On the Use of Probability Calculations in the Critique of Evolution.

It is not easy to test evolution experimentally, mostly due to the near impossibility of controlled experimentation and, consequently, the lack of reproducibility. Thus the evolution theory is not universally accepted even among scientists. The crucial concept of evolution is the spontaneity of evolutionary changes: life as we observe it today emerged and evolved as a result of interactions between environment on one side and biomolecules or, later, cells and organisms, on the other side. No intervention of an intelligent designer is necessary at any point. Scientists opposed to this notion argue that life is so complex, especially at the molecular level, that it is statistically impossible for it to rise and evolve spontaneously by small evolutionary steps. To support their claims they often use probability calculations that invariably lead to the conclusion that the odds against emergence of, e.g., the eye, a biochemical pathway, or life as a whole, are some ridiculously high number. Consequently, organism s and their constituents could not have evolved spontaneously, but must have been designed by a goal-oriented, prescient, intelligent designer.

Enzyme cascades, such as the immune complement system or blood clotting, and biochemical pathways are the favorite targets of the "designists" since the coordinated presence and functioning of many factors, connected in series, seems absolutely necessary for the final result to occur, i.e., destruction of a microbe, formation of a blood clot, or synthesis of a metabolite. Missing only one link in the chain results in no effect at all and thus it is not possible to have a partial and step-wise improvement, which is a central principle of evolution. This apparent paradox disappears with the realization of three facts. First, genes, biochemical pathways, and organs do not evolve de novo and randomly. Evolution does not work as a random number generator and does not create anything from nothing. It only can modify preexisting systems, which greatly limits the number of possible evolution pathways and outcomes. Systems with new small modifications may exhibit selective advantage over the systems without those mod ifications, which is referred to as natural selection. The interplay between the limits, imposed by a system's prehistory, and natural selection imparts a continuity and apparent directionality to the whole process. For example, Dawkins (1996) has solved the darwinists' "difficulty" with the evolution of the eye by proving that intermediary steps do exist and that to sense some light is better (in the evolutionary sense) than not to sense any. Complex structures and pathways were thus forged by natural selection, but probabilistic calculations rarely take it into account. Second, many biological systems did not evolve for the function they fulfill today Rather, they adopted the given new function when the environment allowed for it. For example, the Krebs cycle did not evolve originally to feed NADH to the electron transport chain; it was co-opted for that purpose with the accumulation of oxygen in the atmosphere. And third, many biochemical pathways are not true all-or-none systems. They are organized in cas cades not in order to produce the final effect, but rather to ensure a better control and/or amplification of the process in question. For example, one of the active components of the complement, C3b, is formed spontaneously and is constantly present in serum at a low level; other complement components modulate, i.e., decrease or increase, C3b concentration as necessary. The three above-mentioned notions should be a part of any serious evolutionary considerations, but the scope of the present paper is limited. I do not discuss the mechanics of gene duplication or exon shuffling which are the main means by which new molecules arise (Graur and Li, 2000). I also do not address the big philosophical issues in the discourse between the darwinists and the "designists". My modest goal is to point out flaws in the probabilistic reasoning applied to evolution by the latter and show that, even in the absence of all the higher-level evolutionary mechanisms, mere random shuffling of molecules and their parts, when interp reted correctly, may lead to interesting results. As a particular example, the quantitative argument of Behe (1996) against the evolution of tissue plasminogen activator (TPA) is subjected to criticism.

