Can I use poisson distribution as family in Generalized Additive Model (GAM) for continuous, non-negative data?

Question

I am building a GAM with a data set which distribution resembles poisson-distributed data. However, my data is continuous, ie, it contains information on tree volumes in cubic meters. So, when doing the GAM code in R (with mgcv library) can I use poisson as the family? Or should I choose something else since the data is not count data? I indeed found some threads discussing similar issues but they didn't provide an answer.

My simplified example code with only one explanatory variable:

gam_volumes <- gam(volumes_m3 ~ s(age, k=10), data=training, family=poisson)

Answer 1

I would use a Gamma distribution with log link for this; this distribution will look like a Poisson (right skewed) but it is a continuous distribution. You can't have 0s in the Gamma but that's OK as a 0 volume tree isn't an observable tree.