  We study a size-structured model proposed in [1] C. Barril, \`A. Calsina, O.
Diekmann, J. Z. Farkas, On competition through growth reduction, e-print
arXiv:2303.02981, to describe the dynamics of trees growth in the forest. Our
approach to the associated renewal equation is rather different from the
methods in [1] and is based on ideas developed in [2] F. Herrera, S.
Trofimchuk, Dynamics of one-dimensional maps and Gurtin-MacCamy's population
model. Part I: asymptotically constant solutions, Ukrainian Math. J., (in
Memory of O. Sharkovsky), 75 (2023), 1635-1651,
https://doi.org/10.3842/umzh.v75i12.7678. Assuming relatively weak restrictions
on the reproduction, death and growth rates $\beta, \mu, g$, we establish the
permanence properties of the semiflow $\frak F^t$ generated by the renewal
equation and prove that it possesses a compact global attractor of points
$\mathcal A$. Next we show that the opposite types of monotonicity of $\beta,
g$ assure that $\frak F^t$ is also monotone and that in this case $\mathcal A$
coincides with a unique asymptotically stable equilibrium attracting
neighbourhoods of compact sets with non-zero initial data.
