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Frontiers in Mathematical Biology (Paperback, Softcover reprint of the original 1st ed. 1994)
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Frontiers in Mathematical Biology (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: Lecture Notes in Biomathematics, 100
Expected to ship within 10 - 15 working days
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From a mathematical point of view, physiologically structured
population models are an underdeveloped branch of the theory of
infinite dimensional dynamical systems. We have called attention to
four aspects: (i) A choice has to be made about the kind of
equations one extracts from the predominantly verbal arguments
about the basic assumptions, and subsequently uses as a starting
point for a rigorous mathematical analysis. Though differential
equations are easy to formulate (different mechanisms don't
interact in infinites imal time intervals and so end up as separate
terms in the equations) they may be hard to interpret rigorously as
infinitesimal generators. Integral equations constitute an
attractive alternative. (ii) The ability of physiologically
structured population models to increase our un derstanding of the
relation between mechanisms at the i-level and phenomena at the
p-level will depend strongly on the development of dynamical
systems lab facilities which are applicable to this class of
models. (iii) Physiologically structured population models are
ideally suited for the for mulation of evolutionary questions.
Apart from the special case of age (see Charlesworth 1980, Yodzis
1989, Caswell 1989, and the references given there) hardly any
theory exists at the moment. This will, hopefully, change rapidly
in the coming years. Again the development of appropriate software
may turn out to be crucial."
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