Introduction
Creel surveys allow fisheries scientists and managers to collect data on catch and harvest, an angler popuation (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 3.597536 6.0048773 9.602413
#> 2 3.438553 5.2290034 8.667556
#> 3 7.106046 0.7784606 7.884507
#> 4 8.747507 1.0715760 9.819083
#> 5 8.735652 1.6051185 10.340771
#> 6 1.881686 2.7515846 4.633270In 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 3.6 hours into the fishing day, continued to fish for 6 hours, and left the access point at 9.6 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)
#> Want to understand how all the pieces fit together? Buy the
#> ggplot2 book: http://ggplot2.org/book/
# 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, sampling_prob = 8/12, mean_catch_rate = 2.5)
#> n_observed_trips total_observed_trip_effort n_completed_trips
#> 1 86 586.0279 50
#> total_completed_trip_effort total_completed_trip_catch start_time
#> 1 222.9294 530.1671 0
#> wait_time total_catch true_effort mean_lambda
#> 1 8 795.6116 417.0699 2.39971get_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 accss 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 travelling and waiting;
- wi = waiting time at the ith site (where i = 1, …, n sites);
and
- eij = total time that the jth car (or trailer) is parked at the ith site while the agent is at that shite (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
- ci is the catch for the ith sampling unit
and
* Li is the length of the fishing trip at the tie of the interview.
For incomplete surveys, Li 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 arguent, 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,
sampling_prob = 8/12, mean_catch_rate = 2.5, fishing_day_length = 12)
sim
#> Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 585.9488 2.607587 866.5934 403.0374 2.481576The 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: 1527.9124526.
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 survery 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, sampling_prob = 8/12,
mean_catch_rate = 2.5, fishing_day_length = 12)
sim
#> Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 582.5113 2.197079 744.9890 408.1091 2.238827
#> 2 525.6581 2.610515 962.0484 371.0789 2.788176
#> 3 532.4813 2.593379 774.0897 376.5876 2.364251
#> 4 636.9765 2.069540 776.0824 444.2898 2.275464
#> 5 551.9909 2.255368 816.2178 392.7341 2.518792
#> 6 666.7207 2.161836 799.9225 461.0866 2.379170
#> 7 571.7152 2.399565 817.8163 402.0583 2.547475
#> 8 621.4893 2.069414 731.0183 441.1592 2.134023
#> 9 608.1691 2.328550 854.8820 426.5282 2.305846
#> 10 531.5312 2.260759 764.4231 380.1294 2.258321
#> 11 600.5033 2.910176 844.1526 412.9629 2.757026
#> 12 583.2813 2.542058 836.5646 401.1198 2.613398
#> 13 621.7530 2.526983 886.7834 422.6602 2.482501
#> 14 614.4349 2.658935 782.2079 422.5720 2.459972
#> 15 593.8837 2.748767 936.2094 411.7710 2.764624
#> 16 579.6193 2.344677 833.4941 410.2437 2.377972
#> 17 610.3543 2.395208 911.6421 429.0311 2.658027
#> 18 557.2910 2.300684 862.2922 396.4331 2.498155
#> 19 566.0941 2.073266 729.5827 396.8897 2.138644
#> 20 608.2846 2.128812 731.1389 432.0415 1.974324With 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
#> -185.54 -71.15 -22.28 66.09 322.50
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 474.8766 376.0562 1.263 0.2228
#> true_catch 1.1256 0.4572 2.462 0.0241 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 136.5 on 18 degrees of freedom
#> Multiple R-squared: 0.2519, Adjusted R-squared: 0.2103
#> F-statistic: 6.061 on 1 and 18 DF, p-value: 0.02414Plotting 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)
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
#> -12.0376 -6.0464 -0.9879 3.1929 16.9332
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -51.07503 32.32989 -1.58 0.132
#> true_effort 1.55183 0.07835 19.80 1.14e-13 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 8.011 on 18 degrees of freedom
#> Multiple R-squared: 0.9561, Adjusted R-squared: 0.9537
#> F-statistic: 392.2 on 1 and 18 DF, p-value: 1.141e-13
#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)
Can we observe 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, sampling_prob = 1,
mean_catch_rate = 2.5, fishing_day_length = 12)
sim
#> Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 768.7004 2.470043 824.7229 768.7004 2.511069
#> 2 708.7170 2.599554 806.7401 708.7170 2.495052
