Ice Fishing Survey Analysis

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Overview

Ice fishing creel surveys share the bus-route structure, but all access points are sampled with certainty. Every angler leaving the lake must pass through the single ice access point (the boat ramp area or designated ice-access site), so there is no site-level subsampling. The site inclusion probability is always p_site = 1.0, and the overall inclusion probability reduces to just the period sampling probability:

\[\pi_i = p\_site \times p\_period = 1.0 \times p\_period = p\_period\]

In tidycreel, this is a degenerate bus-route design. The bus-route Horvitz-Thompson estimators still apply; only the probability structure is simpler.

Effort type distinction

Ice fishing surveys collect two distinct effort measures:

time_on_ice — total hours the angler party was physically on the ice, including travel to the fishing hole, breaks, and social time. This is the easiest to record and most commonly used.
active_fishing_time — hours spent with lines in the water, excluding travel, setup, and breaks. This captures actual fishing pressure more precisely but requires more careful interviewing.

The effort_type argument to creel_design() controls which measure the design tracks, and adds a matching column to the estimate_effort() output: total_effort_hr_on_ice for "time_on_ice" and total_effort_hr_active for "active_fishing_time". Both are aliases of estimate, which is present on every design and is what generic code should read.

Shelter mode stratification

Ice anglers fish from open-air setups or enclosed dark-house shelters. Catch rates and effort patterns differ between these groups — dark-house anglers often target specific species and fish longer hours. The estimate_effort() function accepts a by argument to produce separate estimates for each shelter type.

Example Data

This vignette uses two built-in datasets representing a hypothetical Nebraska ice fishing creel survey at Lake McConaughy in January-February 2024. All 12 sampling days are weekends — a common design choice since ice fishing pressure is concentrated on Saturday and Sunday.

library(tidycreel)

data(example_ice_sampling_frame)
data(example_ice_interviews)

head(example_ice_sampling_frame)
#>         date day_type p_period
#> 1 2024-01-06  weekend     0.50
#> 2 2024-01-07  weekend     0.50
#> 3 2024-01-13  weekend     0.50
#> 4 2024-01-14  weekend     0.50
#> 5 2024-01-20  weekend     0.55
#> 6 2024-01-21  weekend     0.55
head(example_ice_interviews)
#>         date n_counted n_interviewed hours_on_ice active_fishing_hours
#> 1 2024-01-06        12             5          5.0                  4.0
#> 2 2024-01-06        12             4          6.5                  5.5
#> 3 2024-01-06        12             3          4.0                  3.5
#> 4 2024-01-06         8             3          3.5                  3.0
#> 5 2024-01-06         8             3          5.0                  4.0
#> 6 2024-01-06         8             2          7.0                  6.0
#>   walleye_catch perch_catch walleye_kept perch_kept trip_status shelter_mode
#> 1             2           5            1          3    complete         open
#> 2             0           8            0          5    complete         open
#> 3             1           3            1          2    complete         open
#> 4             3           0            2          0    complete   dark_house
#> 5             1           4            1          3  incomplete   dark_house
#> 6             0           6            0          4    complete   dark_house

The sampling frame records the survey calendar and the period sampling probability (p_period = 0.5 means each day had a 50% chance of being sampled). The interview data contains 72 interviews with walleye and perch catch, both effort measures, and the shelter type (shelter_mode) for each angler party.

