Abstract. Many studies have shown plant species' dispersal distances to be strongly related to life-history traits, but how well different traits can predict dispersal distances is not yet known. We used cross-validation techniques and a global data set (576 plant species) to measure the predictive power of simple plant traits to estimate species' maximum dispersal distances. Including dispersal syndrome (wind, animal, ant, ballistic, and no special syndrome), growth form (tree, shrub, herb), seed mass, seed release height, and terminal velocity in different combinations as explanatory variables we constructed models to explain variation in measured maximum dispersal distances and evaluated their power to predict maximum dispersal distances. Predictions are more accurate, but also limited to a particular set of species, if data on more specific traits, such as terminal velocity, are available. The best model (R 2 ¼ 0.60) included dispersal syndrome, growth form, and terminal velocity as fixed effects. Reasonable predictions of maximum dispersal distance (R 2 ¼ 0.53) are also possible when using only the simplest and most commonly measured traits; dispersal syndrome and growth form together with species taxonomy data. We provide a function (dispeRsal) to be run in the software package R. This enables researchers to estimate maximum dispersal distances with confidence intervals for plant species using measured traits as predictors. Easily obtainable trait data, such as dispersal syndrome (inferred from seed morphology) and growth form, enable predictions to be made for a large number of species.

Summary 1.Dispersal is fundamental to ecological processes at all scales and levels of organization, but progress is limited by a lack of information about the general shape and form of plant dispersal kernels. We addressed this gap by synthesizing empirical data describing seed dispersal and fitting general dispersal kernels representing major plant types and dispersal modes. 2. A comprehensive literature search resulted in 107 papers describing 168 dispersal kernels for 144 vascular plant species. The data covered 63 families, all the continents except Antarctica, and the broad vegetation types of forest, grassland, shrubland and more open habitats (e.g. deserts). We classified kernels in terms of dispersal mode (ant, ballistic, rodent, vertebrates other than rodents, vehicle or wind), plant growth form (climber, graminoid, herb, shrub or tree), seed mass and plant height. 3. We fitted 11 widely used probability density functions to each of the 168 data sets to provide a statistical description of the dispersal kernel. The exponential power (ExP) and log-sech (LogS) functions performed best. Other 2-parameter functions varied in performance. For example, the lognormal and Weibull performed poorly, while the 2Dt and power law performed moderately well. Of the single-parameter functions, the Gaussian performed very poorly, while the exponential performed better. No function was among the best-fitting for all data sets. 4. For 10 plant growth form/dispersal mode combinations for which we had >3 data sets, we fitted ExP and LogS functions across multiple data sets to provide generalized dispersal kernels. We also fitted these functions to subdivisions of these growth form/dispersal mode combinations in terms of seed mass (for animal-dispersed seeds) or plant height (wind-dispersed) classes. These functions provided generally good fits to the grouped data sets, despite variation in empirical methods, local conditions, vegetation type and the exact dispersal process. 5. Synthesis. We synthesize the rich empirical information on seed dispersal distances to provide standardized dispersal kernels for 168 case studies and generalized kernels for plant growth form/ dispersal mode combinations. Potential uses include the following: (i) choosing appropriate dispersal functions in mathematical models; (ii) selecting informative dispersal kernels for one's empirical study system; and (iii) using representative dispersal kernels in cross-taxon comparative studies.

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The positive relationship between spatial environmental heterogeneity and species diversity is a widely accepted concept, generally associated with niche limitation. However, niche limitation cannot account for negative heterogeneity-diversity relationships (HDR) revealed in several case studies. Here we explore how HDR varies at different spatial scales and provide novel theories for small-scale species co-existence that explain both positive and negative HDR. At large spatial scales of heterogeneity (e.g. landscape level), different communities co-exist, promoting large regional species pool size and resulting in positive HDR. At smaller scales within communities, species co-existence can be enhanced by increasing the number of different patches, as predicted by the niche limitation theory, or alternatively, restrained by heterogeneity. We conducted meta-regressions for experimental and observational HDR studies, and found that negative HDRs are significantly more common at smaller spatial scales. We propose three theories to account for niche limitation at small spatial scales. (1) Microfragmentation theory: with increasing spatial heterogeneity, large homogeneous patches lose area and become isolated, which in turn restrains the establishment of new plant individuals and populations, thus reducing species richness. (2) Heterogeneity confounded by mean: when heterogeneity occurs at spatial scales smaller than the size of individual plants, which forage through the patches, species diversity can be either positively or negatively affected by a change in the mean of an environmental factor. (3) Heterogeneity as a separate niche axis: the ability of species to tolerate heterogeneity at spatial scales smaller than plant size varies, affecting HDR. We conclude that processes other than niche limitation can affect the relationship between heterogeneity and diversity.