Your data is not currently in the correct shape for a poisson/negative binomial regression because you currently have three columns that constitute your response variabl. As such, you will need to reshape your data to answer the question you are interested in.
I think you are actually after a chi-square test but this will require that you reshape your data into a two by two contingency table.
If you want to account for the potential effect of an individual (I.e. a male that is particularly keen on a particular species) you might extend this to be a log-linear model with mixed-effects. You can do the latter in R with the lme package.
Note: A log-linear model is a specific case of a poisson/negative binomial model, and you almost always want negative binomial errors.
A table like this (albeit editted to suit your stats programs needs) would yield the results I think you want by using a chi-square analysis. You wouldn't be combining counts between species so you shouldn't run the risk of doubling as you suggested in the comments.