The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.

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Phenological shifts constitute one of the clearest manifestations of climate warming. Advanced emergence is widely reported in high-latitude ectotherms, but a significant number of species exhibit delayed, or no change in, emergence. Here we present a mechanistic theoretical framework that reconciles these disparate observations and predicts population-level phenological patterns based solely on data on temperature responses of the underlying life history traits. Our model, parameterized with data from insects at different latitudes, shows that peak abundance occurs earlier in the year when warming increases the mean environmental temperature, but is delayed when warming increases the amplitude of seasonal fluctuations. We find that warming does not necessarily lead to a longer activity period in high-latitude species because it elevates summer temperatures above the upper limit for reproduction and development. Our findings both confirm and confound expectations for ectotherm species affected by climate warming: an increase in the mean temperature is more detrimental to low-latitude species adapted to high mean temperatures and low-amplitude seasonal fluctuations; an increase in seasonal fluctuations is more detrimental to high-latitude species adapted to low mean temperatures and high-amplitude fluctuations.

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within-individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long-run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage-duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay-differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long-term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.