# Modelling the difference between two Hubbert curves

I have a large set of time series data, consisting of series from two different conditions, the averages of which are shown below.

I would like to fit a model to this data, to test that a) the peak value is greater in the 'conflict' condition, and b) the peak occurs earlier in this condition.

ggplot(data, aes(x=Time, y=Variable, colour=Condition))
+ stat_summary(fun.data=mean_se, geom="pointrange")


From my own research on this, I know that:

• Growth curve analysis is the usual way of modelling time series data like this, but I can't figure out how I would fit a polynomial for this shape of curve.
• I have some experience fitting GCA models using lme4 in R, mostly following Dan Mirman's tutorials, but I'm still learning.
• Curves of this kind are referred to as Hubbert curves, and typically used to model oil production, as a symmetric logistic curve up and down.
• R package grofit is maybe useful for analyses of this kind, although I would rather know I'm barking up the right tree before investing time in learning how to use this.

Can anyone point me in the right direction here?

• I realize after posting that my reference to 'Hubbert Curves' in the question title may not be appropriate, as all I can say is that my plot looks like Hubbert curves. – Eoin May 19 '14 at 12:33