Progressive Count Surveys • tidycreel

Overview

A progressive count survey replaces the random spot-check of an instantaneous count with a complete traversal of the access corridor. The observer drives or walks the entire shoreline, access road, or boat ramp circuit — counting every angler encountered along the way. This vignette demonstrates the full progressive count workflow: scheduling, data collection structure, effort estimation, and catch estimation.

Instantaneous vs. Progressive Counts

Feature	Instantaneous	Progressive
Observer visits	One spot at a random time	Full circuit of the section
Count meaning	Anglers visible at a moment	Anglers encountered during circuit
Estimator	$\hat{E}_d = C \times T_d$	$\hat{E}_d = C \times T_d$
Additional input	—	`circuit_time` (τ) and `period_length_col` ( $T_d$ )
Circuit time τ	Not needed	Required (cancels algebraically)

The estimators are algebraically identical once the progressive count formula is expanded: $\hat{E}_d = C \times \tau \times (T_d / \tau) = C \times T_d$ . The circuit time $\tau$ cancels, so only the raw count $C$ and the total open hours $T_d$ enter the final calculation. Nevertheless, $\tau$ must be supplied to add_counts() as a check that the field protocol (circuit duration) is documented.

When to Use Progressive Counts

Progressive counts are preferred when:

Anglers are spread along a linear corridor (river, canal, reservoir shoreline road) and a single spot-check would miss substantial activity
The access route is fully enumerable in one traverse within a count period
Observer movement is fast relative to angler turnover (circuit time < 30% of $T_d$ )

Instantaneous counts are preferred when:

The waterbody is large and a complete traverse is impractical
Multiple sections are counted simultaneously by separate crews
Observer presence along the circuit might disturb anglers or alert them to upcoming interviews

Data Requirements

A progressive count dataset needs:

Calendar — sampled dates with day_type and open_hours ( $T_d$ )
Count data — one row per sampled day with raw angler count ( $C$ ) and a column recording $T_d$ (the same open_hours value, or an observed value if the site closed early)
circuit_time — a single numeric value (hours) for the traversal duration $\tau$

A Complete Example

Survey Setup

We survey a 25-km reservoir access road over a 4-week season (July–July). A single crew completes the full circuit in 2 hours ( $\tau = 2$ h). The access road is open 10 hours per day.

library(tidycreel)

# Four-week season: 10 weekdays, 8 weekend days sampled
calendar <- data.frame(
  date = as.Date(c(
    # Weekdays
    "2024-07-01", "2024-07-02", "2024-07-03", "2024-07-04", "2024-07-05",
    "2024-07-09", "2024-07-10", "2024-07-11", "2024-07-12", "2024-07-16",
    # Weekends
    "2024-07-06", "2024-07-07", "2024-07-13", "2024-07-14",
    "2024-07-20", "2024-07-21", "2024-07-27", "2024-07-28"
  )),
  day_type = c(rep("weekday", 10), rep("weekend", 8)),
  open_hours = 10
)

design <- creel_design(calendar, date = date, strata = day_type)
design
#> 
#> ── Creel Survey Design ─────────────────────────────────────────────────────────
#> Type: "instantaneous"
#> Date column: date
#> Strata: day_type
#> Calendar: 18 days (2024-07-01 to 2024-07-28)
#> day_type: 2 levels
#> Counts: "none"
#> Interviews: "none"
#> Sections: "none"

Count Data

Each row is one circuit traversal per sampled day. The shift_hours column records the actual open hours for that day (here always 10, but could vary if a site closed early due to weather).

set.seed(7)
counts <- data.frame(
  date = calendar$date,
  day_type = calendar$day_type,
  n_anglers = c(
    # Weekday counts: moderate activity
    18L, 22L, 15L, 12L, 25L, 20L, 17L, 14L, 23L, 19L,
    # Weekend counts: higher activity
    48L, 55L, 42L, 61L, 53L, 47L, 58L, 64L
  ),
  shift_hours = 10
)

