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| Subject:
Mathematical sustainability models
Category: Science Asked by: evawi-ga List Price: $10.00 |
Posted:
04 Nov 2002 07:17 PST
Expires: 04 Dec 2002 07:17 PST Question ID: 98215 |
Did anyboby ever explore how to make mathematical models of "sustainability" in the meaning "sustainable management of natural resources". There is a new science called "sustainability science" and I found some of relevant wewpages concerning this on the internet. But I am searching in vain for a connection to mathematics. Maybe you can help? | |
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| Subject:
Re: Mathematical sustainability models
From: al_kane-ga on 04 Nov 2002 09:05 PST |
I'd recommend the following two sites: 1. The Alliance for Global Sustainability (AGS) <http://globalsustainability.org/> AGS is mainly a collaboration between four universities (ETH, MIT, UT, and CUT). Many others throughout the world also contribute to AGS. The main goal of AGS is to bring together researchers from all disciplines to understand, promote, and work towards sustainability issues on regional to global scales. Within the AGS site you can find links to mathematical model-based approaches to sustainability. Here's one example, <http://globalsustainability.org/Research/2002/#2116>. 2. MIT Joint Program on the Policy and Science of Global Change <http://web.mit.edu/globalchange/www/> The MIT Joint Program, which is partially tied to AGS, is mainly focused on climate change issues. These issues are, however, intimately tied to sustainability. I recommend this site because there is a detailed description of the mathematical model they use, <http://web.mit.edu/globalchange/www/if.html>. The model contains climate, ecosystem, chemistry, and economic modules that are all coupled to one another. The site also contains many links to publications that detail the various model components and applications of the model. One example is the following paper, which is related to global air quaility and climate, <http://web.mit.edu/globalchange/www/MITJPSPGC_Rpt24.pdf>. Good luck with your sustainability research. |
| Subject:
Re: Mathematical sustainability models
From: mathtalk-ga on 04 Nov 2002 10:01 PST |
Actually there is a huge amount of work done on this, under the rubrik of "mathematical ecology" and "predator-prey" models, generally using a continuous model (systems of ordinary differential equations) to show the viability and equilibria of multiple-species populations with and without "harvesting". About twenty years ago the creation of mathematical ecology programs (at graduate level education institutions) had a lot of momentum. I could provide references either to those programs or to the fruits of their research, but I suspect the keywords above will show you plenty of material. regards, mathtalk-ga |
| Subject:
Re: Mathematical sustainability models
From: evawi-ga on 05 Nov 2002 00:21 PST |
Sorry, but the sites you reccomend shows only non-mathematical models. Mathematical models have equations! The predatory-prey model is a classical example of a simple mathematical model, but it has nothing to do with the much bigger problem of "sustainable management of natural resources", which involves also human actions on nature. |
| Subject:
Re: Mathematical sustainability models
From: al_kane-ga on 05 Nov 2002 06:48 PST |
Just a couple of points regarding your distinction between 'computer' and 'mathematical' models. * Computer models are based on mathematical equations. By examining the various components of computer models you will find your connection to mathematics! * Sustainability issues are complex, and so it is difficult to imagine capturing all of the complexities in an equation or two. Thus, we turn to computers to simulate the sometimes hundreds of interconnected processes that take place simultaneously. For this reason, I believe that you'll have a difficult time finding one equation to describe sustainability. * If it's one equation that you're interested in, however, then take a look at the mass continuity equation, dc/dt = sources - sinks, (where c = mass). The mass continuity equation, for instance, can be used to investigate the nitrogen content in watersheds and forest canopies. Additional equations can be used for other nutrients, such as phosphorus. And humans impacts can play a role by contributing to the 'source' or 'sink' terms. Thus, in this way, very complex models can be built-up from this equation. * If you're interested in the above approach, then take a look at the text 'Earth System Science' from Charlson, Rodhe, and Jacobson, <http://www.amazon.com/exec/obidos/tg/detail/-/012379370X/ref=pd_sim_books_2/103-5790849-8969400?v=glance>. |
| Subject:
Re: Mathematical sustainability models
From: mathtalk-ga on 05 Nov 2002 07:43 PST |
Hi, evawi-ga: Although the simplest versions are "uncontrolled" two-species models, the Lotka-Volterra equations and variants have been used to investigate questions of harvesting and conservation. If this is of interest to you, you might take a look at this paper: "Harvesting and Conservation in a Predator-Prey System" J. Hoekstra and J. van den Bergh (Feb. 2001, Tinbergen Institute) http://www.tinbergen.nl/discussionpapers/01024.pdf and its accompanying references to the literature. A particularly interesting application, to my mind, is using these models to compare implications of fixed-quota versus fixed-effort constraints on harvesting. If you wish I could provide an answer that describes this issue in more mathematical detail. regards, mathtalk-ga |
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