The function also returns a p-value to evaluate whether partitioning the data is statistically warranted.
The function then fits the Two-Innate Rates Model (TIRM) to the lower set of the partitioned data and adds the individuals from the upper set to the estimate of population size
fitTirmPartition(data, max.pop, n.boots.part=100)n.boots.part=100) should be appropriate.
max.popThe PART algorithm first fits the Two-Innate Rates Model (TIRM) to the entire data set. Assuming the distribution of capture counts can be approximated as either a two (null) or three (alternative) class multinomial distribution, the algorithm considers all possible ways to partition the count data under both the null and alternative distributions. The partitioning schemes which maximizes the respective likelihoods is retained. A test-statistic, the ratio of multinomial (log) likelihoods (3:2) is obtained for the observed data.
The MLE for number of individuals in class a, number of individuals in class b and the ratio of capture probabilities (alpha) are used to simulate n.boots.part data sets
under the TIRM. The test-statistic is calculated for each data set as described above.
The observed test-statistic is then compared to the distribution of simulated test-statistics. When the observed test-statistic falls in the tail of the distribution of the test-statisitic from the simulated data, the null model can be rejected.
The TIRM model is then fit to the lower two classes obtained from partitioning the data in order to obtain the MLE for population size. Individuals from the upper class (i.e. those that were captured most often) to the population size estimate. It is therefore assumed that we have captured all individuals in the population with the highest probability of capture and that the class designation has been made without error.
The TIRM model fit by this function assumes that individuals can be assigned to two classes. Class A represent the frequently captured individuals. Class B represents the infrequently captured individuals.
The value is specified for max.pop is not likely to matter as long as it is much greater than the maximum likelihood estimate for population size.
Note that if the data contains only singletons, the data is not informative and the maximum likelihood estimate for population size will be equal to max.pop
Pennell M.W., C.R. Stansbury, L.P. Waits and C.R. Miller. submitted. capwire: A R Package for Estimating Population Census Size from Non-Invasive Genetic Sampling
Stansbury C.R., D.E. Ausband, P. Zager, C.M. Mack, C.R. Miller, M.W. Pennell, and L.P. Waits. in prep. Non-invasive genetic sampling of rendezvous sites and population estimation of grey wolves in Idaho, USA
fitTirm, partitionCountData
## Use dummy data set with a few individuals having very high capture counts
d <- c(1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,6,6,7,8,10,10,14,17,19,22,22,25)
data <- buildClassTable(d)
## Partition the data
## Fit the TIRM to the lower two classes obtained from partitioning data set
res <- fitTirmPartition(data=data, max.pop=200, n.boots.part=10)
res
## Compare population estimate from fitting TIRM
## to partitioned data set to population estimate obtained from fitting all data
res.all <- fitTirm(data=data, max.pop=200)$ml.pop.size
res.all
Run the code above in your browser using DataLab