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<h1 class="title toc-ignore">Exercise Solutions</h1>
</div>
<p> </p>
<div id="exercise-6-basic-programming-in-r" class="section level2">
<h2>Exercise 6: Basic programming in R</h2>
<p> </p>
<p>Read <a href="https://intro2r.com/prog-r.html">Chapter 7</a> to help
you complete the questions in this exercise.</p>
<p> </p>
<p>1. Create a function to calculate the area of a circle. Test the
function by finding the area of a circle with a diameter of 3.4 cm. Can
you use it on a vector of data?</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="co"># area of a circle</span></span>
<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a><span class="co"># the equation to calculate the area of a circle is pi * radius^2</span></span>
<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a></span>
<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a>circle.area <span class="ot"><-</span> <span class="cf">function</span>(d){ </span>
<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a> pi <span class="sc">*</span> (d<span class="sc">/</span><span class="dv">2</span>)<span class="sc">^</span><span class="dv">2</span></span>
<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a>}</span>
<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a></span>
<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="co"># to use your new function</span></span>
<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a></span>
<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a><span class="fu">circle.area</span>(<span class="dv">10</span>)</span>
<span id="cb1-11"><a href="#cb1-11" tabindex="-1"></a><span class="co"># [1] 78.53982</span></span>
<span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a></span>
<span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a><span class="co"># to test on a vector of diameters</span></span>
<span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="co"># first create a vector with diameters ranging from 0 to 50 in steps of 10</span></span>
<span id="cb1-15"><a href="#cb1-15" tabindex="-1"></a></span>
<span id="cb1-16"><a href="#cb1-16" tabindex="-1"></a>cir.diam <span class="ot"><-</span> <span class="fu">seq</span>(<span class="at">from =</span> <span class="dv">0</span>, <span class="at">to =</span> <span class="dv">50</span>, <span class="at">by =</span> <span class="dv">10</span>)</span>
<span id="cb1-17"><a href="#cb1-17" tabindex="-1"></a></span>
<span id="cb1-18"><a href="#cb1-18" tabindex="-1"></a><span class="co"># test your function</span></span>
<span id="cb1-19"><a href="#cb1-19" tabindex="-1"></a></span>
<span id="cb1-20"><a href="#cb1-20" tabindex="-1"></a><span class="fu">circle.area</span>(cir.diam)</span>
<span id="cb1-21"><a href="#cb1-21" tabindex="-1"></a><span class="co"># [1] 0.00000 78.53982 314.15927 706.85835 1256.63706 1963.49541</span></span></code></pre></div>
<p> </p>
<p>2. Write a function to convert farenheit to centegrade (oC = (oF -
32) x 5/9). Get your function to print out your result in the following
format: “Farenheit : <em>value of oF</em> is equivalent to <em>value
oC</em> centigrade.”</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>far.cent <span class="ot"><-</span> <span class="cf">function</span>(a) {</span>
<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a> val <span class="ot"><-</span> (a <span class="sc">-</span> <span class="dv">32</span>) <span class="sc">*</span> <span class="dv">5</span><span class="sc">/</span><span class="dv">9</span></span>
<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a> <span class="fu">print</span>(<span class="fu">paste</span>(<span class="st">"Fahrenheit: "</span>, <span class="fu">round</span>(a, <span class="at">digits =</span> <span class="dv">3</span>), <span class="st">"oF"</span>, <span class="at">sep =</span> <span class="st">" "</span>), <span class="at">quote =</span> <span class="cn">FALSE</span>) <span class="co"># round 3dp</span></span>
<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a> <span class="fu">print</span>(<span class="fu">paste</span>(<span class="st">"Centigrade: "</span>, <span class="fu">round</span>(val, <span class="at">digits =</span> <span class="dv">3</span>), <span class="st">"oC"</span>, <span class="at">sep =</span> <span class="st">" "</span>), <span class="at">quote =</span> <span class="cn">FALSE</span>) <span class="co"># round 3dp</span></span>
<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a>}</span>
<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a></span>
<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a><span class="co"># alternative Fahrenheit to centigrade using cat function</span></span>
