## Introduction

In the sections on the multispecies model and on running a simulation we saw how to set up a model and project it forward through time under our desired fishing scenario. The result of running a projection is an object of class MizerSim. What do we then do? How can we explore the results of the simulation? In this section we introduce a range of summaries, plots and indicators that can be easily produced using functions included in mizer.

We will use the following MizerSim object for these examples, where the effort array is the one we created in the previous section on running a simulation:

sim <- project(NS_params, effort = effort_array, dt = 0.1, t_save = 1)

## Accessing the simulation results

The projected species abundances at size through time can be obtained with N(sim). This returns a three-dimensional array (time x species x size). Consequently, this array can get very big so inspecting it can be difficult. In the example we have just run, the time dimension of n has 10 rows (one for the initial population and then one for each of the saved time steps). There are also 12 species each with 100 sizes. We can check this by running the dim() function and looking at the dimensions of the n array:

dim(N(sim))
## [1]  10  12 100

To pull out the abundances of a particular species through time at size you can subset the array. For example to look at Cod through time you can use:

N(sim)[, "Cod", ]

This returns a two-dimensional array: time x size, containing the cod abundances. The time dimension depends on the value of the argument t_save when project() was run. You can see that even though we specified dt to be 0.1 when we called project(), the t_save = 1 argument has meant that the output is only saved every year.

Often we are particularly interested in the results at the final time-step. These we can access with

finalN(sim)

which is a two dimensional array (species x size).

The projected resource abundances can be accesses similarly with

NResource(sim)

This returns a two-dimensional array (time x size). And if we are only interested in the final time step

finalNResource(sim)

returns a vector with one entry for each size class.

## Summary functions

As well as the summary() methods that are available for both MizerParams and MizerSim objects, there are other useful summary functions to pull information out of a MizerSim object. A description of the different summary functions available is given in the summary functions help page.

All of these functions have help files to explain how they are used. (It is also possible to use most of these functions with a MizerParams object if you also supply the population abundance as an argument. This can be useful for exploring how changes in parameter value or abundance can affect summary statistics and indicators. We won’t explore this here but you can see their help files for more details.)

The functions getBiomass() and getN() have additional arguments that allow the user to set the size range over which to calculate the summary statistic. This is done by passing in a combination of the arguments min_l, min_w, max_l and max_w for the minimum and maximum length or weight. If min_l is specified there is no need to specify min_w and so on. However, if a length is specified (minimum or maximum) then it is necessary for the species parameter data.frame (see the species parameters section) to include the parameters a and b for length-weight conversion. It is possible to mix length and weight constraints, e.g. by supplying a minimum weight and a maximum length. The default values are the minimum and maximum weights of the spectrum, i.e. the full range of the size spectrum is used.

### Examples of using the summary functions

Here we show a simple demonstration of using a summary function using the sim object we created earlier. Here, we use getSSB() to calculate the SSB of each species through time (note the use of the head() function to only display the first few rows).

ssb <- getSSB(sim)
dim(ssb)
## [1] 10 12
head(ssb)
##     sp
## time        Sprat      Sandeel       N.pout      Herring        Dab
##    1 210810187886 5.378411e+12 183159668755 442644004208 6885675636
##    2 157421300798 3.498137e+12 153386837865 499200353502 5278650740
##    3 138701220818 2.510551e+12 135619248024 603931625682 5065030019
##    4 118875574040 1.997337e+12 110306292341 569167018628 4877123531
##    5 114060666493 1.790051e+12 112246876589 420615452917 5224602753
##    6 125640651552 1.736155e+12 124869964868 351468531499 6147959412
##     sp
## time      Whiting        Sole    Gurnard       Plaice      Haddock          Cod
##    1 113572753243 63630241776 9102232924 303365911438 151965178029 531536722956
##    2  87964359889 46775076902 7385280731 232689238362 117830523964 345850203280
##    3  91749455062 45443905458 7528148453 240988454909 135946957263 290183064993
##    4  85038348880 49465062866 6855105119 264670808435 158905104522 308445205952
##    5  77139941423 53555703121 5600934574 279557468426 145778058562 335438386336
##    6  82462061701 56441766035 5398238488 278206590917 123593721267 351386199474
##     sp
## time       Saithe
##    1 327578246185
##    2 218500695506
##    3 197610219846
##    4 228220656964
##    5 271860341040
##    6 287805766571

As mentioned above, we can specify the size range for the getsummaryBiomass() and getN() functions. For example, here we calculate the total biomass of each species but only include individuals that are larger than 10 g and smaller than 1000 g.

