What does instantaneous rate matrix mean?
Reversible At its simplist the GTR rate, is the General Time Reversible model and most importantly infers the matrix is &quot;reversible&quot;, thus as many A mutations will go to C as C mutations go to A and the number of mutations is relative to the G-T mutation rate. The G-T mutation rate is one of the least common mutations (transversion) so all other values are above 1. If you plotted this as a matrix the top right-hand matrix is identical to the bottom left hand matrix because its reversible, i.e. A &lt;-&gt; C . This is cool because you don't need to tell the algorithm which sequence is the root.
Directional The &quot;instantaneous&quot; matrix is a directional matrix, thus A -&gt; C is not the same as C -&gt; A. In order to obtain an accurate directional matrix you need to assign a root, its like lets start from the deepest node in the tree (the one between the root/outgroup and all ingroup sequences) and now - if that is correct - we can remove the restrictions of reversibility and impose directionality on the mutation process. This is needed if you are performing molecular clock type calculations. However, the key is assigning the root/outgroup - if it assigns it e.g. by mid-point rooting that is not necessarily a good idea.
Advice. My advice is if you are building a basic tree and haven't assigned a root/outgroup, obviously using GTR which is a good move, then you don't to worry about the intananeous matrix because it might not be meaningful. If you are running a molecular clock/dating/rate estimate type model and a very clear what the root/outgroup is and that is specified in the input, then the instananeous matrix becomes important.

The mutation rates of GTR and instananeous are not directly comparable because the GTR rate is with respect to G &lt;-&gt; T mutation, whilst instananeous is primarily concerned with the directionality of mutation and is a 12-parameter model, as opposed to GTR which 6-perameters, where one of those parameters is the reference.
Thus G-T is reversible in GTR (the reference) and so e.g. A&lt;-&gt;C is reversible with respect to G&lt;-&gt;T.
In instananeous matrix G -&gt; T and T -&gt; G are two different rates as are A-&gt; C and C -&gt; A, so one approximation based on an assumption with respect to a second approximation based on the same assumption can't directly equate to a mutation rate which removes that assumption.