| Title: | Determine Optimum Stocking Times Used in Fishery Enhancements |
|---|---|
| Description: | A collection of functions that aid in calculating the optimum time to stock hatchery reared fish into a body of water given the growth, mortality and cost of raising a particular number of individuals to a certain length. |
| Authors: | Paul Frater [aut, cre]
|
| Maintainer: | Paul Frater <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.0.2 |
| Built: | 2024-12-16 06:58:35 UTC |
| Source: | CRAN |
This data.frame contains the cost parameters used in
spp_examples. These parameters correspond with the
total_cost and linear_total_cost functions.
cost_parameterscost_parameters
A tibble of variables and 16 records
Species common name
The source of the data. WDNR is from Wisconsin Dep't of Natural Resources Hatchery cost data. AFS is the American Fisheries Society Special Publication 35 on Fishkill Replacement costs
Either "exp" for exponential – corresponds to the
total_cost cost function, or "linear" – corresponds to the
linear_total_cost cost function.
The cost function – either
total_cost or linear_total_cost
A list-col of the parameters necessary for
the respective cost function found in cost_fun
Compute the per-cost fish based on stocking time, time to recruitment, growth, and mortality
cost_per_fish( time_at_stocking, time_at_rec, n_recruits_desired, cost_fun = total_cost, cost_fun_args, mort_fun = constant_mort, mort_fun_args )cost_per_fish( time_at_stocking, time_at_rec, n_recruits_desired, cost_fun = total_cost, cost_fun_args, mort_fun = constant_mort, mort_fun_args )
time_at_stocking |
The time at which fish are stocked (i.e. synonymous with the amount of time that fish are raised in a hatchery) |
time_at_rec |
The time at which a fish enters the fishery (i.e. the
amount of time it takes a fish to grow to a desired length). Use
|
n_recruits_desired |
The number of recruits desired at
|
cost_fun |
The cost function. Defaults to |
cost_fun_args |
Arguments for |
mort_fun |
The mortality function, see ?mort_funs |
mort_fun_args |
List. Named arguments to be passed to |
The per-fish cost fish that lives until time_at_rec based on
time_at_stocking, the cost function and mortality functions.
cost_args <- list( init_cost = 0.05, time_slope = 0.01, time_exp = 1.2, rec_exp = 1 ) mort_args <- list(m_init = (1 / 365)) # the cost-per-fish to stock across a range of times given cost and mortality # assumes fish recruit into the fishery at day 1000 curve(cost_per_fish( x, 1000, 1000, cost_fun_args = cost_args, mort_fun_args = mort_args), xlab = "Days", ylab = "$ per fish stocked", 10, 1200 )cost_args <- list( init_cost = 0.05, time_slope = 0.01, time_exp = 1.2, rec_exp = 1 ) mort_args <- list(m_init = (1 / 365)) # the cost-per-fish to stock across a range of times given cost and mortality # assumes fish recruit into the fishery at day 1000 curve(cost_per_fish( x, 1000, 1000, cost_fun_args = cost_args, mort_fun_args = mort_args), xlab = "Days", ylab = "$ per fish stocked", 10, 1200 )
This is a multivariable function of both time and number of recruits raised. Cost-per-time and cost-per-recruit can be calculated as a quadratic where the slope and exponent can be specified.
daily_cost_fun( time, recruits, daily_cost, time_slope = 0, time_exp = 1, rec_slope = 1, rec_exp = 1, type = "multiplicative" )daily_cost_fun( time, recruits, daily_cost, time_slope = 0, time_exp = 1, rec_slope = 1, rec_exp = 1, type = "multiplicative" )
time |
The time at which fish are raised in hatchery |
recruits |
The number of recruits raised |
daily_cost |
Baseline daily cost to raise a single fish |
time_slope |
The slope term on the amount of time (see details) |
time_exp |
The exponent on the amount of time |
rec_slope |
The slope term on the number of recruits |
rec_exp |
The exponent on the number of recruits |
type |
Either multiply the number of recruits times the cost-at-time or add to it (see Details). |
The cost-per-fish based on time and number of recruits uses the function:
C = sTtα * s2Rβ + bif type = "multiplicative". Otherwise it uses:
C = sTtα + s2Rβ + bif type = "additive"
where C = the cost to rear R number of recruits at time T, the s values are the slopes, α and β, are the exponents on time (T) and recruits (R), respectively, and b is the intercept. The instantaneous cost is really what is of interest, and the number of recruits essentially adjusts the intercept on that dimension of the equation.
