Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions

Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations ( red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated ( white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year (catastrophe) is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme ( catastrophic) events can occur ( strong noise) or sensitivity is high ( overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk.