Indeterminacy loci of iterate maps in moduli space

The moduli space ${\mathrm{r}\mathrm{a}\mathrm{t}}_d$ of rational maps in one complex variable of degree $d\ge 2$ has a natural compactification by a projective variety ${\overline{\mathrm{r}\mathrm{a}\mathrm{t}}}_d$ provided by geometric invariant theory. Given $n \ge 2$,theiterationmap$\Phi_n : $\mathrm{r}\mathrm{a}\mathrm{t}$d \to$\mathrm{r}\mathrm{a}\mathrm{t}${d^n}$, defined by ${\mathrm{\Phi }}_n:[f]\mapsto [f^n]$, extends to a rational map $\Phi_n : \overline{$\mathrm{r}\mathrm{a}\mathrm{t}$}d\dashrightarrow \overline{$\mathrm{r}\mathrm{a}\mathrm{t}$}{d^n}$. We characterize the elements of ${\overline{\mathrm{r}\mathrm{a}\mathrm{t}}}_d$ which lie in the indeterminacy locus of ${\mathrm{\Phi }}_n$.