Design Construction

Build an ice fishing design using creel_design() with survey_type = "ice". The effort_type argument is required and determines the column label in downstream output. We use p_period = 0.5 as a scalar (uniform period sampling probability across all days).

design <- creel_design(
  example_ice_sampling_frame,
  date = date,
  strata = day_type,
  survey_type = "ice",
  effort_type = "time_on_ice",
  p_period = 0.5
)
print(design)
#> 
#> ── Creel Survey Design ─────────────────────────────────────────────────────────
#> Type: "ice"
#> Date column: date
#> Strata: day_type
#> Calendar: 12 days (2024-01-06 to 2024-02-11)
#> day_type: 1 level
#> Counts: "none"
#> Interviews: "none"
#> Sections: "none"
#> 
#> ── Ice Fishing Design ──
#> 
#> Effort type: time_on_ice
#> p_period (global): 0.5

Omitting effort_type or supplying an unrecognized value produces an informative error:

creel_design(
  example_ice_sampling_frame,
  date = date,
  strata = day_type,
  survey_type = "ice"
)
#> Error in `creel_design()`:
#> ! `effort_type` is required for "ice" survey designs.
#> ✖ No `effort_type` supplied.
#> ℹ Valid values: "time_on_ice" and "active_fishing_time".

Attaching Interview Data

Use add_interviews() to attach the survey data to the design. For ice surveys, n_counted and n_interviewed are required — they record how many parties were counted at the access point versus how many were actually interviewed during each visit, providing the enumeration expansion factor.

design <- add_interviews(
  design,
  example_ice_interviews,
  catch         = walleye_catch,
  effort        = hours_on_ice,
  harvest       = walleye_kept,
  trip_status   = trip_status,
  n_counted     = n_counted,
  n_interviewed = n_interviewed
)
#> Warning: ! No `n_anglers` provided — assuming 1 angler per interview.
#> ℹ Pass `n_anglers = <column>` to use actual party sizes for angler-hour
#>   normalization.
#> ℹ If the interviews really are one angler each, pass `n_anglers = 1` to state
#>   that and silence this warning.
#> Warning: 23 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.
#> ℹ Added 72 interviews: 60 complete (83%), 12 incomplete (17%)

Effort Estimation

estimate_effort() dispatches through the bus-route Horvitz-Thompson estimator and returns the total angler-hours with a standard error and confidence interval. The effort column is returned twice: as estimate, the name every design uses and the one generic code should read, and again under a name recording the effort type – total_effort_hr_on_ice because the design was built with effort_type = "time_on_ice".

effort_est <- estimate_effort(design)
print(effort_est)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Total
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Effort target: sampled_days
#> Unit: party-hours
#> 
#> # A tibble: 1 × 6
#>   estimate    se ci_lower ci_upper     n total_effort_hr_on_ice
#>      <dbl> <dbl>    <dbl>    <dbl> <int>                  <dbl>
#> 1    2406.  74.6    2260.    2552.    72                  2406.

To demonstrate the column-naming distinction, rebuild the design using effort_type = "active_fishing_time" and the active_fishing_hours column from the interview data. The effort-type column is then labeled total_effort_hr_active; estimate is present either way.

design_aft <- creel_design(
  example_ice_sampling_frame,
  date        = date,
  strata      = day_type,
  survey_type = "ice",
  effort_type = "active_fishing_time",
  p_period    = 0.5
)

design_aft <- suppressMessages(add_interviews(
  design_aft,
  example_ice_interviews,
  catch         = walleye_catch,
  effort        = active_fishing_hours,
  harvest       = walleye_kept,
  trip_status   = trip_status,
  n_counted     = n_counted,
  n_interviewed = n_interviewed
))
#> Warning: ! No `n_anglers` provided — assuming 1 angler per interview.
#> ℹ Pass `n_anglers = <column>` to use actual party sizes for angler-hour
#>   normalization.
#> ℹ If the interviews really are one angler each, pass `n_anglers = 1` to state
#>   that and silence this warning.
#> Warning: 23 interviews have zero catch.
#> ℹ Zero catch may be valid (skunked) or indicate missing data.

effort_aft <- estimate_effort(design_aft)
print(effort_aft)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Total
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Effort target: sampled_days
#> Unit: party-hours
#> 
#> # A tibble: 1 × 6
#>   estimate    se ci_lower ci_upper     n total_effort_hr_active
#>      <dbl> <dbl>    <dbl>    <dbl> <int>                  <dbl>
#> 1    1990.  69.1    1855.    2126.    72                  1990.

