Journal of Ecology 2004 92, 758– 766 © 2004 British Ecological Society Blackwell Publishing, Ltd. An evaluation of alternative dispersal functions for trees DAVID F. GREENE*§, CHARLES D. CANHAM†, K. DAVID COATES‡ and PHILIP T. LEPAGE§ *Department of Geography, Concordia University, 1455 de Maisonnueve Boulevard, Montreal, Quebec, H3G 1M8, Canada, †Institute of Ecosystem Studies, PO Box AB, Millbrook, New York, USA, ‡British Columbia Forest Service, Research Section, Bag 6000, Smithers, British Columbia, V0J 2N0, Canada, and § Groupe de Recherche en Écologie Forestière Interuniversitaire, Universite du Quebec a Montreal, Montreal, Quebec, Canada Summary 1 We compared three commonly used empirical seed/seedling dispersal functions for trees (lognormal, 2Dt, and two-parameter Weibull) by analysis of published studies where the location of the source is known, as well as by inverse modelling within an old growth hardwood forest in southern Quebec. Almost all the species were wind-dispersed. 2 For the discrete source studies, the lognormal was clearly superior, while for the inverse modelling the performance of the three dispersal functions was somewhat more even. We speculate that collisions with boles spuriously enhanced the likelihood of the 2Dt and the Weibull with inverse modelling, as both these functions assume that the greatest seed/seedling density will occur at the base of the maternal parent bole. 3 We conclude that the lognormal function is to be preferred because, as well as providing a framework for mechanistic interpretation, it tends to provide a closer approximation to observed dispersal curves. 4 We also argue that mean distances travelled by seed crops are far more extensive than indicated by previous studies that used the Weibull function. Key-words: anemochory, inverse modelling, recruitment, seed dispersal, tree regeneration Journal of Ecology (2004) 92, 758 – 766 Introduction Information about seed dispersal and recruitment is crucial for understanding the genetic structure of plant populations, plant invasions and, in some cases, species coexistence (reviewed in Nathan & Muller-Landau 2000). Further, the recruitment subroutine is an essen- tial part of stand dynamics simulators being developed by foresters to predict stand density and volume (LePage et al . 2000). Nonetheless, empirical delineation of seed and seedling dispersal curves within forests has been a difficult task because the individual dispersal curves of conspecific trees usually overlap. There are a number of methods available for determining indi- vidual dispersal curves (Greene & Calogeropoulos 2002), but by far the most economical is the inverse modelling approach pioneered by Ribbens et al . (1994). Under this approach, maximum likelihood methods are used to estimate the terms of the dispersal function, given the spatial distribution and sizes of potential parent trees around each sample location. The inverse modelling approach has now been used in a number of different studies, but with disagreement among practitioners over the most appropriate functional form of the dispersal curve. Ribbens et al . (1994) used a two-parameter Weibull function (sometimes referred to as the exponential family; Clark et al . 1999). Clark et al . (1999) proposed a composite dispersal function (the ‘2Dt’ function) that was exponential in shape, but with a normally distributed variable for the scale parameter. They argued that this function was a better descriptor of dispersal curves than the two-parameter Weibull used by Ribbens et al . (1994). Stoyan & Wagner (2001) claimed the lognormal was superior to the Weibull. Meanwhile, other authors (e.g. LePage et al . 2000 for the Weibull, Tanaka et al . 1998 for the lognormal) have simply adopted one or another of these functions, intuiting, perhaps, that they will perform about equally well. Nonetheless, the choice of the function is critical; as noted by Nathan & Muller-Landau (2000), some functions have far tails that are too thin to permit meta- population persistence (let alone a migrational velocity sufficient to explain the Holocene record). There is general agreement on the basic expression for the dispersal curve: Correspondence. David F. Green (e-mail greene@alcor.concordia.ca).