Smooth motor function is impossible unless all elements of the motor cortex and basal ganglia are present from the beginning. The green arrows denote the electronic feedback system required to produce smooth motor function; another perfect example of Irreducible Complexity.

Materials and Methods

A presentation of the components and interconnection of the motor, and pre-motor cortices, and the basal ganglia of the human brain, and their relationship with the rest of the musculoskeletal system, constitute the material for this Discussion. Application of the laws of probability and stochastic processes constitute the methods employed in this disertation. If a stepwise stochastic process can be excluded as the method of production of the cortical / basal ganglia integration of the neuromotor system of the human body, evolution is falsified; using Darwin's criterion for falsification.

The neuroanatomy, and neurophysiology of the cerebral cortex, basal ganglia, cerebellum, and skeletal neuromotor pathways are well known. The absence of any part of the system leads to specific disease entities. Therefore their interaction can appropriately serve as mathematical material suitable for analysis from the standpoint of a stochastic derivation.

There are several methods of calculation we can use to prove or falsify and evolutionary premise: application of the laws of probability; application of the laws that govern permutations and combinations; consideration of the rules that govern stochastic processes; and, evidence based reasoning (the material for which is set forth in table 1).

The Classic Laws of Probability ^{5, 6, 7}

• First Law: If the probability of an event is 1, then the event must occur.
• Second Law: If the probability of an event is 0, the event will not occur.
• Third Law: The probability of an event occurring, at all, lies somewhere between 0 and 1.
• Fourth Law: The sum of all the probabilities of all simple events which might occur in a sample space must equal 1; and cannot be greater than 1. Whenever something can have more than one outcome, which are equally likely, then the probability of any particular combination of outcomes on two or more independent trials, is the product of their respective probabilities. Note: with trial and error stochastic methods, the probability of success or failure, with each "mutation", is equal).
• Sample Space: A sample space is a compilation of all possible outcomes that might occur, given a set of parameters. For example given 12 plates of different colors, and a table on which to set the plates, there are 12 ways in which the dishes can be arranged around the circumference of the table; starting at the 12 o'clock position.
• Odds Ratio: The odds-ratio is determined by dividing the probability that an event will happen; by the probability that the given event will not happen.

Bound of Probability and Application of the Laws of Probability and the Odds Ratio:

Figures 1 and 2, depicts the schematic relationship between the motor and pre-motor cortices and the basal ganglia of the brain. This representation has an absolute basis in fact ^{8, 9}. Since we know that the subsystem in question actually exists and works as depicted, the probability of its occurrence in nature, as depicted, is one (1).

We also know that smooth motor function will not occur unless all the elements, depicted in the drawing are present and functional. The loss of any element in the depiction will result in akinesia, hypokinesia, or hyperkinesias, i.e. Parkinson's disease, Huntington's chorea, athetoid movements, ballismus, etc. Thus, according to the second Law, the chance of the elements depicted in the sample space of figure 1 producing smoothly controlled motor function in the absence of any single element in the depiction is zero (0).

If we count all the elements of figure 2, we find that the sample space in question, is composed of the motor and pre-motor cortices, the seven nuclei of the basal ganglia (counting the caudate nucleus and putamen as separate nuclei within the striate body), the seven interconnecting pathways, and the four neurotransmitters (distributed in 8 combinations); for a total of 24 elements in the sample space -- on each side of the brain. Therefore, the probability of the arrangement depicted in figure 1 having occurred by chance is 1/48! (factorial) = 1 / 1.2 x 10 ⁶¹ = 8.1 x 10 ^-62 (without considering the cerebellum, or the production of the molecules constituting the various nuclei, or their tracts, or their neurotransmitters).

Bounds of Probability: The concept of a bound to probability asks and answers the question: when does the improbability of a chance occurrence become so great that its occurrence will never take place? Richard Dawkins ¹⁰ set the negative probability bound at 10^-19. Mathematician Emile Borel ^{11, 12}, set the bound of absolute improbability at 10^-50. Mathematician, William Dembski ^{12, 13} sets the bound arguably high, at 10 ^-150. Thus, except for Demski, the negative probability of the system depicted in figure 2 (8.1 times 10^-62), having occurred by chance exceeds reasonable limits.

