LOTKA, ALFRED J.

(1880–1949)

Alfred James Lotka was born in Galicia, in a city that was then part of the Austrian empire known as Lem-berg, and which is now known as L'viv in Ukraine. Lotka's parents, Jacques and Marie (Doebely) Lotka, were U.S. citizens. He grew up in France and studied chemistry, physics and mathematics at Birmingham University in England, the University of Leipzig in Germany, and Cornell University in the United States, earning a D.Sc. from Birmingham in 1912. In 1902, he moved to the United States, where he spent most of the rest of his life. After working as an industrial chemist and at various other jobs, he held a temporary research appointment from 1922 to 1924 in American biometrician and eugenist Raymond Pearl's group at Johns Hopkins University. Lotka worked for the Metropolitian Life Insurance Company in New York City from 1924 until his retirement in 1948. Two months before his 55th birthday he married Romola Beattie; they had no children. He was president of the Population Association of America (1938–1939) and of the American Statistical Association (1943).

Lotka's concept of population embraced mole-cules, equipment, rotifers, Drosophila, humans, interacting species, interacting genotypes, and publications. He developed a powerful mathematical armamentarium for analyzing populations. He remains the population scientist nonpareil, whose five books and more than 100 papers not only shaped demography, the core population-science discipline, but also advanced ecology, evolutionary biology, epidemiology, economics, operations research, and chemistry among other subjects. Although the clarity and charm of his writings make them highly accessible to the reader, their range and profundity demand careful study. Most of the mathematical theory of population developed subsequently by other scientists is still best described as footnotes to Lotka's work.

While at Johns Hopkins University, Lotka completed his multifaceted book, Elements of Physical Biology (1925). Lotka's use of systems of differential equations, his emphasis on comparative statics and his focus on maximal principles and the stability of equilibria led to penetrating insights and opened new analytical perspectives.

A second book, Théorie Analytique des Associations Biologiques, was published in two parts (1934 and 1939). The second part focuses on demographic analysis with special application to humans. It lays out the three basic equations of Lotka's theory of stable populations:

and

as well as the general renewal equation:

where the population is closed to migration and consists of "a large number of essentially similar units" (e.g., human females) and where a is age, b is the birth rate, r is the population growth rate, c(a) is the proportion of the population at age a, p (a) is the probability of survival from birth to age a, m (a) is the maternity rate or rate of reproduction at age a, and B(t) is the number of births at time t, and ω is an upper limit on age. These equations have been of fundamental importance to demographic theory and application. Lotka's research on the renewal equation began in 1908 at Cornell University in collaboration with Professor F. R. Sharpe.

Lotka devoted much thought to cyclical processes, from simple predator-prey interactions to global physico-chemical-biological systems. His re-search on the former led to the Lotka-Volterra equations used in ecology; his thinking about the latter anticipates current concerns about environmental stability.

The range of Lotka's interests is suggested by his study of the number of authors with n publications in lengthy bibliographies, such as Chemical Abstracts. He found that the probability of n is approximately 6/(πn)², which implies that three-fifths of the authors listed contribute one article, 15 percent contribute two articles, and only a one-quarter contribute more than two.

BIBLIOGRAPHY

SELECTED WORKS BY ALFRED LOTKA.

Lotka, Alfred J. [1906] 1977. "Relation Between Birth Rates and Death Rates." In Mathematical Demography: Selected Papers, ed. D. Smith and Nathan Keyfitz. Berlin: Springer-Verlag.

——. [1922] 1977. "The Stability of the Normal Age Distribution." In Mathematical Demography: Selected Papers, ed. D. Smith and Nathan Keyfitz. Berlin: Springer-Verlag.

——. 1925. Elements of Physical Biology. Balti-more: Williams & Wilkins. Reprinted as Elements of Mathematical Biology (1956). New York: Dover Publications.

——. 1926. "The Frequency Distribution of Scientific Productivity." Journal of the Washington Academy of Sciences 16: 317–323.

——. 1934, 1939. Théorie Analytique des Associations Biologiques. Paris: Hermann et Cie.

——. 1998. Analytical Theory of Biological Populations, (Théorie Analytique des Associations Biologiques) trans. David P. Smith and Helene Rossert (New York: Plenum Press.).

Sharpe, F. R., and Alfred J. Lotka. [1911] 1977. "A Problem in Age-Distribution." In Mathematical Demography: Selected Papers, ed. D. Smith and Nathan Keyfitz. Berlin: Springer-Verlag.

SELECTED WORKS ABOUT ALFRED LOTKA.

Arthur, W. Brian, and James W. Vaupel. 1984. "Some General Relationships in Population Dynamics." Population Index 50(2): 214–226.

Samuelson, Paul A. 1977. "Resolving a Historical Confusion in Population Analysis." In Mathematical Demography: Selected Papers, ed. David Smith and Nathan Keyfitz. Berlin: Springer-Verlag.

Simon, Herbert A. 1959. "Review of Elements of Mathematical Biology by Alfred J. Lotka." Econometrica 27(3): 493–495.