[Footnotes]

[Footnotes]
1
S. Kingsland, Modeling nature. Episodes in the history of population ecology (Chicago, 1985)
F. Scudo, "The 'Golden Age' of theoretical ecology: A conceptual appraisal," Revue europeene des sciences sociales, 22 (1984), 11–64.
2
W.B. Provine, The origins of theoretical population genetics (Chicago, 1971)
E. Mayr and W.B. Provine, eds., The evolutionary synthesis: Perspectives on the unification of biology (Cambridge, 1980).
3
T. Vignoli and G.V. Schiaparelli, Peregrinazioni antropologiche e fisiche. Studio com- parativo fra le forme organiche naturali e le forme geometriche pure (Milan, 1898)
D'A.W. Thompson, On growth and form (Cambridge, 1917).
4
B.L. van der Pol and J. Van der Mark, "The heartbeat considered as a relaxation oscilla- tion, and an electrical model of the heart," Philosophical magazine, 6 (1928), 763–775
J. Lot- ka, Elements of physical biology (Baltimore, 1925).
5
Kingsland (ref. 1), 129.
6
G. Israel, "The two paths of the mathematization of the social and economic sci- ences. The decline of the 'mathematique sociale' and the beginnings of mathematical econom- ics at the turn of the eighteenth century," Physis, 30 (1993), 27–78.
7
Israel, "Vito Volterra: Un fisico ma- tematico di fronte ai problemi della fisica del Novecento," Revista di storia della scienza, 1 (1984), 39–72
"II determinismo e la teoria delle equazioni differenziali ordinarie. Un'analisi retrospettiva a partire dalla meccanica ereditaria," Physis, 28 (1991), 305–358.
8
Speeches delivered at a dinner held in University College, London, in honour of Profes- sor Karl Pearson, 23 April 1934 (Cambridge, 1934), 22–23.
9
Israel, "The origins of mathematical modelling in biology: A revival of mechanical reductionism and Darwinism," Science in context, 6 (1993), 469–509
"Volterra e la dinamica delle popolazioni biologiche," in A. Roccheggiani, ed., II pensiero scientifico di Vito Volterra (Ancona, 1990), 87–113
"Volterra's analytical mechanics of biological associations," Ar- chives Internationales d'histoire des sciences, 41 (1991), 57–104, 307–352
"Le equazioni di Volterra e Lotka: una questione di priorita" in O. Montaldo and L. Grugnetti, eds., La storia delle matematiche in Italia (Cagliari, 1982), 495–502
"On the contribution of Volterra and Lotka to the development of modern biomathematics," History and philosophy of life sci- ences, 10 (1988), 37–49.
10
Israel, "L'interminabile crisi del meccanicismo," Rivista di storia della scienza, 1 (1984), 73–99
"Approccio descrittivo e approccio ermeneutico nella modellistica matematica contemporanea," in S. Petruccioli, ed., Immagini, linguaggi, concetti (Rome, 1991)
La mathematisation du reel (Paris, 1996).
B. Ingrao and G. Israel, The invisi- ble hand. Economic equilibrium in the history of science (Cambridge, 1990)
Israel, "The origins" (ref. 9).
11
G. Israel, "Volterra archive at the Accademia Nazionale dei Lincei," Historia mathematica, 9 (1982), 229–238
G. Paoloni, ed., Vito Volterra e il suo tempo (1860-1940) (Rome, 1990).
G. Israel and A. Millan Gasca, "La correspondencia entre Vladimir A. Kostitzin y Vito Volterra (1933-1962) y los i- nicios de la biomatematica," Llull, Revista de la Sociedad Espahola de Historia de las Cien- cias y de las Tecnicas, 16 (1993), 159–224.
12
Volterra, "Variazioni e fluttuazioni del numero d'individui in specie animali conviven- ti," Accademia dei Lincei, Memorie, 2 (1926), 31–113.