Let's put this Negative probability in perspective. A 6 mm cube of air has a volume of 200 ul and contains 4.8 x 10 ¹⁸. atoms. The national solar observatory at Sacramento Peak in New Mexico ¹⁴ estimates the maximum number of atoms in the universe at 6 x 1079. If that is true, and 8.1 x10^-62 is taken as the probability of the arrangement in figure 2 having occurred by chance, the negative probability of a chance occurrence is the centrally the same as finding one specific 6 mm cube of air molecules in a sample of molecules the size of all the atoms in the universe: i.e., an absurdity

Moreover, using the odds-ratio, the probability of the feedback system depicted in figure 2 having occurred by chance as compared to design (design probability = 1) is 1 divided by 8.1 X 10 ^-62. Thus, the basal ganglia system is 120 million billion billion billion billion billion billion times more likely to have occurred by design than by chance. The odds ratio makes it scientifically irresponsible to believe in a chance origin as compared to design.

Probability of the entire neuromuscular system control having occurred by chance:

To determine this probability, we must consider the following minimum components: (1) The cortex, basal nuclei, tracts, and neurotransmitters, in figures 1 and 2: i.e., 24 elements on each side of the brain; (2) the twelve major tracts, pathways and fibers entering and leaving each side of the cerebellum ¹⁵; (3) the three major nerves that innervate each upper extremity; (4) the two major nerves that innervate each lower extremity; (5) at least the three major bones, and two major joints of each upper and each lower extremity (without considering the individual muscles); (6) the wrists, and ankles (as single units); (7) the hand bones as a single unit, plus five fingers; (8) the tarsal and metatarsals of the foot as a single unit, plus the great toe; (9) the dorsal spine and rib cage, and all attached muscles as a single unit; (10) the lumbar spine; (11) the head, atlanto-occipital joint, seven cervical vertebrae and six joints (because of the demands of eye-hand coordination and head positioning)

Thus, the minimum number of components involved in our calculation becomes 61 elements for each side of the body; plus 17 spinal elements;' or, 122, plus 17. The probability is therefore the reciprocal of 139 factorial, or approximately one chance in 9.6 X 10²³⁸.

Taking the universal vanishing point of probability at 10 ^-200 rather than Dawkins' 10^-19, or Borel's 10^-50, or Demski's 10^-150, the probability of a human neuromotor system occurring by chance is 10 ³⁸ times less than no chance at all !! Or, referencing the total number of atoms, photons, and neutrinos in the universe 14 at 6 x 1088, (Sacramento Peak Observatory) the probability of the human neuromuscular system having developed by chance, is essentially the same as finding one specific elementary particle in a sample size larger than all the atoms photons and neutrinos in 10 ¹⁵⁰ universes the size of this one, combined.

There can be only one logical interpretation of this observation: namely, that the human neuromotor system cannot exist in the form it does by chance; remembering that the fourth law of probability doesn't care about method of production, infinite time, infinite energy, stochastic vectors, or anything else. The fourth law of probability only cares about the number of components involved in a system, i.e. the sum of the potential permutations of the parameters in the sample space (there is no coupled probability because each nucleus of the basal ganglia system is free to form independently).

Recursion, and Stochastic Processes:

Some familiarity with recursion, and stochastic processes, is necessary in order to evaluate the possibility of a chance origin of life; familiarity with fractals is not. If life and organic materials were to have arisen by chance; and to have been propagated by chance, then each new generation of life, or the organic materials composing life, would had to have been produced by reiteration of the same mechanism(s.) that produce them in the first place. This type phenomenon is exemplified by recursions; the type of processes/functions which power chance stochastic processes.

A recursion is a mechanism which defines a given results in terms of itself -- as a random variable. Let's take the factorial of the prime No. 5 and describe it as a recursion. If we use the standard method of defining a factorial, which is the product of a sequential series of numbers between 1 and a given variable, the result is described as follows:

But, to perform this function of 5, we had to identify three other terms: 2, 3, and 4. It was not necessary to specify the number 1 because the number 1 is understood in terms of 5, as 1 X 5 = 5. Using recursion, the entire process can be described in terms of only one variable, i.e. 5 (meaning 5 units of 1), as follows:

A fellow physician, Niels Jerne (1911 - 1994) was a co-winner of the Nobel Prize for medicine and physics in 1984; on the basis of his work in immunology. In his banquet speach, he extrapolated Noam Chomsky's transformational -- generative grammar model of language, to explain the human immune system by equating the components of generative grammar to the various features of protein structure - as a recursive process.

