Variation in dispersal ability among the individual organisms in a population could have substantial implications for demography and population spread, community dynamics, and evolution by natural selection. In plants, dispersal ability may vary at both the level of the maternal plant (how far can the plant disperse its offspring?) and the individual seed (how far can one seed disperse relative to its siblings?). In addition, dispersal ability in seeds can covary with other demographic rates. For example, maternal plants may trade-off between productivity (the number of seeds produced) and provisioning of individual seeds (seed size). All else being equal, heavier seeds tend to reduce dispersal ability in primarily wind-dispersed species, but may increase dispersal in some animal-dispersed species, particularly those transported by scatter-hoarding granivores. Finally, many plant species show positive correlations between seed size and germination, seedling vigor, or seedling competitiveness and survival.
I use a series of theoretical models to explore the implications of size-based covariation among maternal productivity, seed dispersal ability, and individual seedling establishment probabilities. Specifically, I compare the seedling shadows that arise when other demographic rates are assumed to be independent of dispersal ability with the shadows that result from models that account for covariation.
For simplicity, I assume that individual seeds are dispersed according to a Gaussian kernel with a standard deviation that varies linearly with seed size. In the absence of a size effect on establishment probabilities, normal variation in size among seeds produces a heavy-tailed, 2Dt-type kernel at the cohort level. When size-dependent establishment probabilities are added to this model, their effect depends on the relationship between seed size and dispersal. Assuming low overall establishment rates that increase linearly with seed size, increased variation in seed size causes recruitment to decline near the source and to increase at longer dispersal distances. In addition, the ratio of recruitment with size-dependent establishment to recruitment without size-dependence approaches a constant, asymptotic value > 1 as dispersal distance increases. The opposite pattern occurs if dispersal is inversely related to seed size. In conclusion, traits that affect seed dispersal may also effect seedling recruitment, leading to covariation among these processes. Depending on its sign, this covariation may either exaggerate or dampen the effects of variation in dispersal ability on spatial recruitment patterns, even in the absence of density- or habitat-dependent survival.