## Research HypothesesThis page contains derivations of analytical solutions to current working hypotheses by Dr. Erik Hobbie. The greek letters lower case delta and upper case delta used in these equations may appear as a d or D, respectively, on some browsers. - Analytical solutions to nitrogen isotope patterns in mycorrhizal symbioses.
- Estimation of carbon allocation to mycorrhizal fungi from nitrogen isotope measurements
- References
Analytical solutions to fungal and plant d (1) d The remainder (1 - T (2)d Of the reduced nitrate in the fungus (T (3)d The remainder (1 - T (4)d Of the original nitrate, a fraction (1 - T (5)d Of the total nitrate supplied, a fraction [T Fortunately, the calculation for ammonium is considerably less onerous,
being essentially identical to equations (1) and (2) in the text. Of the total
ammonium supplied, a fraction T (6) d (7) d With ammonium supplied at a rate A and nitrate supplied at a rate N, the isotopic signatures for plant and fungus are as follows. (8) d Substituting equations (5) and (6) into equation (8) yields equation (9). (9)
d The pattern in fungi is simpler. (10)
d
Below-ground carbon flux to mycorrhizal fungi has been difficult to estimate because of the rapid turnover of mycorrhizal root tips and hyphae, and difficulties in translating any static measurement of hyphal mass into a carbon flux. The close coupling between nitrogen and carbon cycling in plants (Ågren and Bosatta 1996) suggests that a theoretical treatment of plant-mycorrhizal carbon and nitrogen cycles may prove useful in determining carbon flux to mycorrhizal fungi. I start from the basic premise that uptake of available soil nitrogen by fungi (and plants) is proportional to the growth of hyphae (and roots) into previously unexploited areas (Clarkson 1985; Ingestad and Ågren 1988). In other words, because of the limited mobility of available nitrogen in the soil, the flux of nitrogen to the hyphal or root surface is proportional to growth and not mass. Below I've outlined the mathematical framework by which this approach could be used to estimate carbon allocation to mycorrhizal fungi. Observations: - Carbon flux to mycorrhizal fungi results in acquisition of nitrogen.
- Carbon allocation below-ground is proportional to N availability (Ågren and Bosatta 1996).
- Plant d
_{}^{15}N declines with lower N availability (Hobbie et al. 1999, 2000). - What is the relationship among nitrogen isotopes, nitrogen acquisition and carbon flux to mycorrhizal fungi?
Carbon allocation to mycorrhizal fungi can be estimated: (1) C C
Definitions: Equations: (2) C (3) T (5) N Setting (5) and (6) equal to each other: (7) G * n = (1-T Substituting (4) into (7) and dividing by n: (8) G = (1/ T Substituting (8) into (2): (1) C Because both equation (1) and equations of factors controlling nitrogen
isotope patterns in plants use the transfer ratio (T Ågren GI, Bosatta E. 1996. Theoretical ecosystem ecology. Cambridge University Press, Cambridge. Clarkson DT. 1985. Factors affecting mineral nutrient acquisition by plants. Annual Review of Plant Physiology 36:77-115. Hobbie, E.A., S.A. Macko, and H.H. Shugart. 1999. Insights into nitrogen and carbon dynamics of ectomycorrhizal and saprotrophic fungi from isotopic evidence. Oecologia 118:353-360. Hobbie, E.A., S.A. Macko, and M.T. Williams. 2000.
Correlations between foliar d Ingestad T, Ågren GI. 1988. Nutrient uptake and allocation at steady-state nutrition. Physiologia Plantarum 72:450-459. |