Description
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
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