posted 23. March 2003 15:50                   

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Historically, a great many features of organisms have been said to show a trend over the history of life, and many rationales for such trends have been proposed. Here I review eight candidates, eight "live hypotheses" that are inspiring research on largest-scale trends today: entropy, energy intensiveness, evolutionary versatility, developmental depth, structural depth, adaptedness, size, and complexity. For each, the review covers the principal arguments that have been advanced for why a trend is expected, as well as some of the empirical approaches that have been adopted. Also discussed are three conceptual matters arising in connection with trend studies: 1. Alternative bases for classifying trends: pattern versus dynamics; 2. alternative modes in which largest-scale trends have been studied: "exploratory" versus "skeptical"; and 3. evolutionary progress.

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blind variation and selective retention tend to produce increases in both structural and functional complexity of evolving systems

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The history of life shows a clear trend in hierarchical organization, revealed by the successive emergence of organisms with ever greater numbers of levels of nestedness and greater development, or `individuation', of the highest level. Various arguments have been offered which suggest that the trend is the result of a directional bias, or tendency, meaning that hierarchical increases are more probable than decreases among lineages, perhaps because hierarchical increases are favoured, on average, by natural selection. Further, what little evidence exists seems to point to a bias: some major increases are known ± including the origin of the eukaryotic cell from prokaryotic cells and of animals, fungi and land plants from solitary eukaryotic cells ± but no major decreases (except in parasitic and commensal organisms), at least at the cellular and multicellular levels. The fact of a trend, combined with the arguments and evidence, might make a bias seem beyond doubt, but here I argue that its existence is an open empirical question. Further, I show how testing is possible.

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To be precise, this freezing phenomenon has been described before (9), but it was seen as an arcane result of mathematical population genetics of uncertain significance and familiar to only a very few specialists. The significance of the present report is that Waxman and Peck have shown that this obscure property of mutation-selection equations has a connection to a generic property of organisms: complexity. Each gene has many effects and functions, each character is functionally connected to multiple others. Since this is the case, the freezing of genetic and phenotypic states is a necessary outcome, just as many organismal biologists have suspected for more than a century.

This sounds great and simple, but nothing in science is ever really simple. There is always the question whether the models are producing artifacts rather than pointing to fundamental insights. There is also no definite empirical proof as to whether the Bauplan concept is a perceptual artifact or a real pattern. Both are empirical questions that need to be settled. What makes the result by Waxman and Peck nonetheless exciting is that new emergent phenomena can be discovered that are not obvious from the study of simple models. More complexity is not just more of the same, but can lead to qualitatively new phenomena. This has long been know to physicists, but there are only a handful of examples where "complexity effects" were described in population genetic models (10). These and the report by Waxman and Peck show the need to study the population genetic theory of complex adaptations as a separate problem.

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posted 23. March 2003 17:13                   

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A Brief Overview of Some Existing Formulations of Complexity

This is an overview of some of the articles which directly invoke the idea of complexity in their analysis, either by defining it or by specifying its properties. There is no comprehensive overview of this subject across disciplinary borders, but there are some relevant collections:

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posted 13. April 2003 15:59                   

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But an entire ensemble is often much simpler than one of its members. This principle can be stated more formally using the notion of algorithmic information content. The algorithmic information in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler.

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution. The former is described by a few equations, whereas the latter requires the specification of vast amounts of initial data on some hypersurface. The lesson is that complexity increases when we restrict our attention to one particular element in an ensemble, thereby losing the symmetry and simplicity that were inherent in the totality of all the elements taken together. (p. 51; emphasis added)

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