Calculating population estimate on multiple species in same table

I am trying to write a code that will allow me to automate the calculation of a population estimate on summarized capture data based on two-pass depletion methods used in fisheries.

The equation to calculate a population estimate using this method is as follows:

N = (C1)^2/(C1-C2) where N = Population Estimate, C1= Number captured in 1st sampling, C2 = Number captured in second sampling.

I have already summarized a large dataset based on species and the number captured in each "pass" or sampling instance.

An example of this summary dataset looks like this:

dataex <- data.frame(Species= c("BRK","RGN","RGN","RBT","RBT"),
                  PassCaptured = c(1,1,2,1,2),
                  NumberCaptured = c(6,18,5,10,3))

I am having trouble figuring out a code to calculate the population estimate for each species in this summary dataset.

For example, the population estimate for the species RGN using the dataset and the equation would be: (18)^2/(18 - 5) giving N = 24.

I could calculate this manually for each species based on the summarized dataset, but I know there is a more efficient way.

The desired output is a table with population estimate (N) calculated for each species:

data.frame(Species = c("RGN",'RBT'),
           Popest = c(18,35))

Note also that there are cases when a species is captured in the first sampling instance and not the second and thus, a population estimate cannot be calculated (species BRK in the example dataset)

Any help getting me started would be greatly appreciated.

Solution

Here's one way to calculate this population estimate for each species.

library(dplyr)

dataex |>
  arrange(Species, PassCaptured) |>
  summarize(
    Popest = (NumberCaptured[1]^2)/(NumberCaptured[1] - NumberCaptured[2]), 
    .by = Species
  ) |>
  tidyr::drop_na()
#>   Species   Popest
#> 1     RBT 14.28571
#> 2     RGN 24.92308