Lotka, Alfred J.

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Lotka, Alfred J.

WORKS BY LOTKA

PLEMENSUPTARY BIBLIOGRAPHY

Alfred James Lotka (1880–1949) anticipated many of the ideas of cybernetics and did original work in demography, evolutionary processes, and self-renewing aggregates. Born in Austria of American parentage, he spent his boyhood in France and acquired his advanced education in England, Germany, and the United States. He was employed as a chemist, physicist, mathematician, and biolo-gist until 1924, when he joined the Metropolitan Life Insurance Company. There he worked on tasks that made heavy demands upon his actuarial and demographic skills. Lotka’s 95 technical papers and 6 books reflect his deductive acumen, imagination, pragmatism, precision, and erudition. These works, as well as his magazine articles, also manifest a deep appreciation of the arts and humanities. He held the office of president of the Population Association of America and of the American Statistical Association and several posts in the International Union for the Scientific Study of Population.

His key concern was the set of processes underlying self-renewing aggregates and systems under-going change, especially irreversible change; this interest prompted the work to which “the field of demography owes virtually its entire central core of analytical development” (Notestein 1950, p. 23). Having shown in 1907 how a closed population withfixed age distribution grows, Lotka (with F. R. Sharpe 1911) demonstrated how a closed population develops a stable age distribution and a characteristic rate of increase, thereby supplying the most powerful of the modern demographer’s analytical tools, the stable population model. Building on this and later work, Lotka (with L. I. Dublin 1925) showed how to compute a stable age distribution and the“intrinsic”(or “true”) rate of increase, a discovery meriting for himthe title “father of demographic analysis” (Vincent 1950, p.14). This study revealed how misleading crude rates of natural increase can be. Lotka subsequently published many studies of self-renewing aggregates, evolution of ag£ distributions, indices of reproductivity, progeny of population elements, orphanhood, changes in fertility and family size, family extinction, mortality, and so on. Some of this work appeared in the revised editions of Dublin and Lotka’s The Money Value of a Man and Length of Life: A Study of the Life Table, and a great deal was summarized in Lotka’s Theorie analytique des associations biologiques(1934–1939).

Probably most representative of Lotka’s thought is Elements of Physical Biology (1925). Appearing when few social scientists used mathematics, it informed some of them of the uses of differential equations, the mechanics of systems and subsystems and the uses of systemic theory, andan essentially cybernetic view of organismic behavior (Simon 1959, p. 494). The book was the source of certain central modern ideas, and it demonstrates Lotka’s ability to discover significance in diverse phenomena. Even today it contributes to the understanding of statics and dynamics. The book focuses upon the mechanics of one of the “systems under-going irreversible changes in the distribution of matter” among its severalcomponents, namely, the evolving “life-bearing system,” whichis made up of an assembly of biological species, among them man, and collections of certain inorganic materials. Having defined irreversibility and conceived of evo-lution as the redistribution of matter, Lotka described the fundamental equations of the kinetics of evolving systems, along with growth functions and constraints. Under “statics” he treated steady states and diverse equilibria (e.g., chemical, inter-species, moving); Le Chatelier’s principle, displacement of equilibrium, homeostasis, stability conditions, and what is now called “comparative statics”; and the role of parameters which define the state of systems. Under “dynamics” he discussed “the progressive redistribution of the matter of the system” among “aggregations of living organisms” or “energy transformers,” together with the inorganic background within which substance circulatedand parameterscould change, albeit very slowly. He described indetail theelements composing the apparatus which energy transformers usein coping with their externalenvironments, among them depictors, receptors(including communicators), elab-orators, epictors,effectors, adjusters, and “consciousness”involved in depictors and adjusters [see INFORMATION THEORY]. This nonteleological apparatus enables some organisms, especially man, to discriminate, select, andin some environments stem that increase in entropy which dominates irreversible systems; its influence maybe accentuated by favorable orthogenesis.

Joseph J. Spengler

[For discussion of the subsequent development of Lotka’s ideas, seeComputation; Cybernetics; Lifet Tables; Opulation.]

WORKS BY LOTKA

1911 Lotka, Alfredj.; and Sharpe, F. R. A Problem in Age Distribution.Philosophical Magazine 21:435–438.(1925) 1957 Elements of Mathematical Biology. New York: Dover. → First published as Elements of Physical Biology.

1925 Lotka, Alfred J.; and Dublin, Louis I. On the True Rate of Natural Increase.Journal of the American StatisticalAssociation 20:305–339.

(1930) 1946 Dublin, Louis I.; and Lotka, Alfred J.The Money Value of a Man. Rev. ed. New York: Ronald. 1934–1939

Theorie analytique des associations biologiques. 2 vols. Paris: Hermann. → Volume 1: Principes. Volume 2: Analyse demographique avec application particuliere a I’espece humaine.

(1936) 1949 Dublin, Louis I.; Lotka, Alfredj.; and Spiegelman, M.Length of Life: A Study of the Life Table. Rev. ed. New York: Ronald. → Spiegelman is a joint author of the revised editiononly.

PLEMENSUPTARY BIBLIOGRAPHY

Lopez, Alvaro 1961 Problems in Stable Population Theory. Princeton Univ., Office of Population Research.

Notestein, Frank W.1950 Alfred James Lotka.Population Index 16:22-29. → Contains a bibliography.

Simon, Herbert A. 1959 [A Book Review of]Elements of Mathematical Biology, by Alfred J. Lotka.Econometrica 27:493–495.

Vincent, Paul 1950 Alfred J. Lotka: 1880–1949.Population 5:13-14.