Linear mixed effects model and model selection

Hi,
I am looking at the effect of macrophyte allelochemicals on the growth
of phytoplankton. The aim of my project is to compare the effect of
allelochemicals of two different macrophyte species on the growth rate
of two different algal species (the negative effect that is shown as
the area cleared of algae) during 10 days and to compare the effect of
each macrophyte on each algal species at each day. I used linear mixed
effect models for data analysis then I used ANOVAs to do daily
comparisons. I received these comments from my examiner but don?t
understand what he means.

 1. This is part of my methods explaining the data analysis; Linear
mixed effect models was used to compare blah blah...... An Analysis of
Variance (ANOVA) was used to analyse the LMEM.
My examiner?s comment; Not clear why you used ANOVA here. Was it to
compare models?

2.The effects of TREATMENT and TIME and their interaction were all
significant (Table 5). Because of the significant interaction, the
analysis was split by TIME.
 Comment; Given that you have interactions, you should do a model
selection to show whether the interaction model is in fact more
parsimonious.

 Can someone explain these and tell me how and when should I do model
selection?
I have attached a copy of my graph, data and model coding I've used in
R. Can someone check if the model coding I used is correct and what
coding where and how I need to add for model selection. I also don't
know how to put that in words if I want to explain in methods section.

Thanks,
Fariba Moslih