Two-Generation Analysis of Pollen Flow Across a Landscape. II. Relation Between Φft, Pollen Dispersal and Interfemale Distance

We study the behavior of Φ_ft, a recently introduced estimator of instantaneous pollen flow, which is basically the intraclass correlation of inferred pollen cloud genetic frequencies among a sample of females drawn from a single population. Using standard theories of identity by descent and spatial processes, we show that Φ_ft depends on the average distance of pollen dispersal (δ) and on the average distance between sampled mothers (⁠ $x1¯$⁠). Provided that mothers are sampled far enough apart (⁠ $x1¯>5δ$⁠), Φ_ft becomes independent of $x1¯$ and is then inversely proportional to the square of δ. Provided that this condition is fulfilled, δ is directly estimable from Φ_ft. Even when $x1¯<5δ$⁠, estimation can easily be achieved via numerical evaluation. We show that the relation between Φ_ft and δ is only modestly affected by the shape of the distribution function, a result of importance, since this shape is generally unknown. We also study the impact of adult density within the population on Φ_ft, showing that to achieve the correct inference of δ from Φ_ft it must be taken into account, but that it has no effect on the distance at which mothers must be sampled.