  We investigate the time evolution of the second-order R\'enyi entropy (RE)
for bosons in a one-dimensional optical lattice following a sudden quench of
the hopping amplitude $J$. Specifically, we examine systems that are quenched
into the strongly correlated Mott-insulating (MI) regime with $J/U\ll 1$ ($U$
denotes the strength of the on-site repulsive interaction) from the MI limit
with $J=0$. In this regime, the low-energy excited states can be effectively
described by fermionic quasiparticles known as doublons and holons. They are
excited in entangled pairs through the quench dynamics. By developing an
effective theory, we derive a direct relation between the RE and correlation
functions associated with doublons and holons. This relation allows us to
analytically calculate the RE and obtain a physical picture for the RE, both in
the ground state and during time evolution through the quench dynamics, in
terms of doublon holon pairs. In particular, we show that the RE is
proportional to the population of doublon-holon pairs that span the boundary of
the subsystem. Our quasiparticle picture introduces some remarkable features
that are absent in previous studies on the dynamics of entanglement entropy in
free-fermion models. It provides with valuable insights into the dynamics of
entanglement entropy in strongly-correlated systems.
