Lynch and his co-author Reinhard Burger’s big insight was that no amount of genetic variation could keep a population perfectly on track with a moving target. Genes determine how the expression of a heritable trait (or phenotype) is distributed across a population. Often this distribution is modeled as a bell curve: For a trait like body type, some individuals might be fatter than the ideal, others might be skinnier, but most fall somewhere towards the middle. The key to survival, Lynch and Burger found, was that the average expression of the trait couldn’t lag too far behind the optimal expression in the new environment. If it remained close, the population could hang on.

But evolution can only speed up so much, and Lynch found that for a population to avoid extinction the environment would have to change relatively slowly. For a species to survive, it would need leeway from the environment — in scientific terms, “on the order of 1 percent or fewer of a phenotypic standard deviation per generation,” as Lynch and Burger wrote.

Together, these models outline the conditions under which evolution can come to the rescue, and the limits of that power. To beat extinction, according to Gomulkiewicz and Holt’s models, a population should start out large, not decline too quickly, not need to transform too dramatically and have ample genetic variation to make that transformation. In addition, Lynch’s models show that the environment can’t be changing too fast.