There are two theories on the relationship between biodiversity and stability. The ripple effect states that the more species there are, the more likely that any sort of disaster which affects one taxa will automatically affect the whole system, since all species interact very heavily due to lack of space. Therefore, primary systems with few taxa are considered to be more stable. Studies on the effects of environmental disturbances on both primary and climax community level reef ecosystems support this theory.
The other theory states that stability increases with an increase in biodiversity. In the late eighties, James Lovelock built a computer model called 'Daisyworld', of which one of the outcomes was that the more species there were in the ecosystem, the greater its stability. In Daisyworld, a planet/star system identical to ours was created, the only difference being that the only two species on the world were white and black daisies. In the distant past, only the equatorial regions would have received enough heat for the daisies to grow. The dark daisies, which absorb heat, would have flourished on this cold world. Gradually the dark daisies would have covered the planet, eventually warming the overall temperature through their absorption of heat.
As the star's luminosity increased, the temperature would become much warmer, and the lighter daisies, reflecting heat and light, thereby staying much cooler, would become the dominant species. Ultimately, a steady state is reached, with a mean albedo close to what is needed for optimum daisy growth. As the star gradually heats up, the planet is eventually covered in white daisies, until the heat becomes so great they are insufficient to keep a decent temperature. Daisyworld finally expires. (Lovelock, 1995)