Increasing the exponent will dramatically increase the cost of raising
hatchery fish as time goes on. Increasing the exponent dramatically
increases the cost of raising a greater number of fish. Integrating this
equation across time will compute the total cost to raise the number of
recruits to time T. Use the total_daily_cost function to
do this automatically.
A numeric value representing the cost of rearing the number of
recruits at a given time and given the number of recruits raised
# compute the instantaneous cost of raising 1000 fish on day 100 daily_cost_fun(time = 100, recruits = 1000, daily_cost = 0.05, time_slope = 0, time_exp = 1, rec_slope = 0.01, rec_exp = 1) # plot a curve of instantaneous cost against time curve(daily_cost_fun(x, 1000, 0.05, 0.01, 1.2, 0.05, 1), 0, 1000, xlab = "Time", ylab = "$") ## Not run: # 3d plot of costs by time and recruit emdbook::curve3d(daily_cost_fun(x, y, 0.05, 0.01, 1.2, 0.05, 1), from = c(0, 0), to = c(1000, 1000), xlab = "Time", ylab = "Recruits", zlab = "$", sys3d = "wireframe") ## End(Not run)# compute the instantaneous cost of raising 1000 fish on day 100 daily_cost_fun(time = 100, recruits = 1000, daily_cost = 0.05, time_slope = 0, time_exp = 1, rec_slope = 0.01, rec_exp = 1) # plot a curve of instantaneous cost against time curve(daily_cost_fun(x, 1000, 0.05, 0.01, 1.2, 0.05, 1), 0, 1000, xlab = "Time", ylab = "$") ## Not run: # 3d plot of costs by time and recruit emdbook::curve3d(daily_cost_fun(x, y, 0.05, 0.01, 1.2, 0.05, 1), from = c(0, 0), to = c(1000, 1000), xlab = "Time", ylab = "Recruits", zlab = "$", sys3d = "wireframe") ## End(Not run)
This data.frame contains the growth parameters used in
spp_examples. The growth parameters correspond with the von
Bertalanfy growth curve (VBGF – see vbgf)
growth_parametersgrowth_parameters
A data.frame with 7 fields and 6 records:
Species common name
Scientific name for the species
The L_infinity parameters for the VBGF
The k parameter for the VBGF
The t_0 parameter for the VBGF
Number of samples used. For WDNR data this is the number of paired length-at-age data points (WDNR, 2021). For FishBase it is the number of submitted entries.
Where data was retrieved from. WDNR is the Wisconsin Dep't of Natural Resources Fisheries Management Database. FishBase (Froese and Pauly, 2010) is FishBase.
This function calculates the inverse of the VBGF, or, time it takes to grow to a particular length
inv_vb(len, linf, k, t0)inv_vb(len, linf, k, t0)
len |
Numeric. A length at which to determine how long it takes to grow |
linf |
The L∞ parameter of the VBGF |
k |
The k parameter of the VBGF |
t0 |
The t0 |
A numeric vector of how long it takes to grow to length len
time <- 365 len_at_age <- vbgf(time, 30, (0.2 / 365), -0.2) inv_vb(len_at_age, 30, (0.2/365), -0.2)time <- 365 len_at_age <- vbgf(time, 30, (0.2 / 365), -0.2) inv_vb(len_at_age, 30, (0.2/365), -0.2)
This function returns the total cost of raising n recruits to
time. The curve across time can only be linear
with parameters int and beta, but can be non-linear with
respect to recruits
linear_total_cost(time, recruits, int, beta, rec_exp = 1)linear_total_cost(time, recruits, int, beta, rec_exp = 1)
time |
The amount of time that fish are raised in hatchery |
recruits |
The number of recruits raised |
int |
Intercept for the linear total cost curve |
beta |
Slope for the linear total cost curve |
rec_exp |
The exponent on the number of recruits |
A vector the same length as time with the total cost to raise
n recruits to time
curve(linear_total_cost(x, 0.5, 0.001, 100), 0, 1000)curve(linear_total_cost(x, 0.5, 0.001, 100), 0, 1000)
This family of functions produce different shapes of mortality curves across time
exp_mort(time, m_init, m_inf, alpha, t_scale = NULL) decreasing_mort(time, m_init, m_inf, alpha) constant_mort(time, m_init) inv_mort(time, m_init, m_inf) gaussian_mort(time, m_init, m_max, t_scale, alpha) half_gaussian_mort(time, m_init, m_max, m_inf, t_scale, alpha) linear_mort(time, alpha, m_init) parabolic_mort(time, m_min, alpha, t_scale, beta)exp_mort(time, m_init, m_inf, alpha, t_scale = NULL) decreasing_mort(time, m_init, m_inf, alpha) constant_mort(time, m_init) inv_mort(time, m_init, m_inf) gaussian_mort(time, m_init, m_max, t_scale, alpha) half_gaussian_mort(time, m_init, m_max, m_inf, t_scale, alpha) linear_mort(time, alpha, m_init) parabolic_mort(time, m_min, alpha, t_scale, beta)
time |
The time to calculate mortality at |
m_init |
Initial rate of mortality at time 0 (or time t for
|
m_inf |
Final rate of mortality as time approaches infinity |
alpha |
The rate at which mortality decreases across time |
t_scale |
A horizontal scaling parameter |
m_max |
The maximum mortality that is achieved at |
m_min |
The lowest mortality that the curve should reach |
beta |
Slope on the quadratic term for |
These functions produced different shapes of mortality curves that are
commonly found in fisheries. Some of the more common are
constant_mort (which returns constant mortality across time),
exp_mort (S-shaped decreasing curve), and decreasing_mort
(non-linear decreasing curve). Others are less common and represent specific
scenarios such as gaussian_mort (implemented to represent a
bottleneck).
