Abstract
What rates of directional change are species likely to be capable of sustaining indefinitely such as in response to a warming climate? We derive estimates of the maximum rates of phenotypic change that populations can sustain in response to a directionally changing environment, using a quantitative genetics simulation model whose parameters are calibrated with data from natural populations. Sustainable directional change is largely limited to ≤2-4% of a trait standard deviation per generation, in agreement with an estimate derived from quantitative-genetic theory and with published field studies. Data from thirty-seven longitudinal field-studies of species' phenological responses to a warming climate yield rates of change that fall in the 68th-86th percentiles of our predictions for what populations can sustain, and there are suggestions that the rate of climate change may already have diminished their capacities to maintain these rates. Given the pace of climate change, species with generation times greater than four years may be especially at risk.