Relatedness in Single-Mated vs. Multi-Mated Queens

• Single-mated queen: If a queen mates with only one male, all her daughters (workers) are full sisters. In the haplodiploid system, full sisters share all of their father’s genes (since he is haploid) and half of their mother’s, resulting in a relatedness of 0.75 (75%) between sisters.

• Multi-mated queen: If a queen mates with multiple males, her daughters are a mix of full sisters (same father) and half-sisters (different fathers). Full sisters still share 75% of their genes, but half-sisters share only 25% (because they only share genes from their mother).

Calculating Mean Genetic Relatedness

When a queen mates with n males, and sperm is used equally from each, the average relatedness among female offspring is:

Mean relatedness=1n×0.75+n−1n×0.25Mean relatedness=n1×0.75+nn−1×0.25

For example, with two males (n = 2):

Mean relatedness=12×0.75+12×0.25=0.5Mean relatedness=21×0.75+21×0.25=0.5

As the number of males increases, the mean relatedness approaches 0.25, the value for half-sisters.

Empirical Evidence

Studies confirm that in natural honey bee colonies, the mean genetic relatedness among female progeny is significantly lower than 0.75, often around 0.5 or even lower, depending on the number of males the queen mates with. This reduction in relatedness is a direct result of polyandry (multiple mating), which increases genetic diversity in the colony but decreases the average relatedness among workers.

Conclusion

If a honey bee queen mates with multiple males, the mean genetic relatedness among her female progeny is lower than 0.75 and is correctly represented by a value between 0.25 and 0.75, typically around 0.5 for two mates and decreasing further with more mates.

This shift in relatedness is a key factor in the evolution of social behavior and genetic diversity in Hymenoptera colonies.