Introduction

Creel surveys allow fisheries scientists and managers to collect data on catch and harvest, an angler population (including effort expended), and, depending on survey design, biological data on fish populations. Though important methods of collecting data on the user base of the fishery, creel surveys are difficult to implement and, in graduate fisheries programs, creel surveys are paid little attention. As a result, fisheries managers–the first job for many fisheries-program graduates–often inherit old surveys or are told to institute new surveys with little knowledge of how to do so.

Fisheries can cover large spatial extents: large reservoirs, coast-lines, and river systems. A creel survey has to be statistically valid, adaptable to the geographic challenges of the fishery, and cost efficient. Limited budgets can prevent agencies from implementing creel surveys; the AnglerCreelSurveySimulation was designed to help managers explore the type of creel survey that is most appropriate for their fishery, including fisheries with multiple access points, access points that are more popular than others, variation in catch rate, the number of surveyors, and seasonal variation in day-lengths.

The AnglerCreelSurveySimulation package does require that users know something about their fishery and the human dimensions of that fishery. A prior knowledge includes mean trip length for a party (or individual), the mean catch rate of the

The AnglerCreelSurveySimulation package is simple, but powerful. Four functions provide the means for users to create a population of anglers, limit the length of the fishing day to any value, and provide a mean trip length for the population. Ultimately, the user only needs to know the final function ConductMultipleSurveys but because I’d rather this not be a black box of functions, this brief introduction will be a step-by-step process through the package.

A walk-through of the package

This tutorial assumes that we have a very simple, small fishery with only one access point that, on any given day, is visited by 100 anglers. The fishing day length for our theoretical fishery is 12 hours (say, from 6 am to 6pm) and all anglers are required to have completed their trip by 6pm. Lastly, the mean trip length is known to be 3.5 hours.

For the purposes of this package, all times are functions of the fishing day. In other words, if a fishing day length is 12 hours (e.g., from 6 am to 6pm) and an angler starts their trip at 2 and ends at 4 that means that they started their trip at 8 am and ended at 10 am.

The make_anglers() function builds a population of anglers:


library(AnglerCreelSurveySimulation)

anglers <- make_anglers(n_anglers = 100, mean_trip_length = 3.5, fishing_day_length = 12)

make_anglers() returns a dataframe with start_time, trip_length, and departure_time for all anglers.


head(anglers)
#>   start_time trip_length departure_time
#> 1   7.848704   0.7295994       8.578304
#> 2   4.539477   5.8672689      10.406746
#> 3   3.689589   3.9681883       7.657777
#> 4   3.864445   1.1396013       5.004046
#> 5   1.119438   3.0971773       4.216615
#> 6   7.062798   3.0905057      10.153304

In the head(anglers) statement, you can see that starttime, triplength, and departureTime are all available for each angler. The first angler started their trip roughly 7.85 hours into the fishing day, continued to fish for 0.73 hours, and left the access point at 8.58 hours into the fishing day. Angler start times are assigned by the uniform distribution and trip lengths are assigned by the gamma distribution. To get true effort of all the anglers for this angler population, summing trip_length is all that’s needed: 0.

The distribution of angler trip lengths can be easily visualized:


library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)

# Histogram overlaid with kernel density curve
anglers %>%
  ggplot(aes(x=trip_length)) + 
  geom_histogram(aes(y=..density..), 
                 binwidth=.1,
                 colour="black", fill="white") +
  geom_density(alpha=.2, fill="#FF6666")

Once the population of anglers has been created, the next function to apply is the get_total_values() function. In get_total_values(), the user specifies the start time of the creel surveyor, the end time of the surveyor, and the wait time of the surveyor. Here is where the user also specifies the sampling probability of the anglers (in most cases, equal to \(\frac{waitTime}{fishingDayLength}\)) and the mean catch rate of the fishery. There are a number of a default settings in the get_total_values() function; see ?get_total_values for a description of how the function handles NULL values for startTime, endTime, and waitTime. startTime and waitTime are the times that the surveyor started and waited at the access point. totalCatch and trueEffort are the total (or real) values for catch and effort. meanLambda is the mean catch rate for all anglers. Even though we assigned meanCatchRate to get_total_values(), individual mean catch rates are simulated by rgamma() with shape equal to meanCatchRate and rate equal to 1.