13
Volterra, Legons sur la theorie mathematique de la lutte pour la vie, ed. Marcel Brelot (Paris, 1931)
D ell' influenza della stasi peschereccia del periodo 1914–1918 sul patrimonio ittico dell Alto Adriatico, Comitato Talassografico Italiano, Memorie, 126 (Venice, 1926).
14
Volterra, "Fluctuations in the abundance of species considered mathematically," Na- ture, 118 (1926), 558–560, on 559.
15
Darwin, The origin of species by means of natural selection, or the preservation of favoured races in the struggle for life (6th edn., London, 1882), 53–54
Volterra (ref. 14), 559.
16
Ibid., 559–560.
17
Volterra (ref. 14).
18
Draft, Volterra to Larmor, 11 June 1926
Pearson, 21 Sep 1926.
19
Volterra, "Sulle fluttuazioni biologiche," Accademia dei Lincei, Rendiconti, 5 (1927), 3–10
"Leggi sulle fluttuazioni biologiche," ibid., 61–67; "Sulla periodicita delle fluttuazioni biologiche," ibid., 465–470.
20
Volterra, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Comitato Talassografico, Memorie, 131 (Venezia, 1927)
Essai mathematique sur les fluctua- tions biologiques (Paris, 1927)
"Una teoria matematica sulla lotta per l'esistenza," Scientia, 41 (1927), 85–102
ibid., Supplement, 33–48
"Variations and fluctua- tions of the number of individuals in animal species living together," Conseil international pour l'exploration de la mer, Journal, 3 (1928), 3–51
Mathematical theory of the struggle for existence (in Russian) (Moscow, 1928).
21
Volterra to D'Arcy W. Thompson, 28 Nov 1926.
"La theorie mathematique de la lutte pour la vie et 1'experience (a propos de deux ouvrages de C.F. Gause)," Scientia, 60 (1936), 169–174).
Israel, "Le equazioni" and "On the contribution" (ref. 9).
22
E. Pearson, "The application of the theory of differential equations to the solution of problems connected with the interdependence of species," Biometrika, 19 (1927), 216–222, 442
F.S. Bodenheimer, "Welche Faktorem regulieren die Individuenzahl einer Insektenart in der Natur?," Biologisches Zentralblatt, 48 (1928), 714.
23
Thompson to Volterra, 2 Jul 1926
24
M. Mazzocut-Mis, "D'Arcy Thompson, la forme et le vivant," Alliage, 22 (1995), 24–31, on 24
25
Monod Herzen to Volterra, 10 Dec 1927
Memoire CXXXI is Volterra, "Variazioni" (ref. 20).
E. Monod-Herzen, Science et esthetique. Principes de morphologie generate (2 vols., Paris, 1927).
26
Thompson to Volterra, 29 Jul 1927.
27
Chapman to Volterra, 9 Aug 1928.
R.N. Chapman, "The quantitative analysis of en- vironmental factors," Ecology, 9 (1928), 111–122.
28
Kingsland (ref. 1), 95–96
Chapman to Volterra, 28 Jan 1929.
29
Ibid.
Chapman to Volterra, 26 Sep 1928
30
Kingsland (ref. 1), 234.
K. Friederichs, Die Grundfragen und Gesetzmdssigkeiten der land-und forstwirtschaftlichen Zoologie insbesondere der Entomologie (Berlin, 1930)
"Welche Faktoren regulieren die Individuenzahl einer Insektenart in der Natur? Ein kritisches Referat," Anzeiger fiir Schddlingskunde, 6 (1929), 25.
31
Chapman to Volterra, 28 Jan 1929
infra, §6.
32
Graham to Volterra, 1 Nov 1928.
33
Graham to Volterra, 30 Jan 1929.
34
Elton to Volterra, 6 Jan 1931.
Animal ecology (2nd edn., 1925)
35
E.G. Leigh, "The ecological role of Volterra's equations" in Some mathematical problems in biology (Providence, 1968), 1–61.
D.A. MacLulich, Fluctuation in the number of the varying hare (Toronto 1937)
36
Volterra, Legons (ref. 13), 3.
37
Ibid., 210.
38
infra §4.
