Calculate the rate at which biomass of each species is fished

This yield rate is given in grams per year. It is calculated at each time step saved in the MizerSim object.

Usage

getYield(object)

Arguments

object: An object of class MizerParams or MizerSim.

Value

If called with a MizerParams object, a vector with the yield rate in grams per year for each species in the model. If called with a MizerSim object, an array (time x species) containing the yield rate at each time step for all species.

Details

The yield rate $y_i(t)$ for species $i$ at time $t$ is defined as $$y_i(t)=\int\mu_{f.i}(w, t)N_i(w, t)w dw$$ where $\mu_{f.i}(w, t)$ is the fishing mortality of an individual of species $i$ and weight $w$ at time $t$ and $N_i(w, t)$ is the abundance density of such individuals. The factor of $w$ converts the abundance density into a biomass density and the integral aggregates the contribution from all sizes.

The total catch in a time period from $t_1$ to $t_2$ is the integral of the yield rate over that period: $$C = \int_{t_1}^{t2}y_i(t)dt$$ In practice, as the yield rate is only available at the saved times, one can only approximate this integral by averaging over the available yield rates during the time period and multiplying by the time period. The less the yield changes between the saved values, the more accurate this approximation is. So the approximation can be improved by saving simulation results at smaller intervals, using the t_save argument to project(). But this is only a concern if abundances change quickly during the time period of interest.

Examples

yield <- getYield(NS_sim)
yield[c("1972", "2010"), c("Herring", "Cod")]
#>       sp
#> time       Herring          Cod
#>   1972 80002050975 355351719122
#>   2010 30496241734 289022888045

# Running simulation for another year, saving intermediate time steps
params <- setInitialValues(getParams(NS_sim), NS_sim)
sim <- project(params, t_save = 0.1, t_max = 1, 
               t_start = 2010, progress_bar = FALSE)
# The yield rate for Herring decreases during the year
getYield(sim)[, "Herring"]
#>        2010      2010.1      2010.2      2010.3      2010.4      2010.5 
#> 30496241734 30406503779 30297907652 30173956406 30038604629 29896229522 
#>      2010.6      2010.7      2010.8      2010.9        2011 
#> 29751183405 29607379160 29468046935 29335685116 29212159486 
# We get the total catch in the year by averaging over the year
sum(getYield(sim)[1:10, "Herring"] / 10)
#> [1] 29947173834