Two-generation analysis of pollen flow across a landscape. II. Relation between phi(ft), pollen dispersal and...

We study the behavior of Phi(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 Phi(ft) depends on the average distance of pollen dispersal (delta) and on the average distance between sampled mothers (x(1)). Provided that mothers are sampled far enough apart (x(1) > 5delta), Phi(ft) becomes independent of x(1) and is then inversely proportional to the square of delta. Provided that this condition is fulfilled, delta is directly estimable from Phi(ft). Even when x(1) < 5delta, estimation can easily be achieved via numerical evaluation. We show that the relation between Phi(ft) and delta 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 Phi(ft), showing that to achieve the correct inference of delta from Phi(ft) it must be taken into account, but that it has no effect on the distance at which mothers must be sampled.