Numerosity, abstraction, and the emergence of symbolic Thinking

Current Anthropology

Volumn 53, Issue 2, 2012, Pages 204-225

  Coolidge, Frederick L ^a   Overmann, Karenleigh A ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84859146559     PISSN: 00113204     EISSN: None     Source Type: Journal    
DOI: 10.1086/664818     Document Type: Review

References (142)

1. Ambrose, S. H. 2001. Paleolithic technology and human evolution. Science 291(5509):1748-1753.
2. Andres, M., S. Di Luca, and M. Pesenti. 2008. Finger counting: the missing tool? Behavioral and Brain Sciences 31:642-643.
3. Ansari, D. 2008. Effects of development and enculturation on number representation in the brain. Nature Reviews Neurosciences 9:278-291.
4. Ansari, D., N. Garcia, E. Lucas, K. Hamon, and B. Dhital. 2005. Neural correlates of symbolic number processing in children and adults. Neuroreport 16:1769-1773.
5. Ardila, A. 2010. On the evolution of calculation abilities. Frontiers in Evolutionary Neuroscience 2(7):1-7.
6. Ardila, A. 2011. There are two different language systems in the brain. Journal of Behavioral and Brain Science 1:23-36.
7. Ardila, A., L. M. Galeano, and M. Rosselli. 1998. Toward a model of neuropsychological activity. Neuropsychology Review 8:177-189.
8. Ardila, A., and M. Rosselli. 2002. Acalculia and dyscalculia. Neuropsychology Review 12:176-232.
9. Baddeley, A. 2007. Working memory, thought, and action. Oxford: Oxford University Press.
10. Barth, H., K. La Mont, J. Lipton, S. Dehaene, N. Kanwisher, and E. Spelke. 2006. Non-symbolic arithmetic in adults and young children. Cognition 98: 199-222.
11. Biro, D., and T. Matsuzawa. 2001. Chimpanzee numerical competence: cardinal and ordinal skills. In Primate origins of human cognition and behavior. T. Matsuzawa, ed. Pp. 199-225. Tokyo: Springer.
12. Blum, D. 1994. The monkey wars. Oxford: Oxford University Press.
13. Bongard, S., and A. Nieder. 2010. Basic mathematical rules are encoded by primate prefrontal cortex neurons. Proceedings of the National Academy of Sciences of the USA 107:2277-2282.
14. Botha, R. 2008. Prehistoric shell beads as a window on language evolution. Language and Communication 28:197-212.
15. Brannon, E. M. 2005. The independence of language and mathematical reasoning. Proceedings of the National Academy of Sciences of the USA 102: 3177-3178.
16. Bright, M. 2009. The diversity of species. Chicago: Heinemann.
17. Bruner, E. 2004. Geometric morphometrics and paleoneurology: brain shape evolution in the genus Homo. Journal of Human Evolution 47:279-303.
18. Bruner, E. 2010. Morphological differences in the parietal lobes within the human genus: a neurofunctional perspective. Current Anthropology 51(suppl. 1):S77-S88.
19. Bruner, E., J. M. De la Cuétara, and R. L. Holloway. 2011a. A bivariate approach to the variation of the parietal curvature in the genus Homo. Anatomical Record 294:1548-1556.
20. Bruner, E., and R. L. Holloway. 2010. A bivariate approach to the widening of the frontal lobes in the genus Homo. Journal of Human Evolution 58: 138-146.
21. Bruner, E., G. Manzi, and J. L. Arsuaga. 2003. Encephalization and allometric trajectories in the genus Homo: evidence from the Neandertal and modern lineages. Proceedings of the National Academy of Sciences of the USA 100(26): 15335-15340.
22. Bruner, E., M. Martin-Loeches, M. Burgaleta, and R. Colom. 2011b. Midsagittal brain shape correlation with intelligence and cognitive performance. Intelligence 39:141-147.
23. Bruner, E., M. Martin-Loeches, and R. Colom. 2010. Human midsagittal brain shape variation: patterns, allometry, and integration. Journal of Anatomy 216:589-599.
