optistock (version 0.0.2)

recruits_at_time: Calculate the number of recruits left after given time based on mortality

Description

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).

Usage

recruits_at_time(
  time_at_stocking,
  time_at_rec,
  fish_init,
  mort_fun = exp_mort,
  mort_fun_args
)

Value

The number of fish that will be left given the mortality function, its parameters, and the time (time_at_rec - time_at_stocking)

Arguments

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 inv_vb to calculate this.

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 mort_fun

Details

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:

N_t = 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).

Examples

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)