Biostatistics: Pollen dispersal directionality
(This isn't an answer, but hopefully it will help get it past the experimental design into just solving the equation.)

Where did you get that α0 was not determined from their data? On p. 10 (256), they state, "The prevailing direction of effective pollen dispersal within neighbourhoods (a0) that gave the best ﬁt of the model was 91 degrees from north (nearly due east)." 

The best-fit δ parameter value of 0.56 (which determines the size of the effect of the angle between the male tree and the wind) is also determined by their model (table 1, model 9) based on their sample set.

This math is too much for me to solve, but here is how I would go about getting through the experimental setup to just solving the math equation:

Since you're only looking for the effect of wind/directionality, you would set the tree height and distance between trees to be equal. So βd and γh would remain constant and cancel out when you solve for a. 

Then you want to determine what angles would give you the highest and lowest pollen counts. Set a0 to wind direction and aj to the angle between a0 and the half disk. The highest pollen count would happen at aj = a0. The lowest pollen counts would happen at aj = (a0-180) or (a0-π or whatever unit of angle is appropriate. Stupid trig.).

With those settings, it should be possible to determine the values of ϕ where aj = a0 and where aj = a0-180. 

Then you can get the proportion of pollen grain falls into each disk by finding the ratio of ϕj(a0-180) / ϕj(a0).

Assumptions:
1) There's a linear correlation between ϕ, "the mating success (i.e. fertility) of each outcross male in the neighbourhood" and the distribution of pollen grain dispersal.

2) That a0 ("The prevailing direction of effective pollen dispersal within neighbourhoods") is entirely due to wind. Here I could see terrain being a factor, which would make the effect of wind xδ, such that x&lt;1. If this were the case, the calculated ratio of high pollen / low pollen would be higher than actual.