Ecology, 90(8), 2009, pp. 2129–2138 Ó 2009 by the Ecological Society of America Safe sites, seed supply, and the recruitment function in plant populations RICHARD P. DUNCAN, 1 JEFFREY M. DIEZ,JON J. SULLIVAN,STEVEN WANGEN, AND ALICE L. MILLER 2 Bio-Protection Research Centre, P.O. Box 84, Lincoln University, Lincoln 7647 New Zealand Abstract. The extent to which plant populations are seed vs. establishment limited can be understood by quantifying the recruitment function, describing the number of seedlings that establish as a function of the number of seeds added. Here, we derive a general equation for the recruitment function based on a mechanistic model describing how the availability of safe sites (sites suitable for germination and establishment) interacts with the number and distribution of seeds added to a plot to determine the number of recruits. The parameters of this recruitment function have a direct biological interpretation that can provide insight into the processes limiting recruitment in plant populations. Key words: Beverton-Holt function; establishment limitation; Hieracium lepidulum; microsite; plant recruitment; recruitment function; safe site availability; seed-addition experiments; seed limitation; self- thinning. INTRODUCTION The availability of seeds and the availability of sites suitable for seedling establishment (safe sites; Harper et al. 1961) are key determinants of recruitment in plant populations (Harper et al. 1965, Crawley 1990, Eriksson and Ehrle´n 1992). At one extreme, populations are establishment limited, meaning the rate of seed supply is sufficient to ensure that all available safe sites are oc- cupied and population size is constrained by the number of safe sites. At the other extreme, populations are seed limited, meaning the rate of seed supply is low relative to the availability of safe sites so that many safe sites are unoccupied and population size is constrained by seed supply. In reality, most plant populations are probably limited by a combination of the two processes (Eriksson and Ehrle´n 1992). This is because, rather than being a dichotomy, the extent of seed vs. establishment limita- tion falls along a gradient (Manning et al. 2004, Clark et al. 2007, Kollmann et al. 2007) that depends on the rate of seed supply relative to the availability of safe sites. A series of plots may all show seed limitation, in that seed addition results in new seedling recruitment (Turnbull et al. 2000), but the magnitude of the recruitment response could vary markedly between plots. For a given level of seed addition, plots with more available safe sites should have higher recruitment and appear more strongly seed limited. To understand the factors limiting recruitment in plant populations, this interplay between safe-site availability and seed-supply rate is of key interest. One way to understand this interplay is through seed- addition experiments that allow us to quantify the recruitment function (Poulsen et al. 2007). This function describes the relationship between the number of seeds that are experimentally added to plots and the resulting number of recruits, and is typically a monotonically in- creasing curve that reaches an asymptote at high levels of seed addition. Poulsen et al. (2007) show that the form of the recruitment function can be used to infer the relative strength of seed vs. establishment limitation, and to assess the relative importance of density-dependent and density-independent processes in affecting popula- tion recruitment. Central to this approach is quantifying the recruitment function. Poulsen et al. (2007) used the Beverton-Holt function, which has two parameters, one that estimates the proportion of seeds that would recruit in the absence of density-dependent effects, and a second that estimates the asymptotic number of recruits at high levels of seed addition under negative density dependence. While the parameters of the Beverton-Holt function have biolog- ical interpretations, the function was chosen because it often fits observed recruitment data well and the mecha- nistic underpinnings were not discussed. Our aim in this paper is to bridge the gap between the underlying processes hypothesized to control recruit- ment in plant populations, and the functions used to quantify these relationships. To do this, we derive a general recruitment function based on a mechanistic model of how safe sites and seed supply interact to determine the number of recruits. We build on a model of recruitment in which there are a limited number of safe sites capable of supporting a single seedling, with seeds competing to occupy these safe sites. The relationship Manuscript received 31 July 2008; revised 11 November 2008; accepted 20 November 2008. Corresponding Editor: J. Weiner. 1 E-mail: Richard.Duncan@lincoln.ac.nz 2 Present address: National Park Service, Joshua Tree National Park, 74485 National Park Drive, Twentynine Palms, California 92277 USA. 2129