Two blog posts recently collided for me. First, in a blog discussion on Macroevolution vs. Microevolution, Allen MacNeill clarified some issues for me (thanks to TUIBG for bringing it back up):
Add the newly emerging fields of evo-devo and epigenesis to the foregoing, and it is increasingly clear that macroevolution (i.e. cladogenesis) follows different rules than microevolution (i.e. anagenesis), and that these differences are most noticeable in the fossil record cited by Eldredge and Gould as the basis for their theory of punctuated equilibrium. In particular, the basic program that energized the "modern synthesis" â€“ that is, the reduction of all significant evolutionary mechanisms to a series of linked mathematical models, based on grossly simplified reductions of complex biology to quasi-Mendelian point-like "particles of inheritance" (changes in which drive the variation and divergence of phenotypes) â€“ is impossible to apply in any coherent way to macroevolution. The "modern synthesis" was essentially a "Newtonian" program, whose proponents assumed that the underlying law-like processes (i.e. microevoluiton) are (like physics) both ahistorical and universal. However, it is now becoming clear that the emerging science of macroevolution is both irreversibly historically contingent (and therefore not reducible to mathematical formalisms) and driven by fundamentally different processes than those underlying most of microevolution.
Rich Lawler's comment at Gene Expression counter-balances that comment with an item on Formalization and Process:
It's interesting to note that a few of the most insightful observations about the evolutionary process were first promulgated verbally, then later proven mathematically (unlike H-W equilibrium). These include runaway sexual selection (first adumbrated by Fisher, then shown mathematically possible by Lande and Kirkpatrick), the handicap principle (first adumbrated by Zahavi, then–finally–shown to be mathematically possible by Grafen), and, of course, natural selection (first adumbrated by what's-his-face, then formalized by Wright, Fisher, and later Price, among others). And of course, all of these topics were debated back-n-forth until the math made them more clear.
The key words here appear to be complex and process, in determining whether some pattern is historical or can be formalized. Do we know enough to reduce the complex into a process? If we knew enough, the Platonist philosophers of science argue that we could reduce even the complexity of biology to mathematics, much like in the Newtonian program. The number of variables are too great to enumerate. This is the case for any historical description – causation still rules, but not all of the causes can be labeled.
Formalization is also important in molecular and cellular biology – how do we best formally represent the highly interconnected network of protein interactions in the cell? While not a process per se, this network is complex and dynamic. Richard Bonneau et al. had a very recent post in Cell experimentally trying to point the way towards such a formalization with A Predictive Model for Transcriptional Control of Physiology in a Free Living Cell:
This does bring up an obvious question of whether the potential for enormous complexity of a biological system will ever allow the construction of a complete model of a cell. In this regard it has been favorably suggested, at least in the context of metabolism, that despite this potential for complexity, a cell usually functions in one of few dominant modes or states (Barrett et al., 2005). We speculate that this natural property of a biological system simplifies the problem to inferring gene regulatory models for its transitions among relatively few states. In addition, as discussed earlier, the extensive connectivity within EF and biological networks makes it tractable to effectively construct a comprehensive model of cellular responses to changes in multiple EFs from a modest number of well-designed systematic perturbation experiments ([Faith et al., 2007] and [Hayete et al., 2007]). We believe that this type of a model will hold true for environmental responses of all organisms and, more importantly, that it should be possible to construct such models solely from EF perturbation experiments. This will be especially valuable in context of organisms that currently lack tools for genetic analysis.
Thus, Bonneau et al. make the case for formalizing the cellular networks in systems biology. And, as Razib, Lawler, and MacNeill note, microevolution is accessible to formalization. Can macroevolution also be formalized in mathematical terms?
Now it's my turn to punt the ball.