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   2.344548   0.6990596       3.043607
#> 2   8.879916   1.7421654      10.622081
#> 3   2.132229   1.5513144       3.683544
#> 4   2.455847   5.0693691       7.525216
#> 5   5.909529   1.9754853       7.885014
#> 6  10.956395   0.5725891      11.528984

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 2.34 hours into the fishing day, continued to fish for 0.7 hours, and left the access point at 3.04 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               83                   205.6881                51
#>   total_completed_trip_effort total_completed_trip_catch start_time wait_time
#> 1                    125.9844                   402.5573          0         8
#>   total_catch true_effort mean_lambda
#> 1     878.151     298.652    2.868091

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
#> 1 251.5783       2.717137   821.3414    336.6918     2.58303

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: 683.5727596.

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  251.2751       2.715368   891.6315    347.5472    2.502541
#> 2  262.9803       2.697911   950.5193    347.9895    2.744980
#> 3  239.5772       2.140410   701.7522    316.6104    2.261379
#> 4  211.5798       2.563842   757.3305    316.6688    2.278562
#> 5  265.1032       2.089420   765.4021    328.3983    2.180437
#> 6  219.7396       2.669585   851.2098    337.4097    2.530436
#> 7  259.8684       2.135428   880.3317    342.4824    2.544421
#> 8  269.0109       2.733957   881.6512    356.4888    2.527161
#> 9  254.4988       3.200268  1005.9532    346.1834    2.870056
#> 10 265.6539       2.348372   951.6683    343.8136    2.675011
#> 11 236.6423       2.916161   886.9852    338.9313    2.592258
#> 12 253.0033       2.227817   790.3172    346.9199    2.352073
#> 13 247.4905       2.127633   728.1211    330.5219    2.307401
#> 14 273.2019       2.796893   973.5158    355.1038    2.695640
#> 15 244.8440       2.498293   839.0884    313.3245    2.479512
#> 16 289.4480       2.416392   855.9033    373.7626    2.371455
#> 17 250.0151       2.578717   905.4115    352.0875    2.579268
#> 18 234.8942       2.036539   685.8589    306.7750    2.320789
#> 19 238.3071       2.665224   826.9444    333.3004    2.455166
#> 20 256.2799       2.479191   809.7686    331.2354    2.324683

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 
#> -102.169  -11.936   -1.445   26.685   77.225 
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -103.5678   101.9236  -1.016    0.323    
#> true_catch     0.8641     0.1197   7.219 1.03e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 46.87 on 18 degrees of freedom
#> Multiple R-squared:  0.7433, Adjusted R-squared:  0.729 
#> F-statistic: 52.11 on 1 and 18 DF,  p-value: 1.026e-06

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 every 8 hours.
#> 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 
#> -30.761  -7.544   4.046   9.332  21.560 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -10.0047    62.5832  -0.160 0.874770    
#> true_effort   0.7721     0.1848   4.178 0.000565 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 13.35 on 18 degrees of freedom
#> Multiple R-squared:  0.4923, Adjusted R-squared:  0.4641 
#> F-statistic: 17.46 on 1 and 18 DF,  p-value: 0.0005652

#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  355.8481       2.507862   892.4179    355.8481    2.428310
#> 2  340.2682       2.290488   779.3804    340.2682    2.285644
#> 3  371.5307       2.684120   997.2332    371.5307    2.650148
#> 4  304.8843       2.395969   730.4934    304.8843    2.430427
#> 5  371.0462       2.506491   930.0238    371.0462    2.482865
#> 6  306.8586       2.678087   821.7941    306.8586    2.491780
#> 7  343.0437       2.533606   869.1375    343.0437    2.432189
#> 8  353.2809       2.505150   885.0216    353.2809    2.568789
#> 9  349.0948       2.429015   847.9566    349.0948    2.309156
#> 10 357.8227       2.502592   895.4841    357.8227    2.528299
#> 11 322.5526       2.532571   816.8874    322.5526    2.636067
#> 12 356.7094       2.546643   908.4116    356.7094    2.625374
#> 13 349.8136       2.417021   845.5071    349.8136    2.467017
#> 14 330.4801       2.586246   854.7028    330.4801    2.583102
#> 15 339.6830       2.560220   869.6630    339.6830    2.504666
#> 16 350.1321       2.598496   909.8169    350.1321    2.619427
#> 17 338.7259       2.758521   934.3824    338.7259    2.738683
#> 18 350.9463       2.204763   773.7534    350.9463    2.211754
#> 19 313.2939       2.040435   639.2558    313.2939    2.109854
#> 20 340.5213       2.639586   898.8352    340.5213    2.564667

