a, Transmission data from the SARS outbreak in Singapore in 2003 (ref. 5). Bars show observed frequency of Z, the number of individuals infected by each case. Lines show maximum-likelihood fits for Z∼Poisson (squares), Z∼geometric (triangles), and Z∼negative binomial (circles). Inset, probability density function (solid) and cumulative distribution function (dashed) for gamma-distributed ν (corresponding to Z∼negative binomial) estimated from Singapore SARS data. b, Expected proportion of all transmission due to a given proportion of infectious cases, where cases are ranked by infectiousness. For a homogeneous population (all ν = R0), this relation is linear. For five directly transmitted infections (based on k̂ values in Supplementary Table 1), the line is concave owing to variation in ν. c, Proportion of transmission expected from the most infectious 20% of cases, for 10 outbreak or surveillance data sets (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript ‘v’ indicates a partially vaccinated population. d, Reported superspreading events (SSEs; diamonds) relative to estimated reproductive number R (squares) for twelve directly transmitted infections. Lines show 5–95 percentile range of Z∼Poisson(R), and crosses show the 99th-percentile proposed as threshold for SSEs. Stars represent SSEs caused by more than one source case. ‘Other’ diseases are: 1, Streptococcus group A; 2, Lassa fever; 3, Mycoplasma pneumonia; 4, pneumonic plague; 5, tuberculosis. R is not shown for ‘other’ diseases, and is off-scale for monkeypox. See Supplementary Notes for details.