10. Rose, ed. The Richness of Life: The Essential Stephen Jay Gould, 6. See also Turner, “Why We Need Evolution by Jerks”; Rée, “Evolution by Jerks.”
11. Sepkoski, “ ‘Radical’ or ‘Conservative’?”
12. For an urn with 100 balls, 50 being red and 50 being blue, the probability of getting only blue balls by randomly taking 50 balls out of the urn is given by the following considerations:
First, there’s only one way to select only blue balls. Second, in general for an urn with N balls, there are C(N,k) different ways of choosing k balls from among these N (with k greater than or equal to 0 but less than or equal to N). C(N,k) is equal to N! divided by the product of k! and (N-k)!, where the exclamation mark is read “factorial” and equals the product of all numbers less than or equal to the number in question down to 1. Thus “six factorial” = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. Factorials increase very quickly, faster than exponentials. C(N,k) is read “N choose k.”
So for the problem above, the total number of ways to choose 50 specific balls out of 100 balls, ignoring color, is C(100,50), which equals 100! divided by 50! times 50!, or 100!/(50! x 50!).
This number admits an exact calculation, which can be expressed in Mathematica as the following:
C(100,50) = 100,891,344,545,564,193,334,812,497,256 which is approximately 1.00891 x 1029.
Thus, the probability of selecting k specific balls out of N total balls is of course the inverse of that number, and can be distilled to the following equation:
p = k! x (N – k)! / N!
Applied to this problem, the odds of randomly selecting all 50 blue balls in a collection of 50 blue and 50 red balls is 1 divided by C(100,50), or approximately 9.91165 x 10-30.
13. Using the same equation discussed in the above endnote, the probability of selecting 4 specific balls out of 8 total balls is given by the same equation as follows: 4! x (8 - 4)! / 8! = 1 in 70.
14. Gould and Eldredge, “Punctuated Equilibria: The Tempo and Mode of Evolution Reconsidered,” 117.
15. Eldredge and Gould, “Punctuated Equilibria: An Alternative to Phyletic Gradualism,” 84.
16. Lieberman and Vrba, “Stephen Jay Gould on Species Selection: 30 Years of Insight”; Gould, “The Meaning of Punctuated Equilibrium and Its Role in Validating a Hierarchical Approach to Macroevolution.”
17. Gould, The Structure of Evolutionary Theory, 703. As Gould and Eldredge also emphasized elsewhere: “The main insight for revision [of evolutionary theory] holds that all substantial evolutionary change must be reconceived as higher-level sorting based on differential success of certain kinds of stable species, rather than as progressive transformation within lineages [i.e., species]” (“Punctuated Equilibrium Comes of Age,” 224).
18. If natural selection acts upon a larger unit of selection, the species rather than the individual, it followed logically that evolution would occur in larger more discrete jumps. Nevertheless, Gould and Eldredge rarely emphasized this implication of their conception of species selection explicitly, instead highlighting allopatric speciation as the main reason for fossil discontinuity. Stanley did, however, often draw a connection between the activity of species selection as a mechanism of evolutionary change and fossil discontinuity. As he noted, “The validity of the species as the fundamental unit of large-scale evolution depends upon the presence of discontinuities between many species in the tree of life” (Macroevolution, 3).
19. Schopf, Editorial Introduction to Eldredge and Gould, “Punctuated Equilibria: An Alternative to Phyletic Gradualism,” 82; Stanley, Macroevolution: Pattern and Process, 3.
20. Valentine and Erwin, “Interpreting Great Developmental Experiments”; see diagram on p. 92.
21. Valentine and Erwin note that “transitional alliances are unknown or unconfirmed for any of the [Cambrian] phyla,” and yet “the evolutionary explosion near the beginning of Cambrian time was real and produced numerous [new] body plans” (“Interpreting Great Developmental Experiments,” 84, 89).
22. Valentine and Erwin, “Interpreting Great Developmental Experiments,” 96.
23. Gould and Eldredge, “Punctuated Equilibrium Comes of Age.”
24. Gould and Eldredge, “Punctuated Equilibrium Comes of Age.”
25. Schopf, Editorial Introduction to Eldredge and Gould, “Punctuated Equilibria: An Alternative to Phyletic Gradualism,” 84.
