Creel surveys estimate angler effort — the total angler-hours or angler-trips on a waterbody during a survey period. The count data collected in the field can take two forms:
Instantaneous counts (Hoenig et al. 1993): At a
random time within the survey period, an observer records the number of
anglers visible on a section. estimate_effort() expands the
counts to the season and returns angler-days — the
counts themselves, summed over days. It does not multiply by open hours,
so converting the result to angler-hours is a step you take yourself
(see “Units of the instantaneous estimate” below).
Progressive counts (Pope et al., in press): An observer travels the entire section (one “circuit”) and records the number of anglers encountered along the way. Effort is estimated as count × circuit travel time × section open hours / circuit travel time, i.e., Ê_d = C × τ × (T_d / τ) = C × T_d where τ is circuit travel time and T_d is the total open hours on day d.
In addition, observers may complete multiple counts per day (e.g., morning and afternoon circuits). When multiple counts are recorded per sampling unit (PSU), tidycreel aggregates them automatically and decomposes variance into a between-day component and a within-day component via the Rasmussen (1994) two-stage formula.
The examples below show each workflow with inline data.
The classic workflow records one instantaneous count per PSU (day × stratum).
library(tidycreel)
# Survey calendar: four days, two strata
calendar <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")),
day_type = c("weekday", "weekday", "weekend", "weekend")
)
design <- creel_design(calendar, date = date, strata = day_type)
# One count per day
counts <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")),
day_type = c("weekday", "weekday", "weekend", "weekend"),
n_anglers = c(15L, 23L, 45L, 52L)
)
design <- add_counts(design, counts)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
result <- estimate_effort(design)
#> 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.
result$estimates
#> # A tibble: 1 × 7
#> estimate se se_between se_within ci_lower ci_upper n
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 135 10.6 10.6 0 89.3 181. 4With a single count per day, se_within is always zero —
there is no within-day replication to estimate within-day variance. The
se column equals se_between.
The estimate above is 135, which is the sum of the four counts (all
four calendar days were sampled, so the season expansion factor is 1).
It is angler-days, not angler-hours: an instantaneous
count is a snapshot of how many anglers were present at one moment, and
estimate_effort() never multiplies it by the length of the
fishing day. On a 10-hour day the corresponding effort is
135 * 10 = 1350 angler-hours, and that multiplication is
yours to do.
The progressive path below is the one that carries hours, via
period_length_col. If you need angler-hours from
instantaneous counts, either scale the result yourself or supply
pre-expanded daily effort to add_counts() — a column
already in angler-hours — rather than raw counts.
When observers complete multiple circuits on the same day, each
circuit is a sub-sample within the PSU. Supply the circuit identifier
column via count_time_col.
# Two circuits per day: morning ("am") and afternoon ("pm")
calendar_m <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")),
day_type = c("weekday", "weekday", "weekend", "weekend")
)
design_m <- creel_design(calendar_m, date = date, strata = day_type)
multi_counts <- data.frame(
date = as.Date(rep(c(
"2024-06-01", "2024-06-02",
"2024-06-03", "2024-06-04"
), each = 2)),
day_type = rep(c("weekday", "weekday", "weekend", "weekend"), each = 2),
count_time = rep(c("am", "pm"), 4),
n_anglers = c(12L, 18L, 20L, 26L, 40L, 50L, 48L, 56L)
)
design_m <- add_counts(design_m, multi_counts, count_time_col = count_time)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
result_m <- estimate_effort(design_m)
#> 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.
result_m$estimates
#> # A tibble: 1 × 7
#> estimate se se_between se_within ci_lower ci_upper n
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 135 13.1 10.6 7.68 78.6 191. 4The output tibble now contains nonzero se_within values.
