Classic rate estimates for soil support of succession changes on wild Lake Michigan dunes were estimated in Olson’s (1958d) Mercer Award article. Now 60+ years of actual change show which changes fit equations and tables projected; which are set back (as by wind or fire disturbance); which may be accelerating (e.g. by nitorogen inputs from farm, city, and transportation inputs of macrosystems. A world crop legend (Green Globe 1.4) now complements that of mostly wild forests (Gg 1.2), and (partly) nonwoods (Gg1.3) that are most altered by human management and'or degradation. Can projections of future change use updated climate models: from the {G} = {AB} grids worldwide, to landscapes L = [bras], constrained by lake or ocean (hydrosphere h) history, in the case of ocean or Great Lakes dunes? Then from L to local plant/soil systems? Hans Jenny’s (1941, 1980) widely tested state variable formulation express the latter (inter)dependent “state variables” of an ecosystem ed as a function of soil-forming, or ecosystem-conditioning, factors: ideally as “independent variables” eig..With better (super)computer and field strategies, we can “solve”
ed = f(t)e.i . (1
Results/Conclusions
Time in equation (1) can be evaluated as a complex variable: surface age since stabilization is the “real” component; an index of time since recent disturbance(s) is the “imaginary” component (e.g. frequeny of burning or duration(s) since recent disturbance) such as blowdown or human harvest, in case of forest or crop. The (Platonic) ideal of (1) realistically may be resolved as a Taylor’s series approximation allowing departures Δei from conditioning factors besides time (dune age, and disturbance interval). Jenny’s abbreviation is “clorpt” for climate, organisms, relief, parent material, time. (1) then becomes (2) for, allowing for sensitivities ∂ed/∂edwith respect to cl, o, r, and p in the following expansion (Olson 1958d, eq. 1d):
Ed = f(t)e + ∂ed/∂cl + ∂ed/∂o + ∂ed/∂r + ∂ed∂/p + Є, (2a)
or else = f(t)e + ∂ed/∂a + ∂ed/∂b + ∂ed/∂r + ∂ed/∂s + Є (2b)
where (2b) factors are from boldface matrices for the landscape or region L, or world G. (This mY help resolve some confusion about “independence” issues: orthogonal vector space of coordinate basis,vs.“uncorrelated” in the statistical sense.)