Active fishing hours are shorter than time-on-ice because they exclude travel, setup, and breaks. The difference between the two estimates reflects the non-fishing portion of each trip.

Shelter Mode Stratification

Pass by = shelter_mode to estimate_effort() to produce separate effort estimates for open-air anglers and dark-house anglers. This uses the same Horvitz-Thompson framework with the interview data split by the grouping variable.

effort_by_shelter <- estimate_effort(design, by = shelter_mode)
print(effort_by_shelter)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Total
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Grouped by: shelter_mode
#> Effort target: sampled_days
#> Unit: party-hours
#> 
#> # A tibble: 2 × 8
#>   shelter_mode estimate    se ci_lower ci_upper proportion     n
#>   <chr>           <dbl> <dbl>    <dbl>    <dbl>      <dbl> <int>
#> 1 dark_house      1250.  56.7    1139.    1361.      0.520    36
#> 2 open            1156.  23.6    1109.    1202.      0.480    36
#> # ℹ 1 more variable: total_effort_hr_on_ice <dbl>

The proportion column shows each shelter group’s share of total effort. Dark-house anglers tend to fish longer hours on average, which can make their proportional effort contribution larger than their share of party counts alone would suggest.

Catch Rate Estimation

estimate_catch_rate() computes the ratio-of-means CPUE (fish per angler-hour) using the catch and effort columns specified in add_interviews(). By default, only complete trips are used to avoid the well-known incomplete-trip bias in effort-based catch rates.

cpue_est <- estimate_catch_rate(design)
print(cpue_est)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Ratio-of-Means CPUE
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Unit: fish/party-hour
#> 
#> # A tibble: 1 × 5
#>   estimate     se ci_lower ci_upper     n
#>      <dbl>  <dbl>    <dbl>    <dbl> <int>
#> 1    0.198 0.0121    0.174    0.222    60

The estimate column is walleye per hour-on-ice, with a standard error and 95% confidence interval. The n column counts the number of complete interviews used in the ratio.

Total Catch Estimation

On instantaneous designs estimate_total_catch() multiplies a catch rate by a total effort estimate, but ice designs take the bus-route dispatch instead and form no such product. The total is a direct Horvitz-Thompson sum over the interviewed parties, each party’s catch divided by its inclusion probability \(\pi_i\); there is no CPUE term and no effort term. The method is reported as ht-total-catch rather than product-total-catch.

Only completed trips enter the sum. A party still fishing has caught some of its eventual catch, so counting it would expand a partial catch under the inclusion probability of a finished trip. Of the 72 interviews, the 60 complete ones contribute and the 12 incomplete ones are dropped — which is why the n column below reads 60. For the same reason use_trips = "all" is refused on ice and bus-route designs; incomplete trips support a rate, via estimate_catch_rate(use_trips = "incomplete"), not a total.

total_catch_est <- estimate_total_catch(design)
print(total_catch_est)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Total Catch (Horvitz-Thompson)
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Unit: fish
#> 
#> # A tibble: 1 × 5
#>   estimate    se ci_lower ci_upper     n
#>      <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1     398.  20.6     358.     439.    60

The estimate column is the projected total walleye catch across the entire survey period. The standard error and 95% confidence interval come from Taylor linearization on the Horvitz-Thompson sum, not from the delta method — there is no product of two estimates here whose uncertainty would need propagating.

References

Jones, C. M., & Pollock, K. H. (2012). Recreational survey methods: estimation of effort, harvest, and abundance. Chapter 19 in Fisheries Techniques (3rd ed.), pp. 883-919. American Fisheries Society.
Malvestuto, S. P. (1996). Sampling the recreational angler. Chapter 20 in Fisheries Techniques (2nd ed.), pp. 591-623. American Fisheries Society.

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