(please read Part I first.)
3. The Evidence
The first factor in the overthrow of phyletic gradualism was the identification of the actual mechanism by which the information carried by the DNA is expressed. A sequence of DNA codes is nothing like a blueprint for some specific trait. Instead, each DNA code identifies a specific amino acid in one of thousands of strings of amino acids. These strings are called peptides. Each peptide, in turn, may have one or more functions that it performs in the organism: as part of the structure of a protein, or as an enzyme, or a hormone, or a neurotransmitter, or as a part of the molecular "skeleton" that determines the structure of tissues and organs. These, in turn, participate in biochemical pathways and physiological and anatomical structures responsible for the observed traits of the organism. Thus, the correspondences between the codes and the traits are manifold, multivariate, non-linear and often discontinuous. They result in complicated probability-of-reproductive-success surfaces that have many small local optima, most of them low hills whose peaks are far below the high peak of a global optimum.
The second was discovered (see MODPAC: A modular package of programs for fitting model parameters to data and plotting fitted curves. Reed, Behavior Research Methods & Instrumentation, 1976) by mathematicians and computer scientists working on the problem of finding the optimal values of the parameters of a quantitative model to fit a body of data. All the methods, including not only algebraic approximations but also "genetic programming" methods that simulate the mechanisms of genetic evolution (Koza, Genetic Programming, MIT Press 1992) when invoked on a problem with multiple local optima, converge rapidly on some happenstance local optimum near the starting point. Once at this happenstance local optimum, the parameter-fitting mechanisms are at equilibrium. The values of the parameters stay permanently frozen, with a fit often far below the global optimum, unless dislodged by additional computational techniques (exploration, explosion, simulated annealing) that have no equivalent in natural evolution.
The third came from paleontology. In the fossil record, new traits and species appear in the course of only a few dozen generations, only to continue practically unchanged for tens of thousands, and sometimes hundreds of thousands, or millions of generations thereafter. It was this observation that first led to the label "punctuated equilibrium."
The fourth came from engineering. Until the 1970s, it was generally assumed that evolved organs, particularly those that remained unchanged over many millions of generations, and passed unchanged from very ancient classes of organisms to new ones, had evolved to a structure that was optimal for their biological function. Even when the evolved structures were not what an engineer would have designed, it was assumed that the result of evolution was optimal under some set of as yet unidentified constraints. In the 1970s, mechanical and electrical engineers began to look at evolved systems in the hope of identifying designs that might work better than those they already knew. They found only a few rare cases where the results of evolution were anything close to objectively optimal. They were confronted, instead, with all manner of clumsy contraptions just barely good enough for organisms to survive. The vertebrate eye, for example, has not changed in its basic structure from fishes to humans. Yet if an engineer were to design an array of light sensors - as for a digital camera - she would attach the outputs to cabling on the back or the side of the sensors, so that nothing would disperse, or block the path, of light coming into the front of the sensors from the lens. In the vertebrate eye, on the other hand, the optic nerve, which carries the output of retinal sensors from the eye to the brain, comes from the brain into the inside of each eyeball through a hole in the retina. This hole in the array of retinal sensors is why we have a blind spot in each eye (which digital cameras don't have.) The neurons of the optic nerve then pass in front of the light sensors, in the path of incoming light, and connect to the light-sensing rods and cones from the front (where the light comes in.) This is just one of thousands of examples of globally sub-optimal, clumsy structures; just-good-enough-to-survive local optima frozen by evolution.
The fifth was the discovery of recent, ongoing evolutionary changes in human traits whose relevance to reproductive success was affected by recent changes in the human cultural environment. One such change was the introduction of military conscription in Europe in the late 18th and early 19th centuries, and the introduction of footwear with stiff lateral support at around the same time. Before mass production of boots and shoes most humans went barefoot. When most travel was by foot, and most work was done walking or standing, anatomical abnormalities of the feet were severely disabling. The effect of flat feet and other inherited abnormalities was so adverse, and the abnormalities so rare, that men with these abnormalities were (and, in countries with conscription, still are) exempt from conscription. This exemption had two effects. Men with anatomical abnormalities of the foot were much less likely to be killed or maimed in war. More importantly, they stayed and reproduced, while conscripts were away from their neighborhoods and families for a large part of the duration of their prime reproductive years.
Switch to the 1990s. The Achilles Project (Burzykowski et al 2003) measured the incidence of foot disease, including the prevalence of inherited anatomical abnormalities of the feet, in a sample of 1085 randomly selected subjects in 16 European countries. The incidence of anatomical abnormalities of the foot varied between 20.4% (one in five subjects) and 24.8% (one in four.) This in a mere 8 generations after a changed cultural environment moved the local optimum for reproductive success to a different place.
4. Punctuated Equilibrium
Two thousand years ago, Archimedes' formulation and derivation of Archimedes' Principle demonstrated that the laws of nature can be not merely observed and measured, but grounded and understood through the application of reason - of logic and mathematics - to more fundamental and evident laws and facts. The principle of derivation set what is still the highest standard in scientific understanding of how nature works. Punctuated Equilibrium is the fact that when a change in the environment changes the locations of local optima for reproductive success, the traits and species affected by this change are efficiently and quickly moved by natural selection to new local optima - where they may stay, without further modification, until the location of the local optima changes again. The local optima of evolutionary equilibrium do not correspond to "design," in the sense of some global optimum of fitness or health. They are, rather, the product of a random process, which converges on some local optimum without regard to its optimality in any global sense. And this fact can be mathematically derived, in the best tradition of Archimedes, from the application of mathematical measure theory to genetic programming.
(continued in Part III.)