In general, stability means the ability of a system to resist perturbations in the long term. For an ecosystem or biological community, it means to persist in its changing (or fluctuating) environment and in spite of disturbances. Persistence of a multispecies community means therefore that no species goes extinct, nor does any one exhibit population outbreaks, as an outbreak of a species population implies eventual disruption of its resource (or host) species. A common paradigm of ecology consists of the idea that more complex communities, that is, those which involve more species (greater biodiversity) and more interactions among and within them, are more stable than those of lesser complexity. A sound rationale behind the paradigm considers communities of greater diversity to be able to persist under a greater variety of environmental conditions or/and perturbations.

On the one hand, the paradigm relies on the evidence from field studies and laboratory experiments. For example, classical experimental prey-predator systems of two species often prove to be unstable; pest population outbreaks are more typical of agrocenoses than of natural communities, the effects being more disastrous when the crops are monocultures. In contrast, the communities of tropical rain forest, rich in their species composition and interspecies relations, exhibit stable functioning: there are no population outbreaks, while oscillations in the population sizes are much less pronounced than those in boreal forest with lesser species diversity, yet greater population sizes. Boreal communities of simpler structure, amenable to sharp oscillations in population sizes, are thus considered unable to damp out the impacts of perturbations.

On the other hand, each of these arguments or observations may also find another interpretation with no appeal to community complexity or diversity. For instance, the greater stability of natural communities as compared to agricultural ones may rather be caused by better adaptation of the individual species as outcomes of longer coevolution processes than by community organization; the lesser stability of the boreal communities versus the tropic ones can be attributed to destabilizing effects of stronger climatic variations.

So, the debate could hardly be resolved along traditional ways of ecological thinking, and a new dimension was added to the problem by Robert M. May, more than 30 years ago, who coined the 'stability-versus-complexity' theme into the field of mathematical models for multispecies community dynamics. Within the models, the notion of stability always finds a formal definition, hence a quantitative measure, while explicit parameters of a model (like the number of species involved, the number of trophic (or/and other) links among them, the strength of interactions among/within species, etc.) contribute apparently to the greater or lesser complexity. Thereafter, these two pre-conditions provide a formal ground to speculations on whether complexity begets stability, and the further sections illustrate various modes ofreasoning typical for those speculations.

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