The neutral pion, π0, should have an isospin of 0. To be certain, I am referring to the third component of isospin, $I_3$.
The reason for this is very simple: I3 is an additive quantum number. The valence quarks of the neutral pion are up and antiup, or down and antidown. Up and antiup have the opposite (additive inverse) $I_3$ values to each other, as do down and antidown (and just like any particle-antiparticle pair). The sum of opposite numbers is 0 and so, of course, the $I_3$ of the neutral pion is 0.
However, browsing through the Particle Data Group (PDG) particle listings, I noticed something peculiar: the $I^G$ value of the neutral pion is listed as 1-. Here, $I$ is isospin. This is the PDF file from PDG containing this information on the neutral pion.
The same situation occurs with other mesons having the same valence quarks as the neutral pion, such as the neutral rho meson.
So, what is going on here? Are PDG referring to something other than the value which should be 0, as described above? Is there any quantum number notated $I$ that can have a value of 1 while $I_3$ equals 0? (By the way, no, in this case the answer is not "weak isospin".) If so, what is the explanation for this divergence being possible?