24. Burr, D., and J. Ross. 2008. A visual sense of number. Current Biology 18(6): 425-428.
25. Cantlon, J., and E. Brannon. 2006. Shared system for ordering small and large numbers in monkeys and humans. Psychological Science 17:401-406.
26. Cantlon, J., M. Platt, and E. Brannon. 2008. Beyond the number domain. Trends in Cognitive Sciences 30:1-9.
27. Cantlon, J. F., E.M. Brannon, E. J. Carter, and K. A. Pelphrey. 2006. Functional imaging of numerical processing in adults and four-year-old children. PLoS Biology 4:844-854.
28. Cantlon, J. F., M. E. Libertus, P. Pinel, S. Dehaene, E. M. Brannon, and K. A. Pelphrey. 2009. The neural development of an abstract concept of number. Journal of Cognitive Neuroscience 21:2217-2229.
29. Carey, S. 2009. The origin of concepts. Oxford: Oxford University Press.
30. Carreiras, M., M. L. Seghier, S. Baquero, A. Estévez, A. Lozano, J. T. Devlin, and C. J. Price. 2009. An anatomical signature for literacy. Nature 461:983-986.
31. Carruthers, P. 2002. Human creativity: its evolution, its cognitive basis, and its connections with childhood pretence. British Journal for the Philosophy of Science 53:225-249.
32. Chiappe, D. L., and P. Chiappe. 2007. The role of working memory in metaphor production and comprehension. Journal of Memory and Language 56:172-188.
33. Cohen Kadosh, R., and V. Walsh. 2009. Numerical representation in the parietal lobes: abstract or not abstract? Behavioral and Brain Sciences 32:313-373.
34. Coolidge, F. L., K. A. Overmann, and T. Wynn. 2011. Recursion: what is it, who has it, and how did it evolve? Wiley Interdisciplinary Reviews: Cognitive Science 2:547-554.
35. Coolidge, F. L., and T. Wynn. 2001. Executive functions of the frontal lobes and the evolutionary ascendancy of Homo sapiens. Cambridge Archaeological Journal 11:255-260.
36. Coolidge, F. L. 2005. Working memory, its executive functions, and the emergence of modern thinking. Cambridge Archaeological Journal 15:5-26.
37. Crollen, V., X. Seron, and M.-P. Noël. 2011. Is finger-counting necessary for the development of arithmetic abilities? Frontiers in Psychology 2:1-3.
38. Culham, J. C., and N. G. Kanwisher. 2001. Neuroimaging of cognitive functions in human parietal cortex. Current Opinion in Neurobiology 11:157-163.
39. Cummins, D. D., and R. Cummins. 1999. Biological preparedness and evolutionary explanation. Cognition 73:B37-B53.
40. Dart, R. A. 1925. Australopithecus africanus: the man-ape of South Africa. Nature 2884:195-199.
41. Deacon, T. 1997. The symbolic species: the co-evolution of language and the human brain. London: Norton.
42. De Cruz, H. 2008. An extended mind perspective on natural number representation. Philosophical Psychology 21:475-490.
43. De Cruz, H., and J. De Smedt. 2010. Mathematical symbols as epistemic actions. Synthese, doi:10.1007/s11229-010-9837-9.
44. Dehaene, S. 1997. The number sense. New York: Oxford University Press.
45. Dehaene, S. 2007. Symbols and quantities in parietal cortex: elements of a mathematical theory of number representation and manipulation. In Sensorimotor foundations of higher cognition: attention and performance. P. Haggard, Y. Rossetti, and M. Kawato, eds. Pp. 527-574. Oxford: Oxford University Press.
46. Dehaene, S., G. Dehaene-Lambertz, and L. Cohen. 1998. Abstract representations of numbers in the animal and human brain. Trends in Neuroscience 21:355-361.
47. Dehaene, S., E. Spelke, P. Pinel, R. Stanescu, and S. Tsivkin. 1999. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science 284: 970-974.
48. Deloche, G. 1993. Aphasia and acalculia. In Linguistic disorders and pathologies. G. Blanken, J. Dittmann, H. Grimm, J. C. Marshall, and C. W. Wallesch, eds. Pp. 325-332. Berlin: de Gruyter.
