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The calculation of production, reproduction and total growth in the autonomous Vansickle equation

The calculation of production, reproduction and total growth in the autonomous Vansickle equation 1. The VanSickle equation is derived from the Von Foerster equation by a change of variable from age to weight with growth not depending on time explicitly. 2. The author's, previous treatment of Pechen's first graphical method for calculating production is corrected. 3. Pechen's estimate, here called total growth, is reduced to one integration. 4. Production (Thienemann's definition) amounts the calculation of one Stieltjes integral. 5. Production, thus defined, equals reproduction in weight plus total growth (Pechen's estimate). 6. The fact that reproduction is continuous allows an easy estimate of the birth-rate from the age distribution of the number of organisms, by using the Von Foerster boundary condition. 7. The Von Foerster functional boundary condition is consistent with a particular reproductive mechanism called “differentiable reproduction”, in which no discontinuities in the organism's weight because of births are allowed. 8. Numerical calculations on Pechen'sCyclops data are explicitly represented. Production comes at 18.4 instead of 16.6. An averageCyclops individual may spend 13% of its production on reproduction. 9. The calculation of production with the aid of the Stieltjes integral shows that the tail of the age or weight distribution comprising the oldest individuals might be very important. 10. Finally there is a discussion on open problems; mathematically speaking there is still a tremendous lot to be done. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aquatic Ecology Springer Journals

The calculation of production, reproduction and total growth in the autonomous Vansickle equation

Aldenberg, Tom
Aquatic Ecology , Volume 13 (1) – Nov 8, 2005
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References (8)

Publisher
Springer Journals
Copyright
Copyright
Subject
Life Sciences; Freshwater & Marine Ecology; Ecosystems
ISSN
1386-2588
eISSN
1573-5125
DOI
10.1007/BF02260302
Publisher site
See Article on Publisher Site

Abstract

1. The VanSickle equation is derived from the Von Foerster equation by a change of variable from age to weight with growth not depending on time explicitly. 2. The author's, previous treatment of Pechen's first graphical method for calculating production is corrected. 3. Pechen's estimate, here called total growth, is reduced to one integration. 4. Production (Thienemann's definition) amounts the calculation of one Stieltjes integral. 5. Production, thus defined, equals reproduction in weight plus total growth (Pechen's estimate). 6. The fact that reproduction is continuous allows an easy estimate of the birth-rate from the age distribution of the number of organisms, by using the Von Foerster boundary condition. 7. The Von Foerster functional boundary condition is consistent with a particular reproductive mechanism called “differentiable reproduction”, in which no discontinuities in the organism's weight because of births are allowed. 8. Numerical calculations on Pechen'sCyclops data are explicitly represented. Production comes at 18.4 instead of 16.6. An averageCyclops individual may spend 13% of its production on reproduction. 9. The calculation of production with the aid of the Stieltjes integral shows that the tail of the age or weight distribution comprising the oldest individuals might be very important. 10. Finally there is a discussion on open problems; mathematically speaking there is still a tremendous lot to be done.

Journal

Aquatic Ecology – Springer Journals

Published: Nov 8, 2005

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