Phenotypic plasticity plays a key role in modulating how environmental variation influences population dynamics, but we have only rudimentary understanding of how plasticity interacts with the magnitude and predictability of environmental variation to affect population dynamics and persistence. We developed a stochastic individual-based model, in which phenotypes could respond to a temporally fluctuating environmental cue and fitness depended on the match between the phenotype and a randomly fluctuating trait optimum, to assess the absolute fitness and population dynamic consequences of plasticity under different levels of environmental stochasticity and cue reliability. When cue and optimum were tightly correlated, plasticity buffered absolute fitness from environmental variability, and population size remained high and relatively invariant. In contrast, when this correlation weakened and environmental variability was high, strong plasticity reduced population size, and populations with excessively strong plasticity had substantially greater extinction probability. Given that environments might become more variable and unpredictable in the future owing to anthropogenic influences, reaction norms that evolved under historic selective regimes could imperil populations in novel or changing environmental contexts. We suggest that demographic models (e.g. population viability analyses) would benefit from a more explicit consideration of how phenotypic plasticity influences population responses to environmental change.

T he greatest challenges in ecology and evolution are in understanding how physical and biological processes that play out over extensive spatial, temporal, and taxonomic scales interact to affect the dynamics of genes, phenotypes, populations, and ecosystems. The fact that many biological properties are "scale-dependent" has been recognized for decades; biological systems tend to be extremely variable when observed at some scales but relatively invariant at others (Levin 1992). Scale-dependencies in biological systems are produced by non-linear interactions within systems, and from weak or negative covariances in system components across space and time. While fascinating ecologists for decades in terms of quantifying patterns in nature, scale-dependencies have received limited attention in exhibiting portfolio effects, which have important implications for understanding ecological processes and evolutionary dynamics.Here, we show how the "portfolio" concept (WebPanel 1) -a construct that developed out of simple probability theory and has been widely adapted in financial investment theory -applies across ecology and evolution, and provides a framework for understanding how organisms and ecosystems achieve stability in their dynamics despite inherent volatility in their components. The portfolio concept was developed to recognize that diversified financial investment portfolios tended to produce more stable returns than simple portfolios. Thus, the dynamics of financial systems have scale-dependencies analogous to biological systems: dynamics may be extremely volatile at small scales but less variable at more aggregated scales.Modern portfolio theory was first described through the use of graphical and simple analytical models to show the value of diversification for reducing risks in investment strategies (Markowitz 1952). These models introduced the idea that the selection of an efficient investment portfolio should assess the trade-off between the expected return and the variance of alternative asset collections.The key insight was recognizing that the variability of an aggregate portfolio depends critically on the covariation among the component assets. We contend that the nearly ubiquitous scale-dependencies in biological systems (ie that systems are often less variable when viewed at coarse scales than at fine scales; this is the emergent property of interest, where the whole behaves differently than the individual components; Levin 1992), generated by weak and negative covariation within their components, stabilize the emergent properties of many ecological and evolutionary processes. Examples are evident in phenomena ranging from the behavior of individual organisms, to population and ecosystem dynamics, and even to evolutionary strategies. These portfolio effects produce reliable biological functions in a world characterized by stochasticity and unpredictability, and provide underappreciated options for considering risk in natural resource management and conservation. n Species diversity and communitiesEc...

Summary1. Populations are shifting their phenology in response to climate change, but these shifts are often asynchronous among interacting species. Resulting phenological mismatches can drive simultaneous changes in natural selection and population demography, but the links between these interacting processes are poorly understood. 2. Here we analyse 37 years of data from an individual-based study of great tits (Parus major) in the Netherlands and use mixed-effects models to separate the within-and across-year effects of phenological mismatch between great tits and caterpillars (a key food source for developing nestlings) on components of fitness at the individual and population levels. 3. Several components of individual fitness were affected by individual mismatch (i.e. late breeding relative to the caterpillar food peak date), including the probability of doublebrooding, fledgling success, offspring recruitment probability and the number of recruits. Together these effects contributed to an overall negative relationship between relative fitness and laying dates, that is, selection for earlier laying on average. 4. Directional selection for earlier laying was stronger in years where birds bred on average later than the food peak, but was weak or absent in years where the phenology of birds and caterpillars matched (i.e. no population mismatch). 5. The mean number of fledglings per female was lower in years when population mismatch was high, in part because fewer second broods were produced. Population mismatch had a weak effect on the mean number of recruits per female, and no effect on mean adult survival, after controlling for the effects of breeding density and the quality of the autumnal beech (Fagus sylvatica) crop. 6.These findings illustrate how climate change-induced mismatch can have strong effects on the relative fitness of phenotypes within years, but weak effects on mean demographic rates across years. We discuss various general mechanisms that influence the extent of coupling between breeding phenology, selection and population dynamics in open populations subject to strong density regulation and stochasticity.