For this walk through, we’ll schedule the surveyor to work for a total of eight hours at the sole access point in our fishery:


anglers %>%
  get_total_values(start_time = 0, wait_time = 8, circuit_time  = 8, mean_catch_rate = 2.5, 
                   fishing_day_length = 12)
#>   n_observed_trips total_observed_trip_effort n_completed_trips
#> 1               92                   231.3752                49
#>   total_completed_trip_effort total_completed_trip_catch start_time wait_time
#> 1                    133.0505                   300.1805          0         8
#>   total_catch true_effort mean_lambda
#> 1    756.6051    321.6806     2.23846

get_total_values() returns a single row data frame with several columns. The output of get_total_values() is the catch and effort data observed by the surveyor during their wait at the access point along with the “true” values for catch and effort. (Obviously, we can’t simulate biological data but, if an agency’s protocol directed the surveyor to collect biological data, that could be analyzed with other R functions.)

In the output from get_total_values(), n_observed_trips is the number of trips that the surveyor observed, including anglers that arrived after she started her day and anglers that were there for the duration of her time at the access point. total_observed_trip_effort is the effort expended by those parties; because the observed trips were not complete, she did not count their catch. n_completed_trips is the number of anglers that completed their trips while she was onsite, total_completed_trip_effort is the effort expended by those anglers, and total_completed_trip_catch is the number of fish caught by those parties. Catch is both the number of fish harvested and those caught and released.

Estimating catch and effort

Effort and catch are estimated from the Bus Route Estimator:

\[ \widehat{E} = T\sum\limits_{i=1}^n{\frac{1}{w_{i}}}\sum\limits_{j=1}^m{\frac{e_{ij}}{\pi_{j}}} \]

where

E = estimated total party-hours of effort;
T = total time to complete a full circuit of the route, including traveling and waiting;
w_i = waiting time at the i^th site (where i = 1, …, n sites);

and

e_ij = total time that the j^th car (or trailer) is parked at the i^th site while the agent is at that site (where j = 1, …, n sites).

Catch rate is calculated from the Ratio of Means equation:

\[ \widehat{R_1} = \frac{\sum\limits_{i=1}^n{c_i/n}}{\sum\limits_{i=1}^n{L_i/n}} \]

where

c_i is the catch for the i^th sampling unit

and
* L_i is the length of the fishing trip at the tie of the interview.

For incomplete surveys, L_i represents an incomplete trip.

simulate_bus_route() calculates effort and catch based upon these equations. See ?simulate_bus_route for references that include a more detailed discussion of these equations.

simulate_bus_route() calls make_anglers() and get_total_values() so many of the same arguments we passed in the previous functions will need to be passed to simulate_bus_route(). The new argument, nsites, is the number of sites visited by the surveyor. In more advanced simulations (see the examples in ?simulate_bus_route), you can pass strings of values for startTime, waitTime, nsites, and nanglers to simulate a bus route-type survey rather than just a single access-point survey.


sim <- simulate_bus_route(start_time = 0, wait_time = 8, n_sites = 1, n_anglers = 100,
                          mean_catch_rate = 2.5, fishing_day_length = 12)

sim
#>      Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 253.251       2.453602   793.2831    329.9873    2.440061

The output from simulate_bus_route() is a dataframe with values for Ehat, catchRateROM (the ratio of means catch rate), trueCatch, trueEffort, and meanLambda. Ehat is the estimated total effort from the Bus Route Estimator above and catchRateROM is catch rate estimated from the Ratio of Means equation. trueCatch, trueEffort, and meanLambda are the same as before. Multiplying Ehat by catchRateROM gives an estimate of total catch: 621.3772326.