Total variance is se^2 = se_between^2 + se_within^2
(combined in quadrature). When within-day angler counts vary
substantially between circuits, se_within can be the
dominant variance component.
se_within matter?se_within is small when counts are stable throughout the
day (e.g., a lake where angler density is roughly constant). It is large
when activity patterns are strongly bimodal (e.g., a river with a
morning bite and an evening bite but few mid-day anglers). Collecting
multiple counts per day is most valuable when such within-day variation
is expected and needs to be quantified rather than assumed away.
Progressive surveys replace a spot-check count with a complete traversal of the section. The observer counts every angler encountered during one circuit of duration τ hours. The estimator is:
\[\hat{E}_d = C_d \times T_d\]
where C_d is the count on day d and T_d is the total open hours on
day d (the period_length_col argument). The circuit time τ
cancels algebraically; it is only needed internally to compute the
expansion factor κ = T_d / τ.
calendar_p <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")),
day_type = c("weekday", "weekday", "weekend", "weekend")
)
design_p <- creel_design(calendar_p, date = date, strata = day_type)
prog_counts <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02", "2024-06-03", "2024-06-04")),
day_type = c("weekday", "weekday", "weekend", "weekend"),
n_anglers = c(15L, 23L, 45L, 52L),
shift_hours = rep(8, 4)
)
design_p <- add_counts(
design_p, prog_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
result_p <- estimate_effort(design_p)
#> 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.
result_p$estimates
#> # A tibble: 1 × 7
#> estimate se se_between se_within ci_lower ci_upper n
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 1080 85.0 85.0 0 714. 1446. 4Pope et al. (in press) give a worked example with C = 234 anglers encountered during a 2-hour circuit (τ = 2 h) on a day with 8 open hours (T_d = 8 h):
\[\hat{E}_d = 234 \times 8 = 1{,}872 \text{ angler-hours}\]
The code below reproduces this per-day calculation for a two-day
survey. The processed design’s $counts slot stores the
expanded per-day effort (Ê_d), so we can confirm the first-day value
equals 1,872 angler-hours directly.
# Reproduce Pope et al. per-day calculation
cal_pope <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02")),
day_type = c("weekday", "weekday")
)
design_pope <- creel_design(cal_pope, date = date, strata = day_type)
cnt_pope <- data.frame(
date = as.Date(c("2024-06-01", "2024-06-02")),
day_type = c("weekday", "weekday"),
n_anglers = c(234L, 200L),
shift_hours = c(8, 8)
)
design_pope <- add_counts(
design_pope, cnt_pope,
count_type = "progressive",
circuit_time = 2,
period_length_col = shift_hours
)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
# Per-day Ê_d values stored in the design (first day = 1,872 angler-hours)
design_pope$counts
#> date day_type n_anglers
#> 1 2024-06-01 weekday 1872
#> 2 2024-06-02 weekday 1600The n_anglers column in design_pope$counts
shows 1,872 for June 1st — matching the Pope et al. formula exactly.
se_between and se_within| Column | Source | Zero when |
|---|---|---|
se_between |
Between-PSU variance via survey::svytotal() |
Never (always estimated) |
se_within |
Rasmussen (1994) two-stage within-day formula | Single count per PSU |
se |
Combined SE: sqrt(se_between^2 + se_within^2) |
Never |
Practical guidance:
If you collect one count per PSU, se_within = 0 and
se = se_between. The classical creel estimator is recovered
exactly.
If you collect multiple counts per PSU, monitor the ratio
se_within / se. A large ratio (> 0.5) indicates
substantial within-day variation and suggests that daily sampling
intensity (number of circuits) is a meaningful driver of
precision.
For progressive surveys, the estimator variance structure is the same as for instantaneous counts. The key difference is in how the single-PSU effort Ê_d is calculated.
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.
Rasmussen, P. W. (1994). Two-stage variance estimation for creel surveys. Cited in Su, Y.-S., and Liu, P. (2025), equations 17–18.
Su, Y.-S., and Liu, P. (2025). Flexible creel survey estimators. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1–27.