known regulator of early flowering(13)-marking this gene as a drought-escape gene(11,12). The ability to estimate selection strengths provides insights into how selection can shape molecular traits at the core of gene action.

Phenotypic selection analysis is used to estimate the type and strength of selection that acts on more than 15,000 transcripts in rice (Oryza sativa), which provides insight into the adaptive evolutionary role of selection on gene expression.

Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey(1-4). However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods(5-8) and experimental studies indicate that oscillations may be short-lived without external stabilizing factors(9-19). Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events.