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.
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.
February 4th, 2007 at 9:48 pm
I think this argument is flawed. At first glance it may appear to be convincing that chaos may be suppressed in many small disconnected economies than a single large one. The reason why this may appear to be the case boils down to a choice of how the degree of chaos is measured. For example, in the plots above the reason chaos is suppressed is due to averaging. We have many independent populations which are individually chaotic. We then plot the total population of all populations. Because the individual populations are evolving independently from one another it is obvious that the global population will exhibit supressed fluctuation. If you add many independent random functions they inevitably average out. However, because the total population is no longer chaotic, this is not to say the individual populations are not. They are.
Extending this idea to economics, suppose we have a multitude of economies that are completely independent. Of course, if we look at the sum of all these economies then by a simple averaging effect the sum will exhibit far less chaos than any constituent economy. However, this is a flawed way to measure chaos in the this context. The summation is irrelevant. What is of interest is how much chaos individual participants are subject to, not now much chaos is in the summation.
February 5th, 2007 at 10:31 am
Yes, this is an excellent comment: it makes the argument much clearer. It is obvious, of course, that chaos is suppressed in the global economy because fluctuations are superimposed, and that individual economies retain their own dynamics. But this is the point of the argument: because “peaks” and “troughs” of the fluctuations are out of phase, it may be possible to make “social” adjustments. In other words, “help” individual economies to survive their troughs. This would be much more difficult in a general, global slump.
February 5th, 2007 at 3:44 pm
I’m not sure what you mean by ’social adjustments’. It isn’t clear to me at all from what you’re saying that surviving troughs is more difficult in a globalized economy than segregated ones. What reason is there to believe this is the case?
February 5th, 2007 at 6:14 pm
Well, to put it in a nutshell: imagine a world economy which is completely “globalised”, without any economic boundaries, and imagine a world-wide economic collapse caused by excessive debts (or some other factors) at the centre of that economy, for example the United States. It seems to me that the social consequences would be disastrous, in particular for poorer countries, much more so than in a situation where national economies would have retained some degree of independence and would therefore be less affected by the collapse. Furthermore, it would probably be more difficult to get out of a world-wide recession than a more localised one.
February 9th, 2007 at 2:35 pm
> It seems to me that the social consequences would be disastrous, in particular for poorer countries, much more so than in a situation where national economies would have retained some degree of independence and would therefore be less affected by the collapse.
This may or may not be the case. In any case, it has nothing to do with your original argument on fuzzy chaos. I repeat what I said before - The apparent reduction in chaos is not real, it is an artefact of the measure you’ve chosen to measure chaos, by summing up the indivudiuals.
> Furthermore, it would probably be more difficult to get out of a world-wide recession than a more localised one.
What evidence is there to support this. I can think of good counter examples. For example, during the South East Asian economic collapse Australia survived virtually unscathed, despite the fact that our economy is closed linked with Asian ones. More to the point, this has nothing to do with fuzzy chaos as far as I can see.
February 9th, 2007 at 3:11 pm
“For example, during the South East Asian economic collapse Australia survived virtually unscathed, despite the fact that our economy is closed linked with Asian ones.” However, 1) much of Asia, Japan and China in particular, were relatively little affected by the crisis and Australia has much more important economic links with those countries than with the countries that were strongly affected, such as Thailand; 2) Malaysia also was relatively little affected, largely due to Mahatir’s economic measures which “shielded” Malaysia (if I recall this correctly). The latter point supports my argument (if it is correct: I did not check again, it is purely from memory).
“More to the point, this has nothing to do with fuzzy chaos as far as I can see.” In the fuzzy chaos model, subpopulations are superimposed, i.e., if one is close to a maximum and another to a minimum value, the superimposed values tend towards the mean, although each subpopulation still has its own dynamics. Applied to economics, although each national economy has its own dynamics, fluctuations of the global economy (the sum of all national economies) are levelled out, if national economies retain a degree of independence. Appropriate global measures may then facilitate support of economies badly affected by a crash.
February 17th, 2008 at 7:30 pm
I think that it is just a war of the genes - no matter in which organism they reside, they assort to survive.