Testing overdispersion Gamma glmer

Hello,

I want to compare mean trip duration (length.in.hours) across treatment
conditions and colonies. I have 3 colonies and 2 treatments. So, one half
of a colony gets a DWV treatment and the other half a control treatment.

When a histogram is made, it is clear that the data is skewed to the rigth.
So, I am using a Gamma distribution.

This is the model: fit_length = glmer(length.in.hours~treatment*colony +
(1|RFID), family = Gamma(link = "log"), data = datashort)

I use the log link and not the identity link, because the AIC is lower.
RFID is the code used for each subject in the colonies.

I want to test for the overdispersion assumption by using the following
code:

datashort$obs = factor(1:nrow(datashort))> fit_length_obs = glmer(length.in.hours~treatment*colony + (1|RFID) + (1|obs), family = Gamma(link = "log"), data = datashort)
AIC(fit_length, fit_length_obs)                df        AIC

fit_length      8   5646.758
fit_length_obs  9 -74390.105


There is a clear difference between the AIC values, but I was wondering
wether -74390 is a realistic value? Is it not very low? Or am I using the
wrong method to control for overdispersion?

Thank you for some help!

Kind regards,

Sophie