Plant fecundity and seed dispersal in spatially heterogeneous environments: models, mechanisms and estimation

1. Plant fecundity and seed dispersal often depend on environmental variables that vary in space. Hence, plant ecologists need to quantify spatial environmental effects on fecundity and dispersal. 2. We present an approach to estimate and model two types of spatial environmental effects: source effects cause fecundity and dispersal to vary as a function of a source's local environment, whereas path effects depend on all environments a seed encounters during dispersal. Path effects are described by first transforming physical space so that areas of low seed permeability are enlarged relative to others, and then evaluating dispersal kernels in this transformed 'movement space'. 3. Models for source and path effects are embedded into the established inverse modelling (IM) framework. This enables the statistical estimation of environmental effects from easily available data on the spatial distribution of seeds, seed sources and environmental covariates. 4. The presented method is applied to data from a well-studied population of the wind-dispersed Aleppo pine (Pinus halepensis). We use local tree density as an environmental covariate, model fecundity as a function of a tree's basal area, and consider four dispersal kernels: WALD (a closed-form mechanistic model for seed dispersal by wind), log-normal, exponential power and 2Dt. 5. The inclusion of source and path effects of tree density markedly improves IM performance. IM analyses and independent data agree in the parameter range of the mechanistic WALD kernel and in suggesting weak negative density-dependence of fecundity. Of 64 IMs considered, the best four involve the WALD kernel and negative source effects on its shape parameter. The best IM predicts that increasing tree density at the source shortens median dispersal distance while enhancing long-distance dispersal (LDD). Additionally, path effects lead to lower seed permeability of high density areas. These results shed light on the mechanisms by which environmental variation affects fecundity and dispersal of P. halepensis. Moreover, the predicted density-dependent dispersal causes a pronounced lag-phase in simulations of population spread. 6. Synthesis. The presented method can quantify environmental effects on fecundity and dispersal in a wide range of study systems. The movement space concept may furthermore promote a unified understanding of how various organisms move through spatially heterogeneous environments.