Mechanistic Analytical Models for Long‐Distance Seed Dispersal by Wind

Abstract

We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.

Predicting Spatial Patterns of Plant Recruitment Using Animal-Displacement Kernels

“…Most studies on seed shadows and plant recruitment patterns use seed traps and seedling surveys to estimate the relationship between seed (or seedling) density and distance from the seed source (the “dispersal kernel”) using various statistical models [11]–[13]. These models (hereafter referred to as “1D dispersal kernels”) are generally based on unimodal distributions with a peak close to the source and a long tail.…”

Interactions between climate change, competition, dispersal, and disturbances in a tree migration model

“…However, while it is possible to find parameterization based on field data for many forest model components (see Pacala et al 1996), parameterization of dispersal mechanisms is not yet fully available for modelers. Only recently, mechanisms of LDD have been modeled in a way that is satisfying for largescale models (Katul et al 2005). Thanks to this work and others (Higgins and Richardson 1999;Greene et al 2004;Debain et al 2007), we can expect to improve significantly models of tree migration in the future.…”

“…Each seed is dispersed to a given habitat cell according to a dispersal kernel mitigated by the height of the seed source. The dispersal kernel is defined as a double exponential (mixed) kernel, with a typical fat-tailed shape that allows us to take account of the rare but important long-distance events (Clark et al 1998;Higgins and Cain 2002;Katul et al 2005;Debain et al 2007). The density of probability for a single seed is given for d (distance from the seed source) by the following:…”

High seed dispersal ability of Pinus canariensis in stands of contrasting density inferred from genotypic data

“…As was hypothesized, the open pine-wood from site 2 showed much higher mean effective dispersal distance than the dense forest from site 1. This result was expected, because standing vegetation probably acts as a physical barrier to wind dispersed seeds across the landscapes (Pounden et al, 2008), and wind speed increases in open canopies (Katul et al, 2005) promoting long distance dispersal. The trunks and canopies of dense stands intercept seeds, which fall to the ground and are rapidly covered by litter that confers protection against predators, and a favourable microclimate for germination.…”