## Introduction

Matrix population models are a standard method used to assess the viability of structured populations (Morris & Doak 2002). Repeated iterations of the matrix model result in the projection of a population's equilibrium growth rate and extinction risk, providing a measure of the overall performance of populations. Moreover, sensitivity and elasticity analyses of matrix models can identify the life-history stages most critical for the persistence of a species. The results of matrix model analysis and simulation are often used to assess the vulnerability of a population to extinction and to evaluate different management options (Freckleton *et al*. 2003; Garcia 2004; Beverly & Martell 2004; van Mantgem *et al*. 2004).

Several recent studies have investigated how data sampling, parameter estimation and model construction influence the predictions of demographic population viability models (population viability analysis, PVA; Ludwig 1999; Easterling, Ellner & Dixon 2000; Gross 2002; Morris & Doak 2002; Kaye & Pyke 2003). These studies show that model output depends sensitively upon estimated parameters, and that the data used to parameterize models are frequently insufficient. As a result predictions of future population status will be uncertain (Ludwig 1999; Fieberg & Ellner 2000). There is a large literature concerned with how the techniques used to analyse collected data can be adapted to make predictions more accurate (Horvitz, Schemske & Caswell 1997; Ehrlén & van Groenendael 1998; Ludwig 1999; Mills, Doak & Wisdom 1999; de Kroon, van Groenendael & Ehrlén 2000; Caswell 2001; Ehrlén, van Groenendael & de Kroon 2001; Calder *et al*. 2003; Wilcox & Elderd 2003; Hodgson & Townley 2004). In contrast, very little attention has been paid to how the primary data are actually sampled. This is surprising as the accuracy of the data is critical for the quality of predictions of population viability (Lindborg & Ehrlén 2002) and no post-collection procedure can fully compensate for the shortcomings of the data.

Almost all recent plant demographic studies have sampled all individuals within plots (Z. Münzbergová, unpublished data). The most probable explanation for this is that sampling within plots is easy to apply in the field and also provides information on actual stage distribution. However, for any given sampling effort this strategy is unlikely to provide the most accurate estimates of demographic parameters because it often results in a very unequal number of individuals per stage. In the literature it is, in fact, not rare to encounter transition probabilities that are estimated using only one or a few individuals (Z. Münzbergová, unpublished data). A sampling strategy that is able to decrease the problems with already strongly unbalanced sample sizes at the stage of data collection therefore has much larger potential to increase the accuracy of estimates than any post-collection model adjustments.

The only published suggestion on how to sample demographic data other than by a plot-based method is that of Gross (2002). He suggests a method where the number of individuals to be sampled in each stage depends on how much the stages contribute to the growth rate of the population. To apply the method, one needs to make an educated guess on the relative importance of different transitions in the life cycle for population growth; this can be made using data from studies of the same or a related organism, the investigator's prior knowledge, pilot data or comparative demographic studies (Gross 2002).

In this study we suggest a third method for sampling demographic data that is based on sampling an equal number of individuals per stage. It can reduce the problems of plot-based sampling and requires no previous knowledge. We compared the accuracy and precision of this method with both the traditional plot-based sampling method and the alternative method suggested by Gross (2002), using demographic data from 32 plant species under different overall sampling efforts.