Modeling Nutrient Limitation: Ecosystem Consequences of Resource Optimization Nature should weed out sub-optimal strategies of acquiring resources from the environment E.B. Rastetter The Ecosystems Center Marine Biological Laboratory Woods Hole, MA Captiva Island Meeting March 2011

U 1 = g B f(R 1 ) f(T) Uncoupled: U 1 = g B min{f(R 1 ), f(R 2 ), f(R 3 )... } f(T) U 2 = q 2 U 1 U 3 = q 3 U Liebig Limitation: U 1 = g B {f(R 1 ) f(R 2 ) f(R 3 )... } f(T) U 2 = q 2 U 1 U 3 = q 3 U Concurrent Limitation: Strategies for modeling resource acquisition:

Drew 1975 Control (HHH)PO 4 (LHL)NO 3 (LHL) NH 4 (LHL)K (LHL) Barley roots

Length of primary lateral roots (% control) PO 4 NO 3 KNH 4 Nutrient limiting in all layers Nutrient supplied to top and bottom layers Nutrient supplied to middle layer cm cm cm Data from Drew 1975

Data from Wikström and Ericsson Concentration of nutrient in the plant (fraction of optimum) Root:shoot ratio Response of birch seedlings to element limitation

Nadelhoffer et al. 2002

Response of an arctic cotton grass to elevated CO 2 data from Tissue & Oechel 1987

U 1 = g 1 B V 1 f(R 1 ) f(T) Optimized: U 2 = g 2 B V 2 f(R 2 ) f(T) U 3 = g 3 B V 3 f(R 3 ) f(T) V 1 + V 2 + V 2... = 1 U 2 = q 2 U 1 U 3 = q 3 U Maximize U 1 under the constraints that

U i = g i B V i f(R i ) f(T) Adaptive (Optimizing): dV i /dt = a ln{Φ q i U 1 /U i } V i Select Φ so that ∑dV i /dt = 0 (i.e., ∑V i = 1): q 1 ≡ 1 Φ = π (U i /(q i U 1 )) Vi

Uncoupled: U 1U = g B f(R 1 ) f(T) Liebig: U iL = q i g B min{f(R 1 ), f(R 2 ), f(R 3 )} f(T) Concurrent: U iC = q i g B {f(R 1 ) f(R 2 ) f(R 3 )} f(T) Optimized: U iO = g i B V i f(R i ) f(T) If f(R 1 ) doubles: U 1U 2× U iL ≥ 0×, ≤ 2× U iC 2× U iO > 0×, < 2× Comparison of responses for 3-resource models:

U 1U 2× U iL 2× U iC 8× U iO 2× If all three f(R i ) double: Uncoupled: U 1U = g B f(R 1 ) f(T) Liebig: U iL = q i g B min{f(R 1 ), f(R 2 ), f(R 3 )} f(T) Concurrent: U iC = q i g B {f(R 1 ) f(R 2 ) f(R 3 )} f(T) Optimized: U iO = g i B V i f(R i ) f(T) Comparison of responses for 3-resource models:

Plants B C : B N : 74 B P : 11 Inorganic E N : 2.6 E P :0.26 Microbes and soil organic matter D C : D N : 420 D P : 42 U N : 6.5 U P : 1.2 I NF : 0.28 I ND : 0.2 I P : 0.05 L C : 770 L N : 6.5 L P : 1.2 Q N : Q P : Q OC : 255 Q ON : 0.47 Q OP : U mN : U mP : M N : 26 M P : 2.6 R m : 515 P n : 770 U Nfix : 0 Based on Sollins et al HJ Andrews Forest Rastetter 2011

Uncoupled:

Liebig:

Concurrent:

Adaptive: At steady state:

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO 2

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO 2

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO 2

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO 2

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO o C

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO o C 6602

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO o C

Years NPP (g C m -2 yr -1 ) Net N mineralization (g N m -2 yr -1 ) Net P mineralization (g P m -2 yr -1 ) 2 x CO o C 6602

Conclusions: 1.Acclimation toward optimal resource use adds additional dynamics that propagate through and interact with ecosystem resource cycles. 2.These dynamics reflect adjustments within the biotic components of the ecosystem to maintain a metabolic balance and meet stoichiometric constraints 3.These dynamics are not represented in either “Liebig’s Law of the minimum” or “Concurrent” models of resource acquisition. 4.Because of these additional dynamics, initial responses are not likely to reflect long-term responses, making long-term projections from short-term experiments or observations difficult. 5.The optimization of resource use will tend to synchronize ecosystem resource cycles in the long term unless disturbance resets the system. 6.These “acclimation” responses act on many time scales and include activation/deactivation of enzyme systems, allocation of resources to individual tissues, replacement of suboptimal species with other species with more “optimal” uptake characteristics, and even natural selection of more “optimal” uptake characteristics.

Conclusions: 6.Resource optimization in my model is simulated through the reallocation of an abstract quantity I call “effort” (V i ) 7.Because the allocation of “effort” represents many processes within the vegetation, it is difficult to quantify except in terms of the observed long-terms dynamics of the ecosystem; this is the model’s biggest weakness. 8.Currently the allocation of “effort” is tied to a single rate constant. Because of the many processes involved in acclimation, a formulation with several rate constants might be more realistic 9.Model description in Rastetter EB Modeling coupled biogeochemical cycles. Frontiers in Ecology and the Environment 9: Executable code, sample data files, and instructions are available at