Statistical analyses and reproducibility

Details on statistical analysis for Figs. ​Figs.3,3, ​,5,5, ​,77 and ​and88 can be found in ‘Statistical analysis of 3D data’, ‘RNA-sequencing analysis workflow’ and ‘Electrophysiological data analysis and statistics’, respectively. Primary data processing and organization were performed in Microsoft Excel (2010). Statistical analyses were performed using Prism software (GraphPad, V.5.0–V.8.0). Statistical significance for two groups was determined by unpaired two-tailed Student’s t-test. In the case of unequal variance between the two groups, the unpaired Welch’s t-test or unpaired Mann–Whitney U-test was used. For determining differences between more than two groups, one-way ANOVA was applied. Depending on the scientific question, one-way ANOVA was followed by no post hoc test, by Dunnett’s post hoc test (comparing all groups to one control) or by Tukey’s post hoc test (comparing all groups among each other), as indicated in the figure legends. All remaining data (more than two groups, more than one independent factor) were analyzed with two-way ANOVA followed by Sidak’s or Tukey’s post hoc analysis. Data are expressed as the mean, and the error bars indicate the s.e.m. unless specified otherwise. In the violin plots, solid lines represent median values, and dashed lines represent lower and upper quartiles. A detailed description of statistics, including individual data points, tests, P values and further statistical parameters, are provided in the figure legends and as source data. Statistical significance was defined as: *P ≤ 0.05, **P ≤ 0.01, ***P ≤ 0.001 and ****P ≤ 0.0001.

No statistical methods were used to predetermine sample sizes, although sample sizes are similar to those reported in previous publications^6,39,59. Data collection and analysis were carried out in a blinded format throughout the study, unless this was not possible due to the visual differences in cases of varying neuronal numbers resulting from genetic labeling as depicted in Fig. 3a–c. Data distribution was assumed to be normal, but this was not formally tested. Except for animals that died during an experiment, no data were excluded. For metabolic phenotyping, every mouse represents a replicate (n) and the number of replicates is mentioned for each experiment in the figure legend and/or source data. In this case, data were pooled from independent experiments of varying n numbers. For RNA-seq, samples of pooled hypothalami were collected from individual mice of several cohorts. For electrophysiological experiments, the sample numbers indicate the number of cells used in recordings. All measurements that did not require statistical analysis, such as representative images, were obtained from at least two animals and in most cases a minimum of three animals were used.