Stochastic Processes: Using the mathematical terminology of probability, a stochastic process is one defined by an indexed collection of random variables in a domain, "D" of a probability space, which produces a range, "R." when subjected to a particular process/function/law. The results one obtains are entirely the product of chance. The probability that repeated iterations of a process, over time, will produce functional results are infinitely diminished in nature because, as stated, above, the results of time-dependent stochastic processes are non-asymptotic; they diverge more and more from a given path with, each iteration of the process -- as opposed to two-dimensional space-dependent reiteration's of a given function (i.e., fractals)

Though it is true, that this is the type of stochastic process that allows scientists to analyze the behavior of a gas without a detailed analysis of the motion of each individual molecule, it is also the type of probability that Schutzenberger was railing against with regard to the formation of irreducibly complex biologic systems: namely, the improbability of the random production of a complex elephant's trunk being integrated with the random production of a cerebellum, and the chance occurrence of properly integrated wiring patterns required for the use of a trunk. Schutzenberger was a mathematician and computer scientist, who knew the shortcomings of a stochastic process 16. He was also a physician, who knew the magnitude of the problem that persons with less knowledge were asking stochastic processes to solve.

Stochastic processes can be used to analyze an existing system, or duplicate the function of an existing system; but a stochastic process cannot integrate a complex system requiring hundreds or thousands of variables so that the system produces a required specific result, denovo. A system becomes stochastic, i.e. "not treatable by studying the behavior of its individual elements, if the number of elements exceeds 30." ¹⁷ Thus, a stochastic process can be useful in analyzing systems of more than 30 variables; but, not in producing complex systems in living organisms; were the integration of various functions must be asymptotic: and result in a functional end-point.

Paraphrasing Hugo DeVries, the consideration with regard to "evolutionary recursions", and stochastic processes is not that they might have become functional; but the means by which they originated. It is the origin of such processes that must be explained by evolutionists, not the processes, themselves.

Permutations and combinations of a possible stochastic origin of the system depicted in Figure 2: Trial and error, or in the alternative, mutation and selection are the stochastic processes required to power macroeveolution. In the case of mutation and selection, mutation is the variable in the domain space, and selection is the process. In the case of trial and error, error is the variable in the domain space, and trial is the process. There are no other possible mechanisms. Although some prefer to believe that Darwinism is not a chance process, i.e. Professors Dawkins ¹⁸ and Perakh ¹⁹, they do agree that the process by which macroeveolution occurs is stochastic.

The laws that govern the permutations, within a given domain, are the same laws that govern the random functions of stochastic processes.

A permutation is an arrangement of a set of entities in a specified order, i.e. the specific arrangement of the elements of figure 2.

Combinations are variable arrangements of a set of entities without any specified order or arrangement, i.e. the stochastic process by which figure 1 would have been built up by mutation and trial and error selection -- trying various arrangements of the materials available within a given domain.

The laws governing permutations and combinations can be written as follows: where "n" represents the number of elements in a set; and "D" represents the number of objects in that set, integrated into a unit, within that set/domain, which are to be simultaneously considered for any given calculation/process. An exclamation point, "!", indicates a factorial process.

The symbol P^D represents a specific permutation (specific arrangement) of set n using D elements within set n.

The symbol C^D is the number of possible combinations of the elements within set n; with the elements of set n taken D at a time.

The number of permutations in a set of n elements, taken D. at a time, is:
n PD = n (n - 1) (n - 2)(n - 3).....(n - D + 1); or, n PD = n!/(n - D)! = n! if n = D
The number of combinations in a set n, taken D. at a time is:

Using the above functions we can develop the following data regarding a stochastic build-up of the required elements composing the feedback loop between the cortex and basal ganglia of humans, as represented in figure 2:

If we accept the first basal ganglia as preexistent, and each of the four neurotransmitters as preexistent (and not already combined into a system), then we have a set n consisting of five variables in the domain under consideration (one basal ganglia nucleus, and four neurotransmitters) of which we must consider combinations 3 at a time (according to our stated stochastic-function / law). The reason we have to consider them 3 at time is because some of the nuclei of the basal ganglia require two neurotransmitters in order to function; and this remains true for each subsequent nucleus to be added.

