Abstract
The methods of classical mechanics have dominated most areas of population biology since the work of Volterra and Lotka in the 1930’s. These methods revolve around two main principles. First, the state of a system may be observationally determined; second, the future behavior of the system is completely determined by knowledge of the current state and the dynamical laws. These principles are in general valid for models in which there are few degrees of freedom and the trajectory of the system is insensitive to small changes in the initial conditions.
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References
L. Demetrius: Demographic parameters and natural selection. Proceedings National Academy of Sciences 71, 4645–4647 (1974)
L. Demetrius: Adaptive value, entropy and survivorship curves. Nature 275, 231–232 (1978)
L. Demetrius: La valeur adaptative et la sélection naturelle. Comptes Rendus de l’Académie des Sciences 290, 1491–1494 (1980)
L. Demetrius: Macroscopic parameters in complex systems (to appear 1980)
R. Dobrushin: The problem of uniqueness of a Gibbsian random field and the problem of phase transitions Functional Analysis and Applications 2, 302–312 (1968)
F. Dyson: Existence of a phase transition in a one-dimensional Ising ferromagnet. Communications in Mathematical Physics 12, 91–107 (1969)
B. Felderhof, M. Fisher: Phase transitions in one-dimensional cluster interaction fluids. Annals of Physics 58, 176–300 (1970)
F. Hofbauer: Examples for the non-uniqueness of the equilibrium state. Transactions of the American Mathematical Society 228, 223–241 (1977)
P.H. Leslie: On the use of matrices in population mathematics. Biometrika 33, 183–212 (1945)
R. May: Simple mathematical models with very complicated dynamics. Nature 261, 459–466 (1976)
D. Mayer: The Ruelle-Araki Transfer Operator in Statistical Mechanics, in Lecture Notes in Physics, Vol.123 (Springer, Berlin, Heidelberg, New York 1980)
D. Ruelle: Thermodynamic formalism (Addison-Wesley 1978)
Y. Sinai: Markov analysis and C-diffeomorphisms. Functional Analysis and Applications 2, 64–89 (1968)
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Dementrius, L. (1981). The Thermodynamic Formalism in Population Biology. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_29
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DOI: https://doi.org/10.1007/978-3-642-81703-8_29
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