Model litter chemistry and turnover

[hrlai]

See also https://virtual-ecosystem.readthedocs.io/en/662-improve-soil-nutrient-documentation/virtual_ecosystem/theory/soil/litter_theory.html#litter-chemistry

[hrlai]

Currently I am using the SAFE litter data, which seems to be leaf litter. In Elias et al. (2020) their methodology stated that coarse woody debris and partially decomposed leaves were removed. These leaf litter have N, P and lignin measured, so we can eventually link them to the metabolic and structural litter pools. But we do not have chemical data for root and reproductive litter.

[arne-exe]

Currently I am using the SAFE litter data, which seems to be leaf litter. In Elias et al. (2020) their methodology stated that coarse woody debris and partially decomposed leaves were removed. These leaf litter have N, P and lignin measured, so we can eventually link them to the metabolic and structural litter pools. But we do not have chemical data for root and reproductive litter.

Hey, I noticed you mentioned chemical data for root and reproductive litter, I'm currently working on stoichiometry in #48.
The following references may be of interest to you:

• Kitayama et al. (2015; DOI http://dx.doi.org/10.1111/1365-2745.12379), also see supplementary
• Aoyagi et al. (2018; DOI https://doi.org/10.1007/s11284-018-1642-9)
• Proctor et al. (1989; DOI https://doi.org/10.2307/2260752)
• Imai et al. (2010; DOI http://dx.doi.org/10.1017/S0266467410000350)

(Accidentally edited your comment instead of quoting it, my bad)

[hrlai]

THANK YOU! I'll take a look 😄

[hrlai]

Read and see if steady states in this paper makes sense https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.12138

[hrlai]

Also look into Terhi Riutta's datasets.

[jacobcook1995]

So for the decay of litter items that are assumed to have no lignin (i.e. fruit) the decay process should be quite straightforward, i.e.

$$\frac{x(t)}{x_0} = e^{-k_m t},$$

where $k_m$ is the decay rate for metabolic litter. It gets a lot more complex for items that contain lignin as the model does two things:

1. Splits the litter into structural and metabolic based on lignin content
2. Calculates a factor that slows structural litter decay based on lignin content

The fraction of litter input that is considered to be metabolic is given by

$$f_m = f_M - L * (s_N * C:N + s_P * C:P),$$

where $f_M$ is the maximum fraction that can go into the metabolic pool, $L$ is the lignin content of the items, $C:N$ and $C:P$ are the stoichiometric ratios, and $s_N$ and $s_P$ are the "responsiveness" of the split to changes in stoichiometric ratio.

So the full expression for decay of e.g. leaves is given by

$$\frac{x(t)}{x_0} = f_m*e^{-k_m t} + (1 - f_m)*e^{-K(L) t},$$

with

$$K(L) = k_s*e^{rL},$$

where $r$ is a negative parameter determining how much lignin slows litter breakdown, and $k_s$ is the decay rate for structural litter.

Wood contains lignin, but isn't split into separate structural and metabolic pools, so should be modelled as follows

$$\frac{x(t)}{x_0} = e^{-K_w t},$$

with

$$K_w(L) = k_w e^{rL}$$

where $k_w$ is the decay rate for wood.

I think we can assume that the parameters (e.g. $k_s$, $k_m$, $r$) should be the same between different litter items, i.e. fruit, leaves, roots (can't imagine that there's data for this).

There's two big omissions from the above.

1. Decay rates should vary with temperature
2. The relative size of the structural and metabolic components of a litter item should shift as it decays (because the metabolic component breaks down faster).

My gut feeling is that the analysis above will be tricky enough to get to work for the time being and these are things we can worry about later if they become a problem. (@hrlai let me know if you disagree and I can give more detail)

[hrlai]

Thanks @jacobcook1995 your reasoning makes a lot of sense.

For now sharing $k_s$, $k_m$ and $r$ across litter types sound good, as discussed. And will leave temperature dependence for later.

With short enough sampling intervals, I think we might be able to get away for assuming the relative size of structural and metabolic components to be constant (within the narrow window of time). But will keep this in mind.

So the first thing is I'll look for data that measured $x(t)$, $x_0$, $L$ and $t$. And parameters to infer are $f_m$, $k_s$, $k_m$ and $r$.

Just to double check, $t$ is time lapsed since $t_0$ right?

[hrlai]

Hi @jacobcook1995 two more follow-up questions:

1. Would you expect $s_N$ and $s_P$ to be positive bound?
2. Do we expect leaves to be more of metabolic or more or structural? I.e., do we expect $f_m$ to be closer to 0 or closer to 1?

[hrlai]

Sorry another question as I dig deeper on $f_m$:

In Kirschbaum & Paul (2002), their equation 1a had lignin in the denominator; but:-

Fatichi et al. (2019) Equation 99 in the supplementary had lignin in the numerator;

yet they both retain the same -0.018 coefficient, could you explain to me...? I'm going through their constants to pick sensible Bayesian priors for my model.

[hrlai]

So the full expression for decay of e.g. leaves is given by

$$\frac{x(t)}{x_0} = f_m*e^{-k_m t} + (1 - f_m)*e^{rL}*e^{-k_s t},$$

where r is a negative parameter determining how much lignin slows litter breakdown, and k s is the decay rate for structural litter.

Should the second component instead be

$$ (1 - f_m)*e^{-(k_s * \exp(rL)) t} $$ ?

For two reasons:

1. Kirschbaum & Paul (2002) had lignin affecting decomposition rate constant (Equation 3), and I presume their $D_s$ (or $k$) is equivalent to our $k_s$ --- this also extends well if we include temperature dependence later
2. The former does not reduce to one when $t = 0$ because of lignin

[jacobcook1995]

Just to double check, t is time lapsed since t 0 right?

Yes, it is, I should have mentioned that!

1. Would you expect

   $s_N$ and $s_P$  to be positive bound?
   

Yep these have to be positive otherwise the litter could become less recalcitrant as lignin concentrations increase/nutrients become more scarce, which wouldn't make sense.

2. Do we expect leaves to be more of metabolic or more or structural? I.e., do we expect $f_m$ to be closer to 0 or closer to 1?

Hmmm, the dummy values currently used in the model predict an $f_m$ of 0.8, so I would say that leaves are still expected to be mainly metabolic litter. My confidence in that is pretty low though

Sorry another question as I dig deeper on f m :

In Kirschbaum & Paul (2002), their equation 1a had lignin in the denominator; but:-

Fatichi et al. (2019) Equation 99 in the supplementary had lignin in the numerator;

yet they both retain the same -0.018 coefficient, could you explain to me...? I'm going through their constants to pick sensible Bayesian priors for my model.

I think there is a typo in Kirschbaum & Paul (2002), as litter becoming less recalcitrant as lignin decreases makes no sense, in the Parton (1987) paper that they reference the split is determined by the ratio of lignin to nitrogen (so lignin in the numerator).