Using genetic markers to estimate the pollen dispersal curve

Abstract

Pollen dispersai is a critical process that shapes genetic diversity in natural populations of plants. Estimating the pollen dispersal curve can provide insight into the evolutionary dynamics of populations and is essential background for making predictions about changes induced by perturbations. Specifically, we would like to know whether the dispersal curve is exponential, thin-tailed (decreasing faster than exponential), or fat-tailed (decreasing slower than the exponential). In the latter case, rare events of long-distance dispersal will be much more likely. Here we generalize the previously developed TWOGENER method, assuming that the pollen dispersal curve belongs to particular one-or two-parameter families of dispersal curves and estimating simultaneously the parameters of the dispersal curve and the effective density of reproducing individuals in the population. We tested this method on simulated data, using an exponential power distribution, under thin-tailed, exponential and fat-tailed conditions. We find that even if our estimates show some bias and large mean squared error (MSE), we are able to estimate correctly the general trend of the curve • thin-tailed or fat-tailed • and the effective density. Moreover, the mean distance of dispersal can be correctly estimated with low bias and MSE, even if another family of dispersal curve is used for the estimation. Finally, we consider three case studies based on forest tree species. We find that dispersal is fat-tailed in all cases, and that the effective density estimated by our model is below the measured density in two of the cases. This latter result may reflect the difficulty of estimating two parameters, or it may be a biological consequence of variance in reproductive success of males in the population. Both the simulated and empirical findings demonstrate the strong potential of TWOGENER for evaluating the shape of the dispersal curve and the effective density of the population (d^).

Size advantage for male function and size‐dependent sex allocation inAmbrosia artemisiifolia, a wind‐pollinated plant

“…For pollen dispersal, the estimated kernel was fat‐tailed, indicating that the long‐range decay of dispersal probability is slower than the expectation from the exponential distribution (Austerlitz et al., 2004; Figure 5). This finding agrees with a general pattern of pollen dispersal in wind‐pollinated plants (Gerber et al., 2014; Levin & Kerster, 1974; Oddou‐Muratorio, Klein, & Austerlitz, 2005).…”

“…Here, we assumed neighborhood radii as 2, 5, 10, or 15 m, a typing error rate as constant (0.01) and the precision of convergence (“stop” criterion) as 0.001. We used the following exponential power function for estimating pollen dispersal kernel (Austerlitz et al., 2004): $Pfalse(rfalse)=\frac{b}{2\mathrm{\pi }{a}^2\mathrm{\Gamma }\left(\frac{2}{b}\right)}\text{exp}\left[-{\left(\frac{r}{a}\right)}^b\right]$ …”

“…When b  =   1, kernel follows a simple exponential distribution. On the other hand, when b  <   1 or b  >   1, kernel is fat‐tailed or thin‐tailed, respectively (Austerlitz et al., 2004). We estimated the following parameters using the Newton–Raphson algorithm: pollen immigration rate ( m p ), scale and shape parameters of dispersal kernels ( a and b p , respectively), mean pollen dispersal distance ( d p ), directionality effect ( K p ), the prevailing direction of dispersal (θ p ), and selfing rate ( s ).…”

Limiting inbreeding in disjunct and isolated populations of a woody shrub

“…This is the most common pattern found in plants (Ashley 2010), and our observations are also consistent with the pattern frequently reported for insect‐pollinated species (Austerlitz et al. 2004; Smouse and Sork 2004; Vekemans and Hardy 2004). But in H. oldfieldii , most pollen movements were not to nearest neighbors but to plants >10 m away, including significant pollination from distant (>50 m away) sources.…”

The effects of inbreeding, genetic dissimilarity and phenotype on male reproductive success in a dioecious plant

“…a represents the scale parameter (the extent to which pollen disperses) and b is the shape parameter of the dispersal curve, which describes the tail of the distribution: low b corresponds to more leptokurtic curves, with much short-distance dispersal but also a substantial proportion of long-distance dispersal [61].…”