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
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:

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.
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.
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:

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.
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.
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))
)

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"

Scheduling Circuit Start Times

Before field work begins, randomise the circuit start time for each survey day using generate_progressive_start(). This ensures the count is unbiased with respect to time-of-day effort patterns. Two strategies are available:

"discrete" (default): start drawn from the valid τ-aligned offsets — avoids mid-day over-representation caused by the common error. Requires to be a whole number, and aborts if it is not; adjust circuit_time or the open hours to make it one.
"wraparound": start drawn from ; circuit may wrap past the end of the survey day. Carries no divisibility requirement.

The whole-number requirement belongs to "discrete" alone, because that scheme partitions the day into non-overlapping blocks and samples one. Under "wraparound" the count window slides freely, so is an ordinary ratio rather than a count of blocks and need not be a whole number.

This is why add_counts() does not check it. Both schemes give every moment of the day equal probability of being observed, so both are estimated by the same ; a divisibility check in the estimator would reject perfectly valid wraparound designs. The constraint is enforced where it applies — at scheduling time, by generate_progressive_start().

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

(no date column to render calendar)

The returned creel_schedule records circuit_start, circuit_end, is_wrapped, and direction ("forward" / "reverse") for each survey day. Record the scheduled start and direction in your field protocol — both are required for unbiased estimation.

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,
  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.

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.    3243.    4450.   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     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: Instantaneous counts were expanded without a period length.
#> ℹ No `period_length_col` was supplied to `add_counts()`, so the estimate is the
#>   count column summed over days.
#> ! If that column holds an instantaneous angler count, the result is in
#>   angler-days, not angler-hours.
#> ℹ Supply the period each count was randomised within: `add_counts(design,
#>   counts, period_length_col = <col>)`.
#> This warning is displayed once per session.
#> 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.