Conducting multiple simulations

With information about the fishery, the start and wait times of the surveyor, the sampling probability, mean catch rate, and fishing day length, we can run multiple simulations with conduct_multiple_surveys(). conduct_multiple_surveys() is a wrapper that calls the other three functions in turn and compiles the values into a data frame for easy plotting or analysis. The only additional argument needed is the nsims value which tells the function how many simulations to conduct. For the sake of this simple simulation, let’s assume that the creel survey works five days a week for four weeks (i.e. 20 days):


sim <- conduct_multiple_surveys(n_sims = 20, start_time = 0, wait_time = 8, n_sites = 1,
                                n_anglers = 100, 
                                mean_catch_rate = 2.5, fishing_day_length = 12)

sim
#>        Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1  229.5804       2.922077   843.5097    318.4569    2.589429
#> 2  242.2412       2.431374   673.1617    299.8419    2.270287
#> 3  238.2771       2.784609   856.5256    339.3998    2.488253
#> 4  250.4774       2.527403   859.6570    321.3113    2.604803
#> 5  244.7108       2.440642   904.9229    335.9554    2.635200
#> 6  255.9530       2.421817   851.8885    339.6856    2.558691
#> 7  262.7190       2.515356   884.4091    347.7693    2.511190
#> 8  255.1301       2.833122   889.9751    351.9611    2.474098
#> 9  250.0078       2.737806   883.7583    322.5339    2.651930
#> 10 269.4791       2.259227   845.3622    358.6298    2.569356
#> 11 240.4417       2.436507   875.7010    325.0737    2.643493
#> 12 263.5098       2.509888   846.4525    342.9462    2.379685
#> 13 246.1045       2.392697   850.1807    338.6189    2.586232
#> 14 273.0320       2.685496   848.0235    365.7189    2.233682
#> 15 266.8691       2.393276   962.0231    347.2504    2.687680
#> 16 232.0789       2.503812   787.6238    321.6952    2.477968
#> 17 281.9305       2.947629  1047.2571    364.6363    2.914973
#> 18 237.5107       2.432380   900.7840    336.8878    2.580194
#> 19 243.1507       2.469668   759.5665    332.9487    2.400902
#> 20 236.8733       1.983809   758.3912    332.1191    2.293877

With the output from multiple simulations, an analyst can evaluate how closely the creel survey they’ve designed mirrors reality. A lm() of estimated catch as a function of trueCatch can tell us if the survey will over or under estimate reality:


mod <- 
  sim %>% 
  lm((Ehat * catch_rate_ROM) ~ true_catch, data = .)

summary(mod)
#> 
#> Call:
#> lm(formula = (Ehat * catch_rate_ROM) ~ true_catch, data = .)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -106.654  -47.747    1.582   34.698  102.399 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)   
#> (Intercept) 117.4481   152.6798   0.769  0.45172   
#> true_catch    0.6054     0.1776   3.409  0.00313 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 59.63 on 18 degrees of freedom
#> Multiple R-squared:  0.3923, Adjusted R-squared:  0.3586 
#> F-statistic: 11.62 on 1 and 18 DF,  p-value: 0.003129

Plotting the data and the model provide a good visual means of evaluating how close our estimates are to reality:


#Create a new vector of the estimated effort multiplied by estimated catch rate
sim <- 
  sim %>%
  mutate(est_catch = Ehat * catch_rate_ROM)

sim %>% 
  ggplot(aes(x = true_catch, y = est_catch)) +
  geom_point() +
  geom_abline(intercept = mod$coefficients[1], slope = mod$coefficients[2], 
              colour = "red", size = 1.01)
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

The closer the slope parameter estimate is to 1 and the intercept parameter estimate is to 0, the closer our estimate of catch is to reality.

We can create a model and plot of our effort estimates, too:


mod <- 
  sim %>%
  lm(Ehat ~ true_effort, data = .)

summary(mod)
#> 
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -14.2655  -6.6251   0.0526   8.6144  17.0209 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  18.1227    44.1976   0.410    0.687    
#> true_effort   0.6907     0.1309   5.275 5.14e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 9.396 on 18 degrees of freedom
#> Multiple R-squared:  0.6072, Adjusted R-squared:  0.5854 
#> F-statistic: 27.83 on 1 and 18 DF,  p-value: 5.139e-05

#Create a new vector of the estimated effort multiplied by estimated catch rate

sim %>%
  ggplot(aes(x = true_effort, y = Ehat)) +
  geom_point() +
  geom_abline(intercept = mod$coefficients[1], slope = mod$coefficients[2], 
              colour = "red", size = 1.01)

