In the previous pages we have seen that the germination curve gives us the proportion of germinated seeds over time. Such curve is based on a few (basically three) parameters describing the population, such as the germination velocity, capacity and uniformity. A very general model is:
G=P(t<tg)=dΦ(t,β)
where t is the time, d is the maximum germinated proportion (when t→∞), Φ is a cumulative distribution function based on a certain set of a parameters, most frequently a location and a shape parameters (e.g. e and b). One possible line of attack for modelling is to select Φ, d and β and express them as functions of the variables under study. If we have the set of variables X, the model is:
G(X)=d(X)Φ[t,β,X]
Such modelling approach is basically a one-step approach: we input the germination time, the values of parameters and covariates and we get the proportion of germinated seeds.
Another possible line of attack is to proceed in a two-steps fashion:
At the second step, the general model is:
βi=f(X]
We see that the time is no longer included as the independent variable in the second step and the model is fundamentally static.
Both approaches are widely used; the second one is simpler, but the first one is more elegant. The selection is mainly a matter of aims and personal taste. Both approaches pose problems and limitations; I will try to describe all possibilities, so that you can make a more informed selection.
Please, go ahead with reading.