Bet-hedging theory addresses how individuals should optimize fitness in varying and unpredictable environments by sacrificing mean fitness to decrease variation in fitness. So far, three main bet-hedging strategies have been described: conservative bet-hedging (play it safe), diversified bet-hedging (don't put all eggs in one basket) and adaptive coin flipping (choose a strategy at random from a fixed distribution). Within this context, we analyse the trade-off between many small eggs (or seeds) and few large, given an unpredictable environment. Our model is an extension of previous models and allows for any combination of the bet-hedging strategies mentioned above. In our individual-based model (accounting for both ecological and evolutionary forces), the optimal bet-hedging strategy is a combination of conservative and diversified bet-hedging and adaptive coin flipping, which means a variation in egg size both within clutches and between years. Hence, we show how phenotypic variation within a population, often assumed to be due to non-adaptive variation, instead can be the result of females having this mixed strategy. Our results provide a new perspective on bet-hedging and stress the importance of extreme events in life history evolution.

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Population synchrony over various geographical scales is known from a large number of taxa. Three main hypotheses have been put forward as explanations to this phenomenon. First, correlated environmental disturbances (so called Moran effect). Moran showed that at least for linear models, the population synchrony would exactly match that of the corresponding environment. Second, the migration, or dispersal, of individuals is liable to cause population synchrony. Third, nomadic predators have been proposed as a synchronising mechanism. In this paper, I analyse the first two explanations by linearizing a general population model with spatial structure. From this linear approximation I derive an expression for the population synchrony. The major results are: 1) Population synchrony can vary significantly depending on the timing of the population census. 2) The environmental correlation is always important. It sets the ‘base level’ of synchrony. 3) Dispersal is only an effective synchronising mechanism when the local dynamics are at least close to unstable. 4) These results are valid even in a model with delayed density dependence – with possibly cyclic dynamics. Time lag structure has little effect on synchrony.
 Some of the predictions presented here are supported by data from the literature.

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In this paper, we give simple explanations to two unsolved puzzles that have emerged in recent theoretical studies in population dynamics. First, the tendency of some model populations to go extinct from high population densities, and second, the positive effect of autocorrelated environments on extinction risks for some model populations. Both phenomena are given general explanations by simple, linear, sto‐chastic models. We emphasize the predictive and explanatory power of such models.