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Multiple proportions analysis in R

Manuel Spínola 
Dear list members,

The following question is not entirely an R question but I am looking 
how to analyze the below data set in R (I know that sample size is very 
low):

I have a data set corresponding to 12 nests with (20 to 30 eggs each).  
The number of eggs per nest varies.
In each nest I assessed the stage of egg development, location (zone), 
humidity and temperature.

nest  stage0 stage2 stage3 stage4   zone   humidity temp

1        12       8        0        0           a        4.35      34.5
2         0       10       2        14          a        5.56       32.4
3         0       14      0         12          a        6.57       33.7
4         0       12     15        3            b       7.08        33.4
.
.
12      0        6       20       0              c       5.07       34.5
 
I have multiple proportions (one for each stage) in each nest but they 
are not independent. 
I want to assess the effect of zone, humidity and temp on the proportion 
of different stages at each nest.
Is this a case for a multinomial model?
How is a simple way to analyze this data set?
Best,

Manuel Sp?nola