Taken 3 at a time, the number of combinations in the "range" of the first iteration of our stochastic process is 10. When we repeat the process, by stochastically adding another ganglia (and a new connecting pathway), we then have a set of seven variables in our domain rather than just six, because we had to add the connecting pathway between the two ganglia (thus our new iteration will include the new ganglia, the four neurotransmitters (2 for each nucleus), the new pathway, and the old ganglia) Again the combinations must be taken 3 at time. Thus, the number of elements in the "range" becomes 35.

The process must then be repeated six more times in order to produce proper connections between all of our basal ganglia and the cerebral cortex. Thus, we produce the following number of combinations within the range, of our stochastic process, with each "iteration" of the process, as follows: 10; 35; 84; 165; 286; 455; 969; and 1330. Only one combination, in each iteration, of the process satisfies the requirements of figure 2. Accordingly, the probability of each iteration producing success, becomes: 1/10; 1/35; 1/84; 1/165; 1/286; 1/455; 1/969; and 1/1330.

Then, using the fourth law of probability, which states that the total probability in any given series of probabilities is the factorial of that series of elements/iterations of a series, gives us the total probability of the specific permutation presented in figure 2, occurring within the range of our entire stochastic process, is one chance in approximately 814 million billion chances, i.e.:

1/10 X 1/35 X 1/84 X 1/165 X 1/286 X1/455 X 1/968 X 1/1330 = 8.4 X 10 ^-17.

The negative probability, depicted above, is already near the negative bound of probability set by evolutionist, Richard Dawkins. However, that is not the end of the negative probability, as we shall elucidate below.

Recalling Dr. Schutzenberger's example of the elephant's trunk ¹⁶, we must also add in the negative probability of producing the molecules required for the neurotransmitters; the molecules required for the individual basal ganglia nuclei, and their connecting tracts; and the molecules required to produce the genes necessary for each iteration of the stochastic process. To gauge the additional burden on the probability of a stochastic process producing the integration of the cerebral cortex and the basal ganglia, let's just consider the probability of producing one single gene required for the stochastic process.

It has been postulated that organisms of the phylum Arthropoda of which Drosophila is a member, would require approximately 50 different cell types to become functional. The number of purine and pyrimidine base-pairs that constitute the DNA molecular sequences in Drosophila is approximately 180 million ^{20, 21}. The number of genes currently thought to constitute the genome of D. melanogaster is somewhat less than 14,000 ²². Dividing 14,000 into 180 million gives approximately 12,900 base-pairs per gene. However, some of the base pairs are start or stop signals; and other combinations are arguably "junk". So, let's simply accept an average of 1000 base-pairs per functional gene -- with the understanding that there may well be more.

With the conservative assumption that the size of an average gene is 1000 base-pairs; and with the understanding that each position along the 1000 positions of a gene can be filled by any one of 4 base-pair combinations, the probability of getting a single gene right becomes one chance in 4 ¹⁰⁰⁰; this results in a negative probability of approximately 1.2 times 10 ^-632 -- repeated at least eight times (once for each iteration of the stochastic process required to produce the cortical/ganglia system depicted in figure 2).

Then remembering that we are producing only one correct gene when we really have to produce hundreds if not thousands of genes, the bounds of probability are far exceeded into the realm of absolute impossibility.

Results

The laws of mathematics reveal that a stochastic process faces an insurmountably high improbability of producing a functional complex system (such as the basal ganglia system). Darwinism and neo-Darwinism are vanishingly improbable because chance origin at the molecular level exceeds the bound of negative probability.

Discussion and Conclusion

Supporters of Evolution point to changes in the beak size of Galapagos Island finches in response to drought, the emergence of the dark-colored peppered moths in response to industrial mellanism, genetic similarity of hemoglobin in various animals, increased biologic complexity as the geologic strata are ascended, and the emergence of bacterial resistance to antibiotics as evidence of macroevolution. However, close inspection of this evidence reveals its weakness. The beak size of Galapagos Island finches returned to normal when the drought ended. The incidence of light-colored peppered moths returned to normal in England and the northern United States when cities were cleaned up. Motoo Kimura used the genetic polymorphism of hemoglobin molecules (Lewontin and Hubby ²³) to develop the neutral mutation with random drift theory of Evolution ²⁴ as a challenge to natural selection. The Cambrian explosion of thousands of life forms, without precursors, in the geologic strata strongly contradicts Evolution ²⁵. Likewise hospital microbiologists never report a change in species; only a change in resistance to certain antibiotics. Thus, the observations that evolutionists point to as evidence for macroeveolution is in reality only evidence of microevolution i.e. interspecies variation. Paraphrasing, the late Harvard professor of geology and Zoology, Stephen Jay Gould (1941-2002), stated: "macroeveolution is not microevolution extrapolated."

