  Here I investigate some mathematical aspects of the maximum entropy theory of
ecology (METE). In particular I address the geometrical structure of METE
endowed by information geometry. As novel results, the macrostate entropy is
calculated analytically by the Legendre transformation of the log-normalizer in
METE. This result allows for the calculation of the metric terms in the
information geometry arising from METE and, by consequence, the covariance
matrix between METE variables.
