text: user3806: The results of Shekhar et al. (2017) "indicate that ASTRAL requires 
  $\mathcal{O}(f^{-2} \log{n})$ 
  
  gene trees to reconstruct the species tree correctly with high probability where n is the number of species and f is the length of the shortest branch in the species tree. 
  How do I interpret this function, specifically the big O notation, when applying it to my data to estimate whether I have enough loci?
  
  user235: Big O notation means "of the order of". Thus $\mathcal{O}(f^{-2} \log{n})$ means that the number of trees required goes with $\log{n}$ for number of species (i.e. if you square the number of genes, you should double the number of trees) and with the inverse square of the shortest branch length (i.e. if you double the shortest branch length, you quarter the number of trees needed). 
  Big O notation generally allows to to compare two input sizes, but cannot really tell you anything about a single point. I.e. it is hard (impossible?) to tell from this function whether you have sufficient loci. 
  
original_text: 3806: <p>The results of <a href="https://dl.acm.org/citation.cfm?id=3291461" rel="nofollow noreferrer">Shekhar et al. (2017)</a> "indicate that ASTRAL requires </p>
  
  <pre><code><span class="math-container">$\mathcal{O}(f^{-2} \log{n})$</span> 
  </code></pre>
  
  <p>gene trees to reconstruct the species tree correctly with high probability where <code>n</code> is the number of species and <code>f</code> is the length of the shortest branch in the species tree. </p>
  
  <p>How do I interpret this function, specifically the big <code>O</code> notation, when applying it to my data to estimate whether I have enough loci?</p>
   235: <p>Big O notation means "of the order of". Thus <span class="math-container">$\mathcal{O}(f^{-2} \log{n})$</span> means that the number of trees required goes with <span class="math-container">$\log{n}$</span> for number of species (i.e. if you square the number of genes, you should double the number of trees) and with the inverse square of the shortest branch length (i.e. if you double the shortest branch length, you quarter the number of trees needed). </p>
  
  <p>Big O notation generally allows to to compare two input sizes, but cannot really tell you anything about a single point. I.e. it is hard (impossible?) to tell from this function whether you have sufficient loci. </p>
  