<span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a></span>
<span id="cb2-9"><a href="#cb2-9" tabindex="-1"></a>far.cent2 <span class="ot"><-</span> <span class="cf">function</span>(a) {</span>
<span id="cb2-10"><a href="#cb2-10" tabindex="-1"></a> val <span class="ot"><-</span> (a <span class="sc">-</span> <span class="dv">32</span>) <span class="sc">*</span> <span class="dv">5</span><span class="sc">/</span><span class="dv">9</span> <span class="co">#calculation</span></span>
<span id="cb2-11"><a href="#cb2-11" tabindex="-1"></a> <span class="fu">cat</span>(<span class="st">"Fahrenheit: "</span>, <span class="fu">round</span>(a, <span class="at">digits =</span> <span class="dv">3</span>), <span class="st">"oF"</span>, <span class="st">"</span><span class="sc">\n</span><span class="st">"</span>) <span class="co"># use cat function</span></span>
<span id="cb2-12"><a href="#cb2-12" tabindex="-1"></a> <span class="fu">cat</span>(<span class="st">"Centigrade: "</span>, <span class="fu">round</span>(val, <span class="at">digits =</span> <span class="dv">3</span>), <span class="st">"oC"</span>, <span class="st">"</span><span class="sc">\n</span><span class="st">"</span>)</span>
<span id="cb2-13"><a href="#cb2-13" tabindex="-1"></a>}</span></code></pre></div>
<p> </p>
<p>3. Create a vector of normally distributed data, of length 100, mean
35 and standard deviation of 15. Write a function to calculate the mean,
median, and range of the vector, print these values out with appropriate
labels. Also get the function to plot a histogram (as a proportion) of
the values and add a density curve.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="co"># Create a vector of normally distributed data</span></span>
<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a><span class="co"># length 100, mean 35 and standard deviation of 29</span></span>
<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a></span>
<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a>vals <span class="ot"><-</span> <span class="fu">rnorm</span>(<span class="dv">100</span>, <span class="dv">35</span>, <span class="dv">15</span>) <span class="co"># create some norm dist data mean 35, sd = 15</span></span>
<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a></span>
<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a>summary.fun <span class="ot"><-</span> <span class="cf">function</span>(dat){</span>
<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a> mymean <span class="ot"><-</span> <span class="fu">round</span>(<span class="fu">mean</span>(dat), <span class="at">digits =</span> <span class="dv">4</span>) <span class="co"># calc mean</span></span>
<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a> mymedian <span class="ot"><-</span> <span class="fu">round</span>(<span class="fu">median</span>(dat), <span class="at">digits =</span> <span class="dv">4</span>) <span class="co"># calc median</span></span>
<span id="cb3-9"><a href="#cb3-9" tabindex="-1"></a> mymin <span class="ot"><-</span> <span class="fu">round</span>(<span class="fu">min</span>(dat), <span class="at">digits =</span> <span class="dv">4</span>) <span class="co"># calc min</span></span>
<span id="cb3-10"><a href="#cb3-10" tabindex="-1"></a> mymax <span class="ot"><-</span> <span class="fu">round</span>(<span class="fu">max</span>(dat), <span class="at">digits =</span> <span class="dv">4</span>) <span class="co"># calc max</span></span>
<span id="cb3-11"><a href="#cb3-11" tabindex="-1"></a> <span class="fu">print</span>(<span class="fu">paste</span>(<span class="st">"mean:"</span>, mymean, <span class="at">sep =</span> <span class="st">" "</span>), <span class="at">quote =</span> <span class="cn">FALSE</span>) <span class="co"># print mean</span></span>
<span id="cb3-12"><a href="#cb3-12" tabindex="-1"></a> <span class="fu">print</span>(<span class="fu">paste</span>(<span class="st">"median:"</span>, mymedian, <span class="at">sep =</span> <span class="st">" "</span>), <span class="at">quote =</span> <span class="cn">FALSE</span>) <span class="co"># print median</span></span>
<span id="cb3-13"><a href="#cb3-13" tabindex="-1"></a> <span class="fu">print</span>(<span class="fu">paste</span>(<span class="st">"range:"</span>, <span class="st">"from:"</span>, mymin, <span class="st">"to"</span>, mymax, <span class="at">sep =</span> <span class="st">" "</span>), <span class="at">quote =</span> <span class="cn">FALSE</span>) </span>
<span id="cb3-14"><a href="#cb3-14" tabindex="-1"></a> dens <span class="ot"><-</span> <span class="fu">density</span>(dat) <span class="co"># estimate density curve</span></span>
