The simple slope for -1SD is the model predicted slope for someone with a value of the moderator one standard deviation below the mean of the moderator. The simple slope for +1SD is the model predicted slope for someone with a value of the moderator one standard deviation above the mean of the moderator. You're not creating new groups; you're computing the ...
With regard to the first part of your question, i.e.,
how to test the general effect of treatment within each level of environment
You would need to specify the appropriate contrasts to achieve this. The emmeans package seems to offer the possibility to define your own contrasts function; for more info, see here.
With regard to the second part, i.e.,
I think your question is interesting. Actually I don't think @Sympa has answered why the intercept is different between the models with and without the interaction term. A spoiler: I do not have a clear answer to that question but I'll try to do my best to help out.
The function lm() uses, by-default, the dummy coding (have a look at the contrasts argument)....
This is quite standard. See this page for example, clarifying the interpretation of the coefficients in a model with one continuous predictor, one dummy predictor, and their interaction.
The dummy-coding choce will affect the meaning of the coefficients but not the fundamental results of the analysis. If you use treatment contrasts for the analysis (the ...
I'd suggest looking at interaction contrasts; something like this:
emm <- emmeans(m1, ~ treatment * environment)
contrast(emm, "eff", by = "environment") # show the treatment effects
contrast(emm, interaction = c("eff", "pairwise")) # compare the treat effs
This will display, and then compare, the treatment effects (means minus grand means) ...
The interpretation you provided for your model is not correct.
Your fitted model is in effect a collection of 3 fitted sub-models. Each fitted sub-model relates the log odds of being mature rather than immature in a given year to length (lun).
log odds of being mature = -9.15307 + 0.29703*lun
log odds of being mature = (-9.15307 -...