Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild, modified by Louis Gross, Oct. 1995, May 2000, March 2001, June 2003 Allan, Linda J. S. (2003) An Introduction to Stochastic Processes with Applications to Biology. Pearson Prentice Hall, Upper Saddle River, NJ. ISBN 0-13-035218-7 Overview of basic probability and stochastic models common in ecology and epidemiology. Level appropriate for advanced undergraduates in math and graduate students in biology. Non-measure theoretic. Includes numerical examples and MATLAB code. Alstad, Don (2001) Basic Populus Models of Ecology. Prentice-Hall, Inc. Upper Saddle River, NJ. ISBN 0-13-021289-X Guide to the use of the Populus on-line programs (at http://ecology.umn.edu/populus) for teaching basic population models, demographics, competition, predator-prey and epidemic models. Anderson, Roy M. and Robert M. May (1986) The Dynamics of Human Host-Parasite Systems Princeton Univ. Press Beltrami, Edward (1993) Mathematical Models in the Social and Biological Sciences Boston: Jones & Bartlett. 197 p., + 3 (out of 6) chapters on ecological models (incl. a fishery model, measles epidemics, red tide model, pollution model, gray squirrel dispersal model, and a game-theoretical fishery model) Berg, Howard C. (1983) Random walks in biology. Princeton: Princeton Univ. Press, 142p., ISBN 0-691-08245-6 Bossel, Hartmut (1994) Modeling and Simulation. Wellesley, MA: A. K. Peters, 484 p. + a systems dynamics approach to modeling; so most of the applications are drawn from natural resource modeling; great catalog of elementary systems models; comes with software (the SIMPAS simulator, PC-based) as well as STELLA diagrams - no exercises; limited bibliography Brown D. and P. Rothery (1993) Models in Biology: mathematics, statistics and computing Chichester: Wiley, 688 p., ISBN 0-471-93322-8 + lots of (ecological) models, statistics and data, many exercises and references, computer supplement available - ignores age structure Bulmer, Michael (1994) Theoretical Evolutionary Ecology. Sunderland: Sinauer, 352 p., ISBN 0-87893-078-7. + focus on basic population modeling, life history evolution, game theory, and evolution of sex. Has exercises - very little classical population genetics Burgman, M.A. and S. Ferson and H. R. Akcakaya (1993) Risk assessment in conservation biology London: Chapman & Hall, (Population and community biology series 12), 314p., ISBN 0-412-35030-0 + does more than the title might suggest, application of population models to wildlife management Review in Trends in Ecol & Evol., mid 1993 Caswell, Hal (1989) Matrix Population Models. Sunderland: Sinauer, 328 p., ISBN 0-87893-094-9, 0-87893-093-0 + extensive references - no exercises - second greatly expanded edition (2000) Clark, Colin W. (1976) Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley, 352p., ISBN 0-471-15856-9 Cullen, M. R. (1985) Linear Models in Biology--Linear Systems Analysis with Biological Applications. Chichester: Horwood, 213 p. ISBN 0-85312-835-9, 0-85312-905-3, 0-470-20206-8, 0-470-20205-X + all classic linear methods discussed, most examples from ecology, exercises Dale, Virginia H. (ed.) (2003) Ecological Modeling for Resource Management. New York: Springer, 328 p. Collection of papers with emphasis on computational approaches, data colection and decision making. DeAngelis, D. L. (1992) Dynamics of Nutrient Cycling and Food Webs.New York: Chapman & Hall, 270 p., Series Population and community biology series 9; ISBN 0-412-29840-6, 0-412-29830-9 + extensive collection of models, many references - no exercises DeAngelis, D. L and L. J. Gross (eds.) (1992) Individual-Based Models and Approaches in Ecology. Chapman and Hall, New York. ISBN 0-412-031612, 0-412-03171-X. Denny, Mark and Steven Gaines (2000) Chance in Biology: Using Probability to Explore Nature. Princeton University Press, ISBN 0-691-00521-4 Basic introduction to probability for biologists, but not in a standard textbook form. Includes mathematics intertwined with numerous biological examples. Edelstein-Keshet, L. (1988) Mathematical Models in Biology. Random House, New York. ISBN 0-394-35507-5 + good at how and why models are used, assumes only modest math background, good homework problems, good coverage of continuous models - not solely about in ecology, not so good coverage of discrete models, no stochastic models, many errors in the exercises France, J. and J. H. M. Thornley (1984) Mathematical Models in Agriculture. Butterworths Gotelli, Nicholas J. (1995) A primer of ecology. Sunderland: Sinauer Associates, 206 p. Second Edition (1998). + basic updating of the Wilson and Bossert classic, at low mathematical level. Haefner, James W. (1996) Modeling Biological Systems: Principles and Applications. Chapman and Hall, New York. An