Attaching Progressive Counts

Specify count_type = "progressive", the circuit time $\tau$ in hours, and the column holding $T_d$ :

design <- add_counts(
  design, counts,
  count_type = "progressive",
  circuit_time = 2,
  period_length_col = shift_hours
)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

# Per-day expanded effort (C × T_d) stored in design$counts
head(design$counts, 4)
#>         date day_type n_anglers
#> 1 2024-07-01  weekday       180
#> 2 2024-07-02  weekday       220
#> 3 2024-07-03  weekday       150
#> 4 2024-07-04  weekday       120

The n_anglers column now holds $\hat{E}_d = C \times T_d$ , not the raw count. For the first day (18 anglers × 10 hours = 180 angler-hours):

# Verify: C × T_d = 18 × 10 = 180
design$counts$n_anglers[1]
#> [1] 180

Effort Estimation

effort <- estimate_effort(design)
effort$estimates
#> # A tibble: 1 × 7
#>   estimate    se se_between se_within ci_lower ci_upper     n
#>      <dbl> <dbl>      <dbl>     <dbl>    <dbl>    <dbl> <int>
#> 1     6130  249.       249.         0    5601.    6659.    18

The estimate column is the stratified total angler-hours for the 4-week season. The se column is the standard error of that total; se_within is always zero for progressive surveys because there is only one circuit per day (no within-day replication).

Adding Interviews

Interviews are collected during or after the circuit traversal. Attach them exactly as in any other survey type:

set.seed(7)
n_int <- 120 # interviews collected across the season

int_dates <- sample(calendar$date, n_int, replace = TRUE)
catch_total <- rpois(n_int, lambda = 2.1)
interviews <- data.frame(
  date = int_dates,
  day_type = calendar$day_type[match(int_dates, calendar$date)],
  trip_status = "complete",
  hours_fished = round(pmax(rnorm(n_int, mean = 3.8, sd = 1.3), 0.5), 1),
  catch_total = catch_total,
  catch_kept = pmin(rpois(n_int, lambda = 0.7), catch_total)
)

design <- add_interviews(
  design, interviews,
  trip_status = trip_status,
  catch = catch_total,
  effort = hours_fished,
  harvest = catch_kept
)
#> Warning: 10 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.

Catch Rate and Total Catch

cpue <- estimate_catch_rate(design)
cpue$estimates
#> # A tibble: 1 × 5
#>   estimate     se ci_lower ci_upper     n
#>      <dbl>  <dbl>    <dbl>    <dbl> <int>
#> 1    0.606 0.0389    0.530    0.682   120

total_catch <- estimate_total_catch(design)
total_catch$estimates
#> # A tibble: 1 × 5
#>   estimate    se ci_lower ci_upper     n
#>      <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1    3846.  305.    3248.    4445.   120

estimate_total_catch() multiplies the effort estimate by the CPUE estimate and propagates uncertainty via the delta method, producing a season-total catch with a combined standard error.

Harvest Rate and Total Harvest

harvest_rate <- estimate_harvest_rate(design)
harvest_rate$estimates
#> # A tibble: 1 × 5
#>   estimate     se ci_lower ci_upper     n
#>      <dbl>  <dbl>    <dbl>    <dbl> <int>
#> 1    0.161 0.0186    0.125    0.198   120

total_harvest <- estimate_total_harvest(design)
total_harvest$estimates
#> # A tibble: 1 × 5
#>   estimate    se ci_lower ci_upper     n
#>      <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1     989.  121.     752.    1225.   120

Pope et al. Worked Example

Pope et al. (in press) give the canonical calculation: $C = 234$ anglers encountered during a $\tau = 2$ h circuit on a day with $T_d = 8$ open hours.

