258 unidirectional, with chemistry providing the groundwork for biological theories. Rather the opposite applies: much of the work in chemistry was motivated by ideas and experimental observations from biology. None of the players in the unfolding story of chemical self-organisation theories provides a better example for the mutual influence of chemical and biological concepts than the Austrian-American chemist Alfred Lotka (1880–1949). In 1910, Lotka published a paper entitled Contribution to the theory of periodic reactions in the Journal of Physical Chemistry (Lotka 1910). In this paper, he showed that under certain conditions, autocatalysis leads to chemical oscillations. He still assumed an inhomogeneous system in which a substance A is set free with a constant rate from a condensed phase and then reacts to produce a substance B. B influences autocatalytically its own production and decays with a constant rate. Lotka solved the coupled differential equations and showed that the system leads to damped oscillations. At the end of the paper, he states ‘No reaction is known which follows the above law, and as a matter of fact the case here considered was suggested by the consideration of matter lying outside the field of physical chemistry’ (Lotka 1910). In the footnote to this sentence, he mentions the work of Brailsford Robertson, who, motivated by Jacques Loeb, had measured growth curves of different organisms and had come to the conclusion: ‘…cell division has been shown by Loeb to be the expression of an autocatalytic synthesis of nuclear material…in all probabil- ity, cell growth or the synthesis of cytoplasm is also an autocatalytic reaction’ (Brailsford Robertson 1908). While the system Lotka had described in 1910 was producing damped oscillations, he later extended his work to systems with sustained, undamped oscillations and, in particular, also to homogeneous systems. In 1920, he published Undamped oscillations derived from the law of mass action (Lotka 1920a). In the introduction, he states that in the earlier work he believed that the relevant kinetic conditions could only be provided in heterogeneous systems. ‘It is, therefore, somewhat contrary to his first expectations that the writer now finds the conditions for undamped oscillations may occur in the absence of any geometrical causes in a homogeneous system’ (Lotka 1920a). His new system coupled two autocatalytic reac- tions, one consuming the product produced by the other reaction. Again, Lotka cannot point to a realistic example from chemistry and ends the article with a note on biology; ‘Rhythmic phenomena are of particular interest in connec- tion with biological systems (e.g. heart-beat)…’ (Lotka 1920a). He also announces a more general extension of his work to biological problems. This extension, published in PNAS in the same year, contains the equations which were independently discovered by Volterra and today are called Lotka–Volterra equations used to model predator–prey Dev Genes Evol (2011) 221:255–279 relationships in population biology (Lotka 1920b). Lotka extensively cites Spencer’s first principle; ‘Every species of plants and animal is perpetually undergoing a rhythmic variation in number—now from the abundance of food and absence of enemies rising above its average, and then by a consequent scarcity of food and abundance of enemies being depressed below its average…’ (Lotka 1920b). Biology at the population level or physiology seemed to offer applications of his chemically derived equations, while in chemistry, as he notes at the end of his article, oscillations are at best ‘laboratory curiosities’. Later developments showed that neither realistic chemical oscil- lations (see below) nor predator–prey cycles could be described by Lotka’s equations, although they remain extremely popular in ecology (Kot 2001). The lack of applications in chemistry and the obvious affinity of his work to biology made Lotka more and more interested in a physical and mathematical foundation of biology. In particular, he became one of the first authors to point out the limits of the known laws of thermodynamics in explaining life processes; ‘…something more than the first and second laws of thermodynamics is required to predict the course of events’ (Lotka 1922). The thermody- namics available to Lotka only dealt with reversible, i.e. equilibrium, states. However, ‘[r]eal phenomena are irre- versible; and in particular, trigger action, which plays so important a role in life processes, is a typical irreversible process…To deal with these problems, requires the intro- duction of new principles’ (Lotka 1922). Lotka envisages the development of a statistical mechanics for populations of organisms in ‘which the units shall be, not simple material particles in ordinary reversible collision of the type familiar in the kinetic theory…the units in the new statistical mechanics will be energy transformers subject to irreversible collisions…’ (Lotka 1922). These are very visionary comments; however, they seem to imply that an extension of thermodynamics is only required at the population level, while the highly ordered state of the individual organism poses no particular problem in the frame of the existing laws. In 1925, Lotka published Elements of Physical Biology which was reprinted in 1956 under the title Elements of Mathematical Biology. In his programme of a physical biology, he claims to capture all aspects of organismic life. Part I: General remarks deals with a physical theory of evolution; part II: Kinetics with growth; part III: Statics with populations and ecological interactions; and part IV: Dynamics with biochemistry, physiology, behaviour and even consciousness (Lotka 1925). In the introductory chapter Regarding Definitions, Lotka rejects attempts to define life by sharply distinguish- ing it from inorganic phenomena. He explicitly refers to Driesch’s statement that no man-made machine exists which shows self-repair and self-reproduction and spec-