Bøger i Lecture Notes in Biomathematics serien

From the preface by Joel E. Cohen: "e;A century from now humanity will live in a managed - or mismanaged - global garden. We are debating the need to preserve tropical forests. Farming of the sea is providing an increasing part of our fish supply. We are beginning to control atmospheric emissions. In 100 years, we shall use novel farming practices and genetic engineering of bacteria to manipulate the methane production of rice fields. The continental shelf will be providing food, energy, possibly even living space. To make such intensive management possible will require massive improvements in data collection and analysis, and especially in our concepts. A century hence we will live on a wired earth: the oceans and the crust of the earth will receive the same comprehensive monitoring now devoted to weather. As the peoples of currently developing countries increase their levels of wealth, the need for global management will become irresistible as impatience with the accidents of nature and intolerance of mismanagement of the environment - especially of living resources - grow. Our control of physical perturbations and chemical inputs to the environment will be judged by the consequences to living organisms and biological communities. How can we obtain the factual and theoretical foundation needed to move from our present, fragmented knowledge and limited abilities to a managed, global garden?"e; This problem was addressed in the lectures and workshops of a summer school on patch dynamics at Cornell University. The school emphasized the analysis and interpretation of spatial patterns in terrestrial and marine environments. This book contains the course material of this school, combining general reviews with specific applications.

This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe- matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for her very able assistance on all manner of details associated with the organization of the meeting. Finally, a word of thanks to all participants for their con- tributions to the success of the meeting, and to the contributors to this volume for their efforts in preparing their manuscripts.

The "e;raison d'etre"e; of hierarchical dustering theory stems from one basic phe- nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ~ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das- sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first.

This vol ume contains the proceedings of the second U. S. -Austral ia workshop on Renewable Resource Management held at the East-West Center, Honolulu, Hawaii, December 9-12, 1985. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Science and Technology (Austral ia) under the U. S. -Austral ia Cooperative Science Program. The objective of the workshop was to focus on problems associated with the management of renewable resource systems. A particular emphasis was given to methods for handling uncertain elements whieh are present in any real system. Toward this end, the partiei pants were chosen so that the collective expertise included mathematical modeling, dynamical control/game theory, ecology, and practical management of real systems. Each participant was invited to give an informal presentation in his field of expertise as related to the overall theme. The formal papers (contained in this vo 1 ume) were written after the workshop so that the authors coul d util ize the workshop experience in relating their own work to others. To further encourage this exchange, each paper contained in this volume was reviewed by two other participants who then wrote formal comments. These comments (with author's reply in some cases) are attached to the end of each paper.

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.

The idea of organizing a symposium on mathematical models in biology came to some colleagues, members of the Accademia dei Lincei, in order to point out the importance of mathematics not only for supplying instruments for the elaboration and the evaluation of experimental data, but also for discussing the possibility of developing mathematical formulations of biological problems. This appeared particularly appropriate for genetics, where mathematical models have been of historical importance. When the organizing work had started, it became clear to us that the classic studies of Vito Volterra (who was also a Member of the Academy and its President from 1923 to 1926) might be con- sidered a further reason to have the meeting in Rome at the Accademia dei Lincei; thus the meeting is dedicated to his memory. Biology, in its manifold aspects proved to Se ~ difficult object for an exhaustive approach; thus it became necessary for practical reasons to make a choice of problems. Therefore not all branches of biology have been represented. The proceedings of the symposium, as a whole, assume a knowledge of mathematics on the part of the reader; however the problem of teaching mathematics to biologists was the subject of a round table discussion, not recorded in these proceedings. On this were brought up some basic points to be recommended to teachers on an international basis, and a statement was prepared for circulation. The Organizing Committee TABLE OF CONTENTS TOPIC I MODELS OF NATUPAL SELECTION . . . . . . . * . . . .

