Researchers assess the risk of species extinction with conservation models that combine factors that drive down populations—including habitat loss, hunting and overfishing—with the probability of chance disasters affecting the group. Even if human activities greatly affect a species, “all populations that go extinct [ultimately] suffer a string of unfortunate random events, such as a fire, that wipe out the last individuals,” says Brett Melbourne, a mathematical ecologist at the University of Colorado at Boulder.

Until recently, mathematical models of extinction risk included only two types of randomness. The first—variability in the environment, such as rainfall or temperature changes—impacts birth and death rates across the entire population. The second involves random events affecting select individuals within a group. Siblings may have the same probability of dying in a given year, for example, but only one may be lost to, say, an accidental drowning or other chance event.

Ecologists have long known that other types of randomness influence population dynamics, but computational limitations in the early 20th century forced scientists to simplify traditional models. By observing groups of flour beetles in the laboratory, Melbourne and Alan Hastings, a mathematical ecologist at the University of California, Davis, demonstrated that random variations in sex ratios and physical differences, such as body size, greatly contribute to the overall threat of extinction. A large number of males born into a small group, for instance, limits the reproductive potential of the population.

As populations decrease, they become more vulnerable to chance events that precipitate extinction. “With our current understanding, we think that the population size must be very small. But when you add in these new factors, even larger populations may be at risk,” Melbourne explains. Stuart Pimm, a conservation ecologist at Duke University, emphasizes that the model cannot indicate which new species may be threatened with extinction. Rather, he says, “it tells us which species in the emergency room is most at risk” and identifies those that may be in more imminent danger than previously recognized.

From the standpoint of conservation management, “their work could potentially have a big impact, but we need to explore its implications for real species,” notes Sandy Andelman, a senior director at Conservation International. She has recently teamed up with Melbourne to test if his laboratory results can be generalized to the real world. They plan to apply the new model to species such as nonhuman primates and African elephants, for which a great deal of population data exists.

Ultimately, the scientists will examine a variety of populations—from threatened species to those that are critically endangered—to explore the full implications of the model. With 16,000 plant and animal species now threatened by extinction, the stakes couldn’t be higher for global biodiversity.

Note: This article was originally printed with the title, "Random Challenges".