biomass <- getBiomass(sim, min_w = 10, max_w = 1000)
head(biomass)
##     sp
## time        Sprat      Sandeel       N.pout      Herring        Dab
##    1 244119195586 4.589606e+12 238847649463 1.273446e+12 8373096367
##    2 189464604834 2.888858e+12 214678099536 1.413601e+12 6837801607
##    3 169593586308 1.931520e+12 185655249238 1.536104e+12 6536986610
##    4 146468867085 1.409300e+12 166879189209 1.360238e+12 6286073743
##    5 144115814704 1.171670e+12 178630603519 1.175016e+12 6849215327
##    6 159924185834 1.102235e+12 192414189537 1.177930e+12 7904848054
##     sp
## time      Whiting         Sole     Gurnard       Plaice      Haddock
##    1 161515844306 127400523235 24759887586 766087469917 333172493301
##    2 140923805330 112319321368 24087806247 722705573485 335440217763
##    3 139784785126 114244854064 23828541236 743105121821 372682335506
##    4 127051769924 115827036011 20324716177 711903001258 356182595515
##    5 126548669345 116366841999 19072116393 661973266258 323469227911
##    6 137220141191 121684387886 21334281004 668659838352 325245994096
##     sp
## time         Cod       Saithe
##    1 45159646196 158969500338
##    2 52110333051 183496280557
##    3 62885974091 216448253249
##    4 59073484678 214031942473
##    5 51993520691 174593364166
##    6 49544506290 138713867303

## Functions for calculating indicators

Functions are available to calculate a range of indicators from a MizerSim object after a projection. A description of the different indicator functions available is given in the indicator functions help page.. You can read the help pages for each of the functions for full instructions on how to use them, along with examples.

With all of the functions in the table it is possible to specify the size range of the community to be used in the calculation (e.g. to exclude very small or very large individuals) so that the calculated metrics can be compared to empirical data. This is used in the same way that we saw with the function getBiomass() in the section on summary functions for MizerSim objects.. It is also possible to specify which species to include in the calculation. See the help files for more details.

### Examples of calculating indicators

For these examples we use the sim object we created earlier.

The slope of the community can be calculated using the getCommunitySlope() function. Initially we include all species and all sizes in the calculation (only the first five rows are shown):

slope <- getCommunitySlope(sim)
head(slope)
##        slope intercept        r2
## 1 -0.7822250  25.40779 0.8722251
## 2 -0.7970084  25.24922 0.8666363
## 3 -0.8066332  25.21573 0.8665750
## 4 -0.8151679  25.23791 0.8678893
## 5 -0.8229285  25.24489 0.8686275
## 6 -0.8272602  25.23104 0.8673588

This gives the slope, intercept and $$R^2$$ value through time (see the help file for getCommunitySlope for more details).

We can include only the species we want with the species argument. Below we only include demersal species. We also restrict the size range of the community that is used in the calculation to between 10 g and 5 kg. The species argument is a character vector of the names of the species that we want to include in the calculation.

dem_species <- c("Dab", "Whiting", "Sole", "Gurnard", "Plaice", "Haddock",
"Cod", "Saithe")
slope <- getCommunitySlope(sim, min_w = 10, max_w = 5000,
species = dem_species)
head(slope)
##       slope intercept        r2
## 1 -1.096584  26.88942 0.9749307
## 2 -1.177678  27.21999 0.9796408
## 3 -1.148456  27.13231 0.9754412
## 4 -1.060903  26.70050 0.9748899
## 5 -1.026889  26.50463 0.9820432
## 6 -1.061542  26.68677 0.9807863

## Plotting the results

R is very powerful when it comes to exploring data through plots. Two useful packages for plotting are ggplot2 and plotly. These use data.frames for input data whereas many of the mizer functions return arrays or matrices. Fortunately it is straightforward to turn arrays and matrices into data.frames using the melt() function from the reshape2 package that mizer makes available to you. Although mizer does include some dedicated plots, it is definitely worth your time getting to grips with these other plotting packages. This will make it possible for you to make your own plots. We provide some details in the section on using ggplot2 and plotly with mizer.

Included in mizer are several dedicated plots that use MizerSim objects as inputs (see the plots help page.). As well as displaying the plots, these functions all return objects of type ggplot from the ggplot2 package, meaning that they can be further modified by the user (e.g. by changing the plotting theme). See the help page of the individual plot functions for more details. The generic plot() method has also been overloaded for MizerSim objects. This produces several plots in the same window to provide a snapshot of the results of the simulation.

Some of the plots plot values by size (for example plotFeedingLevel() and plotSpectra()). For these plots, the default is to use the data at the final time step of the projection. With these plotting functions, it is also possible to specify a different time, or a time range to average the values over before plotting.

### Plotting examples

Using the plotting functions is straightforward. For example, to plot the total biomass of each species against time you use the plotBiomass() function:

As mentioned above, some of the plot functions plot values against size at a point in time (or averaged over a time period). For these plots it is possible to specify the time step to plot, or the time period to average the values over. The default is to use the final time step. Here we plot the abundance spectra (biomass), averaged over time = 5 to 10:

As mentioned above, and as we have seen several times in this guide, the generic plot() method has also been overloaded. This produces 5 plots in the same window (plotFeedingLevel(), plotBiomass(), plotPredMort(), plotFMort() and plotSpectra()). It is possible to pass in the same arguments that these individual plots use, e.g. arguments to change the time period over which the data is averaged.

plot(sim)

The next section describes how to use what we have learned to model the North Sea.