Exercises on single-species size-spectrum dynamics

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First we need to load some libraries. So run the following code.

library(mizer)
library(tidyverse)
library(plotly)

Exercise 1: Number density plot

Do this exercise only once you have reached the corresponding point in the tutorial notebook. It involves using similar code to that you have seen in the examples in that notebook.

Create a MizerParams object describing a single species in a power-law background where the Sheldon exponent is 2.1. Then plot the number density as a function of weight in the steady state of that model.

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Once you are satisfied with your plot, continue in the tutorial notebook until you reach the next exercise.

Exercise 2: Number of fish in size class

Create the params object used in the tutorial, describing the single-species in a power-law background with exponent 2.05. Run the model to steady state. Then determine the number of fish in the size bracket between 10 grams and 10.5 grams.

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Exercise 3: Mortality rate plot and fit

Make a log-log plot of the mortality rate in the steady state of the model from exercise 2. You can get the mortality rate with the getMort() function. Watch out for a surprise when you look at the variable names in the data frame that you will create.

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Now fit a linear model to determine the slope and and intercept and thus the allometric exponent for the mortality rate and the coefficient, to establish that \[\mu(w) = 1.909\ w^{-1/4}.\]

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Exercise 4: Growth rates

Make a plot showing the growth rates of the original model and of the model with the changed maturity curve.

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Exercise 5: Extra prey

Plot the steady state biomass density in our model when the community abundance is increased by a factor of 10 in the size range from 1mg to 10mg.

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Exercise 6: Predation kernel

Change the paramters of the predation kernel to beta = 500 and sigma = 3 and plot the predation kernel of a predator of size 1g. You should see that the predation kernel is truncated so that the predator never feeds on prey larger than themselves.

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Next, plot the steady state arising with this feeding kernel when the prey abundance is artificially reduced by a factor of 10 in the size range between 1mg and 10mg as in previous examples. What do you observe? Are you surprised?

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Exercise 7: Decreased gamma

What effect will this change in growth rate have on the slope of the juvenile spectrum? Will it be steeper or shallower? Make the plot of the spectrum to see.

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