Marked point pattern analysis on genetic paternity data for uncertainty assessment of pollen dispersal kernels


Correspondence author. Biodiversität und Klima Forschungszentrum, D-60325 Frankfurt am Main, Germany. E-mail:


1.  Obtaining accurate estimates of the pollen dispersal kernel is central to a wide range of ecological studies. Assessing their statistical uncertainty is as important, but rarely considered.

2.  We developed a new method of marked point processes for nonparametric estimation of dispersal kernels based on data of genetic paternity analysis that does not require assumptions about the shape of the dispersal distribution. This allows for construction of Monte Carlo simulation envelopes of a given null model, such as random mating, and for uncertainty assessment of the observed dispersal kernel.

3.  We applied our method to characterize spatial patterns of pollen flow in an isolated population of Populus nigra in Central Germany and to assess the associated statistical uncertainty in estimates of within-population dispersal kernels. We compared our nonparametric within-population kernel estimate with that of established methods of parametric kernel fitting including: (i) a general mating model, (ii) a simplified mating model using categorical paternity data and (iii) least-squares regression of the nonparametric kernel estimate.

4.  Our analysis showed a significant departure from the random mating null model. We found a highly significant excess of mating events at short distances (<400 m) and a weakly significant shortage of mating events at larger distances (1500–2000 m). Simulation envelopes of the null model were very wide at larger distances (>2000 m), indicating large uncertainty on the detailed shape of the kernel’s tail.

5.  Results of the point pattern analysis were consistent with kernel fits using published maximum-likelihood mating models. Model selection revealed that two-component pollen dispersal kernels were the most parsimonious functions.

6. Synthesis. Our approach of nonparametric kernel estimation could be widely applied for dispersal data from genetic paternity analysis and complements traditional kernel estimation by providing a nonparametric kernel estimate and effective methods for an uncertainty assessment in kernel estimation. Our results indicate that statistical model fitting may substantially underestimate the uncertainty in kernel estimation, especially at larger distances.