$\hat{E}_d = 234 \times 8 = 1{,}872 \text{ angler-hours}$

cal_pope <- data.frame(
  date       = as.Date(c("2024-06-01", "2024-06-02")),
  day_type   = c("weekday", "weekday"),
  open_hours = c(8, 8)
)
des_pope <- creel_design(cal_pope, date = date, strata = day_type)

cnt_pope <- data.frame(
  date        = as.Date(c("2024-06-01", "2024-06-02")),
  day_type    = c("weekday", "weekday"),
  n_anglers   = c(234L, 200L),
  shift_hours = c(8, 8)
)
des_pope <- add_counts(
  des_pope, cnt_pope,
  count_type = "progressive",
  circuit_time = 2,
  period_length_col = shift_hours
)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

# First-day Ê_d = 234 × 8 = 1,872 angler-hours
des_pope$counts
#>         date day_type n_anglers
#> 1 2024-06-01  weekday      1872
#> 2 2024-06-02  weekday      1600

Multiple Periods per Day

Some progressive surveys run two circuits per day (e.g., morning and evening). This creates multiple counts per PSU (day), and tidycreel decomposes variance into between-day and within-day components via the Rasmussen (1994) two-stage formula.

For the morning–evening case, use count_time_col to identify the circuit within each day:

# Two circuits per day (morning and evening traversals)
cal_2p <- data.frame(
  date       = rep(as.Date(c("2024-07-01", "2024-07-02", "2024-07-06", "2024-07-07")), 1),
  day_type   = c("weekday", "weekday", "weekend", "weekend"),
  open_hours = 12
)
des_2p <- creel_design(cal_2p, date = date, strata = day_type)

cnt_2p <- data.frame(
  date = rep(as.Date(c(
    "2024-07-01", "2024-07-02",
    "2024-07-06", "2024-07-07"
  )), each = 2),
  day_type = rep(c("weekday", "weekday", "weekend", "weekend"), each = 2),
  count_time = rep(c("am", "pm"), 4),
  n_anglers = c(22L, 18L, 20L, 24L, 55L, 48L, 62L, 58L),
  shift_hours = 12
)

# Note: count_time_col for within-day identification
des_2p <- add_counts(des_2p, cnt_2p, count_time_col = count_time)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

est_2p <- estimate_effort(des_2p)
#> Warning: 2 strata have fewer than 3 observations:
#> • Stratum weekday: 2 observations
#> • Stratum weekend: 2 observations
#> ! Sparse strata produce unstable variance estimates.
#> ℹ Consider combining sparse strata or collecting more data.
est_2p$estimates
#> # A tibble: 1 × 7
#>   estimate    se se_between se_within ci_lower ci_upper     n
#>      <dbl> <dbl>      <dbl>     <dbl>    <dbl>    <dbl> <int>
#> 1     154.  10.0       8.73      4.92     110.     197.     4

The se_within column is now non-zero, reflecting variability between the morning and evening circuits within each day.

Assemble a Summary Report

summary_tbl <- season_summary(list(
  effort  = effort,
  catch   = total_catch,
  harvest = total_harvest
))

summary_tbl$table
#> # A tibble: 1 × 17
#>   effort_estimate effort_se effort_se_between effort_se_within effort_ci_lower
#>             <dbl>     <dbl>             <dbl>            <dbl>           <dbl>
#> 1            6130      249.              249.                0           5601.
#> # ℹ 12 more variables: effort_ci_upper <dbl>, effort_n <int>,
#> #   catch_estimate <dbl>, catch_se <dbl>, catch_ci_lower <dbl>,
#> #   catch_ci_upper <dbl>, catch_n <int>, harvest_estimate <dbl>,
#> #   harvest_se <dbl>, harvest_ci_lower <dbl>, harvest_ci_upper <dbl>,
#> #   harvest_n <int>

References

Hoenig, J. M., Robson, D. S., Jones, C. M., and Pollock, K. H. (1993). Scheduling counts in the instantaneous and progressive count methods for estimating sportfishing effort. North American Journal of Fisheries Management, 13, 723–736.
Pope, K. L., Wilde, G. R., and Gabelhouse, D. W. Jr. (in press). Creel Surveys. Chapter 17 in Fisheries Techniques, 4th ed. American Fisheries Society, Bethesda, MD.
Rasmussen, P. W. (1994). Two-stage variance estimation for creel surveys.
Su, Y.-S., and Liu, P. (2025). Flexible creel survey estimators. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1–27.