Multi-Scale Analysis of Seed Dispersal Contributes tothe Resolution of Reid’s Paradox

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"Reid's paradox" is the mismatch between theoretical estimates of invasion rates for plants and "observed" rates of plant migration, particularly in the Holocene postglacial migration northwards. While Reid couched his paradox in terms of the migration of oaks in Great Britain, observers have documented the same problem in a wide variety of species. In almost all cases, these authors suggest that occasional, long-distance events, probably mitigated by active dispersal factors (ants, birds, rodents) are responsible. Clark and co-workers have shown that order statistics can bridge the gap between theory and predictions, essentially using "fat- tailed" dispersal kernels raised to high powers corresponding to rare, distant dispersal events. However, the spatial caching structure induced by most active dispersers has not been specifically examined. In this paper we develop a complementary approach to order statistics, based on the theory of homogenization, to describe the long-distance dispersal probabilities of seeds. The homogenization approach includes the spatial structure of active dispersal explicitly, and generates a corrective factor to current estimates of migration rates. This corrective factor is the "caching scale ratio," the ratio of mean scatter-hoard size to mean separation between cache sites, and is, in principle, directly observable. The methodology is not limited to animal dispersers and can be used to address any set of dispersal agencies operating at differing scales, in one or more spatial dimensions. This approach is tested for three dispersal mutualisms where Reid's paradox is known to operate: harvester ant/wild ginger, Blue Jay/ oaks, and nutcracker/stone pine. Migration rates predicted using the homogenized approach compare favorably with estimates for tree species based on the paleo-ecological record. However, these rates do not seem to explain the Holocene migration of wild ginger.