# One-step approach

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:

$G = P(t < t_g) = d \,\, \Phi(t, \beta )$

where $$t$$ is the time, $$d$$ is the maximum germinated proportion (when $$t \rightarrow \infty$$), $$\Phi$$ 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 $$\Phi$$, $$d$$ and $$\beta$$ and express them as functions of the variables under study. If we have the set of variables $$X$$, the model is:

$G(X) = d(X) \Phi \left[ t, \beta, X\right]$

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.

# Two-steps approach

Another possible line of attack is to proceed in a two-steps fashion:

1. determine the germination curve for each seed lot (e.g. Petri dish, tray or container) in each experimental conditions and derive some relevant population based parameter (e.g. the maximum germinated fraction or the median germination time);
2. model the effect of experimental variables on the selected population parameter.

At the second step, the general model is:

$\beta_i = f\left(X\right]$

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.