Differential Models for Evolutionary Compositions

General systems are frequently decomposable into parts and these parts can evolve in time or space, a frequent occurrence in the field of Geosciences. In most cases, fitting models to forecast future states of the system is a goal of the analysis. Modelling interactions between parts may also be of...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical geosciences 2014-05, Vol.46 (4), p.381-410
Main Authors: Egozcue, Juan José, Jarauta-Bragulat, Eusebi
Format: Article
Language:English
Subjects:
Chemistry and Earth Sciences
Computer Science
Crystals
Differential equations
Earth and Environmental Science
Earth Sciences
Evolution
Evolutionary biology
Geosphere
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical models
Modelling
Physics
Regression
Reserves
Statistics for Engineering
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:General systems are frequently decomposable into parts and these parts can evolve in time or space, a frequent occurrence in the field of Geosciences. In most cases, fitting models to forecast future states of the system is a goal of the analysis. Modelling interactions between parts may also be of common interest. The system can be analysed from different points of view; the traditional one consists in modelling each part of the system in time. Alternatively, modelling the evolution of the parts as proportions is proposed herein and attention is centred on the compositional evolution. The compositions are expressed in orthogonal coordinates (ilr) and then modelled using first-order differential equations with constant coefficients. Simple models are shown to be very flexible, including many of the standard growth curve models. The models are fitted using regression techniques on the integrated coordinates. The use and interpretation of these differential models is illustrated with several examples: a simulated example; urban waste in Catalonia (Spain); oil production and reserves; and growth of a luzonite crystal.
ISSN:1874-8961
1874-8953
DOI:10.1007/s11004-014-9533-2