Source: Statist. Sci. Volume 16, Number 1
(2001), 23-34.
In 1924 Yule observed that distributions of number of species per
genus were typically longtailed, and proposed a stochastic model to fit
these data. Modern taxonomists often prefer to represent relationships between
species via phylogenetic trees; the counterpart to Yule’s observation is
that actual reconstructed trees look surprisingly unbalanced. The imbalance can
readily be seen via a scatter diagram of the sizes of clades involved in the
splits of published large phylogenetic trees. Attempting stochastic modeling
leads to two puzzles. First, two somewhat opposite possible biological
descriptions of what dominates the macroevolutionary process (adaptive
radiation; “neutral” evolution) lead to exactly the same
mathematical model (Markov or Yule or coalescent). Second, neither this nor any
other simple stochastic model predicts the observed pattern of imbalance. This
essay represents a probabilist’s musings on these puzzles, complementing
the more detailed survey of biological literature by Mooers and Heard,
Quart. Rev. Biol. 72 [(1997) 31–54].
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