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9/7/04
Elements of Mathematical Ecology

Reviewed by Victor Niederhoffer

 

The book Elements of Mathematical Ecology by Mark Kot contains a gold mine of suggestive techniques and applications for those interested in markets and other fathomless subjects where populations cover a landscape with different niches and resource limitations. 

It contains chapters on population models with limited and unlimited resources in continuous and discrete time, delay models, predator prey models, competition and mutualism models, and harvest models. It covers stochastic growth, branching, bifurcation, and cycle  processes. Good biological examples, especially involving the author's hobby birding, and diagrams are given to supplement the mathematical techniques which mainly involve various extensions of differential and difference equations, with emphasis on open form, intuitive and simulatory solutions.

I found the sections on the interactions between one market and the other, i.e. the predator prey, competition and mutualism sections particularly relevant to trading. And all markets should be looked at in terms of their changing structure of positive and negative influence on others, with particular reference to mutualistic markets.

The author describes mutualism in seed dispersal by animals, pollination mutualism (by insects and flowers, digestive mutualisms (the bacteria of cows) and protection mutualisms ( the ants and the acacias and the clown fish and the anemones) .. many simple models based on these mutualisms lead to an unlimited growth which has been called "an orgy of mutual benefaction."

If this and other areas of interaction can be quantified and predicted, an imperial path of beneficent growth for one's profits could be rewarding in two markets at the same time. And the gap between such things as the dismal performance of pairs trading in practice versus the excellent retrospection it shows on paper might be reduced.

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