Johnson, D.L.; Keller, E.A.; Rockwell, T.K. 1990. Dynamic pedogenesis: new views on some key soil concepts, and a model for interpreting Quaternary soils. Quaternary Research, 33, 306-319.
Past researchers have attempted to create a model for soil formation (pedogenesis). Starting with Dokuchaev in the 19th c., climate was viewed as the dominant factor in pedogenesis. Thus, a soil was said to be zonal or monogenic if it was in equilibrium with its driving factor, climate. Johnson et al argue against this, stating that climate can change rapidly through time. Since we know this to be true, how can a given soil ever truly be zonal, or mature? A new model is needed.
As stated above, the authors discredit the monogenic concept, saying that no soil can truly be created by only one factor (climate). This seems fairly obvious, but it bears emphasis: soils are mixtures of solids, liquids, and gases. Various fluxes and processes occur within soils all the time. For example, plant roots can greatly speed up mineral weathering. While one could argue that climate is the ultimate driver of vegetation, I would state that many species (and mosaics) can be present in a given climate. It would be naive to think that they would all behave similarly in regards to soil weathering.
Thus the authors embrace the polygenic concept: that soils are formed from many different things. Further, these things can change through time. The authors give an example of a soil which develops distinct horizons with time. At some point, a new species of plant moves in, which encourages high worm populations. These worms mix (bioturbate) the soil, which blurs the horizons. Thus, a soil can be thought of as progressive (increasing complexity, organization) or regressive (decreasing complexity, organization).
While the authors don't explicitly state that the model of Jenny is incorrect, they may as well have. The Jenny model goes like this: a soil is a function of many factors, including climate, organisms, topography, parent material (rock) and time: S=f(Cl,O,R,P,T). This makes sense, and it is still widely used today. However, the Jenny model must assume that the factors remain more or less steady through time. For example, the climate must remain the same, even though we know it does not. Thus, the Johnson et al model (which they term the Dynamic-Rate Model) is an attempt to address varying factors. Here is the equation:
S = f (D, P, dD/dt, dP/dt)
S = degree of soil pedogenesis
D = dynamic vectors (aka more influential factors)
P = passive vectors (aka less influential factors)
dD/dt, dP/dt = change of the vectors any any chosen time
My interpretation of their use of the word 'vector' is, more or less, where the factor is going. As an example, water flux is considered a dynamic vector. How much pedogenesis would X amount of water percolating through the system cause? With this in mind, placing D and P individually in the equation makes them a sort of description of pedogenesis, or the rate or pedogenesis. The variables dD/dt, dP/dt are a bit more abstract. the little d is a calculus term: differential. To make a long and complicated story short, it basically tells you the rate of change of the vector at any chosen time. In other words, where is D going at time X? What about time Y? The sum of dD/dt, dP/dt can be positive or negative. Positive values indicate soil progression; that is, the soil in undergoing increasing complexity and organization. A negative value means regression; just the opposite.
The D and P of the dynamic-rate model is simply a copy of the Jenny model: it accounts for all of the factors and processes which can change a soil. The variables dD/dt, dP/dt are new. They account for changes in the factors through time. Of course, this makes the model infinitely complex: how does a soil scientist account for a large set of factors which can change in any way and at any time?