26. Foote argued that “given estimates of [a] completeness [of the fossil record], [b] median species duration, [c] the time required for evolutionary transitions, and [d] the number of … higher-level transitions, we could obtain an estimate of the number of major transitions we should expect to see in the fossil record.” His method provided a way to evaluate, as he puts it, “whether the small number of documented major transitions provides strong evidence against evolution” (“On the Probability of Ancestors in the Fossil Record,” 148).
Because variables [a], [b], and [d] are reasonably well established, [c] the time required for plausible mechanisms to produce macroevolutionary transitions stands as the crucial variable in the analysis of any specific evolutionary model, including punctuated equilibrium. If the time required to produce major evolutionary change is high, as it is for the neo-Darwinian mechanism of change, then given current estimates of [a], [b], and [d], neo-Darwinism fails to account for the data of the fossil record. Conversely, if a theory such as punctuated equilibrium can identify a fast enough acting mechanism, then it could account for the paucity of transitional intermediates.
27. Foote and Gould, “Cambrian and Recent Morphological Disparity,” 1816.
28. Darwin, On the Origin of Species, 177.
29. As Gould and Eldredge explained: “Most evolutionary change, we argued, is concentrated in rapid (often geologically instantaneous) events of speciation in small, peripherally isolated populations (the theory of allopatric speciation)” (“Punctuated Equilibria: The Tempo and Mode of Evolution Reconsidered,” 116–17). See also Lewin, “Punctuated Equilibrium Is Now Old Hat.”
30. Shu et al., “Lower Cambrian Vertebrates from South China.”
31. Dawkins, The Blind Watchmaker, 265.
32. Levinton, Genetics, Paleontology, and Macroevolution, 208.
33. Gould, The Structure of Evolutionary Theory, 710.
34. Charlesworth, Lande, and Slatkin, “A Neo-Darwinian Commentary on Macroevolution,” 493. As David Jablonski concluded in 2008, “The extent and efficacy of the specific processes [of species selection] remain poorly known” (“Species Selection,” 501).
35. Gould, The Structure of Evolutionary Theory, 1005.
36. Gould, The Structure of Evolutionary Theory, 55, emphasis added.
37. Gould and Eldredge, “Punctuated Equilibria: The Tempo and Mode of Evolution Reconsidered,” 134.
38. Sepkoski, “ ‘Radical’ or ‘Conservative’?” 307.
39. Sepkoski, “ ‘Radical’ or ‘Conservative’?” 7.
40. Gould, “Is a New and General Theory of Evolution Emerging?” 120. Because his colleagues understood Gould to be offering a theory of macroevolution, many of Gould’s scientific colleagues at the time thought of him, as Sepkoski notes, as an “ardent proponent of a radical (and perhaps misguided) view of evolutionary change” (“ ‘Radical’ or ‘Conservative’?” 302).
41. Sepkoski, “ ‘Radical’ or ‘Conservative’?” 302.
42. Valentine and Erwin, “Interpreting Great Developmental Experiments,” 96.
Chapter 8: The Cambrian Information Explosion
1. Bowler, Theories of Human Evolution, 44–50.
2. Vorzimmer, “Charles Darwin and Blending Inheritance,” 371–90.
3. Jenkins, Genetics, 13–15.
4. Muller, “Artificial Transmutation of the Gene,” 84–87.
5. As Mayr and Provine put it, “Various geneticists … demonstrated that seemingly continuous variation is caused by discontinuous genetic factors [mutations] that obey the Mendelian rules in their mode of inheritance” (The Evoluti
onary Synthesis, 31).
6. Bowler, Evolution: The History of an Idea, 331–39.
7. Huxley, “The Evolutionary Vision,” 249, 253.
8. Huxley, quoted in “ ‘At Random’: A Television Preview,” 45.
9. Watson and Crick, “A Structure for Deoxyribose Nucleic Acids,” 737–38.
10. For an animated demonstration, see the short video “Journey Inside the Cell” on my website at SignatureintheCell.com.
11. Valentine, “Late Precambrian Bilaterians.”
12. Brocks et al., “Archean Molecular Fossils and the Early Rise of Eukaryotes.”
13. Grotzinger et al., “Biostratigraphic and Geochronologic Constraints on Early Animal Evolution.”
14. Ruppert et al, Invertebrate Zoology, 82.
15. Bowring et al., “Calibrating Rates of Early Cambrian Evolution.”
16. Valentine, Origin of the Phyla, 73.
17. Koonin, “How Many Genes Can Make a Cell?”
18. Gerhart and Kirschner, Cells, Embryos, and Evolution, 121; Adams et al., “The Genome Sequence of Drosophila melanogaster”; see also www.ncbi.nlm.nih.gov/genome/?term=drosophila%20melanogaster (accessed November 1, 2012).