Observing all trips

If the start and wait time equals 0 and the length of the fishing day, respectively, the creel surveyor can observe all completed trips, though she’d likely be unhappy having to work 12 hours. The inputs have to be adjusted to allow her to arrive at time 0, stay for all 12 hours, and have a probability of 1.0 at catching everyone:


start_time <- 0
wait_time <- 12
sampling_prob <- 1

sim <- conduct_multiple_surveys(n_sims = 20, start_time = start_time, wait_time = wait_time,
                                n_sites = 1, n_anglers = 100, 
                                mean_catch_rate = 2.5, fishing_day_length = wait_time)

sim
#>        Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1  332.0663       2.349496   780.1882    332.0663    2.233772
#> 2  310.2316       2.345465   727.6373    310.2316    2.401297
#> 3  349.4687       2.273135   794.3896    349.4687    2.279459
#> 4  326.6218       2.490133   813.3317    326.6218    2.546587
#> 5  373.0840       2.482969   926.3561    373.0840    2.419584
#> 6  362.7309       2.260795   820.0605    362.7309    2.286468
#> 7  331.4206       2.539359   841.5960    331.4206    2.496688
#> 8  336.0798       2.242067   753.5133    336.0798    2.305268
#> 9  314.2443       2.404395   755.5673    314.2443    2.416626
#> 10 331.5918       2.355994   781.2284    331.5918    2.448446
#> 11 329.2100       2.369170   779.9543    329.2100    2.418265
#> 12 362.9428       2.217553   804.8448    362.9428    2.278491
#> 13 307.4774       2.241739   689.2840    307.4774    2.350678
#> 14 321.6525       2.731679   878.6515    321.6525    2.664301
#> 15 326.2025       2.401278   783.3030    326.2025    2.488387
#> 16 343.5115       2.249306   772.6625    343.5115    2.270312
#> 17 324.2404       2.549892   826.7780    324.2404    2.592544
#> 18 357.3667       2.622113   937.0559    357.3667    2.516724
#> 19 334.1312       2.548756   851.6189    334.1312    2.562402
#> 20 343.2094       2.637184   905.1062    343.2094    2.657982

#> Warning in summary.lm(mod): essentially perfect fit: summary may be unreliable
#> 
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#> 
#> Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -5.609e-14 -8.850e-16 -6.360e-16  1.800e-17  5.624e-14 
#> 
#> Coefficients:
#>              Estimate Std. Error   t value Pr(>|t|)    
#> (Intercept) 7.458e-14  8.082e-14 9.230e-01    0.368    
#> true_effort 1.000e+00  2.403e-16 4.162e+15   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 1.884e-14 on 18 degrees of freedom
#> Multiple R-squared:      1,  Adjusted R-squared:      1 
#> F-statistic: 1.732e+31 on 1 and 18 DF,  p-value: < 2.2e-16

More complex surveys

If our hypothetical fishery suddenly gained another access point and the original 100 anglers were split between the two access points equally, what kind of information would a creel survey capture? We could ask our surveyor to split her eight-hour work day between both access points, but she’ll have to drive for 0.5 hours to get from one to another. Of course, that 0.5 hour of drive time will be a part of her work day so she’ll effectively have 7.5 hours to spend at access points counting anglers and collecting data.


start_time <- c(0, 4.5)
wait_time <- c(4, 3.5)
n_sites = 2
n_anglers <- c(50, 50)
fishing_day_length <- 12
# sampling_prob <- sum(wait_time)/fishing_day_length

sim <- conduct_multiple_surveys(n_sims = 20, start_time = start_time, wait_time = wait_time,
                                n_sites = n_sites, n_anglers = n_anglers, 
                                mean_catch_rate = 2.5, 
                                fishing_day_length = fishing_day_length)

