JOHN J. ALEXANDER Universily of Cincinnati Cincinnati. 45221
A Popular Approach to Reaction Kinetics Michael P. S. Collins Buyero University P.M.B. 3011 Kano, Nigeria
a stable population density.
Ideas and phrases such as "steady state approximation," "zero population growth" and the like are penetrating everyday life. In the undergraduate physical chemistry course there is scope for interjecting some rigor into these concepts by making reference to population dynamics when discussing kinetic problems. nonulation An elementarv introduction to basic bioloeical . . dynamics including discussion of the logistic equation and the Verhulst-Pierls curve is rewired hackeround. The introand ~ a y n a r d - S m i t h(2) are ductory texts by Solomon most useful. It must be stressed that ecoloeical oooulation dynamics do not necessarily lend themselvestto easy analysis; but then i t may he pointed out that many chemical reactions are like this (3)! If desired, additional links may he made between molecular kinetics and population dynamics. In particular, there is a fruitful analogy between microorganism-substrate population dvnamics in the chemical hemostat and Michaelis-Menton enzyme.substrate kinetics. Williamson ( 4 ) gives a neat summarv of this with an analvsis uf the wurk of Herhrrt. et n l . ( 5 ) on Aerobacter cloacae.
(i)
Literature Cited (1) Solomon. M. E., "Population Dynamics: Edward Arnold & Son. Leeds, 1976. (2) Smith, J. M.. "Mathematical Idem in Biolugv,"Cambridge University Press, l96S. (3) Farrow. L. A.andEdelaon,O.,lnlamsl. l lChom Kin., 6,787 (1974). (4 Williamson, M. -TheAnalyslr .,fBiOlG$.ieal Pop"iatim8,"EdvB.d Amold & son, Loeds, 1912. ( 5 ) Herberl,D.,Ellsworth,R.,sndTeilinp,R.C.,J. Cen. Micmbiol., 14,601 (1956). Question
Mathematical models, closely analogous to those used for chemical kinetics, can be used in other contexts. Here we consider a verv simole model for the dvnamics of wild animal population density. Under some circumstances for certain soecies the oopulation densitv (number of animals per km2 ahalogous to the chemical concentration in molecules~perml) is found to maintain a reasonably steady value over a considerable period of time. A particular species of predatory animals, M, lives as mated pairs (M-MI. These pairs reproduce an average once per year and an average of 2.2 offspring survive to maturity. ra)
two competing individuals (either male or female in our model):
On theassumption that no mnturcanimalsdir cff,calculntetha time r~quiredior the pupulstiw 10 mcrease hy a factor of t i ) 10 and ( i l l 10n. Thp pruccss ma). br reprrrrn~wlhy
(b) Such predatory animals die off, in fact, by two principal mechanisms: first, a "natural death," analogous to a unimolecular C1 chemical reaction M