Erwin Schroedinger, the father of molecular biology, and quantum mechanics has stated:"Darwin was mistaken." ²⁶. Evolutionist Richard Dawkins has stated: "it is grindingly, creakingly, crushingly obvious that if Darwinism was really a theory of chance, it couldn't work." ²⁷. Evolutionists Stearns and Hoekstra stated: "Darwin -- was mistaken." ²⁸. Richard Goldsmith (1878-1958) (University of California, Berkely), saw "bridgeless gaps" in Darwin's descent with many small steps ^{29, 30, 31}. We have gone a step further by providing evidence that a stochastic, step-by-step origin of the basal ganglia system lays beyond the bound of negative probability; removal of any single component will induce diseases such as Huntington's chorea, Parkinson's disease, ballismus, tremor, past-pointing, limping, spasticity etc. These abnormalities would absolutely interfere with evolutionary fitness and reproductive advantage.

Our conclusion supports Michael Behe's irreducible complexity³²; and William Dembsk's mathematics of CSI (Complex Specified Information) ³³ in proving Darwin's hypothesis extremely tenuous. Readers should consider design parameters as well as "evolution" in evaluating biologic systems.

Serial References For The Above Treatise

1. Behe M, referenced in: Pennock, R.T. Editor: Design Creationism and its Critics; MIT press, Cambridge; 2001, p. 247
2. Pramanik, A.: Respiratory Distress Syndrome; e-medicine Editors: Donn, S.M.; Konop, R.; Clark,D.A.;and Wagner, C.L.: 7-2-02; p 1
3. Rhoads, R.. Pflanzer, R.: Human Physiology, 4th edition: Thompson; Brooks/Cole, Pacific Grove California; 2003; pp. 648.
4. Berne, R.M.: Levy, M.N.: Physiology, 4th edition; Mosby, St. Louis 1998; p 536-538
5. Carr, Joseph: A Crash Course in Statistics Hightext Salana Beach CA; 1994; p 24.
6. Hoel, P;G;, Port, S.C and Stone,C.J.: Introduction to Probability Theory; Houghton Mifflin Co., Boston; 1971; pp 6 -10
7. Jaisingh, L. R. ; Statistics; McCraw-Hill, New York San Francisco Washington D.C.; 2000; p. 122 - 127
8. Berne, R.M.: Levy, M.N.: Physiology, 4th edition; Mosby, St. Louis 1998; p 228-9
9. Rhoads, R.. Pflanzer, R.: Human Physiology, 4th edition: Thompson; Brooks/Cole, Pacific Grove California; 2003; pp. 330 - 333.
10. Dawkins, R.: The Blind Watchmaker; W. W. Norton & Co., N. Y., 1996; p: 146
11. Borel, Emile: Probabilities and Life; M. Baudin, New York; 1962; p 28
12. International Society for Complexity Information and Design: http//www.iscid.org/encyclopedia/Universal Probability)
13. Dembski, W.A.: Cites Design Inference, sec. 6.5: Intelligent Design; Intervarsity Press, Downer's Grove California; 1999; p. 143
14. Crozet, Y Referenced by National Solar Observatory, Sacramento Peak NM; www.sunspot.noao.edu/sunspot/pr/answerbook/un
15. Williams, P. L. and Warwick, R.: editors: Gray's Anatomy, 36 edition; W. B. Saunders Company, Philadelphia; 1980; pp. 916-919.
16. Schutzenberger, M-P: The Miracles of Darwinism And Interview with Marcel-Paul Schutzenberger; La Recherche: (French) La Recherche, N: 283: Jan. 1996, p 87)
17. (Perakh, M.: Unintelligent Design; Prometheus Books; 59 John Glenn Drive, Amherst NY; 2004, p.339
18. Dawkins, R.: The Blind Watchmaker; W. W. Norton & Co., N. Y., 1996; p: 43
19. (Perakh, M.: Unintelligent Design; Prometheus Books; 59 John Glenn Drive, Amherst NY; 2004, p.98 - 102
20. Adams, M.: The Genome Sequence of Drosophila melanogaster; Science: 287, 2185-2195
21. Gerhard, J. and Kirschner, M.: Cells, Embryos, and Evolution; Blackwell, 1997; London