This volume collects the contributions presented at the "e;Working Conference on System Theory in Immunology"e;, held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under- standing of basic immunological facts. Conversely, the complexity of experimental results and of interpretative models should stimulate mathematicians to formulate new problems and to design appropriate procedures of analysis. The multitude of scientific publications in theoretical biology, appeared in recent years, confirms this trend and calls for extensive interaction between mat- matics and immunology. The material of this volume is divided into five sections, along the scheme of the Conference program.

This book presents the proceedings of a workshop on community ecology organized at Davis, in April, 1986, sponsored by the Sloan Foundation. There have been several recent symposia on community ecology (Strong et. al., 1984, Diamond and Case, 1987) which have covered a wide range of topics. The goal of the workshop at Davis was more narrow: to explore the role of scale in developing a theoretical approach to understanding communities. There are a number of aspects of scale that enter into attempts to understand ecological communities. One of the most basic is organizational scale. Should community ecology proceed by building up from population biology? This question and its ramifications are stressed throughout the book and explored in the first chapter by Simon Levin. Notions of scale have long been important in understanding physical systems. Thus, in understanding the interactions of organisms with their physical environment, questions of scale become paramount. These more physical questions illustrate the role scale plays in understanding ecology, and are discussed in chapter two by Akira Okubo.

The contents of this volume involve selection, emendation and up-dating of papers presented at the NATO Conference "e;Mathe- matical Analysis of Decision problems in Ecology"e; in Istanbul, Turkey, July 9-13, 1973. It was sponsored by the System Sciences Division of NATO directed by Dr. B. Bayraktar with local arrange- ments administered by Dr. Ilhami Karayalcin, professor of the Department of Industrial Engineering at the Technical University of Istanbul. It was organized by A. Charnes, University professor across the University of Texas System, and Walter R.Lynn, Di- rector of the School of Civil and Environmental Engineering at Cornell Unjversity. The objective of the conference was to bring together a group of leading researchers from the major sciences involved in eco- logical problems and to present the current state of progress in research of a mathematical nature which might assist in the solu- tion of these problems. Although their presentations are not herein recorded, the key- note address of Dr. John A. Logan, president, Rose-Hulman Institute of Technology and the presentation of Dr. Michael J. L. Kirby, then Assistant principal Secretary to the premier of Nova Scotia, Canada, greatly influenced the discussion of papers and their subsequent emendations and revisions.

These Proceedings have been assembled from papers presented at the Conference on Models of Biological Growth and Spread, held at the German Cancer Research Centre Heidelberg and at the Institute of Applied Mathematics of the University of Heidelberg, July 16-21, 1979. The main theme of the conference was the mathematical representation of biolog- ical populations with an underlying spatial structure. An important feature of such populations is that they and/or their individual com- ponents may interact with each other. Such interactions may be due to external disturbances, internal regulatory factors or a combination of both. Many biological phenomena and processes including embryogenesis, cell growth, chemotaxis, cell adhesion, carcinogenesis, and the spread of an epidemic or of an advantageous gene can be studied in this con- text. Thus, problems of particular importance in medicine (human and veterinary), agriculture, ecology, etc. may be taken into consideration and a deeper insight gained by utilizing (more) realistic mathematical models. Since the intrinsic biological mechanisms may differ considerably from each other, a great variety of mathematical approaches, theories and techniques is required. The aims of the conference were (i) To provide an overview of the most important biological aspects. (ii) To survey and analyse possible stochastic and deterministic approaches. (iii) To encourage new research by bringing together mathematicians interested in problems of a biological nature and scientists actively engaged in developing mathematical models in biology.

