Find out if the growth of two populations is statistically different I am creating an artificial model that will simulate the growth of two populations of bacteria under different conditions. Specifically, I am interested in whether adding a certain compound to the 'culture' will alter the growth rate of the populations.
Without adding compound 'X', class A of bacteria grows more rapidly than class B and ultimately forces B into extinction.
My hypothesis is that adding 'X' will facilitate the growth of A, leading more rapidly to the extinction of B.
My knowledge of statistics is rather limited, but I was wondering if there was some test I could use for such an analysis, i.e. something a bit more formal than "the curve on the graph looks more steep"?
 A: The hypothesis has nuances that are difficult to capture in a simulation. I see a number of papers in the microbiology literature dealing with similar situations.
I try to simulate your problem as follows: Bacterium B cultures grow differently depending on the presence of an interaction between Bacterium A and Compound X, which together act as an "Inhibitor". My focus is on the different growth over time of Bacterium B depending on the factor "Inhibitor".
The set-up would involve two logistic growth curves as follows:

A quick look at the fictional data:
    Time      Concentration    Inhibitor
1    0.0      -0.06400915        0
2    0.1       0.03670019        0
...

601  29.9      0.7763743         1
602  30.0      1.0704737         1

To test for differences between growth without and with "Inhibitor" we can use a linear mixed-effects model as such:
require(nlme)
fit <- lme(Concentration ~ Inhibitor,random=~1|Time,data=dat)
anova.lme(fit, adjustSigma = F)

            numDF denDF  F-value p-value
(Intercept)     1   300 573.8239  <.0001
Inhibitor       1   300 206.2185  <.0001

And the presence of "Inhibitor" would predictably have a significant effect on Bacterium B growth.
I'm sure it can be markedly improved, but it is possibly a start.