49. De Smedt, J., and H. De Cruz. 2011. The role of material culture in human time representation: calendrical systems as extensions of mental time travel. Adaptive Behavior 19:63-76.
50. Diester, I., and A. Nieder. 2007. Semantic associations between signs andnumerical categories in the prefrontal cortex. PLoS Biology 5:e294.
51. Diester, I. 2008. Complementary contributions of prefrontal neuron classes in abstract numerical categorization. Journal of Neuroscience 28:7737-7747.
52. Domahs, F., K. Moeller, S. Huber, K. Willmes, and H.-C. Nuerk. 2010. Embodied numerosity: implicit hand-based representations influence symbolic number processing across cultures. Cognition 116:251-266.
53. Durand, J. B., R. Peeters, J. F. Norman, J. T. Todd, and G. A. Orban. 2009. Parietal regions processing visual 3D shape extracted from disparity. Neuroimage 46(4):1114-1126.
54. Everett, D. L. 2005. Cultural constraints on grammar and cognition in Pirahã: another look at the design features of human language. Current Anthropology 46:621-646.
55. Falk, D. 2007. Evolution of the primate brain. In Handbook of paleoanthropology, vol. 2. W. Henke, I. Tattersall, and T. Hardt, eds. Pp. 1133-1162. Berlin: Springer.
56. Feigenson, L., S. Dehaene, and E. Spelke. 2004. Core systems of number. Trends in Cognitive Sciences 8:307-314.
57. Fias, W., J. Lammertyn, B. Caessens, and G. A. Orban. 2007. Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. Journal of Neuroscience 27:8952-8956.
58. Frank, M. C., D. L. Everett, E. Fedorenko, and E. Gibson. 2008. Number as a cognitive technology: evidence from Pirahã language and cognition. Cognition 108:819-824.
59. Geary, J. 2011. I is an other: the secret life of metaphor and how it shapes the way we see the world. New York: HarperCollins.
60. Gelman, R., and C. R. Gallistel. 2004. Language and the origin of numerical concepts. Science 306:441-443.
61. Geschwind, N. 1964. The development of the brain and the evolution of language. Monograph Series on Language and Linguistics 17:155-169.
62. Geva, S., P. S. Jones, J. T. Crinion, C. J. Price, J.-C. Baron, and E. A. Warburton. 2011. The neural correlates of inner speech defined by voxel-based lesionsymptom mapping. Brain: A Journal of Neurology 134:3071-3082.
63. Gilmore, C. K., S. E. McCarthy, and E. S. Spelke. 2010. Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition 115:394-406.
64. Grefkes, C., and G. R. Fink. 2005. The functional organization of the intraparietal sulcus in humans and monkeys. Journal of Anatomy 207(1):3-17.
65. Gunz, P., S. Neubauer, B. Maureille, and J. J. Hublin. 2010. Brain development after birth differs between Neanderthals and modern humans. Current Biology 20:R921-R922.
66. Hagmann P., L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, V. J. Wedeen, and O. Sporns. 2008. Mapping the structural core of human cerebral cortex. PLoS Biology 6:e159.
67. Harnad, S. 1990. The symbol grounding problem. Physica D: Nonlinear Phenomena 42:335-346.
68. Haun, D. B. M., F. M. Jordan, G. Vallortigara, and N. S. Clayton. 2010. Origins of spatial, temporal and numerical cognition: insights from comparative psychology. Trends in Cognitive Sciences 14(12):552-560.
69. Hauser, M. D., N. Chomsky, and W. T. Fitch. 2002. The faculty of language: what is it, who has it, and how did it evolve? Science 298:1569-1579.
70. Henshilwood, C. S., F. d'Errico, M. Vanhaeren, K. van Niekerk, and Z. Jacobs. 2004. Middle Stone Age shell beads from South Africa. Science 304:404.
71. Holloway, I. D., and D. Ansari. 2009. Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology 103(1):17-29.
72. Holloway, R. L. 1981. Exploring the dorsal surface of hominoid brain endocasts by stereoplotter and discriminant analysis. Philosophical Transactions of the Royal Society B: Biological Sciences 393:155-166.