19. Moreover, in addition to requiring a vast amount of new genetic information, building a new animal from a single-celled organism also requires a way of arranging gene products—proteins—into higher levels of organization, including cell types, organs, and body plans. Later, in Chapter 14, I will discuss the importance of these higher-level arrangements and why they also constitute a kind of information—one that, although not stored in genes alone, nevertheless has to be explained as well.
20. Shannon, “A Mathematical Theory of Communication.”
21. To determine how much Shannon information is present in any sequence of characters, information scientists use a formula that converts probability measures into informational measures using a negative logarithmic function. A simple form of that equation can be expressed as I = –log2 p, where the negative sign indicates the inverse relationship between probability and information.
22. Yockey, Information Theory and Molecular Biology, 110.
23. Shannon and Weaver, The Mathematical Theory of Communication, 8.
24. Schneider, “Information Content of Individual Genetic Sequences”; Yockey, Information Theory and Molecular Biology, 58–177.
25. DNA clearly does not convey meaningful information in the sense of “knowledge” conveyed to, and comprehended by, a conscious agent, although the precise sequences of bases could be said to be meaningful in the sense that they are ‘significant’ to the function DNA performs. Clearly, however, the cellular machinery that uses and “reads” the information in DNA to build proteins is not conscious. Nevertheless, semantically meaningful information—a message, the meaning of which is understood by a conscious agent—represents only a special kind of functional information. And all sequences of characters containing functional information can be distinguished from mere Shannon information in that the precise arrangement of characters or symbols in such sequences matters to the function that they perform.
26. Crick, “On Protein Synthesis,” 144, 153. See also Sarkar, “Biological Information,” 191.
Chapter 9: Combinatorial Inflation
1. Eden, “Inadequacies of Neo-Darwinian Evolution as a Scientific Theory,” 11.
2. The quotation and the historical material about the Geneva gathering are drawn from G. R. Taylor, Great Evolution Mystery, 4.
3. Schützenberger, “Algorithms and the Neo-Darwinian Theory of Evolution,” 73–75.
4. Schützenberger, “Algorithms and the Neo-Darwinian Theory of Evolution,” 74–75.
5. Commenting on the symposium thirty years later in a now infamous article in Commentary magazine, mathematician David Berlinski amplified Eden’s argument. As he explains, “However it may operate in life, randomness in language is the enemy of order, a way of annihilating meaning. And not only in language, but in any language-like system” (“The Deniable Darwin”).
6. King and Jukes, “Non-Darwinian Evolution,” 788.
7. Eden, “Inadequacies of Neo-Darwinian Evolution as a Scientific Theory,” 110.
8. Schützenberger, “Algorithms and the Neo-Darwinian Theory of Evolution,” 74.
9. Ulam, “How to Formulate Mathematically Problems of Rate of Evolution,” 21.
10. Eden, “Inadequacies of Neo-Darwinian Evolution as a Scientific Theory,” 7.
11. Denton, Evolution: A Theory in Crisis, 309–11.
12. Maynard Smith, “Natural Selection and the Concept of a Protein Space.”
13. Denton, Evolution, 324.
14. Reidhaar-Olson and Sauer, “Functionally Acceptable Substitutions in Two Alpha-Helical Regions of Lambda Repressor.”
15. Yockey, “On the Information Content of Cytochrome C.”
16. Yockey, “On the Information Content of Cytochrome C.”
17. Behe, “Experimental Support for Regarding Functional Classes of Proteins,” 66.
18. Lau and Dill, “Theory for Protein Mutability and Biogenesis.”
19. Behe, “Experimental Support for Regarding Functional Classes of Proteins.”
Chapter 10: The Origin of Genes and Proteins
1. Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design, 46–47.
2. For a critique of Dawkins’ simulation see Chapter 13 of Signature in the Cell. See also Ewert, et al., “Efficient Per Query Information Extraction from a Hamming Oracle,” 290–97; Dembski, No Free Lunch, 181–216. See also Weasel Ware–Evolutionary Simulation at http://evoinfo.org/weasel.