<span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a> <span class="fu">hist</span>(dat, <span class="at">main =</span> <span class="st">""</span>,<span class="at">type =</span> <span class="st">"l"</span>,<span class="at">freq =</span> <span class="cn">FALSE</span>) <span class="co"># plot histogram</span></span>
<span id="cb3-16"><a href="#cb3-16" tabindex="-1"></a> <span class="fu">lines</span>(dens, <span class="at">lty =</span> <span class="dv">1</span>, <span class="at">col =</span> <span class="st">"red"</span>) <span class="co"># plot density curve</span></span>
<span id="cb3-17"><a href="#cb3-17" tabindex="-1"></a>}</span>
<span id="cb3-18"><a href="#cb3-18" tabindex="-1"></a></span>
<span id="cb3-19"><a href="#cb3-19" tabindex="-1"></a><span class="co"># use the function</span></span>
<span id="cb3-20"><a href="#cb3-20" tabindex="-1"></a><span class="fu">summary.fun</span>(vals)</span></code></pre></div>
<p> </p>
<p>4. Write a function to calculate the median value of a vector of
numbers (yes I know there’s a <code>median()</code> function already but
this is fun!). Be careful with vectors of an even sample size, as you
will have to take the average of the two central numbers (hint: use
modulo %%2 to determine whether the vector is an odd or an even size).
Test your function on vectors with both odd and even sample sizes.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="co"># calculate a median</span></span>
<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a></span>
<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a>ourmedian <span class="ot"><-</span> <span class="cf">function</span>(x){</span>
<span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a> n <span class="ot"><-</span> <span class="fu">length</span>(x)</span>
<span id="cb4-5"><a href="#cb4-5" tabindex="-1"></a> <span class="cf">if</span> (n <span class="sc">%%</span> <span class="dv">2</span> <span class="sc">==</span> <span class="dv">1</span>) <span class="co"># odd numbers</span></span>
<span id="cb4-6"><a href="#cb4-6" tabindex="-1"></a> <span class="fu">sort</span>(x)[(n <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">/</span><span class="dv">2</span>] <span class="co"># find the middle number by adding 1 to length and div 2</span></span>
<span id="cb4-7"><a href="#cb4-7" tabindex="-1"></a> <span class="cf">else</span> { <span class="co"># even numbers</span></span>
<span id="cb4-8"><a href="#cb4-8" tabindex="-1"></a> middletwo <span class="ot"><-</span> <span class="fu">sort</span>(x)[(n<span class="sc">/</span><span class="dv">2</span>) <span class="sc">+</span> <span class="dv">0</span><span class="sc">:</span><span class="dv">1</span>] <span class="co">#find the two middle numbers</span></span>
<span id="cb4-9"><a href="#cb4-9" tabindex="-1"></a> <span class="fu">mean</span>(middletwo)</span>
<span id="cb4-10"><a href="#cb4-10" tabindex="-1"></a> }</span>
<span id="cb4-11"><a href="#cb4-11" tabindex="-1"></a>}</span>
<span id="cb4-12"><a href="#cb4-12" tabindex="-1"></a></span>
<span id="cb4-13"><a href="#cb4-13" tabindex="-1"></a><span class="co"># use the function</span></span>
<span id="cb4-14"><a href="#cb4-14" tabindex="-1"></a>mydat <span class="ot"><-</span> <span class="fu">sample</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">50</span>, <span class="at">size =</span> <span class="dv">10</span>, <span class="at">replace =</span> <span class="cn">TRUE</span> )</span>
<span id="cb4-15"><a href="#cb4-15" tabindex="-1"></a></span>
<span id="cb4-16"><a href="#cb4-16" tabindex="-1"></a><span class="co"># our function</span></span>
<span id="cb4-17"><a href="#cb4-17" tabindex="-1"></a><span class="fu">ourmedian</span>(mydat)</span>
<span id="cb4-18"><a href="#cb4-18" tabindex="-1"></a></span>
<span id="cb4-19"><a href="#cb4-19" tabindex="-1"></a><span class="co"># R median function</span></span>
<span id="cb4-20"><a href="#cb4-20" tabindex="-1"></a><span class="fu">median</span>(mydat)</span></code></pre></div>
<p> </p>
<p>5. You are a population ecologist for the day and wish to investigate
the properties of the <a
href="https://en.wikipedia.org/wiki/Ricker_model">Ricker model</a>. The
Ricker model is defined as:</p>
<p> </p>
<p><span class="math display">\[ N_{t+1} = N_{t} exp\left[r\left(1-
\frac{N_{t}}{K} \right) \right] \]</span></p>
<p> </p>
<p>5. (cont) Where <em>N<sub>t</sub></em> is the population size at time
<em>t</em>, <em>r</em> is the population growth rate and <em>K</em> is
the carrying capacity. Write a function to simulate this model so you
can conveniently determine the effect of changing <em>r</em> and the
initial population size N0. <em>K</em> is often set to 100 by default,
but you want the option of being able to change this with your function.
