Estimate angler population size via closed-population mark-recapture

Computes a closed-population mark-recapture estimate of total angler population size (N_hat) using one of three estimators:

• Chapman (default, method = "chapman"): A bias-corrected version of the Petersen estimator recommended when recaptures are small. \(\hat{N} = \frac{(M+1)(n+1)}{(m+1)} - 1\)

• Petersen (method = "petersen"): The unadjusted Lincoln-Petersen estimator. Requires at least 7 recaptures (\(m \geq 7\)) to avoid large positive bias; use Chapman for smaller recapture counts. \(\hat{N} = \frac{M \cdot n}{m}\)

• Schnabel (method = "schnabel"): A multi-occasion weighted estimator for \(K \geq 2\) sampling occasions. \(\hat{N} = \frac{\sum M_k n_k}{\sum m_k}\) CI uses the Poisson branch when \(\sum m_k < 50\) and the normal approximation on \(1/\hat{N}\) otherwise.

Usage

estimate_angler_n(M, n, m, method = "chapman", conf_level = 0.95)

Arguments

M

integer or numeric. Number of marked animals released (first sample). For method = "schnabel", a vector of cumulative marked-at-large counts before each sampling occasion (M[1] = 0).

n

integer or numeric. Number captured in second sample. For Schnabel, a vector of per-occasion catch counts (same length as M).

m

integer or numeric. Number of recaptures. Scalar for Chapman and Petersen; vector (same length as M) for Schnabel.

method

character(1). One of "chapman" (default), "petersen", or "schnabel".

conf_level

numeric. Confidence level for the CI. Default 0.95.

Value

A creel_estimates S3 object with method = "mark-recapture-chapman" (or petersen/schnabel) and an estimates tibble with columns: parameter, estimate, se, ci_lower, ci_upper, n (total recaptures).

References

Hansen, M. J., & Van Kirk, R. W. (2018). A mark-recapture-based approach for estimating angler harvest. North American Journal of Fisheries Management, 38(2), 400–410. doi:10.1002/nafm.10038

See also

Other Estimation: estimate_exploitation_rate(), estimate_mr_harvest()

Examples

# Chapman (default) — bias-corrected Petersen
result <- estimate_angler_n(M = 200L, n = 50L, m = 10L)
print(result)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: mark-recapture-chapman
#> Variance: chapman
#> Confidence level: 95%
#> 
#> # A tibble: 1 × 6
#>   parameter estimate    se ci_lower ci_upper     n
#>   <chr>        <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1 N_hat         931.  232.     477.    1385.    10

# Petersen — requires m >= 7
result_p <- estimate_angler_n(M = 200L, n = 50L, m = 10L, method = "petersen")
print(result_p)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: mark-recapture-petersen
#> Variance: petersen
#> Confidence level: 95%
#> 
#> # A tibble: 1 × 6
#>   parameter estimate    se ci_lower ci_upper     n
#>   <chr>        <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1 N_hat         1000  283.     446.    1554.    10

# Schnabel — multi-occasion with parallel vectors
result_s <- estimate_angler_n(
  M = c(0L, 47L, 91L, 131L),
  n = c(50L, 50L, 50L, 50L),
  m = c(0L,  4L,  6L,  8L),
  method = "schnabel"
)
print(result_s)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: mark-recapture-schnabel
#> Variance: delta
#> Confidence level: 95%
#> 
#> # A tibble: 1 × 6
#>   parameter estimate    se ci_lower ci_upper     n
#>   <chr>        <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1 N_hat         747.  176.     498.     1345    18