3. Reidhaar-Olson and Sauer, “Functionally Acceptable Substitutions in Two Alpha-Helical Regions of Lambda Repressor,” 315.
4. Protein scientists recognize an additional level of structure called quaternary structure. Quaternary structures are formed from multiple protein folds, or multiple whole proteins.
5. As Reidhaar-Olson and Sauer note: “At [amino-acid] positions that are buried in the structure, there are severe limitations on the number and type of residues allowed. At most surface positions, many different [amino-acid] residues and residue types are tolerated” (“Functionally Acceptable Substitutions in Two Alpha-Helical Regions of Lambda Repressor,” 306).
6. Axe, “Extreme Functional Sensitivity to Conservative Amino Acid Changes on Enzyme Exteriors.”
7. Dawkins, Climbing Mount Improbable.
8. Jensen, “Enzyme Recruitment in Evolution of New Function,” 409–25.
9. Axe, “Extreme Functional Sensitivity to Conservative Amino Acid Changes on Enzyme Exteriors.”
10. Axe, “Extreme Functional Sensitivity to Conservative Amino Acid Changes on Enzyme Exteriors,” 585–96. Experimental work that Axe performed with colleague Ann Gauger, published in 2011, also confirmed this result. See Gauger and Axe, “The Evolutionary Accessibility of New Enzyme Functions: A Case Study from the Biotin Pathway.”
11. Axe, “Extreme Functional Sensitivity to Conservative Amino Acid Changes on Enzyme Exteriors.”
12. Unfolded proteins also stick to other molecular entities within the cell or form what are called inclusion bodies, in both cases impeding proper protein function. Moreover, even slight elevations in temperature will accelerate the unfolding of already destabilized protein folds.
13. Axe’s experiments using a more sensitive screen for function had shown him that even most single amino-acid changes will diminish the function of a protein enough to diminish its fitness, even in cases where such changes do not eliminate function altogether.
14. Blanco, Angrand, and Serrano, “Exploring the Conformational Properties of the Sequence Space Between Two Proteins with Different Folds: An Experimental Study.” As they explain, “Both the hydrophobic core residues and the surface residues are important in determining the structure of the proteins” (741).
15. Neutral evolution in this context refers to a process alleged to explain the origin
of new functional genes and proteins from gene duplicates unhinged from selection pressure. A neutral model of gene evolution is part of a more expansive and general neutral theory of evolution proposed by Motoo Kimura in 1968. As Long et al. explain, Kimura’s model helped “describe how gene duplicates could acquire new functions and ultimately be preserved in a lineage” (“The Origin of New Genes,” 868). However, Kimura’s model of neutral evolution attempted to explain facts and phenomena beyond just the origin of new genes. Thus, not everyone who accepts a neutral model of gene origins subscribes to the whole of Kimura’s theory. Kimura, The Neutral Theory of Molecular Evolution.
16. Matthew Hahn notes that, “There appear to be 4 major mechanisms by which DNA is duplicated: (1) unequal crossing-over, (2) duplicative (DNA) transposition, (3) retrotransposition, and (4) polyploidization” (“Distinguishing Among Evolutionary Models for the Maintenance of Gene Duplicates,” 606).
17. Axe, “Estimating the Prevalence of Protein Sequences Adopting Functional Enzyme Folds.”
18. Dembski, The Design Inference, 175.
19. Michael Behe made this calculation in The Edge of Evolution based on a paper in Proceedings of the National Academy of Sciences U.S.A. that observed that approximately 1030 prokaryotes are formed on earth each year. [Whitman, “Prokaryotes: The unseen majority,” 6578–83.] Since prokaryotes make up the overwhelming majority of organisms, he multiplied that number by 1010, which is about twice the number of years the age of the earth. This allowed him to estimate the total number of organisms that have lived on earth as “slightly fewer than 1040 cells.” Behe, The Edge of Evolution, 64.
20. Bowring et al., “Calibrating Rates of Early Cambrian Evolution”; “A New Look at Evolutionary Rates in Deep Time”; “Geochronology Comes of Age”; Kerr, “Evolution’s Big Bang Gets Even More Explosive”; Monastersky, “Siberian Rocks Clock Biological Big Bang.”
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