a, Power spectrum of all recorded odour plumes (mean ± SD of log power, n = 132 plumes). b, Cross correlation of all recordings at different lateral separation distances. c, Correlation coefficients over all recordings for odours from the same source and for odour sources separated by 50 cm in a controlled laboratory environment with complex airflow (indoors; ethyl valerate (EV) vs. tripropylamine (TPA); n = 25 for same source, n = 27 for sources separated by 50 cm; p < 0.0001, unpaired two-sided t-test). Box indicates 25th – 75th percentiles, thick line is median, whiskers are most extreme data points not considered outliers; see Methods. d, Same as Figure 4b (for odours α-Terpinene and ethyl butyrate) but for radial distances to the PID of 20 cm and 60 cm (p < 0.0001, unpaired two-sided t-test). e, Same as d but measured outdoors (n = 7 for same source, 10 for sources separated by 50 cm; p < 0.001, unpaired t-test; Indoors versus outdoors, one source: p = 0.0060, s = 50 cm: p = 0.0632, unpaired two-sided t-test). f, Example plume structures originating from the same one source or separated sources as recorded with a PID (blue) and replayed with the multi-channel high bandwidth odour delivery device (orange). g, Correlation coefficients over all recordings of replayed plumes for one source (n = 53 plumes) and for sources separated by 50 cm from each other (n = 74 plumes; p = 2.27e-41, unpaired two-sided t-test). h, Odour signals integrated over 2 s for all recordings of replayed plumes for one source (n = 53 plumes) and for sources separated by 50 cm (n = 74 plumes; p = 0.75, unpaired two-sided t-test). i, Odour plume signals integrated over 2 s for rewarded and unrewarded trials (n = 150 trials each; Odour 1: p = 0.4739, Odour 2: p = 0.0923, unpaired two-sided t-test). j, Overlaid power spectra (mean ± SD of log power) of all plumes (n = 127 plumes) recorded in complex, natural airflow conditions (blue) and replayed plumes (orange). k, Schematic of plume reproduction: First, a 2s long window is selected from the PID recording, starting around the middle of the trace and such that odour is present during the first 500 ms. Secondly, the trace is normalised between 0 and 1. Thirdly, the trace is converted into a series of binary opening and closing commands directly related to the value of the normalised signal. A value of 1 translates to a continuous opening, and a value of 0 translates to continuously closed. This series of commands is relayed to an odour valve and an inverted version of the commands is relayed to a mineral oil valve to generate a compensatory airflow. The resulting output resembles the original plume, as measured with a PID, and there is constant airflow throughout the trial, as measured with a flow meter. The same procedure is then applied to the accompanying odour, to create both plumes needed for each trial. l, Group learning curves (mean ± SD) for the two groups of animals trained on the virtual source separation task, but on different set of valves. Group 1 (n = 6 mice, blue) were trained on the task from the start, while Group 2 (n = 6 mice, cyan) were first exposed to a scrambled version of the task and were later transferred to the same plumes as Group 1. This served as a control that the cue required for learning is indeed olfactory information contained in the odour plumes. For the 3rd stage of learning, the plumes were refined to ensure odour was always present in the first 500 ms of the trial and performance stabilised for the two groups. Mice progressed through these learning stages as a group, based on time elapsed from the beginning of training. Therefore, some mice performed more trials than others. The last trial performed by a mouse in each phase is represented by a colour-coded circle above the plot. Accuracy is calculated over a 100-trial sliding window. m, Rejection fraction (fraction of trials the mouse abstained from licking) calculated for each plume pair plotted in relation to the correlation between the two odour traces in that plume pair. Animals are trained to lick (expected low rejection fraction) for source separated trials (low correlation) and abstain from licking (high rejection fraction) for one source trials (high correlation). n, Difference in lick rates in response to source separation training trials (n = 9 mice, mean ± SD), calculated for each mouse as lick rate (licks / 100 ms) in response to S+ trials minus the lick rate in response to S- trials, normalized to averaged lick rate for all trials across the corresponding time period. o, Reaction times for each mouse, calculated as the time point when the difference in lick rate for each mouse crossed a threshold (mean + 3 SDs over the baseline, defined as the first 200 ms of the trace, when odour was not present). Box indicates 25th - 75th percentiles, thick line is median, see Methods. p, Trial map of all animals during virtual source separation tasks before and after introduction of control valves similar to Extended Data Fig. 4 (n = 40 trials pre-, n = 40 trials post-new valve introduction, new valve introduction indicated by black vertical line). Each row corresponds to an animal, each column within the row represents a trial. Light green: hit, dark green: correct rejection, light red: false alarm, dark red: miss. q, Mean performance of animals (n = 11 mice) that reached performance criterion during training during pre- and post-control. r, Discrimination accuracy split by stimulus valence (green, S+; black, S-) for odour correlation fluctuation frequencies 2, 20 and 40 Hz (Fig. 4e; n = 9 mice, data is mean ± SD, unpaired two-sided t-test). s, Group performance for the square pulse probe trials at different frequencies, in animals trained on the source separation task (blue dots, n = 9 mice, data is mean ± SD), compared to group performance where animals were trained on correlated and anti-correlated square pulse trains (from Fig. 2k, black line and SEM band, n = 33 mice; 2 Hz: p = 0.0018, 20 Hz: p = 0.19, 40Hz: p = 0.94, unpaired two sided t-test). Violin plots in g-i show the median as a black dot and the first and third quartile by the bounds of the black bar.