## Introduction

Repeated censuses of permanent forest plots can be used to describe the dynamics of tree populations, i.e. to determine recruitment rate and mortality. There are, however, problems in assessing these rates (Sheil 1995a; Sheil *et al*. 1995; Sheil & May 1996), which raise a debate about whether or not turnover of forests increases with time (Phillips & Gentry 1994; Sheil 1995b; Phillips 1995). These problems arise partly because, in order to obtain demographic estimates in terms of population density, trees from different environments and of different life-history stages are combined.

One way of avoiding these problems is to incorporate the distribution of tree sizes into demographic analyses, because the fate of individual trees is influenced by both their size and their position in the size structure of the whole forest at a particular census (Kohyama 1992, 1993). Growth rate (usually increase in trunk girth or diameter) can be easily determined from repeated census data for each survivor over the period, providing the position of measurement is marked. However, estimation of mortality in a given size class is less precise because it is obtained on a size-class basis, and will therefore be affected by the sample size. Estimation of recruitment into the minimum size is even more difficult, because the number recruited will vary widely depending on the census timing and plot size.

Precise estimates of recruitment rate and mortality therefore require observation of more trees in large-sized plots, although this carries the disadvantages of increasing the effects of the environmental heterogeneity in space and the large cost of such research efforts. Several such large-scale forest plots with an area of 50 ha or more (Condit 1995; Condit *et al*. 1996) have, however, been established for the purpose of analysing the spatial pattern of populations and estimating demographic parameters using large sample sizes.

Forest studies may use ‘stand table analysis’ to calculate the transition probability in a given time interval from a particular size class to the next size class; this procedure multiplies the density of trees in a given class by their size growth rate (Vanclay 1994). Similar calculation can be used to estimate recruitment rates from permanent plot censuses. Here we present a theoretical basis for a procedure for estimating recruitment rate into the minimum size class in a small plot. We apply this procedure to census data from actual plots and model plots generated in a computer. We then examine the validity of this procedure by comparing these estimates with census observations of recruitment events.