Ecological Modelling 251 (2013) 271–278 Contents lists available at SciVerse ScienceDirect Ecological Modelling jo ur n al homep ag e: www.elsevier.com/locate/ecolmodel Effects of space partitioning in a plant species diversity model Jinbao Liao a,b,c , Zhenqing Li b,∗ , Jan J. Quets a , Ivan Nijs a a Research Group Plant and Vegetation Ecology, Department of Biology, University of Antwerp (Campus Drie Eiken), Universiteitsplein 1, B-2610 Wilrijk, Belgium b State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China c Graduate University of Chinese Academy of Sciences, Beijing 100049, China a r t i c l e i n f o Article history: Received 27 July 2012 Received in revised form 23 November 2012 Accepted 28 December 2012 Available online 31 January 2013 Keywords: Grid-based model Spatially explicit model Species coexistence Species richness Trait variation Voronoi partitioning a b s t r a c t Understanding the mechanisms of species diversity maintenance within plant communities has become a fundamental issue in ecology over the past decades. While some models have tried to explore these mechanisms, few studies have integrated the dynamic interactions with neighbours in a spatially explicit way. The present model uses Voronoi polygons to dynamically partition a landscape patch into areas occupied by individual plants. It thus incorporates neighbourhood competition for space, unlike grid- based models with nearest-neighbour competition. In closed two-species communities, dynamic Voronoi partitioning promoted species coexistence, especially under local dispersal. This suggests that grid-based models overestimate species extinction rates. Likewise, multispecies communities without immigration had substantially greater species richness in the space partitioning model than in the grid-based model but only under distance-limited dispersal. In contrast, richness levels were similar in both models under global dispersal or with immigration from the metacommunity. Trait variation among species reduced species richness, but more so for traits associated with competition for space. This suggests that some traits are more important than others in governing species richness. Overall, our study demonstrates that combining species identity (traits) with partitioning of physical space can improve understanding of diversity regulation. © 2013 Elsevier B.V. All rights reserved. 1. Introduction A fundamental issue of ecology is to understand the forces that maintain species diversity within communities (Hutchinson, 1959; Levins, 1970; May, 1975; Pacala and Tilman, 1993; Chesson, 2000; Hubbell, 2001). Two of the most influential theories are the niche theory (Hutchinson, 1959) and the neutral theory (Hubbell, 2001). The niche theory stresses a role for meaningful differences in the niche of coexisting species (Weiher and Keddy, 1999; Wright, 2002; Chase and Leibold, 2003; Silvertown, 2004), which originate from interspecific tradeoffs in the ability to exploit different Abbreviations: A, actual area occupied by an individual resulting from Voronoi partitioning; ¯ A, area need for a species in order not to be affected by density depend- ent mortality; B, probability that an empty site is occupied by an individual; D, death probability of an individual; L, length of a simulated patch; M, number of species in a patch; n, number of neighbours for an individual; (ω), discriminant function that represents the degree of competition between the target individual and its neigh- bours; s, intrinsic seed production rate per individual of a species; m, density of species m in the community; , seed influx rate at a given site; ˛, species sensitivity to plant local density; , intrinsic (density-independent) mortality. ∗ Corresponding author at: 20 Nanxincun, Xiangshan, Haidian District, Beijing 100093, China. Tel.: +86 10 62836956; fax: +86 10 62836956. E-mail addresses: jinbaoliao@ibcas.ac.cn (J. Liao), lizq@ibcas.ac.cn (Z. Li), jan.quets@ua.ac.be (J.J. Quets), ivan.nijs@ua.ac.be (I. Nijs). environments or resources (MacArthur and Levins, 1967; Levin, 1970; MacArthur, 1972; Tilman, 1982; Chesson, 2000). However, in the light of niche theory, it remains unclear why competitive exclusion does not occur when species compete for the same resources for a very long time, and why hundreds of species with very similar resource needs can coexist (May, 1990; Alonso and Solé, 2000; Hubbell, 2001; Bell, 2000, 2001, 2003). Given the problems with niche theory, the neutral model of bio- diversity was developed (Bell, 2000, 2001; Hubbell, 2001), which aimed to explain coexistence in diverse communities with dis- persal and stochastic demographic processes. For its good fit to empirical relative abundance curves (Hubbell, 2001; Gilbert et al., 2006; Halley and Iwasa, 2011), the neutral biodiversity theory has increasingly been applied in both theoretical and empirical stud- ies (Volkov et al., 2005, 2007; Etienne et al., 2007; Chase, 2007; Allouche and Kadmon, 2009). However, major controversies have also arisen, in particular concerning the neutral assumption that species have identical functional traits, which is obviously not the case (Harte, 2003). Bell (2000, 2001) and Hubbell (2001), how- ever, put forward that interspecific differences generally lead to the existence of trade-offs that equalize overall fitness, and thus are insufficient to affect community structure and species abundance. Rather than continuing the controversy on which model pro- vides a better explanation of species coexistence, further study should unify the essence of both the niche and the neutral theory 0304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ecolmodel.2012.12.030