We explain how the spectral curve can be extracted from the ${\cal
    W}$-representation of a matrix model. It emerges from the part of the ${\cal
    W}$-operator, which is linear in time-variables. A possibility of extracting
    the spectral curve in this way is important because there are models where
    matrix integrals are not yet available, and still they possess all their
    important features. We apply this reasoning to the family of WLZZ models and
    discuss additional peculiarities which appear for the non-negative value of the
    family parameter $n$, when the model depends on additional couplings (dual
    times). In this case, the relation between topological and $1/N$ expansions is
    broken. On the other hand, all the WLZZ partition functions are
    $\tau$-functions of the Toda lattice hierarchy, and these models also celebrate
    the superintegrability properties.

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