Figure 1

How many clusters are there in a particular sample? In this simulated instance (main panel), are there two, three or more? The problem is that adding additional clusters, by definition, explains more variation until each individual sits isolated in a cluster by itself [26]. If the cluster limits are robust, statistical methods should be able to identify them without resorting to a priori patterns. Cosine-smoothed kernel density plots [continuous analogues of histograms, [65]] highlight the difference induced by centering around the median (dot-dashed long lines) rather than the mean (dashed long lines) and scaling by the median absolute deviation rather than by standard deviations (the short, perpendicular lines are one median absolute deviation or standard deviation, as appropriate). In symmetric distributions, means and medians are similar, but median absolute deviations can still differ from standard deviations (right panel). If part of the population is an incipient species diverging from the majority, then medians and means also give different values (top panel).