Sharon Kingsland

Department of History of Science and Technology, Johns Hopkins University, Baltimore, MD 21218

Ecology, being an interdisciplinary subject, has often advanced by borrowing perspectives and methods from numerous other disciplines. Of the many cross-disciplinary transfers that have contributed to the science of ecology, one unusual source of inspiration has been physical chemistry, which in a round-about way served to stimulate the development of population ecology in the 1920s. This transfer from physical chemistry into biology was the brainchild of Alfred James Lotka (1880–1949), a man of exceptional creativity and one of the fathers of what would later become theoretical population ecology.

Alfred James Lotka, 1880–1949. Image courtesy of MetLife Archives.

Lotka’s story has an ironic twist because he did not intend to contribute to the discipline of ecology. His goal was to create a new biological discipline called “physical biology,” by which he meant the “broad application of physical principles and methods in the contemplation of biological systems” (1). The analogy between physical chemistry and physical biology lay in the idea that the same basic laws governed both kinds of systems. In both systems, all processes could be reduced to two kinds of changes: those involving exchanges of matter between the components of the system, and those involving exchanges of energy. In the chemical system the components were molecules. In the biological system the components were organisms plus the raw materials in their environment, and the exchanges of matter and energy took place through the web of food relationships, growth, and reproduction. Understanding these relationships mathematically was the goal of physical biology. Because of his attention to systems, Lotka’s approach was strongly ecological, but when he started his project in the early 20th century, ecology barely existed as a discipline and he did not think, even two decades later, that ecologists would be his main audience.

Lotka received his undergraduate education in physics and chemistry at the University of Birmingham in the United Kingdom, where he was influenced by John Henry Poynting, a student of James Clerk Maxwell. After graduation in 1901 Lotka spent a year at the Physical-Chemical Institute at Leipzig, where Wilhelm Ostwald was advancing the idea that energy was the central organizing concept of the physical and biological sciences. Ostwald’s lectures prompted Lotka to explore the idea of developing a new discipline, which would be a biological analog to physical chemistry. After moving to the United States in 1902, Lotka started publishing articles on various aspects of physical biology while working at short-term jobs, completed a master’s degree at Cornell University in 1909, and on the basis of 12 publications earned a Doctorate of Science from Birmingham in 1912 (2).

As time passed, Lotka perceived growing interest in the application of mathematics to biology. One sign was D’Arcy Wentworth Thompson’s 1917 study, On Growth and Form, which applied methods commonplace in the physical sciences to problems of morphology and growth (3). Lotka, working in isolation, was frustrated that his own work had failed to gain recognition. That situation changed in 1920 when his publications came to the attention of Raymond Pearl, a biostatistician at the Johns Hopkins University’s School of Hygiene and Public Health. Pearl had noticed a connection between some of Lotka’s articles and Pearl’s own interests in population growth in single species. Pearl contacted Lotka, started communicating his articles to PNAS, and eventually invited him to Johns Hopkins for an extended stay so that he could gather his ideas into a book.

The first article that Pearl communicated to PNAS in 1920, “Analytical note on certain rhythmic relations in organic systems,” typified Lotka’s approach by opening with discussion of chemical systems and then moving to biological examples (4). The biological case was a hypothetical interaction between two species (a plant and an herbivore feeding on the plant). Lotka arrived at the unexpected result that their interaction would produce undamped or indefinitely continued oscillations in the two populations. Lotka developed this analysis into a general study of predator–prey (or host–parasite) interactions in his subsequent book, Elements of Physical Biology (1925), written in Pearl’s laboratory. That book was reprinted posthumously in 1956 as Elements of Mathematical Biology (1). It is now considered an ecological classic.

In the expanded treatment in Elements, Lotka fleshed out the analysis by building on research in entomology and epidemiology that dealt with host–parasite interactions. His elementary treatment of the problem resulted in undamped oscillations of the two populations, but a more exact treatment led to a damped oscillation (Fig. 1). Later, Lotka revisited the “mathematical theory of capture” to explore how the interaction of predator and prey populations would be affected by refuges that enabled prey to escape capture

See more http://www.pnas.org/content/112/31/9493.full

PNAS August 4, 2015 vol. 112 no. 31 9493-9495