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-c8bb9b59
+83218c15

_tex/index.tex

@@ -247,22 +247,26 @@ \subsection{Metacommunity model}\label{metacommunity-model}
 \endhead
 \bottomrule\noalign{}
 \endlastfoot
-Plant-plant & -1 -- 0 \\
-Plant-herbivore & 0 -- 0.1 \\
-Plant-carnivore & 0 \\
-Herbivore-plant & -0.3 -- 0 \\
+Plant-plant & -1.0 -- 0.00 \\
+Plant-herbivore & 0.0 -- 0.10 \\
+Plant-carnivore & 0.0 \\
+Herbivore-plant & -0.3 -- 0.00 \\
 Herbivore-herbivore & -0.2-- -0.15 \\
-Herbivore-carnivore & 0 -- 0.08 \\
-Carnivore-plant & 0 \\
-Carnivore-herbivore & -0.1 -- 0 \\
-Carnivore-carnivore & -0.1 -- 0 \\
+Herbivore-carnivore & 0.0 -- 0.08 \\
+Carnivore-plant & 0.0 \\
+Carnivore-herbivore & -0.1 -- 0.00 \\
+Carnivore-carnivore & -0.1 -- 0.00 \\
 \end{longtable}
 
 \(A_{ij}(t)\) is the effect of the environment in patch \(j\) on species
 \(i\) at time \(t\) and can be further expanded as follows:
 
+\[
+\hat{A}_{ij}(t)=h\times\frac{1}{\sigma\sqrt{2\pi}}\exp-\frac{1}{2}\left(\frac{(E_{j}(t)-H_{i})^2}{\sigma}\right)^2
+\]
+
 \begin{equation}\phantomsection\label{eq-metacomm_env}{
-A_{ij}(t)=h\left(exp-\frac{(E_{j}(t)-H_{i})^2}{2\sigma^2}-1\right)
+A_{ij}(t)= \hat{A}_{ij}(t) - max(\hat{A})
 }\end{equation}
 
 Species environmental optima (\(H_i\)) are evenly distributed across the
@@ -304,7 +308,7 @@ \subsection{Metacommunity model}\label{metacommunity-model}
 \bottomrule\noalign{}
 \endlastfoot
 Plant & 0.3 & 0.075 \\
-Herbivore & 0.2 & 0.05 \\
+Herbivore & 0.2 & 0.050 \\
 Carnivore & 0.1 & 0.025 \\
 \end{longtable}
 

index.html

@@ -199,7 +199,7 @@ <h2 id="toc-title">Table of contents</h2>
   <li><a href="#conclusion" id="toc-conclusion" class="nav-link" data-scroll-target="#conclusion"><span class="header-section-number">3</span> Conclusion</a></li>
   <li><a href="#references" id="toc-references" class="nav-link" data-scroll-target="#references">References</a></li>
   </ul>
-<div class="quarto-alternate-notebooks"><h2>Notebooks</h2><ul><li><a href="notebooks/data-screening-preview.html"><i class="bi bi-journal-code"></i>Data Screening</a></li></ul></div></nav>
+</nav>
 </div>
 <div id="quarto-margin-sidebar" class="sidebar margin-sidebar zindex-bottom">
 </div>
@@ -238,48 +238,51 @@ <h3 data-number="2.1" class="anchored" data-anchor-id="metacommunity-model"><spa
 <tbody>
 <tr class="odd">
 <td>Plant-plant</td>
-<td style="text-align: center;">-1 – 0</td>
+<td style="text-align: center;">-1.0 – 0.00</td>
 </tr>
 <tr class="even">
 <td>Plant-herbivore</td>
-<td style="text-align: center;">0 – 0.1</td>
+<td style="text-align: center;">0.0 – 0.10</td>
 </tr>
 <tr class="odd">
 <td>Plant-carnivore</td>
-<td style="text-align: center;">0</td>
+<td style="text-align: center;">0.0</td>
 </tr>
 <tr class="even">
 <td>Herbivore-plant</td>
-<td style="text-align: center;">-0.3 – 0</td>
+<td style="text-align: center;">-0.3 – 0.00</td>
 </tr>
 <tr class="odd">
 <td>Herbivore-herbivore</td>
 <td style="text-align: center;">-0.2– -0.15</td>
 </tr>
 <tr class="even">
 <td>Herbivore-carnivore</td>
-<td style="text-align: center;">0 – 0.08</td>
+<td style="text-align: center;">0.0 – 0.08</td>
 </tr>
 <tr class="odd">
 <td>Carnivore-plant</td>
-<td style="text-align: center;">0</td>
+<td style="text-align: center;">0.0</td>
 </tr>
 <tr class="even">
 <td>Carnivore-herbivore</td>
-<td style="text-align: center;">-0.1 – 0</td>
+<td style="text-align: center;">-0.1 – 0.00</td>
 </tr>
 <tr class="odd">
 <td>Carnivore-carnivore</td>
-<td style="text-align: center;">-0.1 – 0</td>
+<td style="text-align: center;">-0.1 – 0.00</td>
 </tr>
 </tbody>
 </table>
 </div>
 </figure>
 </div>
 <p><span class="math inline">\(A_{ij}(t)\)</span> is the effect of the environment in patch <span class="math inline">\(j\)</span> on species <span class="math inline">\(i\)</span> at time <span class="math inline">\(t\)</span> and can be further expanded as follows:</p>
+<p><span class="math display">\[
+\hat{A}_{ij}(t)=h\times\frac{1}{\sigma\sqrt{2\pi}}\exp-\frac{1}{2}\left(\frac{(E_{j}(t)-H_{i})^2}{\sigma}\right)^2
+\]</span></p>
 <p><span id="eq-metacomm_env"><span class="math display">\[
-A_{ij}(t)=h\left(exp-\frac{(E_{j}(t)-H_{i})^2}{2\sigma^2}-1\right)
+A_{ij}(t)= \hat{A}_{ij}(t) - max(\hat{A})
 \tag{2}\]</span></span></p>
 <p>Species environmental optima (<span class="math inline">\(H_i\)</span>) are evenly distributed across the entire range of environmental conditions for each trophic level, meaning that species from different trophic levels will be at, or near the same environmental optima. <span class="math inline">\(h\)</span> is a scaling parameter (set to 300), <span class="math inline">\(E_j(t)\)</span> is the environment in patch <span class="math inline">\(j\)</span> at time <span class="math inline">\(t\)</span> and <span class="math inline">\(\sigma\)</span> is the standard deviation (set to 50).</p>
 <p><span class="math inline">\(I_{ij}(t)\)</span> is the abundance of species <span class="math inline">\(i\)</span> immigrating to patch <span class="math inline">\(j\)</span> at time <span class="math inline">\(t\)</span> and can be expanded as follows:</p>
@@ -310,7 +313,7 @@ <h3 data-number="2.1" class="anchored" data-anchor-id="metacommunity-model"><spa
 <tr class="even">
 <td>Herbivore</td>
 <td style="text-align: center;">0.2</td>
-<td style="text-align: center;">0.05</td>
+<td style="text-align: center;">0.050</td>
 </tr>
 <tr class="odd">
 <td>Carnivore</td>