Conclusion

The discovery that simple non-linear relationships, common in ecological systems, could generate extremely complicated dynamics was nothing short of a revelation. The associated finding that these complicated dynamics exhibited extreme sensitivity to initial conditions carries with it implications for all of ecology. In the intervening three decades since these discoveries were made, ecologists have worked hard to find evidence for this chaos in natural populations. Chaos has been formally defined, and methods have been developed to help test for it in the short and noisy data sets that ecologists are forced to deal with. We now know that populations can indeed be manipulated to generate all the features of chaos seen in mathematical models, and there is reasonable evidence of chaos arising in certain cases, such as childhood measles and some microbial systems. So, chaos can occur. Nevertheless, the majority of attempts to find chaos in natural populations have either drawn a blank or remain controversial.

Early in the ecological study of chaos, Schaffer and Kot50 likened chaos to 'the coals that Newcastle forgot'. With painful irony, their paper was published shortly after the UK national miners' strike and all of the coal pits in the Newcastle area are now closed (as from 2007, only six pits remain in operation in the entire United Kingdom). Surveying the literature here leads one to suggest that many of the richest seams (to stretch the coal metaphor) of available ecological data have now also been explored, and few have provided much return. There may be good reasons why natural populations do not exhibit chaos, but only time will tell whether chaos is indeed rare.

Given the wonderful diversity of the natural world and knowledge that many systems have the propensity to exhibit chaos, perhaps a better question to have asked is 'when and how often are natural systems chaotic?' rather than 'is this system chaotic?'. We have seen already that voles can exhibit very different dynamics in different populations, and both the blowfly and the lynx data are suggestive of a marked change in dynamics at some point in their history. Likewise, flour beetles can exhibit a range of different dynamics dependent on underlying experimental conditions. So, it is perhaps naive to characterize a population as 'non-chaotic' or 'chaotic', because dynamics can change according to the prevailing conditions. Human activities could yet turn non-chaotic dynamics into chaotic dynamics by increasing the degree of non-linearity involved—as has been suggested for some fisheries.90 This may particularly be the case for insect pests, such as the migratory locust mentioned in our opening paragraph, if drastic control measures are only implemented if pest density reaches a high level.73

Chaos theory continues to grow and develop in a variety of scientific fields where it has found wide application. As May noted in one of his early seminal papers,9 'Not only in research, but also in the everyday world of politics and economics, we would all be better off if more people realized that simple non-linear systems do not necessarily possess simple dynamic properties'.

Ecologists are now much more aware of the subtle effects of non-linearities, and appreciate the wide variety of dynamical behaviours they can generate. Yet the truly surprising thing in all this is how long it took scientists to discover chaos. As James Yorke, one of the early pioneers, has recently said 'I continue to wonder, if nearly all scientists missed this pervasive phenomenon, what other obvious phenomenon might we all be missing now?'.91

Named after the mathematician Benoit Mandelbrot, the Mandelbrot set has become one of the icons of chaos theory. This rather complex object is generated by a relatively simple set of rules and has self-similarity at different scales (hence fractal dimensions), such that zooming in one sees the same patterns at an increasingly finer scale. Due to their aesthetic appeal, fractals have long attracted the interest of graphic designers and artists. Image by TNS.

Named after the mathematician Benoit Mandelbrot, the Mandelbrot set has become one of the icons of chaos theory. This rather complex object is generated by a relatively simple set of rules and has self-similarity at different scales (hence fractal dimensions), such that zooming in one sees the same patterns at an increasingly finer scale. Due to their aesthetic appeal, fractals have long attracted the interest of graphic designers and artists. Image by TNS.

This page intentionally left blank

Was this article helpful?

0 0

Post a comment