Ecological Modelling 179 (2004) 487–498 Directionality in fruit dispersal models for anemochorous forest trees Sven Wagner a,∗ , Konrad Wälder b , Eric Ribbens c , André Zeibig a a Institut für Waldbau und Forstschutz, Technical University Dresden, Postfach 1117, Tharandt D-01735, Germany b Institut für Stochastik, TU Bergakademie Freiberg, Freiberg 09596, Germany c Department of Biological Sciences, Western Illinois University, Macomb, IL 61455-1390, USA Received 10 April 2003; received in revised form 4 February 2004; accepted 17 February 2004 Abstract Despite the progress which has been achieved in modelling the seed dispersal of plants by ‘seed shadow models’, the accuracy of the predictions made by those models still needs improvement, especially in regard to long distance dispersal. One assumption in recent parameterization techniques of seed shadow models is isotropy of the distribution around the mother tree. However, published data show non-isotropic features of that distribution. Non-isotropy—or directionality—is understood here as any relevant heterogeneity in seed density by azimuth directions in regard to the mother trees position. We present an approach to estimate the degree of directionality in seed dispersal data by implementing azimuth directions in seed shadow models. This leads to anisotropic models. In all three of the datasets we tested (seed dispersion of Fraxinus excelsior L. and Betula pendula Roth) the model predictions were improved by the anisotropic approach when compared to the isotropic one. However, to get proper estimations the number of seed traps must be high in relation to the number of seed trees. The efficacy of dispersal in relation to available safe site area and seed production, taking directionality into account, was tested by comparing the predicted production of offspring of the non-isotropic model with that of the isotropic model in order to determine the relative advantage of non-isotropic dispersion. To do this we adapted a mean field approach of Geritz et al. [Oecologia 62 (1984) 219] to the two-dimensional model and ran several simulations. We found that when a medium directionality pattern in combination with larger values for mean dispersal distance is modelled, seed dispersal efficacy is high. In contrast, highly pronounced directionality patterns are less efficient, even if larger values of mean dispersal distances are modelled. The capacity to compensate for directionality with larger dispersal distances should occur mostly in species with far flying seeds and large habitat sizes. In contrary, directionality seems always at an evolutionary disadvantage in small habitats. © 2004 Elsevier B.V. All rights reserved. Keywords: Seed dispersal; Directionality; Efficacy; Fraxinus excelsior; Betula pendula ∗ Corresponding author. Tel.: +49-35203-3831300; fax: +49-35203-3831397. E-mail addresses: wagner@forst.tu-dresden.de (S. Wagner), waelder@math.tu-freiberg.de (K. Wälder), e-ribbens@wiu.edu (E. Ribbens), andy@forst.tu-dresden.de (A. Zeibig). 1. Introduction Recently Ribbens et al. (1994) and Clark et al. (1998b) have pointed out the key function of fruit dis- persal in the recruitment process of forests. Malanson and Armstrong (1996) have extended this concept to fragmented landscapes. 0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2004.02.020