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

摘要

We study the behavior of Φft, 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 Φft depends on the average distance of pollen dispersal (δ) and on the average distance between sampled mothers (mml:math xmlns:mml=quot;http://www.w3.org/1998/Math/MathMLquot; display=quot;inlinequot; id=quot;M1quot; overflow=quot;scrollquot;mml:mover accent=quot;truequot;mml:mrowmml:msubmml:mix/mml:mimml:mn1/mml:mn/mml:msub/mml:mrowmml:mo¯/mml:mo/mml:mover/mml:math ). Provided that mothers are sampled far enough apart (mml:math xmlns:mml=quot;http://www.w3.org/1998/Math/MathMLquot; display=quot;inlinequot; id=quot;M2quot; overflow=quot;scrollquot;mml:mrowmml:mover accent=quot;truequot;mml:mrowmml:msubmml:mix/mml:mimml:mn1/mml:mn/mml:msub/mml:mrowmml:mo¯/mml:mo/mml:movermml:mo/mml:momml:mn5/mml:mnmml:miδ/mml:mi/mml:mrow/mml:math ), Φft becomes independent of mml:math xmlns:mml=quot;http://www.w3.org/1998/Math/MathMLquot; display=quot;inlinequot; id=quot;M3quot; overflow=quot;scrollquot;mml:mover accent=quot;truequot;mml:mrowmml:msubmml:mix/mml:mimml:mn1/mml:mn/mml:msub/mml:mrowmml:mo¯/mml:mo/mml:mover/mml:math and is then inversely proportional to the square of δ. Provided that this condition is fulfilled, δ is directly estimable from Φft. Even when mml:math xmlns:mml=quot;http://www.w3.org/1998/Math/MathMLquot; display=quot;inlinequot; id=quot;M4quot; overflow=quot;scrollquot;mml:mrowmml:mover accent=quot;truequot;mml:mrowmml:msubmml:mix/mml:mimml:mn1/mml:mn/mml:msub/mml:mrowmml:mo¯/mml:mo/mml:movermml:mo/mml:momml:mn5/mml:mnmml:miδ/mml:mi/mml:mrow/mml:math , estimation can easily be achieved via numerical evaluation. We show that the relation between Φft 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 Φft, showing that to achieve the correct inference of δ from Φft it must be taken into account, but that it has no effect on the distance at which mothers must be sampled.