Calculate the rate at which biomass of each species is fished
Source:R/summary_methods.R
getYield.RdThis yield rate is given in grams per year. It is calculated at each time step saved in the MizerSim object.
Value
If called with a MizerParams object, a named numeric vector with
the yield rate in grams per year for each species in the model. If called
with a MizerSim object, an ArrayTimeBySpecies object (time x species)
containing the yield rate in grams per year at each saved time step.
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.
See also
Other summary functions:
getBiomass(),
getDiet(),
getGrowthCurves(),
getN(),
getSSB(),
getTrophicLevel(),
getTrophicLevelBySpecies(),
getYieldGear()
Examples
yield <- getYield(NS_sim)
yield[c("1972", "2010"), c("Herring", "Cod")]
#> Yield rate (2 times x 2 species) [g/year]
#> Herring: min=3.05e+10 mean=5.52e+10 max=8e+10
#> Cod: min=2.89e+11 mean=3.22e+11 max=3.55e+11
# 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 approximate the total catch in the year by averaging over the year
sum(getYield(sim)[1:10, "Herring"] / 10)
#> [1] 29947173834