My original question was going to be : How do you estimate the proportion of species in a population from count data of their individual body parts, provided that you can identify each part as belonging to a specific species.
Is it just enough to take the average number of body parts found per species? (keeping in mind some species might have a higher frequency of a certain body part than others).
Edit: More Explanation
EXAMPLE 1 - you take samples of animals that are coming out in pieces. A normal animal called Species 1 has 1 leg, 1 nose, and 1 eye, Each of these traits you can see and count.
Species 2 has 2 traits you can identify: ears (of which it also has only 1), and wings (Also only 1).
(assume this is true for K Species, with K_y traits)
You take 1 sample from x locations each time you count traits. the following is an example from 1 location:
1 leg, 5 noses, 12 eyes, 6 ears, and 8 wings... Which means the following
Number of Species 1's possible are : Minimum 12 individuals ; Maximum 18 individuals (1+5+12):
number of Species 2's possible are : Minimum 8 individuals ; Maximum 14 individuals (8+6).
So in a bag with 1 eye and 1ear I know I have 1 individual of each species(no variation), in a bag with 1 ear 1eye 2 wings and 5 legs I know I have a maximum of 6 individuals (5+1) of species 1 and a min of 5. Species 2, max of 4 min of 3.
So here we have possible limits for Species 1 and Species 2 at sample location x1.
What is the correct way to estimate and compare the proportions of each animal.
We identify each part as belonging to a specific species; the eyes, noses and legs (any eye nose or legs found) belong to species 1, the highest count of individual traits means I have a bigger possible number of individuals belonging to Species 1, the more traits mean I have a larger range to predict the number of individuals.
EXAMPLE 2 You could also think of them as real animals, say chickens, lambs, Piglets with parts in a single bag.
You can easily tell the difference between the three animals limbs, you know that if you get 18 chicken wings and only 3 drumsticks, then the maximum number of chicken slaughtered (assuming the drumsticks, and wings all come from different animals) is 18+3.
Where as the minimum possible number of chicken slaughtered is where the wings are paired 18/2 (9 individuals), and the drumsticks are paired 3/2 (so only a min of 2 whole individuals) per chicken, and the wings and the drumsticks come from the same chickens(and some limbs are lost obviously). So the min# of individuals is the minimum number of pairs [9 whole chicken], and the more likely possible #individuals is the sum of all pairs[9+2 chickens],(but not necessarily???)
So as you can see possible limits of chicken found by calculating their individual parts is : min- 9 chickens, and maximum 21 chickens…… the true number is probably somewhere in the middle(THIS is what I would like to calculate with a high degree of certainty, It could be 11 but I'm not sure of this. I want to be sure of this).
Now let's count the number of pork chops, and pig heads…. etc
Except With the first example the question is simpler, because each trait is exclusive and only occurs once for species. different species will also have different traits (You cannot count pork-chops and lamb chops and consider them from the same species.)
Should I :
-- Calculate a midpoint/mean as (( Maximum - Minimum )/(number of traits)) + Minimum for each species. The calculate the Standard deviation (for each) and compare the Coefficient of variances across each sample x?
-- Take the Midpoint/mean calculated above, rank them and do non parametric pairwise comparisons of my x's
-- Take the Maximum once and minimum once, rank each proceed non parametrically once for the upper limit once for the lower limit.
--- There is probably a way to more accurately find the "true" number (or something close to it) of Individuals per species... If you have any ideas, please let me know.
(I realize 1 sample is not nearly enough, if you would like more information see the link, I can only get 1 sample per location, i'd like to treat each trait as a separate sampling unit, these traits aren't really from animals etc..)