QUANTITATIVE LAWS June 13 -June 24

1. Resource Ratios and Primary Productivity in the
Ocean
George I. Hagstrom, Simon Levin, Adam Martiny
Princeton University
Department of Ecology and Evolutionary Biology

2. Stoichiometry Couples Nutrient Cycles
Photosyntheis in surface ocean pumps carbon to the deep.
Phytoplankton require nitrogen, phosphorus, iron, and
sometimes other nutrients (sillicon)
Depletion of these nutrients in surface ocean slows biological
pump, couples Carbon cycle to nutrient cycles.
Strength of coupling is elemental stoichiometry of
phytoplankton.
C OO
C OO
C OO

3. Nutrient Timescales
Each major nutrient has different chemistry in the ocean:
Inorganic Phosphorus: Residence time of 105 years.
Inorganic Nitrogen: N-Fixation and denitrification.
N2 + 8H+
+ 8e−
+ 16ATP → 2NH3 + 16ADP + H2
Iron residence time 100 years.

4. Redfield-Tyrrell Paradigm
Biologists: N is ULN
Geochemists: P is ULN
dBp
dt
= Bp γp − m ,
dBd
dt
= Bd (γd − m)
dNS
dt
=
(ND − NS )
τS
+
fN
DS
+ (rS − DN )m(Bp + Bd ) − γpBp
dPS
dt
=
(PD − PS )
τS
+
fP
DS
+
(rS m − γp)Bp
(N:P)org
+
(rS m − γd )Bd
(N:P)org
dND
dt
= τ
−1
D (NS − ND ) + mrD (Bp + Bd )
DS
DD
dPD
dt
= τ
−1
D (PS − PD ) + mrD
Bp + Bd
(N:P)org
DS
DD
− kP PD
P is ultimate limiting nutrient
(TPP) = m Bd + Bp =
fP (N:P)p
kP DD (1−rS )
Homeostasis
(N:P)deep ∼ (N:P)p 1 −
DN
1−rS
(N:P)p

5. Challenges to Tyrrell/Redfield: Iron Limitation and
Stoichiometry
Widespread iron limitation, HNLC regions and diazotrophs.
High (N:P)org in subtropical gyres, low (N:P)org in subpolar
gyres.

6. Simple Biogeochemical Model
Three nutrients: N, P, Fe
Three phytoplankton types: diazotrophs, prokaryotes,
eukaryotes
Three ocean regions: High latitude, low-latitude, deep ocean.

7. Ultimate Limiting Nutrient Controlled by Supply and
Demand
Resource Supply:
JP,L =
1
τL
(PD − PL) +
fP,L
dL
, JFe,L =
1
τL
(FeD − FeL) +
fFe,L
dL
, JN,L =
1
τL
(ND − NL) +
fN,L
dL
JP,U =
1
τU
(PD − PU ) +
fP,U
dL
, JFe,U =
1
τL
(FeD − FeU ) +
fFe,U
dU
, JN,U =
1
τU
(ND − NU ) +
fN,U
dU
Normalize by resource demand:
φP,L = (N:P)pJP,L. φFe,L = (N:Fe)pJFe,L, φN,L = JN,L
φP,U = (N:P)uJP,U , φFe,U = (N:Fe)uJFe,U , φN,U = JN,U
Limiting nutrients set by lowest supply to demand ratio:
WL =P,Fe (φP,L, φFe,L), WU =N,P,Fe (φP,U, φFe,U, φN,U)
TPP = α1
ALφWL
(1 − rS )
+ α2fN,L +
AUφWU
(1 − rS )
α1 = 1, α2 = 0 when (N:P)p = (N:P)d or
(N:Fe)p = (N:Fe)d .

8. Iron Supply Shifts Nutrient Limitation Scenarios

9. Deep Ocean N Regulated by Limiting Nutrient Supply to
LL
Fe Limited: ND
JFe,LτL
= (N:Fe)p − DN
1−rS
(N:Fe)p +
JFe,U
JFe,L
(N:Fe)u
P Limited: (N:P)deep = (N:P)p + DN
1−rS
−(N:P)p − kU
kL
(N:P)u
Reconciliation: Iron limitation, high kU
kL
, lateral transport of P depleted
waters (Weber and Deutsch).

10. Response to Nutrient Flux Changes
How would ocean respond to increases in nutrient fluxes?
Redfield picture: Rapid transition to P limitation, no change
in TPP.
John Martin and others: Iron/nitrate fertilization may be
important.
Perform experiments: biogeography and stoichiometry give
new mechanisms.

11. Future Directions: Evolution of Phytoplankton
Stoichiometry
Many Directions to Go
Stoichiometry more plastic than indicated here.
Frugality?
Growth Rate Hypothesis?
Temperature, Phylogeny, Luxury Storage?
Incorporate eco-evolutionary feedbacks.
Could the ocean evolve to colimitation?

12. Thanks!