39
Volterra, Legons (ref. 13), 198–99.
40
R. Pearl, "The influence of density of population upon egg pro- duction in Drosophila melanogaster," Journal of experimental zoology, 63 (1932), 57–84
Kingsland (ref. 1), 77–83.
41
Volterra, Legons (ref. 13), 32.
42
Ibid., 201–202.
43
Brelot to Volterra, 25 Oct 1929.
44
W.R. Thompson to Volterra, 4 May 1930.
45
Volterra, "Una teoria matematica" (ref. 20), 100.
46
Brelot to Volterra, 12 Aug 1929.
47
Draft, Volterra to Brelot, 20 Aug 1929.
48
Volterra, "Una teoria matematica" (ref. 20), 101.
49
Ref. 47.
50
D'Ancona to Volterra, 10 Mar 1930.
51
Volterra, Legons (ref. 13), 7–8.
52
V. Kostitzin, Symbiose, parasitisme et evolution (Paris, 1934), 35–36.
53
D'Ancona to Volterra, 4 Apr 1931.
54
M. Falcone and G. Israel, "Qualitative and numerical analysis of a class of prey- predator models," Acta applicandae mathematicae, 4 (1985), 225–258.
55
Draft, Volterra to D'A. Thompson, ca. Jan 1931
Volterra to Elton, draft, 20 Jan 1932
Chapman to Volterra, 4 May 1931
56
R.N. Chapman, Animal ecology, with special reference to insects (New York, 1931).
57
Kingsland (ref. 1).
58
R.N. Chapman, "The causes of fluctuations in populations in insects," Hawaiian Entomological Society, Proceedings, 8 (1933), 279–292.
59
D. Weiner, Ecology, conservation and cultural revolution in Soviet Russia (Bloom- ington, 1988)
R. Balandine, La vie et Voeuvre de Vernadski (Moscow, 1982); K. Bailes, Sci- ence and Russian culture in the age of revolutions: V.I. Vernadsky and his scientific school, 1863-1945 (Bloomington, 1990)
J. Grinevald, "On a holistic concept for deep and global ecology: The Biosphere," Fundamenta scientiae, 8 (1987), 197–226.
60
M.B. Adams, "Svertsov and Schmalhausen: Russian morphology and the evolutionary synthesis," in Mayr and Provine (ref. 2), 193–225
"Sergei Chetverikov, the Kol'tsov In- stitute, and the evolutionary synthesis," ibid., 242–278.
61
Kingsland (ref. 1), 146 ff.
62
Gause to Volterra, 12 Nov 1932
63
A. Pave, Modelisation en biologie et en ecologie (Paris, 1994), 98.
64
Regnier to Volterra, 12 Mar 1932.
S. Lambin, Jean Regnier (1892–1946) (Paris, 1969).
Suzanne Lambin (b. 1902)
65
D'Ancona to Volterra, 3 Nov 1933.
66
E. Mayr, "The arrival of Neo-darwinism in France," in Mayr and Provine (ref. 2), 321–322
D. Buican, Histoire de la genetique et de Vevolutionisme en France (Paris, 1984).
67
Israel and Millan Gasca (ref. 11)
F. Scudo and J.R. Ziegler, "Vladimir Alex- androvich Kostitzin and Theoretical Ecology," Theoretical population biology, 10 (1976), 395-412.
68
Volterra and D'Ancona, Les associations biologiques etudiees au point de vue mathematique (Paris, 1935)
Le associazioni biologiche studiate dal punto di vista matematico (Rome, 1995), ed. Giorgio Israel.
69
D'Ancona to Volterra, 10 Feb 1929.
70
D'Ancona to Volterra, 28 Mar 1930.
71
Regnier to Volterra, 11 June 1933.
72
Regnier to Volterra, 16 Jul 1933.
73
D'Ancona to Volterra, 26 Jul 1933.
74
Regnier to Volterra, 14 Mar 1934.
75
D'Ancona to Volterra, 2 Dec 1934.
