This volume represents the edited proceedings of the International Symposium on Mathematical Biology held in Kyoto, November 10-15, 1985. The symposium was or­ ganized by an international committee whose members are: E. Teramoto, M. Yamaguti, S. Amari, S.A. Levin, H. Matsuda, A. Okubo, L.M. Ricciardi, R. Rosen, and L.A. Segel. The symposium included technical sessions with a total of 11 invited papers, 49 contributed papers and a poster session where 40 papers were displayed. These Proceedings consist of selected papers from this symposium. This symposium was the second Kyoto meeting on mathematical topics in biology. The first was held in conjunction with the Sixth International Biophysics Congress in 1978. Since then this field of science has grown enormously, and the number of scientists in the field has rapidly increased. This is also the case in Japan. About 80 young japanese scientists and graduate students participated this time. . The sessions were divided into 4 ; , categories: 1) Mathematical Ecology and Population Biology, 2) Mathematical Theory of Developmental Biology and Morphogenesis, 3) Theoretical Neurosciences, and 4) Cell Kinetics and Other Topics. In every session, there were stimulating and active discussions among the participants. We are convinced that the symposium was highly successful in transmitting scientific information across disciplines and in establishing fruitful contacts among the participants. We owe this success to the cooperation of all participants.

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Introductory Lectures.- Chaos and fractals.- Recurrent themes in mathematical biology.- I. Mathematical Ecology and Population Biology.- The Structure of Populations and Communities.- Fantastic voyage into the deep: marine biofluid mechanics.- On the mathematical synthesis of physiological and behavioural mechanisms and population dynamics.- A necessary and sufficient assembly rule for real ecosystems.- Markovian foraging models.- The theory of population dynamics: back to first principles.- Dispersal.- Ecological and evolutionary aspects of dispersal.- The speeds of traveling frontal waves in heterogeneous environments.- Quantitative modeling of growth and dispersal in population models.- The interaction between dispersal and dormancy strategies in varying and heterogeneous environments.- Segregation structures of competing species mediated by a diffusive predator.- A spatially aggregating population model involving size-distributed dynamics.- Evolution.- Evolution of the number of sexes.- A lattice model for population biology.- Population genetical mechanism of molecular evolution - stochastic selection as an alternative to random drift -.- Evolutionary and ecological stability of prey-predator systems with predatory switching.- II. Mathematical Theories of Pattern and Morphogenesis.- Morphogenesis and Pattern Formation.- Pattern formation by coupled oscillations: the pigmentation patterns on the shells of molluscs.- From map systems to plant morphogenesis.- The cortical tractor: a new model for epithelial morphogenesis.- Pattern Formation in Dictyostelium discoideum.- An equilibrium theory of cell distribution in Dictyostelium discoideum.- A model for pattern formation in Dictyostelium discoideum.- A density dependent model for prestalk/prespore pattern formation in Dictyostelium discoideum I. Basic mathematical framework.- Origin of bursting and birhythmicity in a model for cyclic AMP oscillations in Dictyostelium cells.- III. Theoretical Neurosciences and Related Problems in Physiology.- Neurosciences.- Mathematical modelling of macroscopic brain phenomena.- A formal classification of bursting mechanisms in excitable systems.- On the topological representation of signals in self-organizing nerve fields.- The dynamics of a glia-modulated neural network and its relation to brain functions.- Self-organization in nervous systems: some illustrations.- Physiology and Related Problems.- Toward molecular sensory physiology: mathematical models.- Outline of some recent results on the first-passage-time problem in biological modeling.- Active rotator model for large populations of oscillatory and excitable elements.- The harnessing and stability of striated muscle.