## Introduction

Understanding the population dynamics of species is a central theme in ecology. Within species, life stages – defined by size, age or reproductive status – may respond differently to biotic or abiotic factors in ways that have important consequences for population dynamics. One way to capture how variation in vital rates among life stages affects population dynamics is to use demographic matrix models. Matrix models are widely used in basic and applied ecological and evolutionary research, in part because their general and versatile structure allows them to be applied broadly across taxa (Boyce 1992; Menges 2000; Mills & Lindberg 2002; Morris & Doak 2002; Franco & Silvertown 2004). The power of these models is that they can summarize complex demographic data into simple, straightforward descriptors for whole population dynamics, including metrics such as population growth rate (λ), net reproductive rate (*R*_{0}) and measures of the relative contribution of each life stage to overall population growth (Caswell 2001; Morris & Doak 2002). However, common measures of population growth (λ_{1}, *r*) require the assumption that the relative proportion of individuals in each life stage has stabilized even when the total population size is changing (Caswell 2001).

Theoretically, a population would reach an equilibrium or asymptotic state with a corresponding stable stage distribution (SSD) that is determined solely by the demographic rates in the matrix when demographic rates are constant. In reality, a population may never arrive exactly at its SSD, due to stochasticity and disturbance. Recent theoretical advances can overcome the dependence on a stable distribution by allowing population descriptors to depend on time and initial starting conditions (Fox & Gurevitch 2000; Yearsley 2004; Caswell 2007; Haridas & Tuljapurkar 2007; Koons, Holmes & Grand 2007; Townley *et al.* 2007; Tenhumberg, Tyre & Rebarber 2009; Wiedenmann, Fujiwara & Mangel 2009). The results from these transient analyses can differ greatly from equivalent asymptotic analyses, depending on the initial stage distribution (e.g. McMahon & Metcalf 2008; Ezard *et al.* 2010; Maron, Horvitz & Williams 2010). For example, using models from six vertebrate species, Koons *et al.* (2005) found that after 5 years, transient population growth rates could differ from asymptotic growth rates by as much as 59% and transient sensitivities by as much as 200%. In practice, the transient response that a population experiences depends on the structure of the matrix, time scale of interest and the relationship between a population’s initial and asymptotic stage distributions.

A population is expected to behave more similarly to its asymptotic dynamics if it is ‘close’ to its theoretical asymptotic stage distribution (Bierzychudek 1999). Yet, forces that could move populations away from asymptotic stage distributions by affecting particular life stages are common, including stochastic events such as disturbance and weather, as well as disease, herbivory, harvest and temporal changes in environmental conditions. At the same time, it is unknown whether differences from SSD are infrequent occurrences or typical patterns, and thus it is unknown how often the assumption of populations being in their SSD is violated. We conducted an analysis of published demographic models of plant populations for which both the projection matrix and current stage distribution were reported to determine: (i) how similar populations are to their theoretical stable distributions, (ii) how the observed divergence from stable distribution affects near-term projections of population size and growth rate, and (iii) whether there are characteristics of populations based on life history or model attributes that relate to the distance between current and asymptotic stage distributions.