Introduction for biologists

Summary

Striking a balance

If we repeated Noah's experiment — starting a new ecosystem with one couple of each species — we would certainly not expect a restoration of the old régime. Numbers matter. The fate of a population depends on the frequencies of other populations.

The interdependency of different species can be wonderfully intricate. Darwin relished working out ‘how plants and animals, most remote in the scale of nature, are bound together by a web of complex relations’, pointing out, as an instance, that bumble-bees are indispensable to the fertilization of heartsease, and that field-mice cause havoc among the nests and combs of bumble-bees. Since the number of mice is largely dependent on the number of cats, it is consequently ‘quite credible that the presence of a feline animal in large numbers might determine, through the intervention first of mice and then of bees, the frequency of certain flowers!’

This self-regulation of population frequencies has been a dominant theme of mathematical ecology. It started in the 1920s with Alfred Lotka modelling the cycle of mosquitoes and humans in transmitting malaria, and Vito Volterra analysing the dynamics of predators and prey among fish in the Adriatic. They came up with differential equations describing the dynamics of such systems. But the first generations of mathematical ecologists concentrated mostly on investigating static aspects of ecological communities.