Gould, Trends as Changes in Variance: A New Slant on Progress and Directionality in Evolution

GOULD--PRESIDENTIAL ADDRESS
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 CRETACEOUSPALEOGENENEOGENE

FIGURE 6--Modal decades, as defined in text, for each of the three radiations (Cretaceous in five-million-year intervals; Paleogene and Neogene in three-million-year intervals). Except for an initial rise in the Cretaceous, modal decades show no trend to increase.

in the shallows as well, but subclades in these environments did not prevail. The trend would then represent a decrease in variance-a differential removal of the shallow water tail, not a retreat to abyssal safety.

Symmetrical trends.--For interesting psychological reasons, this category is not usually read as a simple inverse of symmetrical increase trends. If an increase trend spreads out symmetrically on both tails and alters no measure of central tendency, we usually don't choose to speak of a trend at all, unless the extreme values at one tail hold a particular fascination for us. This is why, as argued above in the paradox of "life's little joke" (p. 321), we do not recognize as trends the greatest success stories in mammalian evolution--the not clearly directional explosions of species diversity in antelopes, rodents, and bats. But symmetrical decrease trends around an unchanged mean do tend to catch our attention for several reasons. On the other side of life's little joke, single survivors are misread as termini of anagenetic trends--so we spin the classic tales of horse and Homo.

Each type of symmetrical decrease trend leads readily to backward misinterpretation when we misfocus upon entities moving rather than variance decreasing. Consider two examples: 1) when variance drops because number of species plummets, we often think in terms of motion to an optimal form, when the primary phenomenon is reduction (perhaps random or nonselective) to a point of near extinction; 2) when the number of entities remains constant, but variance drops by reducing disparity, we often lament for an intriguing, lost extreme that seems to define some particular excellence--while reduced variance really measures a beneficial stabilization of the system, and the valued extreme was never a "thing" at all, but should have been read as an edge of a system.

Lest this claim seem overly abstract or improbable, I present

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