생물 종의 개체 수 변화를 기술하는 수학적 모델에 대한 고찰 = A study on mathematical models describing population changes of biological species

다국어 초록 (Multilingual Abstract)

Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

참고문헌 (Reference)

1 R.O. PETERSON, "Wolves, Moose, and the Allometry of Population Cycles" 224 (224): 1350-1352, 1984

2 A.J. Nicholson, "The self adjustment of populations to change" 22 : 153-173, 1957

3 P.M.G. Harris, "The history of human populations" Indianapolis 2000

4 J.A.J. Metz, "The dynamics of physiologically structured populations, Lecture Notes in Biomathematics" Springer-Verlag 1986

5 R.M. May, "Stability and Complexity in Model Ecosystems" Princeton Univ. Press 1975

6 P.-F. Verhulst, "Recherche mathémathiques sur le loi d’accroissement de la population" 18 : 3-38, 1845

7 D. Ludwig, "Qualitative analysis of insect outbreak systems: the spruce budworm and forest" 47 : 315-332, 1978

8 J.H. Myers, "Population cycles in rodents" 38-46, 1974

9 P.H. Leslie, "On the use of matrices in certain population mathematics" 33 : 183-212, 1945

10 J.R. Beddington, "Harvesting natural populations in a randomly fluctuatingenvironment" 197 : 463-465, 1977

11 B. Charlesworth, "Evolution in Age-structured Populations" Cambridge University Press 1980

12 A.J. Lotka, "Elements of Physical Biology" Williams and Wilkins 1925

13 P.-F. Verhulst, "Deuxième mémoire sur la loi d’accroissement de la population, Mémoires de l’Academie Royale des Sciences" 20 : 1-32, 1847

14 G. Caselli, "Demography: Analysis and Synthesis" Academic Press 2005

15 F. Brauer, "Constant rate population harvesting: equilibrium and stability" 8 : 12-30, 1975

16 W.A. Calder, III, "An allometric approach to population cycles of mammals" 100 (100): 275-282, 1983

17 T.R. Malthus, "An Essay on the Principle of Population" Penguin Books 1970

18 G.A. De Leo, "Allometry and simple epidemic models for microparasites" 379 : 720-722, 1996