Wind dispersal of seeds from a forest into a clearing

Ecology, March, 1996 by D.F. Greene, E.A. Johnson

INTRODUCTION

Seed dispersal plays an important role in both applied and theoretical problems. Decades of forestry research have shown that clearcuts with diameters exceeding [approximately equal to]200-400 m will be poorly stocked by naturally regenerating tree species because of dispersal constraints (e.g., Barrett 1966, Ronco 1970). Two empirical solutions to the problem (narrow strip-cuts or residual patches of "seed trees" in large cuts) could become landscape design solutions if we had a model relating seed deposition to distance and source strength.

There are at least two broad classes of arguments for landscape-scale persistence of tree species where seed dispersal plays a crucial role. The "shifting mosaic" model of Bormann and Likens (1979) views poor competitors (shade intolerants) as good dispersers who have therefore the advantage of early arrival in rare, ephemeral, large gaps. At the opposite extreme, metapopulation models argue that species are effectively equivalent competitors whose constituent local populations are randomly walking toward extinction or monoculture, but the rate of change is slowed by seed exchange within the metapopulation (Hanski and Gilpin 1991). More empirically, it has been demonstrated by field experiments that seed dispersal can be a serious constraint on local species distribution (e.g., Primack and Miao 1992).

Nonetheless, we know surprisingly little about the process of seed dispersal (Levin 1984). Simple analytical models for the dispersion by wind of heavy particles (such as seeds) from a point source (for example, a tall tree) have been derived and tested (e.g., Walker 1965, Stewart 1968, Greene and Johnson 1989). Such models could easily be extended to the dispersal of seeds from an area source (a collection of point sources) by computer simulation. The area source models must not assume that the horizontal wind velocity is independent of lateral distance from the source. It is well known that horizontal wind velocities at a given height change significantly with distance leeward of an obstacle such as a forest (e.g., Nageli 1953, Caborn 1957, Flemming 1968, Raynor 1971), and therefore these models cannot be applied to the dispersal of seeds across a forest/clearing edge. Instead, these models are limited to cases such as (1) an isolated tree in a field, and (2) a tree dispersing seeds solely within a forest. This is unfortunate as it has become clear that many plant species require a canopy gap for successful recruitment into the canopy (Pickett and White 1985), that is, the more significant dispersal events involve flight trajectories across forest/clearing edges.

The objective of this paper is to construct a micro-meteorological model of the dispersal of seeds from a forest to an adjacent clearing. The model will be tested using forestry studies of dispersal into clearcuts as well as our own studies of dispersal into burns and clearcuts.

One might wonder: why rely on models when seed deposition can be measured directly in the field? There are two reasons. First, accurate characterization of a dispersal curve requires a dense network of seed traps and we may have to wait as much as 5 yr to obtain an adequate seed production year. In addition, this time-consuming enterprise will not permit us to generalize to other species or other sites where, for example, forest height may be different.

THE MODEL

The dispersal model is for an array (forest) of point sources (single trees) with each point source idealized as abscising all seeds from a point in three-dimensional space. Model derivation requires four steps. First, we assume a log-normal distribution of horizontal wind speeds at a standard meteorological reporting station. We then modify this distribution to account for the nonrandom nature of seed abscission. Third, we link the reference station wind speed to the speed at the top of a forest, and subsequently down through the forest to the ground. Fourth, we relate the reference station wind speed to the speeds within the clearing. At this point, the wind structure in both forest and clearing has been established and therefore the seed disposition from any tree to any Cartesian coordinate in the clearing can be estimated. A list of symbols and recommended model default values can be found in the Appendix.

Distribution of wind speeds at a reference station

Assume a log-normal distribution of wind speeds at height [z.sub.r] (the standard height is 10 m) at a reference station (typically an airport) where air flow is unobstructed by the fetch (drag) of trees or buildings (Greene and Johnson 1989). Although we will modify this shortly, assume further that abscission is random with respect to wind speed. Then, the number of seeds abscising from a source at any wind speed (u) is

[Mathematical Expression Omitted],

where Q is the number of seeds on the tree, [u.sub.g] is the median horizontal wind speed, and [[Sigma].sub.ln] is the standard deviation of the natural logarithms of the horizontal wind speeds. At 10 m height, North American airports give a long-term average [u.sub.g] of 4.3 m/s (range of 2.0-6.5 m/s: Hare and Thomas 1974, Luna and Church 1974) and average [[Sigma].sub.ln] of 0.55 (Luna and Church 1974).