1993). In Figure 3, a computer model of random change in cell-type number in diversifying lineages over 4000 steps produced the upper bound shown by the shaded line (Valentine et al., 1994). In that model the number of lineages began at one and increased logistically to 2000; the addition or subtraction of a cell type in each lineage in any step was treated as a Markov process. The model curve is scale to geological time by being pinned to landmarks at 30 and 210 cell types but is free elsewhere.

The chief caveats in interpreting this model relate to the estimates of cell-phenotype numbers indicated on Figure 3. The estimates represent a sampling of cell types and are made with a lumper's approach, and nerve cell types are not distinguished (Valentine et al., 1994). For the simpler organisms the numbers may be fairly accurate, but for increasingly complex forms the figures increasingly underestimate true cell-type numbers. However, the intent is not to measure an increasing developmental complexity, or an increasing information content of metazoan genomes, but simply to reflect the gross morphological complexity of the body plans. Nevertheless, that portion of the curve represented by chordates should be treated with caution. As the early portion of the curve should be on the firmer footing, it is worth considering its implications for the early history of the metazoans and for the Cambrian explosion.

Although the model is not meant to replicate the history of metazoan complexity, the behavior of the upper bound suggests that no forcing mechanism may be necessary to account for the empirical complexity increase in early metazoan body plans. The relatively rapid initial increase in complexity, created partly by a "floor" of two cell types and partly by the diversification of clades, may have been a feature of real clades even in the absence of forcing agents. The origin of metazoans may thus be hypothesized to have been near 600 my ago, more recently than is usually supposed. The rise in complexity is parabolic in the model. At present there is no evidence of a major step in body-plan complexity during the Cambrian explosion. The implication is that when animals with, say, 45 cell types appear during the explosion, there were ancestors of that clade with 44 cell types (or in that general region) that we don't see, and complexities should dwindle, perhaps at an increasing rate as we go back farther in time. Again, the ancestors may be known today only by the late Precambrian traces.

Phylogenetic Models and Body Plans

The Molecular Phylogenetic Model. Expectations as to the body plans of late Precambrian bilaterians depend partly upon phylogenetic models.



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