Progressive Count Surveys

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

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
• The observer can travel the circuit faster than anglers move between fishing spots (see the conditions below — this is a requirement of the method, not a preference)

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

Conditions for an Unbiased Estimate

\(\hat{E}_d = C \times T_d\) is unbiased only when the field protocol satisfies three conditions (Hoenig et al. 1993, p. 725). They are properties of how the count is collected, so no check inside add_counts() can confirm them — they are the analyst’s responsibility:

1. The starting location on the circuit is chosen randomly. Always beginning at the boat ramp biases the count toward whatever is happening there at that hour.
2. The direction of travel is chosen randomly from the two alternatives. generate_progressive_start() draws this for you and returns it in the direction column — it is a field instruction, not decoration.
3. The observer travels faster than the anglers move while those anglers are fishing. If anglers can outpace the observer they may be counted twice or missed.

Two further cautions from the same paper:

• Do not interrupt the circuit to conduct interviews. The derivation assumes constant travel speed; stopping to interview breaks it and is one of the four errors Hoenig et al. single out. Interview on a separate pass.
• The count estimates angler-days of effort, not the number of trips. Reading \(C\) as a trip count “results in a negative bias that can be severe” (Hoenig et al. 1993). \(C\) counts anglers present, and an angler fishing all day is counted once per circuit — not once per trip.

Scheduling the circuit start correctly is the fourth condition, and it is the subject of the section below.

Data Requirements

A progressive count dataset needs:

1. Calendar — sampled dates with day_type. The calendar carries no hours column: creel_design() reads only the date and the strata, so \(T_d\) must travel with the counts.
2. Count data — one row per sampled day with raw angler count (\(C\)) and a column recording \(T_d\), passed as period_length_col. This is the only place the estimator looks for the open hours.
3. circuit_time — a single numeric value (hours) for the traversal duration \(\tau\)

A Complete Example

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))
)

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"

starts <- generate_progressive_start(
  open_start    = "06:00",
  open_end      = "16:00",
  circuit_time  = 2,          # τ = 2 h; T = 10 h → k = 5 valid starts
  strategy      = "discrete",
  n             = nrow(calendar),
  seed          = 42
)
starts

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
)

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

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

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

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,
  n_anglers = 1, # every interview is a single angler
  harvest = catch_kept
)
#> Warning: 10 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.

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.    3243.    4450.   120

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     966.  129.     711.    1222.   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")
)
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")
)
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)
)

# 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.

This chunk shows the within-day variance decomposition on its own; it does not apply the progressive \(T_d\) expansion, so est_2p is in counts rather than angler-hours. To get both, add count_type = "progressive", circuit_time, and period_length_col as in the sections above — add_counts() supports multiple circuits per day on the progressive path.

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.