Bulletin of the National Speleological Society - ISSN 0146-9517
Volume 22 Part 1: 66-75 - January 1960
A publication of the National Speleological Society
Stochastic Models of
Rane L. Curl
A population of caves evolves from a population of cave precursors consisting of joint systems of different complexity, which are subject to the invasion of solvent water whose source, composition, and availability vary in space and time. Although phenomenological theories have had considerable success in identification and explanation of the succession of geomorphic processes responsible for cave development, these processes also produce manifestations in a cave population related to processes of a random or stochastic nature.
Stochastic models have been constructed to mathematically reproduce the evolution of a particular population manifestation, namely the distribution of cave lengths. Intuitively "simple" mechanisms for the rate of cave growth and decay have been used for this purpose. The theories provide a quantitative description of the evolution of cave length distributions and, conversely, some attributes of cave precursors which would lead to present-day length distribtuions. An estimate of the length distribution of all caves more than 100 feet long in West Virginia is used for these comparisons.
The complexity of the evolutionary mechanisms which are subjectively simple as well as mathematically tractable are perhaps contradictory; but stochastic-process concepts are essential for a more quantitative understanding of the cavern cycle, and simple models may serve as a point of departure.
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