Are the ratios of bill crossing morphs in crossbills the result of frequency-dependent selection?

The direction the lower mandible curves in crossbills (Loxia) is an example of a discrete polymorphism. The lower mandible crosses with equal frequency to the left and to the right in several crossbill populations. I hypothesize that the 1:1 ratio results from negative frequency-dependent selection favouring the rarer morph. A crossbill always orients toward closed conifer cones so that its lower mandible is directed towards the cone axis. Thus, only part of the cone can be reached easily when crossbills have few perch sites and the cone cannot be removed from the branch or otherwise turned round. Since crossbills may visit cones which have previously been foraged on by other individuals, an equal frequency of left-to-right mandible crossings may minimize overlap in the use of cones and enhance foraging efficiency. Experimental data support this hypothesis. Moreover, the variation in the ratio of mandible crossing directions among crossbill populations is consistent with this hypothesis.