I have replicated a study of estimating macaw population size, whereby several point counts were made. I am now looking at the original study and trying to work out how to calculate the estimated population size and the associated variance, in the same way as the original study.
The original study (in Spanish here, with snapshot) does not state the name of the equation, nor why they chose it. Furthermore, it only includes half a key, which in English reads:
$m$ = parcel area, $M$ = potential sampling area
$y_i$ = animals detected , $A$ = study area
Obviously there is an error in what $A =$, and I have assumed that instead the following is true:
$m$ = area of plot , $M$ = total range of population
$A = a / M$ , $y_i$ = animals detected
$a$ = total area studied
I know that $M = 11500$ $\text{km}^2$. And from working backwards from the provided $\hat{N}$ in table 4, and assuming that $a = 13$ X m (as they used 13 of the 16 sites in there calculation by the looks of the tables. However this might be completley wrong, and now that I am thinking about it perhaps a=total #muestros X mbar), thus $\bar m$ must equal $3.9605$.
So my question is: are my assumptions (and maths) correct, and also where can I find the source of this equation so I can apply it correctly to my own data?
Further information: As my study is a replica, the same plots were used, however I did more repetitions of each area but for fewer hours each time. So is the area studied the same as the original, or greater?
1.Please note in the link for the study half of the equation is missing, so please use the link below to see the image of the full equation.
2. I have no idea what to tag this, so any suggestions for changes are greatly appreciated.