Extended Data Figure 5: Evaluation of metrics for partner mixing.

The degree of partner intermixing within an aggregate was calculated using two metrics (see Supplementary Information for detailed description of metrics). For the modified join metric (J), 1 represents random mixing, while for Moran’s I, 0 represents random mixing. For both metrics increasing positive values represent increasing partner segregation and increasing negative values represent increasing ordered mixing (like a checkerboard). a, Examples of mock aggregates which were used to verify the behaviour of the two metrics. b, c, The determined values for either J or Moran’s I are represented by the large coloured data points for each of the 41 AS aggregates or 21 AD aggregates analysed in this study, respectively. The black data points represent the values for J or Moran’s I that were calculated in 300 permutation tests where the x and y coordinates of the archaea and bacteria cells were randomly reassigned. When the observed mixing was more segregated than 95% of the random permutation tests, the data points were coloured green and considered significant. Similarly, when the observed mixing was found to be more orderly mixed than 95% of the permutation tests the data points were coloured purple. When the observed mixing was found to be less extreme in either direction than 95% of the random test aggregates the data points were coloured red. The two metrics, while different in their formulation, gave very similar results. It is noteworthy that only a single aggregate contained cells that were more mixed than random. As expected, the permutation tests hover around the random mixing values for each metric, 1 and 0 for J and I, respectively.