22. Watson, J., Baker, T., Bell S., Gann, A., Levine, M., Losick, R.: Molecular Biology of the Gene, 5th Edition, 2004; Pearson Education Inc., Benjamin Cummings, CSHL Press San Francisco California; p: 636
23. (Lewontin, R.C.: cited in: Electrophoresis in the Development of Evolutionary Genetics; Genetics, 128; 1991; p: 657-662
24. Kimura, M: The Neutral Theory of Molecular Evolution: A Review of Recent Evidence; Japanese Journal of Genetics 66, 1991: p: 367-386)
25. Meyer, S.C.: The Origin of Biological Information and the Higher Taxonomic Categories; Proceedings of the Biological Society of Washington; 117 (2); August 2004; pp. 214-218
26. Schrodinger, Erwin: What is Life? Cambridge University Press, Cambridge Massachusetts: 2000: p. 32
27. Dawkins, R.: Climbing Mount Improbable; W. W. Norton & Co., N. Y., 1997; p: 77
28. Stearns,S.C. and Hoekstra, R.: Evolution an Introduction; Oxford University Press Inc., New York; 2002; p 64
29. Goldschmidt, R.: Material Basis of Evolution; (Silliman Milestones in Science); Yale University Press, New Haven CT 1982.
30. Schutzenberger, M-P.: The Return of the Hopeful Monsters; Natural History Magazine: 86, June 1976 page 24-30)
31. Smith, M.: The Theory of Evolution, Canto Edition; Oxford University Press, Cambridge; 2000; p. 317 - 318
32. Behe, M. J.: Darwin's Black Box; Simon and Schuster, New York; 1996; p 71
33. Dembski, W.A.: Intelligent Design; Intervarsity Press, Downer's Grove California; 1999; p. 166-67
34. Yokey, H.P.: Information Theory, Evolution, and the Origin of Life; Cambridge University Press, Cambridge; 2005; 1-189
35. Stearns,S.C. and Hoekstra, R.: Evolution an Introduction; Oxford University Press Inc., New York; 2002; p 282-3
36. Gillespie, J.H Molecular Evolution and the Neutral Allele Theory: in Oxford Surveys in Evolutionary Biology; Harvey P. H., Partridge,L., 4; 1987: pages 10-37
37. Gould, J.L. and Keeton, W.T.: biological science, 6 edition; W. W. Norton & Co., New York; 1996; p 455
38. Stearns,S.C. and Hoekstra, R.: Evolution an Introduction; Oxford University Press Inc., New York; 2002; p 145-6
39. Andersson, D. I, and Huges, D.: Muller's Ratchet Decreases Fitness of a DNA Based Microbe; Proceedings of the National Academy of Sciences of the USA; volume 93, January 23, 1996; p. 906-907).
40. Gould, J.L. and Keeton, W.T.: biological science, 6 edition; W. W. Norton & Co., New York; 1996; p 256-9
41. Lewin B: Genes VII, Oxford U. Press, Oxford; 2002; p 68
42. Hirotsune, S., Yoshida, N., et al.: An Expressed Pseudogene Regulates the Messenger-RNA Stability of Its Homologous Coding Gene, Nature, 423: 2003; 91-96
43. Lee, J. T.: Complicity of Gene and Pseudogene; Nature, 423: 2003; 26-28
44. Whinshaw-Boris, A: Effect of Pseudogenes; UCSD Internet News; April 30, 2003; embargoed by Nature
45. Gould, S. J.: The Structure of Evolutionary Theory; Belknap Press of Harvard University Press, Cambridge; 2002; 38-39
46. Gould, J.L. and Keeton, W.T.: biological science, 6 edition; W. W. Norton & Co., New York; 1996; p 508-9
47. Behe, M. J.: Darwin's Black Box; Simon and Schuster, New York; 1996; p 39
48. Tigner, P.M..: Personal Communication, Scripps Institute of Oceanography, La Jolla California; October 24, 1989
49. Wells J: Icons of Evolution; Regnery Publishing, Wash. DC, 2000; p 168-72
50. Gould, J.L. and Keeton, W.T.: biological science, 6 edition; W. W. Norton & Co., New York; 1996; p 506-7
51. Wells J: Icons of Evolution; Regnery Publishing, Wash. DC, 2000; p 143-57