Quantifying seed dispersal kernels from truncated seed-tracking data

1. Seed dispersal is a key biological process that remains poorly documented because dispersing seeds are notoriously hard to track. While long-distance dispersal is thought to be particularly important, seed-tracking studies typically yield incomplete data sets that are biased against long-distance movements. 2. We evaluate an analytical procedure developed by Jansen, Bongers & Hemerik (2004) to infer the tail of a seed dispersal kernel from incomplete frequency distributions of dispersal distances obtained by tracking seeds. This censored tail reconstruction (CTR) method treats dispersal distances as waiting times in a survival analysis and censors nonretrieved seeds according to how far they can reliably be tracked. We tested whether CTR can provide unbiased estimates of long-distance movements which typically cannot be tracked with traditional field methods. 3. We used a complete frequency distribution of primary seed dispersal distances of the palm Astrocaryum standleyanum, obtained with telemetric thread tags that allow tracking seeds regardless of the distance moved. We truncated and resampled the data set at various distances, fitted kernel functions on CTR estimates of dispersal distance and determined how well this function approximated the true dispersal kernel. 4. Censored tail reconstruction with truncated data approximated the true dispersal kernel remarkably well but only when the best-fitting function (lognormal) was used. We were able to select the correct function and derive an accurate estimate of the seed dispersal kernel even after censoring 5060% of the dispersal events. However, CTR results were substantially biased if 5% or more of seeds within the search radius were overlooked by field observers and erroneously censored. Similar results were obtained using additional simulated dispersal kernels. 5. Our study suggests that the CTR method can accurately estimate the dispersal kernel from truncated seed-tracking data if the kernel is a simple decay function. This method will improve our understanding of the spatial patterns of seed movement and should replace the usual practice of omitting nonretrieved seeds from analyses in seed-tracking studies.