So, you will need a function with the following arguments; nzero which
sets the initial population size, <em>r</em> which will determine the
population growth rate, time which sets how long the simulation will run
for and <em>K</em> which we will initially set to 100 by default.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="co"># function to simulate Ricker model</span></span>
<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a></span>
<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a>Ricker.model <span class="ot"><-</span> <span class="cf">function</span>(nzero, r, time, <span class="at">K =</span> <span class="dv">1</span>) {</span>
<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a> <span class="co"># sets initial parameters</span></span>
<span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a> N <span class="ot"><-</span> <span class="fu">numeric</span>(time <span class="sc">+</span> <span class="dv">1</span>) <span class="co"># creates a real vector of length time+1 to store values of Nt+1</span></span>
<span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a> N[<span class="dv">1</span>] <span class="ot"><-</span> nzero <span class="co"># sets initial population size in first element of N</span></span>
<span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>time) {</span>
<span id="cb5-8"><a href="#cb5-8" tabindex="-1"></a> <span class="co"># loops over time</span></span>
<span id="cb5-9"><a href="#cb5-9" tabindex="-1"></a> N[i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot"><-</span> N[i] <span class="sc">*</span> <span class="fu">exp</span>(r <span class="sc">*</span> (<span class="dv">1</span> <span class="sc">-</span> N[i]<span class="sc">/</span>K))</span>
<span id="cb5-10"><a href="#cb5-10" tabindex="-1"></a> }</span>
<span id="cb5-11"><a href="#cb5-11" tabindex="-1"></a> Time <span class="ot"><-</span> <span class="dv">0</span><span class="sc">:</span>time <span class="co"># creates vector for x axis</span></span>
<span id="cb5-12"><a href="#cb5-12" tabindex="-1"></a> <span class="fu">plot</span>(Time, N, <span class="at">type =</span> <span class="st">"o"</span>, <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, time), <span class="at">xlab =</span> <span class="st">"Time"</span>, <span class="at">ylab =</span> <span class="st">"Population size (N)"</span>, <span class="at">main =</span> <span class="fu">paste</span>(<span class="st">"r ="</span>,</span>
<span id="cb5-13"><a href="#cb5-13" tabindex="-1"></a> r, <span class="at">sep =</span> <span class="st">" "</span>)) <span class="co"># plots output</span></span>
<span id="cb5-14"><a href="#cb5-14" tabindex="-1"></a>}</span>
<span id="cb5-15"><a href="#cb5-15" tabindex="-1"></a></span>
<span id="cb5-16"><a href="#cb5-16" tabindex="-1"></a><span class="co"># To run play around with the different parameters, especially r</span></span>
<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a><span class="fu">Ricker.model</span>(<span class="at">nzero =</span> <span class="fl">0.1</span>, <span class="at">r =</span> <span class="dv">1</span>, <span class="at">time =</span> <span class="dv">100</span>)</span></code></pre></div>
<p> </p>
<p>End of Exercise 6</p>
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