sim
#>         Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1  1073.0361       2.136732   889.3546    371.1335    2.482785
#> 2   950.6238       2.081875   848.4074    323.9579    2.542817
#> 3   977.5594       2.346412   881.0611    346.8195    2.454725
#> 4  1103.8019       2.130647   736.0677    354.5028    2.185741
#> 5   991.3314       2.386394   958.7163    370.5217    2.582096
#> 6   988.1584       3.319931   983.9394    360.5094    2.765659
#> 7   960.2328       2.783050   853.0638    342.8843    2.532346
#> 8   947.7904       2.181505   705.8306    334.3205    2.233893
#> 9  1109.6304       2.535476   823.4347    343.1908    2.445997
#> 10 1040.4163       2.739175   900.4431    329.3077    2.700439
#> 11  976.6533       2.385551   821.9913    340.0579    2.520625
#> 12 1025.6042       2.272252   782.3169    350.2939    2.252351
#> 13  929.5455       2.370111   902.1140    323.9536    2.640390
#> 14  961.1415       2.354007   873.9887    344.0762    2.586497
#> 15 1050.2158       2.252650   832.5109    332.6180    2.469718
#> 16  996.8416       2.658754   874.4433    343.2334    2.555044
#> 17  818.6322       2.432671   756.1011    319.5939    2.343483
#> 18  888.7214       2.831334   915.3094    342.8267    2.756298
#> 19  890.0733       2.431894   696.9834    303.8410    2.214772
#> 20  974.4155       2.622142   907.5017    343.5489    2.589945

#> 
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -112.165  -27.396   -7.721   18.313  121.754 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)  
#> (Intercept) 157.7237   294.5754   0.535   0.5989  
#> true_effort   2.4189     0.8627   2.804   0.0117 *
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 62.02 on 18 degrees of freedom
#> Multiple R-squared:  0.304,  Adjusted R-squared:  0.2653 
#> F-statistic: 7.861 on 1 and 18 DF,  p-value: 0.01174

Even more simulations

Ultimately, the creel survey simulation can be as complicated as a creel survey. If a survey requires multiple clerks, several simulations can be coupled together to act as multiple surveyors. To accommodate weekends or holidays (i.e., increased angler pressure), additional simulations with different wait times and more anglers (to simulate higher pressure) can be built into the simulation. For example, if we know that angler pressure is 50% higher at the two access points on weekends, we can hire a second clerk to sample 8 hours a day on the weekends–one day at each access point–and add the weekend data to the weekday data.


#Weekend clerks
start_time_w <- 2
wait_time_w <- 10
n_sites <- 1
n_anglers_w <- 75
fishing_day_length <- 12
sampling_prob <- 8/12

sim_w <- conduct_multiple_surveys(n_sims = 8, start_time = start_time_w, 
                                  wait_time = wait_time_w, n_sites = n_sites, 
                                  n_anglers = n_anglers_w, 
                                  mean_catch_rate = 2.5, 
                                  fishing_day_length = fishing_day_length)

sim_w
#>       Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 364.1994       3.099086   784.1936    253.0403    3.162699
#> 2 363.7366       2.591261   654.5392    252.5948    2.532314
#> 3 351.9882       2.372916   581.9455    245.5611    2.424276
#> 4 366.1034       2.232428   567.5691    254.2385    2.280246
#> 5 357.6785       2.387432   593.2924    249.0428    2.337480
#> 6 363.1619       2.502503   635.4235    254.0747    2.430667
#> 7 380.0270       3.104976   819.4271    263.9077    2.938617
#> 8 397.5087       2.807544   775.7808    277.4534    2.834117

#Add the weekday survey and weekend surveys to the same data frame
mon_survey <- 
  sim_w %>%
  bind_rows(sim)

mod <- 
  mon_survey %>% 
  lm(Ehat ~ true_effort, data = .)

summary(mod)
#> 
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -171.677  -28.103   -8.317   30.289  169.033 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -1292.8543   127.8607  -10.11 1.68e-10 ***
#> true_effort     6.6281     0.4002   16.56 2.49e-15 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 86.76 on 26 degrees of freedom
#> Multiple R-squared:  0.9134, Adjusted R-squared:  0.9101 
#> F-statistic: 274.2 on 1 and 26 DF,  p-value: 2.488e-15

Choose your own adventure

Hopefully, this vignette has shown you how to build and simulate your own creel survey. It’s flexible enough to estimate monthly or seasonal changes in fishing day length, changes in the mean catch rate, increased angler pressure on weekends, and any number of access sites, start times, wait times, and sampling probabilities. The output from conduct_multiple_surveys() allows the user to estimate variability in the catch and effort estimates (e.g., relative standard error) to evaluate the most efficient creel survey for their fishery.

- Introduction
  - A walk-through of the package

Simulating Creel Surveys