73. Hubbard, E. M., M. Piazza, P. Pinel, and S. Dehaene. 2009. Numerical and spatial intuitions: a role for posterior parietal cortex? In Cognitive biology: evolutionary and developmental perspectives on mind, brain and behavior. L. Tommasi, L. Nadel, and M. A. Peterson, eds. Pp. 221-246. Cambridge, MA: MIT Press.
74. Hurford, J. 1987. Language and number: the emergence of a cognitive system. Oxford: Blackwell.
75. Hutchins, E. 2005. Material anchors for conceptual blends. Journal of Pragmatics 37:1555-1577.
76. Imbo, I., A. Vandierendonck, and W. Fias. 2011. Passive hand movements disrupt adults' counting strategies. Frontiers in Psychology 2:1-5.
77. Jackendoff, R. 1996. How language helps us think. Pragmatics and Cognition 4:1-34.
78. Jordan, N. C., D. Kaplan, M. N. Locuniak, and C. Ramineni. 2007. Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research and Practice 22:36-46.
79. Jung, R. E., and R. J. Haier. 2007. The parieto-frontal integration theory (PFIT) of intelligence: converging neuroimaging evidence. Behavioural and Brain Sciences 30:135-187.
80. Kaufman, E. L., M. W. Lord, T. W. Reese, and J. Volkmann. 1949. The discrimination of visual number. American Journal of Psychology 62:498-525.
81. Kaufmann, L., F. Koppelstaetter, C. Siedentopf, I. Haala, E. Haberlandt, L. B. Zimmerhackl, S. Felber, and A. Ischebeck. 2006. Neural correlates of the number-size interference task in children. Neuroreport 17:587-591.
82. Kirsh, D. 1995. The intelligent use of space. Artificial Intelligence 73:31-68.
83. Klein, E., K. Moeller, K. Willmes, H.-C. Nuerk, and F. Domahs. 2011. The influence of implicit hand-based representations on mental arithmetic. Frontiers in Psychology 2:1-7.
84. Lakoff, G., and M. Johnson. 1999. Philosophy in the flesh: the embodied mind and its challenge to Western philosophy. New York: Basic.
85. Lakoff, G., and R. E. Núñez. 2000. Where mathematics comes from: how the embodied mind brings mathematics into being. New York: Basic.
86. Le Corre, M., and S. Carey. 2007. One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition 105(2):395-438.
87. Libertus, M. E., L. Feigenson, and J. Halberda. 2011. Preschool acuity of the approximate number system correlates with school math ability. Developmental Science 14:1292-1300.
88. Lurito, J. T., D. A. Kareken, M. J. Lowe, S. H. A. Chen, and V. P. Mathews. 2000. Comparison of rhyming and word generation with fMRI. Human Brain Mapping 10:99-106.
89. Malafouris, L. 2008. Beads for a plastic mind: the "blind man's stick" (BMS) hypothesis and the active nature of material culture. Cambridge Archaeological Journal 18:401-414.
90. Malafouris, L. 2010a. The brain-artefact interface (BAI): a challenge for archaeology and cultural neuroscience. Social Cognitive and Affective Neuroscience 5(2/3):264-273, doi:10.1093/scan/nsp057.
91. Malafouris, L. 2010b. Grasping the concept of number: how did the sapient mind move beyond approximation? In The archaeology of measurement: comprehending heaven, earth and time in ancient societies. C. Renfrew and I. Morley, eds. Pp. 35-42. Cambridge: Cambridge University Press.
92. Maloney, E. A., E. F. Risko, F. Preston, D. Ansari, and J. Fugelsang. 2010. Challenging the reliability and validity of cognitive measures: the case of the numerical distance effect. Acta Psychologica 134(2):154-161.
93. Mantovan, M. C., M. Delazer, M. Ermani, and G. Denes. 1999. The breakdown of calculation procedures in Alzheimer's disease. Cortex 35:21-38.
