Optimality, Acclimation and Photosynthesis

The following is a theoretical derivation of a generalized
acclimation model of time-averaged photosynthesis (Pmean) and photosynthetic capacity (Pmax) based on optimality theory and empirical evidence for a highly conservative ratio between Pmax and Pmean (Schulze 2006). Numerous studies have found the actual quantum yield of photosynthesis as well as the light-use efficiency of photosynthesis (εmean=Pmean/APARmean) to be about one-half of its theoretical maximum value (Landsberg 1986, Norman 1993, Haxeltine and Prentice 1996).

Time-averaged photosynthesis (
Pmean) may be expressed as a functionof time-averaged radiation (PARmean), light absorptance (fAPAR), and the efficiency of photosynthetic CO2 uptake per unit absorbed radiation (εmean):


Similarly, photosynthetic capacity (Pmax), may be expressed as function of time-averaged radiation (PARmean), light absorptance (fAPAR), and the maximum efficiency of photosynthetic CO2 uptake per unit absorbed radiation (εmax):


It follows that


If measurements (Landsberg 1986, Schulze 2006) and modeling studies (
Norman 1993, Haxeltine and Prentice 1996) laboratory indicated that ε=Pmean/APARmean, it follows that

If it is true that 

Pmax=2*Pmean                                                                                                            Eqn 1


Pmax=LUEmax*APARsat                                                                                              Eqn 2


Pmean=LUEmean*APARmean                                                                                          Eqn 3

then it follows from sustitution that

LUEmax*APARsat=2*LUEmean*APARmean                                                                                     Eqn 4        

Further, optimality theory suggests that plants acclimate to their light environment by adjusting photosynthetic capacity in tune with the availability of light (Arnon 1982, Farquhar 1989). It follows that for an optimally acclimated plant, Pmax should occur at the average absorbed growth irradiance, that is, light saturation should occur at the average light level such that APARsat = APARmean.

Therefore, substituting APARmean for APARsat in Eqn 4 gives


which simplifies to

LUEmax=2*LUEmean                                                                                                              Eqn 5

Since the upper limit to LUEmax is the maximum quantum yield of photosynthesis (q), LUEmax can be replaced to give



LUEmean=1/2*q                                                                                                          Eqn 6

Therefore, sustituting for LUEmean in Eqn 3 gives Pmean as a function of the quantum yield and mean growth irradiance

Pmean=1/2*q*APARmean                                                                                                 Eqn 7

Similarly, combining Eqns 2, 5 and 6 gives Pmax as a function of the quantum yield and mean growth irradiance

Pmax=q*APARmean                                                                                                        Eqn8

Equations 7 and 8 provide simple theoretical models for predicting time-averaged photosynthesis (Pmean) and photosynthetic capacity (Pmax) from the maximum quantum yield and time-averaged absorbed radiation (APARmean), notwithstanding reductions in the quantum yield and absorbed irradiance due to suboptimal growth conditions (i.e. seasonal temperature and moisture stress). To summarize, there are two main assumptions in these derivations; the first is that Pmax=2*Pmean and the second is that plants acclimate by adjusting photosynthetic capacity to the mean growth irradiance so that APARsat=APARmean (optimal acclimation). The first assumption can be verified empirically using continuous leaf level gas exchange (e.g. Zotz and Winter 1993, see also Schulze 2006) and canopy scale eddy covariance measurements (e.g. Sims et al. 2005). The second assumption can be verified by analyzing photosynthetic light response curves from the same two types of measurements. This second assumption is expected based on ecophysiological and optimality theory of photosynthetic acclimation to growth irradiance. However, we currently lack a theoretical explanation of the 2:1 ratio of maximum to mean photosynthesis, although it has been suggested that this ratio allows for maximum performance in a variable environment (Schulze 2006).


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