Long distance seed dispersal by wind: measuring and modelling the tail of the curve

Abstract

The size and shape of the tail of the seed dispersal curve is important in determining the spatial dynamics of plants, but is difficult to quantify. We devised an experimental protocol to measure long-distance dispersal which involved measuring dispersal by wind from isolated individuals at a range of distances from the source, but maintaining a large and constant sampling intensity at each distance. Seeds were trapped up to 80 m from the plants, the furthest a dispersal curve for an individual plant has been measured for a non-tree species. Standard empirical negative exponential and inverse power models were fitted using likelihood methods. The latter always had a better fit than the former, but in most cases neither described the data well, and strongly under-estimated the tail of the dispersal curve. An alternative model formulation with two kernel components had a much better fit in most cases and described the tail data more accurately. Mechanistic models provide an alternative to direct measurement of dispersal. However, while a previous mechanistic model accurately predicted the modal dispersal distance, it always under-predicted the measured tail. Long-distance dispersal may be caused by rare extremes in horizontal wind speed or turbulence. Therefore, under-estimation of the tail by standard empirical models and mechanistic models may indicate a lack of flexibility to take account of such extremes. Future studies should examine carefully whether the widely used exponential and power models are, in fact, valid, and investigate alternative models.

An investigation into effects of long-distance seed dispersal on organelle population genetic structure and colonization rate: a model analysis

“…The speed of colonization remains constant and is determined by the frequency and length of rare longdistance dispersal events. This is in agreement with other models of seed dispersal (Hewitt, 1996;Ibrahim et al, 1996;Le Corre et al, 1997;Clark, 1998;Clark et al, 1999;Clark et al, 2001;Bullock and Clark, 2000;Pakeman 2001;Petit et al, 2000). The results from this study additionally show that the speed of colonization is robust to changes in the periodicity of dispersal, a barrier of seedling establishment and a staggered start of colonization.…”

“…It is argued that it is better to represent dispersal by two different mechanisms so the central tendency and the tail can be varied independently (Clark, 1998;Clark et al, 1999;Pakeman, 2001). Stratified dispersal kernels have been used to simulate realistically the ecto/endozoochorous dispersal of woodland herbaceous species (Pakeman 2001); the rapid colonization of the forest herb Asarum canadense (Cain et al, 1998); the behaviour of Hieracium pilosella (Winkler and Stocklin, 2002); and the dispersal of Calluna vulgaris and Erica cinera by wind (Bullock and Clark, 2000). Simulation models based on the oak system concluded that long-distance dispersal events not only allowed for rapid expansion but they were also the most important factor determining the spatial genetic structure of maternally inherited genes (Le Corre et al, 1997;Petit et al, 2000).…”

Patterns of pollen dispersal in a small population of Pinus sylvestris L. revealed by total-exclusion paternity analysis

“…Even though this study uses a wider scale than most previous paternity analyses of wind-pollinated trees, the data do not allow reliable estimates of the tail of the distribution, which, as suggested by the observed portion of long-distance immigrants, may extend over tens of kilometres. On the other hand, long-distance dispersal events are likely to be governed by complex stochastic atmospheric processes that are poorly predicted by standard empirical or mechanistic models (Bullock and Clarke, 2000), and they may require novel experimental and analytical approaches (Nathan et al, 2003).…”

Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels

“…The ID model with a Gaussian dispersal kernel is essentially equivalent to the classical RD model, in a sense that will be made precise in this paper. Alternative dispersal kernels with heavier tails model the faster and wider spreading observed in many field studies (Bullock and Clarke, 2000;Clark et al, 1999Clark et al, , 2001Katul et al, 2005;Klein et al, 2006;Paradis et al, 2002). This paper proposes a new fractional RD equation…”