94. Mazzocco, M. M., L. Feigenson, and J. Halberda. 2011. Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development 82:1224-1237.
95. McGuire, P. K., D. A. Silbersweig, R. M. Murray, A. S. David, R. S. J. Frackowiak, and C. D. Frith. 1996. Functional anatomy of inner speech and auditory verbal imagery. Psychological Medicine 26:38-39.
96. Menninger, K. 1992. Number words and number symbols: a cultural history of numbers. P. Broneer, trans. New York: Dover.
97. P. Broneer, Trans Miller, E. K., A. Nieder, D. J. Freedman, and J. D. Wallis. 2003. Neural correlates of categories and concepts. Current Opinion in Neurobiology 13: 198-203.
98. Mundy, E., and C. K. Gilmore. 2009. Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology 103:490-502.
99. Nieder, A. 2009. Prefrontal cortex and the evolution of symbolic reference. Current Opinion in Neurobiology 19:99-108.
100. Nieder, A., and S. Dehaene. 2009. Representation of number in the brain. Annual Review of Neuroscience 32:185-208.
101. Nieder, A., I. Diester, and O. Tudusciuc. 2006. Temporal and spatial enumeration processes in the primate parietal cortex. Science 313:1431-1435.
102. Nieder, A., and E. K. Miller. 2004. A parieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Sciences of the USA. 101:7457-7462.
103. Orban, G. A. 2011. The extraction of 3D shape in the visual system of human and nonhuman primates. Annual Review of Neuroscience 34:361-388.
104. Orban, G. A., K. Claeys, K. Nelissen, R. Smans, S. Sunaert, J. T. Todd, C. Wardak, J. B. Durand, and W. Vanduffel. 2006. Mapping the parietal cortex of human and non-human primates. Neuropsychologia 44:2647-2667.
105. Overmann, K., T. Wynn, and F. L. Coolidge. 2011. The prehistory of number concept. Behavioral and Brain Sciences 34:142-144.
106. Owen, W. J., R. Borowsky, and G. E. Sarty. 2004. FMRI of two measures of phonological processing in visual word recognition: ecological validity matters. Brain and Language 90:40-46.
107. Patel, A. D. 2008. Music, language, and the brain. New York: Oxford University Press.
108. Peeters, R., L. Simone, K. Nelissen, M. Fabbri-Destro, W. Vanduffel, G. Rizzolatti, and G. A. Orban. 2009. The representation of tool use in humans and monkeys: common and uniquely human features. Journal of Neuroscience 29(37):11523-11539.
109. Peirce, C. 1955. Philosophical writings of Peirce. J. Buchler, ed. New York: Dover.
110. Penn, D. C., K. J. Holyoak, and D. J. Povineli. 2008. Darwin's mistake: explaining the discontinuity between human and nonhuman minds. Behavioral and Brain Sciences 31:109-178.
111. Piazza, M. 2010. Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences 14(12):542-551.
112. Piazza, M., and V. Izard. 2009. How humans count: numerosity and the parietal cortex. Neuroscientist 15(3):261-273.
113. Ramachandran, V. S. 2004. A brief tour of human consciousness: from impostor poodles to purple numbers. New York: Pi.
114. Reuland, E. 2010. Imagination, planning, and working memory: the emergence of language. Current Anthropology 51(suppl. 1):S99-S110.
115. Rips, L. J., A. Bloomfield, and J. Asmuth. 2008. From numerical concepts to concepts of number. Behavioral and Brain Sciences 31:623-642.
116. Rivera, S. M., A. L. Reiss, M. A. Eckert, and V. Menon. 2005. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex 15:1779-1790.
117. Roggeman, C., S. Santens, W. Fias, and T. Verguts. 2011. Stages of nonsymbolic number processing in occipitoparietal cortex disentangled by fMRI adaptation. Journal of Neuroscience 31(19):7168-7173.
118. Roux, F. E., S. Boetto, O. Sacko, F. Chollet, and M. Trémoulet. 2003. Writing, calculating, and finger recognition in the region of the angular gyrus: a cortical stimulation study of Gerstmann syndrome. Journal of Neurosurgery 99:716-727.