76
Volterra, "Remarques sur la note de M. Régnier et Mile. Lambin," CRAS, 199 (1934), 1684–1686
J. Regnier and S. Lambin, "Etude d'un cas d'antagonisme micro- bien (Bacillus Coli-Staphylococcus aureus)," CRAS, 199 (1934), 1682–1683.
Volterra, "The general equations of biological strife in the case of historical ac- tions," Edinburgh Mathematical Society, IIs., Proceedings, 6 (1939), 4–10.
77
V. Kostitzin, Biologie mathematique (Paris, 1937), 67.
78
Volterra and D'Ancona (ref. 68), 21–23, 32–33.
79
Regnier to Volterra, 9 Dec 1934.
80
Regnier to Volterra, 19 May 1935.
81
D'Ancona to Volterra, 2 Dec 1934
The biology of population growth (New York, 1925)
ref. 41.
82
G.F. Gause, The struggle for existence (Baltimore, 1934).
Gause, Verifications expirimentales de la lutte pour la vie (Paris, 1935).
83
Volterra, "La thdorie mathematique" (ref. 21)
Gause to Volterra, 23 Dec 1935.
84
D'Ancona to Volterra, 31 Jan 1935.
85
D'Ancona to Volterra, 6 Feb 1935
Regnier to Volterra, 18 Nov 1934.
D'Ancona to Volterra (ref. 75)
ref. 22.
86
D'Ancona to Volterra, 25 Apr 1935
Volterra to Koshitzin, draft 13 Nov 1935
Chapman (ref. 56).
87
J. Stanley, "A mathematical theory of the growth of populations of the flour beetle, Tri- bolium confusum Duval," Canadian journal of research, 6 (1931), 632 ff., 7
(1932), 126 ff.
Stanley to Volterra, 29 Mar 1935.
88
Volterra and D'Ancona (ref. 68), 73.
89
Ibid., 8–9.
90
Ibid., 83–84.
91
Ibid., 82–83.
V.A. Bailey, "The interaction between host and parasites," Quarterly journal of mathematics, 2 (1931), 68–77
AJ. Nicholson, "The balance of animal popula- tions," Journal of animal ecology, 2 (1933), 132–178
Nicholson and Bailey, "The balance of animal populations," Zoological Society of London, Proceedings, part 3 (1935), 551–598
Kingsland (ref. 1), 139 ff.
92
Gause, Verifications (ref. 82), 9-10
Israel, "The origins" (ref. 9).
93
Gause, Verifications (ref. 82), 42–43.
94
Israel, "Volterra's analytical mechanics" (ref. 9).
95
Volterra, "Population growth, equilibria and extinction under specified breeding condi- tions: A development and extension of the theory of the logistic curve," Human Biology, 10 (1938), 1–11
"Calculus of variations and the logistic curve," ibid., 11 (1939), 173–178.
96
D'Ancona to Volterra, 24 Oct 1937
Volterra to D'Ancona, draft, 5 Nov 1937
D'Ancona to Volterra, 11 Nov 1937.
Leon Brillouin, Notions elementaires de mathematiques pour les sciences experimentales (Paris, 1935)
"Sur une generalisation des equations biologiques dans le cas d'une population intoxiquee," CRAS, 204 (1937), 1683
Kostitzin to Volterra, 5 May 1938
97
Kostitzin (ref. 52)
Evolution de 1'atmosphere, circulation organique, epoques gla- ciaires (Paris, 1935).
98
Kostitzin (ref. 77)
Mathematical biology (London, 1939).
Scuds and Ziegler, The "Golden Age" of theoretical ecology, 1923–1940 (Berlin, 1978).
99
Kostitzin to Volterra, 13 Aug 1935.
"Sur l'intoxication d'un milieu par les produits cata- boliques d'une population," CRAS, 201 (1935), 516-518.
100
Kostitzin to Volterra, 24 Aug 1935.
101
Kostitzin (ref. 77), 66–72
Israel and Millin Gasca (ref. 11).
Regnier to Volterra, 3 Nov 1935
Kostitzin to Volterra, 6 Nov 1935.