overview of many applications of different mathematical approaches, including modern computational ones, to many areas of biology. Hallam, T. G. and S. A. Levin (eds.) (1986) Mathematical Ecology: an Introduction. Springer, Series Biomathematics 17; 457p., ISBN 3-540-13631-2, 0-387-13631-2 Hannon, B. & Ruth, M. (1994) Dynamic Modeling. New York: Springer, 248p. systems approach to modeling; covers economic, engineering, as well as genetic and ecological models; is a tutorial in STELLA II, with most of the book relying on the use of this package; comes with software (Mac or Windows). Hastings, Alan (1997) Population Biology: Concepts and Models. New York: Springer, 220p. Basic overview of deterministic models and data of population biology and population genetics. Hoff, John and Michael Bevers (2002) Spatial Optimization in Ecological Applications. New York: Columbia University Press, 257p. Collection of case studies dealing with mathematical programming in application to forest management, conservation biology and develops this for discrete reaction-diffusion models. Hoppensteadt, Frank C. (1982) Mathematical methods of population biology. Cambridge: Cambridge Univ. Press (Cambridge studies in mathematical biology 4), 149p., ISBN 0-521-23846-3, 0-521-28256-X + good intro to topic - population dynamics only Jeffries, Clark. (1989) Mathematical Modeling in Ecology--a Workbook for Students. Boston: Birkhauser. 193 p., ISBN 0-8176-3421-5 thin, eclectic book; easily covered in a semester; a dynamical systems approach to ecosystem modeling, see review in Ecology Vol. 71:2400-2401 (1990) + exercises with solutions - limited references for each chapter Jones, D. S. and B. D. Sleeman (2003) Differential Equations and Mathematical Biology. Boca Raton: CRC Press, 390 p. Ordinary and partial differential equations in application to various biological problems including heart physiology, nerve impulses, tumour growth and epidemics. Keen, Robert E., Spain, James D. (1992) Computer simulation in biology: a BASIC introduction. New York (etc.) : Wiley-Liss, 498p., incl. disk, ISBN 0-471-50971-X + assumes only elementary knowledge of calculus and linear algebra, goes from simple growth models to complex simulation models, ecological examples, strong emphasis on programming - examples are in BASIC Kot, Mark (2001) Elements of Mathematical Ecology. Cambridge University Press, 453 p. Covers classical differential and partial differential equation models in ecology, includes basic stochastic models and introduction to optimal control. Levin, S. A., Hallam, T. G. and L. J. Gross (eds.) (1989) Applied Mathematical Ecology.Springer, Series Biomathematics 18; ISBN 3-540-19465-7, 0-387-19465-7 Logofet, Dmitrii O. (1993) Matrices and Graphs--Stability Problems in Mathematical Ecology Boca Raton: CRC Press, 308p. Deals only with issues of multicomponent and multispecies assemblages with emphasis on Lyapunov stability. Topics include: Leslie models, graph-theoretical analysis, food webs, competition, spatial distribution - no exercises Marcus-Roberts, H. and M. Thompson (eds.) (1983) Life Science Models. Springer, 366p., ISBN 0-387-90739-4, 3-540-90739-4 Maynard Smith, John (1968) Mathematical Ideas in Biology.Cambridge: Cambridge Univ. Press, 152p. Maynard Smith, J. (1974) Models in Ecology. Cambridge: Cambridge University Press. 146 p. + old, but a classic, insightful text - no exercises. Maynard Smith, John (1982) Evolution and the Theory of Games. Cambridge: Cambridge Univ. Press, 224p., ISBN 0-521-24673-3, 0-521-28884-3 Mazumbar, J. (1989) An Introduction to Mathematical Physiology and Biology. Cambridge: Cambridge Univ. Press, 208 p., ISBN 0-521-37002-7, 0-521-37901-6. Differential equation modeling introduction, including applications to diffusion, population biology, biogeography, biofluids, and pharmacokinetics. Murray, J. D. (1989) Mathematical Biology. Springer, Series Biomathematics 19, 767p., ISBN 3-540-19460-6, 0-387-19460-6 R.M.Nisbet, W.S.C.Gurney (1982) Modelling Fluctuating Populations. Chichester: Wiley, 379p., ISBN 0-471-28058-5 + good for discrete models - out of date Okubo, Akira (1980) Diffusion and ecological problems: mathematical models. Springer (Biomathematics, vol.10), 254p., ISBN 3-540-09620-5. 0-387-09620-5 Classic overview of deterministic diffusion models - updated as Okubo and Levin, (2001) Othmer, H. G., F. R. Adler, M. A. Lewis and J. C. Dalton (eds). (1997) Case Studies in Mathematical Modeling: Ecology, Physiology and Cell Biology. Prentice-Hall, Inc. Upper Saddle River, NJ. ISBN 0-13-574039-8 Collection of numerous brief review articles by various experts on math modeling problems, utilizing mainly undergraduate-level math. Pielou, E. C. (1977) Mathematical Ecology. New York: Wiley; 385 p., ISBN 0-471-01993-3 covers stochastic and deterministic population models, spatial models, predation, competition, diffusion models, diversity, as well as multivariate statistical techniques such as ordination, CCA, and discriminant analysis. + a classic, good reference - out of date, no exercises Pielou, E. C. (1974) Population and Community Ecology: Principles and Methods. New York: Gordon and Breach. 