Environmental Engineering Reference
In-Depth Information
For the understanding of time-dependent dynamics, numerical approximation is
necessary. This, of course, poses the problems both that numerical results may be in
error and that generalizations based on numerical results are difficult. Plausibility
considerations are to some extent inevitable. Personal experience of the modeller
who works with differential equations is not only the basis to adequately understand
and formulate the code, but also generates a kind of gut feeling for solutions that are
adequate to capturing the relevant ecological patterns and processes. A brief outline
on some of the major points to be considered for successfully working with this
model category can be found at
http://www.mced-ecology.org
.
With the beginning of the elementary contributions from Malthus (late eigh-
teenth century), James Lotka and Vito Volterra (1925, 1926), and Fisher
(1930-1940) the method of differential equations is well established in biology
and ecology; for a detailed historical overview: see Chap 3; for further develop-
ments: see Chap. 7; example applications are given in Chaps. 17-20.
Since their introduction, differential equations have had a leading role in eco-
logical modelling. During the last decades the field of ecological modelling has
expanded considerably. Today, differential equations still contribute to scientific
progress, though side by side with a wide variety of other approaches which are
outlined in the following chapters.
Further Readings
Many textbooks exist on ordinary differential equations, often with a very specific
focus. A list of topics relating to the ecological context can be found at
http://
homepage.ruhr-uni-bochum.de/michael.knorrenschild/embooks.html
(Knorrenschild
M (2010) List of textbooks on ecological modelling). From our perspective we would
select the following topics and webpages that expand on the contents provided in this
chapter:
Edelstein-Keshet L (2004) Mathematical models in biology, 2nd edn. SIAM, 586 p
Jeffries C (1989) A workbook in mathematical modeling for students of ecology. Springer,
Heidelberg
Kot M (2001) Elements of mathematical ecology. Cambridge University Press, Cambridge,
http://
www.cambridge.org/us/catalogue/catalogue.asp?isbn
ΒΌ
9780521001502
Sharov A (n.d) Quantitative population ecology. On-Line Course.
http://home.comcast.net/~sharov/
PopEcol/popecol.html
William SC, Gurney WSC, Nisbet RM (1989) Ecological dynamics. Oxford University Press,
Oxford, New York.
http://www.stams.strath.ac.uk/ecodyn/
Wiki topic on differential equations.
http://en.wikibooks.org/wiki/Differential_Equations
Yodzis P (1989) Introduction to theoretical ecology. Harper & Row, New York
