> What do the figures 0.15 to 0.375 mean and how are they derived?  

This is the so-called relatedness between members of the colony. Francis Ratnieks wrote, when he was at Cornell:

> As the number of males that mate with a queen increases, the relatedness (G) between a worker and the male offspring of the queen remains constant (G = 0.25), whereas the mean relatedness between workers and the male offspring of other workers declines from 0.375 to 0.125. 

> Therefore, when queens mate once, the hierarchy of worker "preferences" for the mother of the colony's males would be (1) self (G = 0.5); (2) randomly chosen worker (sister) (G = 0.375); (3) queen (mother) (G = 0.25). However, when queens mate with many males, this sequence becomes (1) self, (2) queen, (3) randomly chosen worker (G < 0.25). 

In this example he is using the ratio of relatedness to show how bees favor those that are more closely related, as in the much lauded theory of Kinship Selection. This is an area where the math whizzes have dominated for years. Unfortunately, the weakness is that honey bees don't seem to respect kinship all that much, joining other colonies will nilly and accepting unrelated workers and even queens when circumstances require.

PLB

ref

Reproductive Harmony via Mutual Policing by Workers in Eusocial Hymenoptera Author(s): Francis L. W. Ratnieks
Source: The American Naturalist, Vol. 132, No. 2 (Aug., 1988), pp. 217-236

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