424 p., ISBN 0-677-03580-2 + lower-level more widely ranging coverage of mathematical ecology than her "Mathematical Ecology"; very clear development of theory. - no exercises. Renshaw, Eric (1991) Modelling biological populations in space and time. Cambridge Cambridge University Press, (Cambridge studies in mathematical biology 11) 403p., ISBN 0-521-30388-5 (hardcover 1991), ISBN 0-521-44855-7 (paperback 1993) An advanced book. Covers discrete and continuous, deterministic and stochastic models. Covers all the standard topics (competition, predator-prey, birth-death processes, epidemics) plus population growth models with time lags and spatial population models - no exercises Roberts, Fred S. (1976) Discrete Mathematical Models, with applications to Social, Biological and Environmental Problems. Prentice-Hall Rose, Michael R. (1987) Quantitative Ecological Theory--An Introduction to Basic Models. Baltimore: J. Hopkins Univ. Press, 203 p., ISBN 0-7099-2289-2, 0-7099-2288-4 Essentially the lecture notes for a course in theoretical ecology. Topics include population growth, competition, predation, simple ecosystems, complex ecosystems, and migration. + very clear, intuitive development of the mathematics - no exercises, primitive typesetting. Roughgarden, J. (1989) Perspectives in ecological theory. Princeton: Princeton Univ. Press, 394p., ISBN 0-691-08507-2, 0-691-08508-0 Roughgarden, J. (1998) Primer of ecological theory. Prentice Hall, New Jersey, 456 p. An overview with extensive MATLAB code of many areas of ecological theory including basic genetics and ecosystems. Schneider, David C. (1994) Quantitative Ecology: Spatial and Temporal Scaling. Academic Press, 395p. ISBN 0-12-627860-1. Focuses entirely on issues of scale in ecology, with very basic models for allometry, spatial scaling and units and dimensionality discussed. Segel, Lee A. (1984) Modeling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge Univ. Press. Smitalova, Kristina & Sujan, Stefan (1991) A Mathematical Treatment of Dynamical Models in Biological Science. New York: Ellis Horwood, 183p., ISBN 0-13-221771-6, 80-224-0245-1 Deals exclusively with the mathematical theory of community models-- single species, two-species, and n-species ending with a chapter on chaos theory in ecology. + many references - no exercises Starfield T. M. and A. L. Bleloch (1986) Building models for conservation and wildlife management. New York: Macmillan, (Biological resource management) 253p., ISBN 0-02-948040-X + easy to read, plenty of good explanation Starfield, A. M., Smith, K.A. & Bleloch, A.L. (1990) How to model it: problem solving for the computer age. New York: McGraw-Hill, 206p., ISBN 0-07-005897-0 + good introduction to the modelling process in general, comes (in the 2nd ed.) with a disk that contains the spreadsheet examples and WinEXPERT (a small expert system) Suter, G. W. (ed. and principal author; contrib. authors: L. W. Barnthouse et al.) (1993) Ecological Risk Assessment. Lewis Publishers, Chelsea, Michigan 48118 USA Taubes, Clifford Henry (2001) Modeling Differential Equations in Biology. Prentice-Hall, Inc. Upper Saddle River, NJ. ISBN 0-13-017325-8 Unique in that it includes within each chapter that describes some aspect of differential equations, appropriate recent scientific journal articles that illustrate the mathematics discussed. Thornley, John H. M. and Ian R. Johnson (1990) Plant and Crop Modelling. Clarendon Press, Oxford, Tuchinsky, Philip M. (1981) Man in Competition with the Spruce Budworm--An Application of Differential Equations. Boston: Birkhauser, 77 p. + careful derivation of one of the classic mathematical models in ecology, exercises with solutions Vandermeer, J. H. (1981) Elementary Mathematical Ecology. Wiley and Sons, NY, 294p. 1981 Malabar, Fla: Krieger, 1990, 294p., ISBN 0-89464-465-3 programmed learning text + lots of exercises with solutions - boils away a great deal of the biology in favor of the math, holes in coverage Wilson, Will (2000) Simulating Ecological and Evolutionary Systems in C. Cambridge University Press, 301 p. Covers numerous ecological models, simulated using an individual-based perspective. Relatively few evolutionary examples. Yodzis, Peter (1989) Introduction to theoretical ecology.New York (etc.): Harper & Row, 384 p., ISBN 0-06-047369-X + good intuitive development of the equations, many exercises and references