  In this paper, we investigate the asymptotic behavior of the number $s_q(g)$
of isogeny classes of simple abelian varieties of dimension $g$ over a finite
field $\mathbb{F}_q$. We prove that the logarithmic asymptotic of $s_q(g)$ is
the same as the logarithmic asymptotic of the number $m_q(g)$ of isogeny
classes of all abelian varieties of dimension $g$ over $\mathbb{F}_q$. We also
prove that $$ \limsup_{g \rightarrow \infty} \frac{s_q(g)}{m_q(g)}=1. $$ This
suggests that there are much more simple isogeny classes of abelian varieties
over $\mathbb{F}_q$ of dimension $g$ than non-simple ones for sufficiently
large $g$, which can be understood as the opposite situation to a main result
of Lipnowski and Tsimerman (Duke Math 167:3403-3453, 2018).
