What kind of maternal effects can be selected for in fluctuating environments?

Just as phenotypic plasticity can evolve when developing individuals get informational cues about their future adult environment, deterministic maternal effects, where offspring trait values depend on the maternal environment, can evolve when mothers gain reliable information about the environments their offspring will face. Randomizing maternal effects (a type of diversifying bet hedging), where offspring trait values are randomized, can evolve by natural selection even when information about future environments is unavailable. We investigate selection on both randomizing and deterministic maternal effects in environments that show correlated fluctuations between two environmental states. We compare the strength of selection for deterministic and randomizing maternal effects and explicitly consider maternal fitness costs of producing offspring with different phenotypes. Only a small set of environmental parameters allow randomizing maternal effects to outcompete deterministic maternal effects; not only must there be little or no information available about future environments, but the frequency of each environment must fall within a narrow range. By contrast, deterministic maternal effects can always invade an ancestral state lacking a maternal effect even if the amount of environmental information available is low. The long-term outcome may involve offspring trait value randomization but only if trait values first evolve to cause extreme differences in environment-specific fitness. Overall, deterministic maternal effects are more likely to evolve by natural selection than randomizing maternal effects.