119. Santens, S., C. Roggeman, W. Fias, and T. Verguts. 2009. Number processing pathways in human parietal cortex. Cerebral Cortex 20(1):77-88.
120. Sato, M., L. Cattaneo, G. Rizzolatti, and V. Gallese. 2007. Numbers within our hands: modulation of corticospinal excitability of hand muscles during numerical judgment. Journal of Cognitive Neuroscience 19:684-693.
121. Sawamura, H., G. A. Orban, and R. Vogels. 2006. Selectivity of neuronal adaptation does not match response selectivity: a single-cell study of the fMRI adaptation paradigm. Neuron 49(2):307-318.
122. Smith, N. 2004. Chomsky: ideas and ideals. 2nd edition. Cambridge: Cambridge University Press.
123. Sterelny, K. 2010. Minds: extended or scaffolded? Phenomenology and the Cognitive Sciences 9:465-481.
124. Tang, Y., W. Zhang, K. Chen, S. Feng, Y. Ji, J. Shen, E. Reiman, and Y. Liu. 2006. Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences of the USA 103:10775-10780.
125. Tattersall, I. 2009. Language and the origin of symbolic thought. In Cognitive archaeology and human evolution. S. de Beaune, F. L. Coolidge, and T.Wynn, eds. Pp. 109-116. Cambridge: Cambridge University Press.
126. Tobias, P. V. 1987. The brain of Homo habilis: a new level of organization in cerebral evolution. Journal of Human Evolution 16:741-761.
127. Tomasello, M., and M. Carpenter. 2007. Shared intentionality. Developmental Science 10:121-125.
128. Trinkhaus, E. 1995. Neanderthal mortality patterns. Journal of Archaeological Science 22:121-142.
129. Vanduffel, W., D. Fize, H. Peuskens, K. Denys, S. Sunaert, J. T. Todd, and G. A. Orban. 2002. Extracting 3D from motion: differences in human and monkey intraparietal cortex. Science 298(5592):413-415.
130. Van Essen, D. C., and D. L. Dierker. 2007. Surface-based and probabilistic atlases of primate cerebral cortex. Neuron 56(2):209-225.
131. VanMarle, K., and K. Wynn. 2010. Tracking and quantifying objects and noncohesive substances. Developmental Science, doi:10.1111/j.1467-7687.2010.00998.
132. Vygotsky, L. S. 1962. Thought and language. Cambridge, MA: MIT Press.
133. Wadley, L., T. Hodgskiss, and M. Grant. 2009. Implications for complex cognition from the hafting of tools with compound adhesives in the Middle Stone Age, South Africa. Proceedings of the National Academy of Sciences of the USA 106:9590-9594.
134. Wagner, J. B., and S. C. Johnson. 2011. An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition 119(1):10-22.
135. Weidenreich, F. 1936. Observations on the form and proportions of the endocranial casts of Sinanthropus pekinensis, other hominids and the great apes: a comparative study of brain size. Palaeontologia Sinica, ser. D, 3:1-50.
136. Whitehead, A. N. 1911. An introduction to mathematics. New York: Holt.
137. Wiese, H. 2003. Iconic and non-iconic stages in number development: the role of language. Trends in Cognitive Sciences 7:385-390.
138. Wynn, T. 2009. Hafted spears and the archeology of cognition. Proceedings of the National Academy of Sciences of the USA 106:9544-9545.
139. Wynn, T., and F. L. Coolidge. 2005. The effect of enhanced working memory on language. Journal of Human Evolution 50:230-231.
140. Wynn, T. 2012. How to think like a Neandertal. Oxford: Oxford University Press.
141. Zamarian, L., A. Ischebeck, and M. Delazer. 2009. Neuroscience of learning arithmetic: evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews 33:909-925.
142. Zilhão, J., D. E. Angelucci, E. Badal-García, F. d'Errico, F. Daniel, L. Dayet, K. Douka, et al. 2010. Symbolic use of marine shells and mineral pigments by Iberian Neandertals. Proceedings of the National Academy of Sciences of the USA 107:1023-1028.