#> 3 759.9584 2.416612 854.5432 759.9584 2.358045
#> 4 783.3415 2.715485 892.3400 783.3415 2.663605
#> 5 728.9695 2.126378 691.4138 728.9695 2.128315
#> 6 724.7953 2.183654 724.3334 724.7953 2.273502
#> 7 695.8944 2.599302 844.9681 695.8944 2.614189
#> 8 789.6448 2.410761 814.9992 789.6448 2.467584
#> 9 781.7185 2.672259 876.0535 781.7185 2.706500
#> 10 753.8212 2.370904 822.9531 753.8212 2.410414
#> 11 814.7701 2.519984 879.0222 814.7701 2.583332
#> 12 811.6684 2.305741 759.6655 811.6684 2.385969
#> 13 751.8314 2.374681 773.6552 751.8314 2.429269
#> 14 753.1468 2.419120 836.7430 753.1468 2.436932
#> 15 776.5254 2.162192 817.4036 776.5254 2.237419
#> 16 738.9103 2.666906 885.2465 738.9103 2.609013
#> 17 784.0078 2.284436 807.6391 784.0078 2.316637
#> 18 784.3040 2.603432 874.8825 784.3040 2.618557
#> 19 802.6489 2.429314 860.2270 802.6489 2.333058
#> 20 774.0712 2.567579 905.7421 774.0712 2.469119#> 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
#> -1.008e-13 -9.010e-16 1.612e-14 2.442e-14 1.043e-13
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.034e-13 2.840e-13 7.160e-01 0.483
#> true_effort 1.000e+00 3.712e-16 2.694e+15 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 5.282e-14 on 18 degrees of freedom
#> Multiple R-squared: 1, Adjusted R-squared: 1
#> F-statistic: 7.258e+30 on 1 and 18 DF, p-value: < 2.2e-16
Another simulation
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,
sampling_prob = sampling_prob, mean_catch_rate = 2.5,
fishing_day_length = fishing_day_length)
sim
#> Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 336.3974 2.446137 842.4591 194.2340 2.501437
#> 2 459.4682 2.461493 794.7933 216.4546 2.514877
#> 3 363.0755 2.157886 760.6865 233.0647 2.359580
#> 4 422.7744 2.310826 787.1008 223.0891 2.374984
#> 5 413.9636 2.549926 906.0712 222.9362 2.577263
#> 6 409.6488 2.585385 743.7690 217.4829 2.351497
#> 7 429.4646 2.806555 889.1171 245.4681 2.555515
#> 8 437.3585 2.494798 869.9422 237.6559 2.438136
#> 9 418.4751 3.389806 927.2633 225.8867 2.674165
#> 10 435.0700 2.468669 836.1957 246.1885 2.289779
#> 11 508.9174 2.480358 840.6856 247.3459 2.325625
#> 12 401.5740 2.808633 922.8538 218.0649 2.880003
#> 13 380.6494 3.202355 953.2290 230.1477 2.686220
#> 14 411.1600 2.460808 957.5743 214.7786 2.713318
#> 15 438.6053 2.880876 742.9910 224.8079 2.279269
#> 16 501.4253 1.962584 753.3787 231.2408 2.422737
#> 17 482.2694 2.375788 803.4919 234.8892 2.316639
#> 18 502.1387 2.132380 843.9224 234.5807 2.393269
#> 19 420.0203 2.400470 734.3253 223.6434 2.292050
#> 20 492.1539 2.721672 858.8633 215.6486 2.493468#>
#> Call:
#> lm(formula = Ehat ~ true_effort, data = .)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -80.775 -20.218 -7.547 36.599 78.212
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 43.6023 173.5401 0.251 0.8045
#> true_effort 1.7173 0.7637 2.249 0.0373 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 42.55 on 18 degrees of freedom
#> Multiple R-squared: 0.2193, Adjusted R-squared: 0.1759
#> F-statistic: 5.056 on 1 and 18 DF, p-value: 0.0373
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 surveryors. To accomodate 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, sampling_prob = sampling_prob,
mean_catch_rate = 2.5, fishing_day_length = fishing_day_length)
sim_w
#> Ehat catch_rate_ROM true_catch true_effort mean_lambda
#> 1 654.4297 2.405069 636.0419 437.8568 2.514499
#> 2 635.3440 2.498353 602.0437 423.5627 2.453219
#> 3 711.8827 2.314211 618.1801 474.5885 2.379199
#> 4 596.5517 2.349445 590.9965 398.3901 2.403765
#> 5 683.4622 2.632500 697.3532 457.2936 2.603457
#> 6 649.8841 2.303446 573.7912 434.3805 2.387601
#> 7 589.8644 2.657115 752.9906 394.7195 2.607380
#> 8 647.9023 2.553308 651.7656 431.9349 2.489279
#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
#> -75.643 -17.224 -5.803 10.862 71.865
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 192.08255 22.16532 8.666 3.82e-09 ***
#> true_effort 1.05823 0.07377 14.345 7.29e-14 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 36.71 on 26 degrees of freedom
#> Multiple R-squared: 0.8878, Adjusted R-squared: 0.8835
#> F-statistic: 205.8 on 1 and 26 DF, p-value: 7.291e-14
Choose your own advenure
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 estiate variability in the catch and effort estimates (e.g., relative standard error) to evaluate the most efficient creel survey for their fishery.