Fuzzy chaos modelling in ecology and economics

The aim of this post is to draw the attention of economists to some results obtained for ecological systems, because they may provide insights into how economic systems work. In a paper published a few years ago (Klaus Rohde and Peter P. Rohde 2001. Fuzzy chaos: reduced chaos in the combined dynamics of several independently chaotic populations. American Naturalist 158, 553-556) we have shown that chaos in populations is reduced in metapopulations consisting of several largely independent subpopulations with different reproductive rates. Examples are given in figures 1 and 2. Population sizes x are plotted as fractions of carrying capacities (0-1) at different reproductive rates r of the population. Figure 1 shows a bifurcation diagram for a single population; the insets show population sizes plotted against time for a few selected reproductive rates. Note that chaotic fluctuations in population size begin at r=3.57. Figure 2 shows a bifurcation diagram for a metapopulation consisting of 5000 subpopulations, illustrated only for reproductive rates of r=3.50 and larger. Note that there still are chaotic fluctuations, but the width of the fluctuations is significantly reduced.


Figure 1: Bifurcation diagram for a single population.
Fig.2. Bifurcation diagram for 5000 subpopulations.

Figure 2: Bifurcation diagram for a metapopulation consisting of 5000 subpopulations.

This may suggest that chaotic fluctuations are much stronger in single large economies, for example due to globalisation, than in the world economy consisting of national economies that are largely separated.

I invite comments to point out any errors in the argument.

recent papers

This is a test run, i.e., my first blog. I am using it to draw your attention to some recent papers on ecological/evolutionary modelling done jointly with Dietrich Stauffer of the Institute of Theoretical Physics, Universität Köln, Germany. Dietrich Stauffer is one of the leading computational physicists in the world. His “Introduction to Percolation Theory” has been cited around 4000 times. His many papers include applications of models to physics, chemistry, genetics, immunology, language evolution, geology and biology. His most recent book, published jointly with some colleagues, is on “Biology, Sociology, Geology by Computational physicists” (Elsevier 2006).

Our papers are:

Rohde, K. and Stauffer, D. 2005. Simulation of geographical trends in the Chowdhury ecosystem model. Advances in Complex Systems 8, 451-464. http://arxiv.org/q-bio/0505016

Stauffer, D and. Rohde, K. 2006. Simulation of Rapoport’s rule for latitudinal species spread. Theory in Biosciences 125, 55-65. http://arxiv.org/q-bio/0507033

Stauffer, D., Schulze C., Rohde K. submitted. Habitat width along a latitudinal gradient. View et Milieu http://arxiv.org/q-bio/0612012

In the first of these papers, we use the Chowdhury ecosystem model to analyse latitudinal gradients in species diversity. We found that complexity of foodwebs increases with time and at a higher rate at low latitudes. Keeping many niches empty makes the results correspond more closely to natural gradients.

In the second paper, we use the Chowdhury ecosystem model to test Rapoport’s rule, according to which latitudinal ranges of species are greater at high latitudes. We did not find support for the rule, in agreement with empirical studies.

In the third paper, we use the Chowdhury ecosystem model to test the latitude-niche breadth hypothesis, which explains the higher species diversity in the tropics by narrower niches there. We did not find support for the hypothesis, in agreement with some empirical studies.

I have examined the same ecological/evolutionary problems in a number of earlier papers using empirical data. References can be found at http://www-personal.une.edu.au/~krohde/