TPA is an enzyme that participates in the biochemical cascade of blood clotting. Behe's argument is reproduced below, almost verbatim (p. 93 of Behe, 1996). A model animal with blood-clotting cascades is said to have about 3 x [10.sup.4] genes, which code for proteins or protein domains. TPA has four different types of domains. Therefore, putting the four specific domain types together in the enzyme molecule by chance is an event with the probability of about [10.sup.-18]18. Behe's calculation is straightforward and simple, although simplified: TPA actually consists of five domains, two of the five being identical; also, all the details of the machinery necessary for gene shuffling and protein expression have been neglected. But the calculation is followed by sheer demagoguery, whose only aim is to disorient the reader and to make the probability of forming TPA look extremely small. Behe continues: "Now, if the Irish Sweepstakes had odds of winning of one-tenth to the eighteenth power, and if a million peopl e played the lottery each year, it would take an average of about a thousand billion years before anyone (not just a particular person) won the lottery. A thousand billion years is roughly a hundred times the current estimate of the age of universe." (p. 94). It is most puzzling why only million people participate in Behe's Irish Sweepstakes and why the drawing is carried out only once a year, but such numbers conveniently assure the author the desired small probability. Are such numbers relevant to the world of molecular or cellular biochemistry? I am afraid not. One just needs to realize that the model animal consists of about [10.sup.12] cells and each cell carries the whole set of genes. Therefore, a single animal provides the opportunity to carry out [10.sup.12] different shufflings in its cells to make a TPA molecule. If we multiply that number by the number of animals of the given species populating the whole Earth, say [10.sup.9], suddenly we have the opportunity to carry out [10.sup.21] shufflings wh en the cells in all the animals divide. How often cells divide depends on the cell type and the tissue. Let us assume that an average cell divides once in three days, which means that in one year it divides about [10.sup.2] times. Thus, in one year, the population of our model animals can undergo [10.sup.23] gene reshufflings to create the TPA molecule by chance. Comparing this result to Behe's number leads to the conclusion that the animal population (of a single species) on the planet can carry out sufficient number of reshufflings to produce about [10.sup.5] TPA molecules each year--by blind chance! This, of course, is an overestimation; the cell-division concept employed is more applicable to microorganisms than to animals with blood-clotting cascades. In a more sober estimate, we may include into our reasoning the fact that only those changes that occur in germ cells are carried over to the next generation and thus are meaningful for evolution. Since males usually produce many more germ cells than female s, we can leave the females out from the calculation. Assuming that a male produces [10.sup.8] sperm cells in a year, a population of [10.sup.9] individuals can carry out [10.sup.17] inheritable gene shufflings in a year. How many of these shuffling will actually be realized in an offspring depends on reproductive strategies and cycles in the species. If the average male produces only ten offspring a year, the population will carry out [10.sup.10] inheritable gene shufflings. The average time, in which a TPA molecule is expected to be formed by chance permutations of all the gene products within the germ cells of our population, is [10.sup.8] years ([10.sup.18]/[10.sup.10]. This time is well within the bio- or geological time domain and significantly shorter than Behe's thousand billion ([10.sup.12]) years. And if we did not limit ourselves to a single species, but considered the whole biosphere, the odds for producing TPA by chance would increase by several orders of magnitude. The numbers in our examples ar e arbitrary, but in contrast with those of Behe, they are more relevant to the real world of biology and, even more importantly, they are not demagogically misinterpreted.

Those colleagues, who undertake similar probabilistic calculations in the good faith that it is not a baseless and meaningless mathematical exercise, should not forget that the world contains more than just a single model animal and certainly more than just a single cell. This realization is even more important in the case of prebiotic evolution, where one deals with molecules instead of cells. Every high school kid knows that 1 liter of a 1 millimolar solution contains 6 x [10.sup.20] molecules which constantly collide and interact with each other with high frequency. The time scale relevant for molecular processes is typically between nanoseconds and seconds. The large number of particles and the high frequency of molecular interactions in every drop of the biosphere, whether in the cell or in a test tube, must be a part of any serious probabilistic considerations concerning Darwinian evolution.

ACKNOWLEDGMENTS

I thank the editor and two anonymous reviewers for suggestions that helped to improve the clarity of the argument.

LITERATURE CITED

Behe, M.J. 1996. Darwin's Black Box. Simon & Schuster, New York, NY.

Dawkins, R. 1996. Climbing Mount Improbable. W.W. Norton & Co., New York, NY.

Graur, D., and W.H. Li. 2000. Fundamentals of Molecular Evolution, 2nd Ed. Sinauer Associates, Sunderland, MA.