Statistical test for comparing overall preference of 3 groups based on count data I am struggling to find any examples online of a data structure and appropriate statistical test which matches my data. 
My dataset has counts of the number of courtships events of individual males towards different species of female. My hypothesis to test is that overall the males courted more towards the females of their own species. 
I have looked at GLMs with poisson/negative binomial distributions, but this doesn't seem appropriate as I have 3 response variables which I want to compare. I want the model to take into account the differences in the overall number of courtship counts of individual males (which I think rules out Chi-square).
This is what my data looks like:

Does anyone have any ideas with this? And perhaps any links/descriptions of how you would go through the analysis on R? 
 A: Disclaimer: This answer is quite speculative because I don't exactly understand
your experimental procedure or your data. And, after a (short) wait, I don't yet
have an answer to my question. If the answer is No, if you think I am
using your data improperly, or if you don't understand my analysis,
please leave a comment. At least, maybe we'll have a framework for
clarification, so we can start again.

If all six males are from Species b, then we could treat this
as a block design and do a Friedman test. The 'main effect' is Species
with three levels; the block effect is Males. It is assumed that Males
may react differently, and the Friedman test does not test for differences among Males. (An analogous situation is
that six judges taste three varieties of wine and give scores
to each. In this case 'scores' are numbers of courtship events.)
Here are results from a Friedman test:
a = c(4,5,0,8,5,13)
b = c(33,17,1,63,14,14)
c = c(5,1,0,7,6,14)
DTA=cbind(a,b,c)
friedman.test(DTA)

        Friedman rank sum test

data:  DTA
Friedman chi-squared = 8.4545, df = 2, p-value = 0.01459

So taken as a group, the males have a pattern of consistent preferences
among species. You don't have much data--barely enough to get significant results from such a rank-based test. Also two of the males stand out
as very different:  #3 is remarkably non-frisky, and #6 is remarkably 
non-discriminatory. So the small P-value indicating a clear difference
in preference is surprising.
By eye it seems that most of the males have some preference for species b.
A Wilcoxon signed rank (paired) tests find significant preferences of b over a and also of b over c. In both cases there are cautionary notes
about ties or 0's, so P-values are probably not exact.  (In comparing b against a there are two differences of $1$; in comparing b against c, there is a difference of 0.)
The difference between b and a is stronger. 
wilcox.test(b-c, alte="g")$p.val
[1] 0.02952911
Warning message:
In wilcox.test.default(b - c, alte = "g") :
  cannot compute exact p-value with zeroes

wilcox.test(b-a, alte="g")$p.val    
[1] 0.01776117
Warning message:
In wilcox.test.default(b - a, alte = "g") :
  cannot compute exact p-value with ties

In doing such ad hoc tests
there is some danger of 'false discovery', and I judge the difference
between b and c to be only borderline significant (only 5 out of 6 males
showed a difference, and one of them only barely).
