Life history and population size impact both ecological dynamics and evolutionary trajectories[76,77], In turn, population size is inherently linked to adaptive potential, as larger populations have more standing genetic variation available for natural selection, [38,78] (see section 2). Thus, the importance of phenotypic plasticity in adaptive evolution depends on changes in population size, which also influences the likelihood of local extinctions[79–82]. Such impacts of population size depend on life history; long-lived species can persist longer at small population sizes than short-lived species, which can collapse quickly[83,84].

Much evidence shows that higher rates of environmental change lead to decreases in population size[85], suggesting that rates of local extinction rates of many bird and mammal species will increase as the rate of climate warming exceeds the rate of adaptive responses[86]. However, population size can increase in some species under higher rates of environmental change. For instance, bird species adapted to drier climates can utilize agricultural land and are predicted to persist in and colonize into drier habitats under climate change[87]. Mechanistically, however, the explicit links between increasing rate of environmental change and population dynamics remains largely unresolved.

The interplay between increasing environmental variability and population size has now been intensively studied both theoretically and empirically[88]. Despite the usual assumption that a more variable environment is detrimental for populations, recent syntheses across systems show that the effect of environmental variability is highly context-dependent and can have positive as well as negative effects on population growth rates[24,89]. Demographically-explicit theories have made important progress in elucidating the mechanisms for why increased environmental variability can have different influences on population size[90]. The mechanisms that produce the disparities in demographic responses to variable environments usually depend on system-specific density-dependent effects, which influence transient dynamics of population trends[91].

Temporal autocorrelation in the environment has gained much attention in population biology and climate change research[31,34]. Here too, the emerging message is that autocorrelated environments can have positive[92,93] or negative[93] impacts on population size and extinction risk, depending on life history strategies[94], and phylogenetic history[95]. For example, annual plants have lower extinction risks when the environment is more positively temporally autocorrelated compared to perennial plants[93]. Moreover, in some cases, population size itself can become more variable through time under positive environmental autocorrelations, thereby increasing extinction risk[34].