In February 1985 a small international meeting of scientists took place at the recreation resort of the Polish Academy of Sci- ences in Mogilany, near Cracow, Poland. The initiative for holding the workshop came from a working meeting on mathematical immunology and related topics at the International Institute for Applied Sys- tems Analysis in Laxenburg, Austria, in November 1983. In addition to representatives of IIASA, delegates of the IIASA National Member Organizations (NMO) of Czechoslovakia, Italy, and the soviet Union took part in that working meeting. The participants came to the conclusion that IIASA could play an important role in facilitating the development of research in this field. The first step that they recommended to I IASA was to organize a workshop on mathematical immunology. The purpose of the workshop was to review the progress that has been made in applying mathematics to problems in immunology and to explore ways in which further progress might be achieved, especially by more efficient interactions between scientists working in mathematical and experimental immunology. Some National Member Organizations contributed to the success of the workshop by nominat- ing further participants working in this or related fields. For instance, thanks to a suggestion of the British NMO, the meeting also included analyses of the interactions between the immune state of a population and epidemiological phenomena. There were 33 participants at Mogilany from 11 countries, namely Canada, Czechoslovakia, Federal Republic of Germany, Hungary, Japan, Netherlands, Poland, Sweden, united Kingdom, USA, and USSR.

"e; . . . behavior is not, what an organism does itself, but to what we point. Therefore, whether a type of behavior of an organism is adequate as a certain configuration of movements, will depend on the environment in which we de- scribe it. "e; (Humberto Maturana, Francisco Varela: El arbol del conocimiento, 1984) "e;A thorough analysis of behavior must result in a scheme, that shows all regularities that are to be found between the sensorical input and the motorical output of an animal. This scheme is an abstract representation of the brain. "e; (Valentin Braitenberg: Gehirngespinste, 1973) During the 70ies, when Biomathematics (beyond Biomedical Statistics and Com- puting) became more popular at universities and research institutes, the problems dealt with came mainly from the general fields of 'Population Biology' and 'Complex Systems Analysis' such as epidemics, ecosystems analysis, morphogenesis, genetics, immunology and neurology (see the first series of Springer Lecture Notes in Biomathematics). Since then, the picture has not considerably changed, and it seems that "e;a thorough analysis of behavior"e; of single organisms and, moreover, of their mutual interactions, is far from being understood. On the contrary, mathematical modellers and analysts have been well- advised to restrict their investigations to specific aspects of 'biological behavior', one of which is 'biological motion'. Until now, only a few Conference Proceedings or Lecture Notes have paid attention to this important aspect, some of the earlier examples being Vol. 24: 'The measurement of biological shape and shape changes' (1978) or Vol.

The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ- ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con- tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "e;Chance and Necessity"e; (Monod 1971) as integrated components of adaptation in nature.

The E M B 0 course on "e;Formal Analysis of Genetic Regulation"e; A course entitled "e;Formal analysis of Genetic Regulation"e; was held at the University of Brussels from 6 to 16 September 1977 under the auspices of EMBO (European Molecular Biology Organization). As indicated by the title of the book (but not explicitly enough by the title of the course), the main emphasis was put on a dynamic analysis of systems using logical methods, that is, methods in which functions and variables take only a limited number of values - typically two. In this respect, this course was complementary to an EMBO course using continuous methods which was held some months later in Israel by Prof. Segel. People from four very different laboratories took an active part in teaching our course in Brussels : Drs Anne LEUSSLER and Philippe VAN HAM, from the Laboratory of Prof. Jean FLORINE (Laboratoire des Systemes logiques et numeriques, Faculte des Sciences appliquees, Universite Libre de Bruxelles). Dr Stuart KAUFFMAN (Dept. of Biochemistry and Biophysics, School of Medicine, Philadelphia). Prof. Gregoire NICOLlS (Service de Biophysique Theorique, Faculte des Sciences, Universite Libre de Bruxelles) and his temporary coworker Dr David RIGNEY (presently at the Center for Statistical Mechanics and Thermodynamics of the University of Texas at Austin, Texas).

When we consider the main object of forestry, the tree, it immediately becomes clear why experimental population geneticists have been so hesitant in making this object a primary concern of their research. Trees are very long-living organisms with generation intervals frequently exceeding those of their investigators by multiples. They virtually exclude, therefore, application of the classical methods of population genetics since these are based on observing genetic structures over generations. This situation, where the limits set to observation are so severe, particularly requires close cooperation between theory and experiment. It also requires careful consideration of results obtained for organisms other than trees, in order to gain additional insights by comparing the results for trees with those for other organisms. Yet, the greatest challenge to population and ecological genetics probably originates from the fact that forests are very likely to be the most complex ecosystems of all, even in some cases where they are subject to intense management. This complexity, which equally comprises biotic and abiotic factors varying both in time and space, makes extremely high demands on the adaptational capacity and thus flexibility of the carriers of such an ecosystem. Longevity combined with immobility during the vegetative phase, however, appears to contradict the obvious necessity of adaptational flexibility in forest tree populations when compared with short lived and/or mobile organisms.

In August 1988. the Sixth International Coral Reef Symposium was held in Townsville resulting in an influx of most of the world's coral reef sCientists to the city. We seized this opportunity at the Australian Institute of Marine Science to run a small workshop immediately before the symposium on the outbreaks of the crown-of-thorns starfish. Aeanthaster planei. We invited that small band of mathematicians who had been modelling the phenomenon, (and who may not have normally attended an international meeting so thoroughly dedicated to natural science) to meet with those SCientists who had been been actively working on the phenomenon in the field. John Casti notes in his delightful new book Alternate Realities (Wiley, 1989): 'If the natural role of the experimenter is to generate new observables by which we know the processes of Nature, and the natural role of the mathematician is to generate new formal structures by which we can represent these processes. then the system SCientist finds his niche by serving as a broker between the two. ' I think our book shows the fruits of that brokerage through the wide range of models explored within its pages. the high level of collaboration and interaction across disciplines evident in the individual papers, and in the emerging synthesis that reflects a far deeper understanding of this complex phenomenon than was possible even a few years ago.

These are the proceedings of the Second R. Yorque Workshop on Resource Management which took place in Ashland, Oregon on July 23-25, 1984. The purpose of the workshop is to provide an informal atmosphere for the discussion of resource assessment and management problems. Each participant presented a one hour morning talk; afternoons were reserved for informal chatting. The workshop was successful in stimulating ideas and interaction. The papers by R. Deriso, R. Hilborn and C. Walters all address the same basic issue, so they are lumped together. Other than that, the order to the papers in this volume was determined in the same fashion as the order of speakers during the workshop -- by random draw. Marc Mangel Department of Mathematics University of California Davis, California June 1985 TABLE OF CONTENTS A General Theory for Fishery Modeling Jon Schnute Data Transformations in Regression Analysis with Applications to Stock-Recruitment Relationships David Ruppert and Raymond J. Carroll ******. **. **. . ***************. * 29 A Conceptual Model for Multispecies, Multifleet Fisheries Wayne M. Getz, Gordon L. Swartzman, and Robert C. Francis . **. ***. *** 49 Risk Adverse Harvesting Strategies Richard Der iso . . *. . ****. . *. . . . . . . . ******. *. . . . . *. **. *********. *. *** 65 A Comparison of Harvest Policies for Mixed Stock Fisheries Ray Hilborn . . *******. **. **. ******. ************. . ******. . . . . ******. . * 75 Pathological Behavior of Managed Populations When Production Relationships are Assessed from Natural Experiments Carl J. Walters ******. **********. *. **. ******. *. **********. *****. . .

The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis- cipline with its own repertoire of techniques. The purpose of the Workshop on sto- chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap- plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important feature of the Workshop and one of the reasons for organizing it has been the fact that the theory of stochastic differential equations (SDE's) has found a rich source of new problems in the fields of population genetics and neuro- biology. This is especially so for the relatively new and growing area of infinite dimensional, i. e. , measure-valued or distribution-valued SDE's. The papers in II and III and some of the papers in the remaining categories represent these areas.