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2003-Knorrenschild-Gross-Text Books on Mathematical Modeling in Biology

Author(s): Michael Knorrenschild


Keywords: biology Mathematical Biology textbook text

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Resource Image Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild,


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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 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



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



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,


   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  



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,



Mazumbar, J. (1989) An Introduction to Mathematical Physiology and

Biology. Cambridge: Cambridge Univ. Press, 208 p., ISBN 0-521-37002-7,


    Differential equation modeling introduction, including applications

    to diffusion, population biology, biogeography, biofluids, and



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.


    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



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



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



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



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



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


    programmed learning text  + lots of exercises with solutions - boils

    away a great deal of the biology in favor of the math,  holes in



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



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