Asymptotics of Masur-Veech volume of strata of quadratic differentials with many simple poles

We provide large $n$ asymptotics of the Masur-Veech volumes for strata of quadratic differentials of the form ${\mathcal{Q}}_g(n,d_1,\dots ,d_k,-1^{n+D-4g+4})$, where all positive integers $d_i$ are fixed and $D=d_1+\cdots +d_k$. Our formulae are particularly explicit in genus $1$. For the two series of non-varying strata ${\mathcal{Q}}_1(n,-1^n)$ and ${\mathcal{Q}}_1(n,1,-1^{n+1})$ we give simple closed formulae for the volumes for any $n$.