Uncertainties in interpretation of isotope signals for estimation of fine root longevity: theoretical considerations

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Abstract
This paper examines uncertainties in the interpretation of isotope signals when estimating fine root longevity, particularly in forests. The isotope signals are depleted δ13C values from elevated CO2 experiments and enriched Δ14C values from bomb 14C in atmospheric CO2. For the CO2 experiments, I explored the effects of six root mortality patterns (on–off, proportional, constant, normal, left skew, and right skew distributions), five levels of nonstructural carbohydrate (NSC) reserves, and increased root growth on root δ13C values after CO2 fumigation. My analysis indicates that fitting a linear equation to δ13C data provides unbiased estimates of longevity only if root mortality follows an on–off model, without dilution of isotope signals by pretreatment NSC reserves, and under a steady state between growth and death. If root mortality follows the other patterns, the linear extrapolation considerably overestimates root longevity. In contrast, fitting an exponential equation to δ13C data underestimates longevity with all the mortality patterns except the proportional one. With either linear or exponential extrapolation, dilution of isotope signals by pretreatment NSC reserves could result in overestimation of root longevity by several‐fold. Root longevity is underestimated if elevated CO2 stimulates fine root growth. For the bomb 14C approach, I examined the effects of four mortality patterns (on–off, proportional, constant, and normal distribution) on root Δ14C values. For a given Δ14C value, the proportional pattern usually provides a shorter estimate of root longevity than the other patterns. Overall, we have to improve our understanding of root growth and mortality patterns and to measure NSC reserves in order to reduce uncertainties in estimated fine root longevity from isotope data.