Darwin and Lotka

Abstract

Abstract Population was the subject of two major conceptual developments in the second quarter of the 20th century. Both were inspired by biology. Lotka developed a mathematics of evolution in human and other species by analogy to thermodynamic models. His theory followed demographic practice in treating populations as closed units, commonly macro-scale, and in inferring underlying processes of change from aggregate outcomes. In contrast, the - a collaborative product of research in experimental and population genetics, natural history, and related fields of biology - followed Darwin in insisting that close observation of small-scale population processes and local environments is necessary to understand population change. Because gene-environment interactions rely on expanding and contracting networks of individuals, the populations in question are by nature open. Despite the apparent conflict between these positions, the broke new ground in the history of population thought by showing how the two approaches could be combined. Demography, however, moved away from and population biology as a source of theory in the early post-war era, and this conceptual redevelopment of population was scarcely remarked upon. More recently, the tremendous development of genetics has recalled demographers' attention to theory as an inescapable element of modern population thought. This paper provides a historical introduction to mid-20th-century developments in Darwinian population thinking, and the implications of its dual conceptualisation of population for demography. Its potential importance extends beyond the problem of gene-environment interactions to many aspects of social network analysis. 1. Introduction The theory of population proposed in Lotka's two main works was formulated as a contribution to biology. The Elements of Physical Biology (1925) elaborated a general mechanics of evolution in which relations between species are modelled as isolated systems obeying laws analogous to thermodynamics. This was reiterated in Part One of the Theorie analytique des associations biologiques (1934), and human populations were then treated as a special case in Part Two (1939). The period in which Lotka was writing was one of tremendous ferment in biology. The major contemporary breakthrough, which has come to be known as the evolutionary synthesis (Mayr and Provine 1998), was, however, formulated in terms that contrasted sharply to Lotka's. It addressed the dynamics of intra-species variation (Dobzhansky 1937). This focus, emphasizing relationships between individuals making up distinctive sub-populations, rather than species as undifferentiated wholes, was to have a lasting impact on the utility and reception of Lotka's work as a general theory of population for biology. Lotka's method acquired an eminent role only in a sub-field of population ecology, the study of predator-prey relations, where it parallels work by Volterra (Scudo and Ziegler 1978; Kingsland 1985). This marginalisation is reflected in histories of theory, in which the reader looks in vain even for mention of Lotka's two works (e.g. Provine 1971; Mayr 1982; Gould 2002). Lotka's fate as a theorist of population evolution has not troubled demographers, assuming they are aware of it. His papers on American demographics (e.g., 1925 [with L.I. Dublin], 1936) established his pre-eminence in the mathematics of human populations, and no effort was made to translate the Theorie for almost half a century after his death (Lotka 1998). The argument that Lotka formulated the core of demographic theory was consolidated in a series of influential syntheses in the early post-war era: a magisterial survey of the social scientific domain of population research by Hauser and Duncan (1959: 1-117); Ryder's elegant sociological generalisation of Lotka's concept of population, taking account of subsequent developments in cohort analysis (1964); and a summary of the development of modern population thought (Lorimer 1959). …