Do new life-forms appear explosively in Earth-history?

Introduction

Question: In geologic time, do new life-forms appear explosively in life-history on Earth? (By “explosively,” we loosely mean at a rate which, on the surface, seems incompatibe with Darwinian gradualism).

“Yes, after all…

…like whales

The evolution or appearance of whales as been extraordinarily explosive (non-gradual). On the traditional evolutionary model, a coyote-like creature (Pakicetus)¹ was transformed into a fully-aquatic whale within 4 million years, (perhaps significantly less) despite the requirements:

• Counter-current heat exchanger for intra-abdominal testes
• Ball vertebra
• Tail flukes and musculature
• Blubber for temperature insulation
• Ability to drink sea water (reorganization of kidney tissues)
• Fetus in breech position (for labor underwater)
• Nurse young underwater (modified mammae)
• Forelimbs transformed into flippers
• Reduction of hindlimbs
• Reduction/loss of pelvis and sacral vertebrae
• Reorganization of the musculature for the reproductive organs
• Hydrodynamic properties of the skin
• Special lung surfactants
• Novel muscle systems for the blowhole
• Modification of the teeth
• Modification of the eye for underwater vision
• Emergence and expansion of the mandibular fat pad with complex lipid distribution
• Reorganization of skull bones and musculature
• Modification of the ear bones
• Decoupling of esophagus and trachea
• Synthesis and metabolism of isovaleric acid (toxic to terrestrial mammals)
• Emergence of blowhole musculature and their neurological control²

Carl Zimmer, Evolution: The Triumph of an idea (Harper Perennial, 2002), 163.
Adapted from an online lecture, “Whale Evolution Vs. Population Genetics” - Richard Sternberg (PhD. in Evolutionary Biology).
Jonathan McLatchie: “According to Richard Sternberg's calculations, and based on the equations of population genetics applied in a 2008 paper by Durrett and Schmidt in the Journal of Genetics, one may reasonably expect to see two co-ordinated mutations to achieve fixation in the timeframe of around 43.3 million years. When one considers the magnitude of the engineering feat, such a scenario can only be ruled incredible. This problem is accentuated further when one considers that the majority of anatomical novelties unique to aquatic cetaceans (Pelagiceti) appeared during just a few million years -- probably within 1-3 million years.” [Fact-Checking Wikipedia on Common Descent: The Evidence from Paleontology, online at evolutionnews.org]

…like the Cambrian fauna

They appear explosively in fossil records

New life-forms appear suddenly in the fossil record.¹ This is relevant because, unless life were appearing suddenly in life-history, the fossil record would not be this way.

But so what if the fossil record only shows new life-forms arriving suddenly. Couldn't it be that the relevant rocks have been eroded or remain undiscovered (i.e. the appearance is an “artifact” of an incomplete sampling).

This is widely acknowledged [Forthcoming]. In a now famous quote, a prominent paleontologist explains why he advocates a rapid stop-and-start model for Darwinian evolution (contra Darwin's gradualism):

Stephen Jay Gould (Professor at Harvard, Paleonotologist): “The extreme rarity of transitional forms in the fossil record persists as the trade secret of paleontology. The evolutionary trees that adorn our textbooks have data only at the tips and nodes of their branches; the rest is inference, however reasonable, not the evidence of fossils. … We fancy ourselves as the only true students of life's history, yet to preserve our favored account of evolution by natural selection we view our data as so bad that we never see the very process we profess to study. For several years, Niles Eldredge of the American Museum of Natural History and I have been advocating a resolution to this uncomfortable paradox.” [“Evolution's Erratic Pace” in Natural History 86(5)(1977): 12-16.]