Lincoln index
lincoln_index.Rd
Estimate the size of the wild-male population.
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 $S$.