#> 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 
#> -4.696e-14 -4.680e-16  2.437e-15  4.626e-15  1.550e-14 
#> 
#> Coefficients:
#>              Estimate Std. Error   t value Pr(>|t|)    
#> (Intercept) 1.017e-13  5.200e-14 1.955e+00   0.0663 .  
#> true_effort 1.000e+00  1.517e-16 6.592e+15   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 1.244e-14 on 18 degrees of freedom
#> Multiple R-squared:      1,  Adjusted R-squared:      1 
#> F-statistic: 4.346e+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   747.0897       2.395948   781.2451    349.6246    2.411676
#> 2  1049.7223       1.765272   887.2324    351.9553    2.407386
#> 3  1001.8543       2.015416   860.2979    342.3451    2.486909
#> 4   939.5718       2.676889   845.5717    337.8541    2.480168
#> 5   836.0630       3.020539   842.3358    341.2702    2.428031
#> 6  1168.0913       2.110574   682.2155    324.0263    2.025390
#> 7   861.9932       2.231022   811.7799    331.9898    2.491920
#> 8   970.4394       2.133755   786.4610    319.8154    2.441453
#> 9   909.1530       2.293082   845.3929    348.6101    2.478829
#> 10 1076.2712       2.201420   790.6962    348.3613    2.314308
#> 11 1003.6039       2.961193   901.8364    336.2231    2.752778
#> 12  994.7747       2.093049   833.1171    346.3091    2.379673
#> 13  996.2269       2.234408   839.4745    356.3127    2.448600
#> 14 1020.5084       1.891334   832.9888    335.3736    2.443650
#> 15  843.4247       2.861870   771.0300    326.6157    2.437588
#> 16  936.2151       2.107805   799.7216    313.7693    2.565320
#> 17  947.0207       2.595076   801.8594    324.4572    2.488821
#> 18  974.9905       2.724325   753.4912    324.6000    2.405841
#> 19 1077.8457       2.430041   946.5520    368.0249    2.557546
#> 20  804.6284       3.158537   838.6308    326.1016    2.615504

#> 
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -226.09  -69.24   20.17   51.98  227.50 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  527.989    579.589   0.911    0.374
#> true_effort    1.273      1.715   0.742    0.467
#> 
#> Residual standard error: 104 on 18 degrees of freedom
#> Multiple R-squared:  0.02972,    Adjusted R-squared:  -0.02419 
#> F-statistic: 0.5513 on 1 and 18 DF,  p-value: 0.4674

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
#> 1 394.9863       2.523206   697.4651    276.2823    2.652318
#> 2 383.8820       2.436196   649.4526    266.5847    2.409292
#> 3 395.5739       2.755471   756.9392    274.7041    2.744176
#> 4 354.8569       2.734374   674.7273    247.3653    2.931638
#> 5 379.7376       2.622277   695.1953    265.0997    2.685504
#> 6 367.8180       2.804485   722.4389    256.8065    2.863010
#> 7 380.3324       2.454154   648.1905    264.1197    2.526219
#> 8 401.1485       2.456887   684.4281    278.5754    2.463277

#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 
#> -278.17  -77.48  -11.91   64.92  326.12 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -1478.1192   207.6681  -7.118 1.47e-07 ***
#> true_effort     7.1602     0.6507  11.004 2.79e-11 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 119.4 on 26 degrees of freedom
#> Multiple R-squared:  0.8232, Adjusted R-squared:  0.8164 
#> F-statistic: 121.1 on 1 and 26 DF,  p-value: 2.79e-11

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