# Appropriate test (in R) for proportion data that aren't normally distributed, aren't based on counts, and include 0's and 1's?

I'm studying differences in tree health among 5 species of trees across 3 different green infrastructure types. Here are the first few lines of data:

                   Species  Type Dieback Discolor      FvFm Transparency
1      Quercus palustris STree    0.00     0.05        NA    0.3870864
2      Quercus palustris  ROWB    0.20     0.05 0.7146000    0.2957104
3          Ginkgo biloba STree    0.80     0.90 0.6514000    0.6012480
4  Gleditsia triacanthos   SGS    0.05     0.35 0.8052500    0.4581673
5  Gleditsia triacanthos STree    0.05     0.50 0.8218000    0.6596218


All of the tree health metrics are proportions: Dieback=percentage of canopy dieback (in 5% increments), Discolor=percentage of canopy discoloration (in 5% increments), FvFm=a measure of photosynthetic efficiency (out of 100%), Transparency=percentage of canopy transparency. Canopy transparency is normally distributed, so I just used lm in R to analyze it. Dieback and discoloration are really skewed because most trees are pretty healthy, so there are a lot of 0's. I also found a few dead trees, which means they have 100% canopy dieback. FvFm is similar: there were lots of trees with high FvFm's, and the dead trees had 0 FvFm.

I'm interested in how tree species, green infrastructure types, and the interaction of the two influence tree health. Using lm, this would mean:

 Model <- lm(Transparency ~ Species + Type + Species:Type, data=Trees)


I've read that proportion data can be analyzed using logistic regression (using glm) or beta regression (using betareg). This might be a silly question, but I thought that logistic regression is more for count data and betareg only works for proportions between 0 and 1, NOT including 0 and 1. Is this correct? Or are there ways to use logistic regression or beta regression on my data? Are there other tests that would be more appropriate? Any advice would be greatly appreciated.