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Estimate the size of the wild-male population.

Usage

lincoln_index(released, survival_rate, age, marked_recaptured, wild_catch)

Arguments

released

Numeric. Number of sterile males released.

survival_rate

Numeric. Estimated survival rate.

age

Numeric. Number of days since release.

marked_recaptured

Numeric. Number of re-captured sterile males.

wild_catch

Numeric. Number of wild males captured.

Details

A simple estimate is obtained as follows (Thompson 2012, Ch. 18). Let the total captures at a day $t$ be the sum of $m_t$ marked and $n_t$ wild mosquitoes. Assuming that the proportion of marked individuals in the sample equals that in the population of size $P$: $$\frac{m_t}{m_t + n_t} = \frac{M_t}{M_t + P},$$ where $M_t = R\,S^a_t$ is the number of marked individuals captured at time $t$, with $R$ the number of released adults, $S$ the daily survival rate and $a_t$ the number of days since release (age). I.e., the number of marked individuals at time $t$ is the remaining number from those released that survived for $a_t$ days.

The Lincoln Index (a.k.a. the Petersen estimator) has been used as a simple estimate of the wild male population size, assuming that the survival rate of an individual remains constant. Here we use a modified version that corrects for small samples and compensates for daily survival. $$P_t = R\,S^{a_t}\,(n_t + 1) / (m_t + 1).$$

The values of $R$, $n_t$, $m_t$ and $t$ can be gathered from the adult surveys data. The calculation required the estimation of the survival rate $S$.

References

Thompson, Steven K. 2012. Sampling. 3rd ed. Wiley Series in Probability and Statistics. Hoboken, N.J: Wiley.

Examples

lincoln_index(
  released         = 1e4,
  survival_rate    = .80,
  age              = 1,
  marked_recapture = 15,
  wild_catch       = 5
)
#> [1] 3000