A vector of numeric values for mortality rate at time
# an example in years curve(exp_mort(x, 0.2, 0.1, 0.25), 0, 20) # an example in days curve(exp_mort(x, (1 / 365), (0.2 / 365), 0.005), 0, 1000)# an example in years curve(exp_mort(x, 0.2, 0.1, 0.25), 0, 20) # an example in days curve(exp_mort(x, (1 / 365), (0.2 / 365), 0.005), 0, 1000)
This function is essentially the inverse of recruits_at_time.
Given the number of fish desired at a certain time and the mortality
function and parameters this function will calculate how many fish should be
stocked into a system.
n_to_stock( time_at_stocking, time_at_rec, n_recruits_desired, mort_fun = exp_mort, mort_fun_args )n_to_stock( time_at_stocking, time_at_rec, n_recruits_desired, mort_fun = exp_mort, mort_fun_args )
time_at_stocking |
The time that fish are stocked (i.e. synonymous with the amount of time that fish are raised in a hatchery) |
time_at_rec |
The time at which a fish enters the fishery (i.e. the
amount of time it takes a fish to grow to a desired length). Use
|
n_recruits_desired |
The number of recruits desired at
|
mort_fun |
The mortality function, see ?mort_funs |
mort_fun_args |
List. Named arguments to be passed to |
The number of fish to be stocked at time_at_stocking to
get the desired number of fish at time_at_rec based on the mortality
function and associated parameters
# how many fish to stock on day 100 if you want 10000 fish on day 1000 n_to_stock(10000, 100, 1000, mort_fun = exp_mort, mort_fun_args = list(m_init = (1 / 365), m_inf = (0.2/365), alpha = 0.005))# how many fish to stock on day 100 if you want 10000 fish on day 1000 n_to_stock(10000, 100, 1000, mort_fun = exp_mort, mort_fun_args = list(m_init = (1 / 365), m_inf = (0.2/365), alpha = 0.005))
This function will open a Shiny app where you can play around with parameters to see how the resulting CPF curve will change.
optistock_app()optistock_app()
NULL. Opens and runs the Shiny application that comes with the
optistock package
This function will use the provided mortality function and parameters along
with the length of time from stocking until the time in question to determine
how many fish will be left at that time (i.e. how many fish die between
time_at_stocking and time_at_rec).
recruits_at_time( time_at_stocking, time_at_rec, fish_init, mort_fun = exp_mort, mort_fun_args )recruits_at_time( time_at_stocking, time_at_rec, fish_init, mort_fun = exp_mort, mort_fun_args )
time_at_stocking |
The day that fish are stocked (i.e. synonymous with the amount of time that fish are raised in a hatchery) |
time_at_rec |
The time at which a fish enters the fishery (i.e. the
amount of time it takes a fish to grow to a desired length). Use
|
fish_init |
The initial number of fish stocked |
mort_fun |
The mortality function, see ?mort_funs |
mort_fun_args |
List. Named arguments to be passed to |
This function calculates how many fish are left at a certain time based on the initial number of fish stocked and the integral of the mortality function. The number of fish left are computed using the following equation:
Nt = N0 exp(∫ f(t))where N0 is the initial number of fish
stocked and f(t) is the mortality function. The amount of time is provided
to the function as the time at which fish are recruited into the fishery
minus the time at which they are stocked. The time at which fish are
recruited into the fishery can be calculated using the inverse von
Bertalanffy growth function (see inv_vb).