102
Regnier to Volterra, 13 Apr 1936.
103
Kostitzin "Sur une generalisation des equations biologiques dans le cas d'une popula- tion intoxiquee par les produits de son activite chimique," CRAS, 204 (1937), 1683–1685.
Kostitzin to Volterra, 12 June 1937.
104
Lambin to Volterra, 17 Jul 1938.
105
Volterra a Regnier, draft, n.d.
106
Regnier to Volterra, 11 Oct 1938
Kostitzin to Volterra, 12 Oct 1938
Kostitzin to Vol- terra, 27 Oct 1938.
107
Kostitzin to Volterra, 2 Nov 1938.
ref. 101.
108
Regnier and Lambin, "Etude sur le croit microbien en fonction de la quantite de sub- stance nutritive des milieux de culture," CRAS, 207 (1938), 1263
Kostitzin and Volterra, "Remarques sur Faction toxique du milieu a propos de la note de M. Regnier et Mile. Lam- bin," CRAS, 207 (1938), 1146–1148.
109
Kostitzin to Volterra, 27 Oct 1938
Kostitzin to Volterra, 6 Dec 1938
9 Mar 1939
3 June 1939
Kostitzin, "Sur les equations integro-differentielles de la theorie de Faction toxique du milieu," CRAS, 208 (1939), 1545-1547.
110
Volterra, "Sui tentativi di applicazione delle matematiche alle scienze biologiche e so- ciali," in Universita di Roma, Annuario (1901), 3–28.
111
Volterra, "Fluctuations dans la lutte pour la vie: leurs lois fondamentales et de reciprocity," in Opere matematiche. Memorie e note (Rome, 1960), 5, 482–495, on 482
Vol- terra, "Applications des mathematiques a la biologie," L'Enseignement mathematique, 36 (1937), 297–330.
ref. 81–83.
112
D'Ancona to Volterra, 23 Feb 1935.
113
D'Ancona to Volterra, 28 Feb 1935.
114
D'Ancona to Volterra, 1 May 1936.
115
E. Mayr, "The arrival of neo-Darwinism in France," in Mayr and Provine (ref. 2), 322
116
D'Ancona to Volterra, 14 Mar 1937.
117
D'Ancona to Volterra, 18 Mar 1937.
118
Kostitzin to Volterra, 5 Apr 1937.
119
Kostitzin to Volterra, 12 June 1937.
A. Sutherland, The origin and growth of the moral instinct (2 vols., London, 1898).
A. Millan Gasca, "Immagini matema- tiche della vita," Prometeo, 10 (1993), no. 43, 88–96.
120
Kostitzin to Volterra, 12 June 1937.
121
Kostitzin to Volterra, 15 May 1938.
Kostitzin, "Selection naturelle et transformation des especes du point du vue analytique, statistique et biologique,' CRAS, 206 (1938), 1442– 1444.
122
Kostitzin to Volterra, 19 Sep 1939.
123
Kostitzin to Volterra, 31 Dec 1935.
D'Ancona to Volterra, 30 Nov 1933.
124
Kostitzin to Volterra, 4 Mar 1937.
125
Kostitzin to Mrs. Volterra, 14 Feb 1946.
Kostitzin, "Sur le developpement des populations bactériennes," CRAS, 242 (1956), 611–612.
126
Robert K. May, "Will a large complex system be stable?," Nature, 238 (1972), 413
Stability and complexity in model ecosystems (Princeton, 1974).
127
E. Mayr, The growth of biological thought. Diversity, evolution and inheritance (Cam- bridge, 1982), chapt. 1.
128
Ingrao and Israel (ref. 10).
129
S. Levin, ed., Frontiers in mathematical biology (Berlin, 1994), ix.
130
J.M. Smith, Models in ecology (Cambridge, 1974).
131
G. Oster and J. Guckenheimer, "Bifurcation phenomena in population models," in J.E. Marsden, M. McCracken, eds. The Hopf bifurcation and its applications (New York, 1976), 327-328.
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