The number of fish that will be left given the mortality function,
its parameters, and the time (time_at_rec - time_at_stocking)
mort_args <- list( m_init = (1 / 365), m_inf = (0.2/365), alpha = 0.005 ) recruits_at_time(100, 1000, 1000, mort_fun = exp_mort, mort_fun_args = mort_args)mort_args <- list( m_init = (1 / 365), m_inf = (0.2/365), alpha = 0.005 ) recruits_at_time(100, 1000, 1000, mort_fun = exp_mort, mort_fun_args = mort_args)
This family of functions opens R scripts to run the scenarios that are used in the optistocking paper. Simply call the function to open the file that contains R code for the species' of interest.
walleye_example() musky_example() rainbow_trout_example() chinook_example()walleye_example() musky_example() rainbow_trout_example() chinook_example()
NULL. Opens an R script with an example
## Not run: walleye_example() ## End(Not run)## Not run: walleye_example() ## End(Not run)
This function computes the total cost to raise fish in a hatchery until
time. This function differs from total_daily_cost by
directly computing the total cost rather than integrating a daily cost
estimate.
total_cost( time, time_slope = 1, time_exp = 1, init_cost = 0, recruits = 1, rec_exp = 1 )total_cost( time, time_slope = 1, time_exp = 1, init_cost = 0, recruits = 1, rec_exp = 1 )
time |
The amount of time that fish are raised in hatchery |
time_slope |
Controls how quickly the slope increases over time |
time_exp |
Controls the non-linearity of the curve over time |
init_cost |
The initial cost (i.e. intercept of the curve) |
recruits |
The number of recruits |
rec_exp |
Controls the non-linearity of the curve across recruit number |
The total_cost function computes a cost curve according to the
following equation:
where α corresponds to the
time_slope argument,
γ is the time_exp parameter,
β is the intercept (or
init_cost),
R is the number of recruits, and
τ is the recruitment exponent
corresponding to rec_exp
A vector of values representing cost for the given time, recruit number, and associated variables
curve(total_cost(x, time_slope = 0.05, time_exp = 1.2), 0, 100) curve(total_cost(x, time_slope = 0.05, time_exp = 0.5), 0, 100)curve(total_cost(x, time_slope = 0.05, time_exp = 1.2), 0, 100) curve(total_cost(x, time_slope = 0.05, time_exp = 0.5), 0, 100)
This function takes the definite integral from time t = 0 until the
given time of the daily_cost_fun.
This integral is then the total cost of raising x number of fish until
time given the other cost function parameters.
total_daily_cost( time, recruits, daily_cost, init_cost = 0, time_slope = 0, time_exp = 1, rec_slope = 1, rec_exp = 1, type = "multiplicative" )total_daily_cost( time, recruits, daily_cost, init_cost = 0, time_slope = 0, time_exp = 1, rec_slope = 1, rec_exp = 1, type = "multiplicative" )
time |
The time at which fish are raised in hatchery |
recruits |
The number of recruits raised |
daily_cost |
Baseline daily cost to raise a single fish |
init_cost |
An intercept on the total cost function |
time_slope |
The slope term on the amount of time (see details) |
time_exp |
The exponent on the amount of time |
rec_slope |
The slope term on the number of recruits |
rec_exp |
The exponent on the number of recruits |
type |
Either multiply the number of recruits times the cost-at-time or add to it (see Details). |
The total cost across time to raise the number of recruits.
This is simply the integral from time t = 0 until time of the
daily_cost_fun function.
# total cost of raising 1000 fish for 100 days at given parameters total_daily_cost(time = 100, recruits = 100, daily_cost = 0.05, time_slope = 0.01, time_exp = 1.2, rec_slope = 0.05, rec_exp = 1)# total cost of raising 1000 fish for 100 days at given parameters total_daily_cost(time = 100, recruits = 100, daily_cost = 0.05, time_slope = 0.01, time_exp = 1.2, rec_slope = 0.05, rec_exp = 1)
Basic von Bertalanffy growth function (VBGF)
vbgf(time, linf, k, t0)vbgf(time, linf, k, t0)
time |
Time at which to calculate size |
linf |
The L∞ parameter of the VBGF |
k |
The k parameter of the VBGF |
t0 |
The t0 |
A numeric vector of lengths given the age (or amount of time) and parameters
curve(vbgf(x, 30, 0.25, -0.2), 0, 10) curve(vbgf(x, 30, (0.25 / 365), -0.2), 0, 10 * 365)curve(vbgf(x, 30, 0.25, -0.2), 0, 10) curve(vbgf(x, 30, (0.25 / 365), -0.2), 0, 10 * 365)