Forest Soil Carbon and Nitrogen Cycles under Biomass Harvest: Stability, Transient Response, and Feedback

Biomass harvest generates an imbalance in forest carbon (C) and nitrogen (N) cycles and the nonlinear biogeochemical responses may have long-term consequences for soil fertility and sustainable management. We analyze these dynamics and characterize the impact of biomass harvest and N fertilization on soil biogeochemistry and ecosystem yield with an ecosystem model of intermediate complexity that couples plant and soil C and N cycles. Two harvest schemes are modeled: continuous harvest at low intensity and periodic clear-cut harvest. Continuously-harvested systems sustain N harvest at steady-state under net mineralization conditions, which depends on the C:N ratio and respiration rate of decomposers. Further, linear stability analysis reveals steady-state harvest regimes are associated with stable foci, indicating oscillations in C and N pools that decay with time after harvest. Modeled ecosystems under periodic clear-cut harvest operate in a limit-cycle with net mineralization on average. However, when N limitation is strong, soil C–N cycling switches between net immobilization and net mineralization through time. The model predicts an optimal rotation length associated with a maximum sustainable yield (MSY) and minimum external N losses. Through non-linear plant–soil feedbacks triggered by harvest, strong N limitation promotes short periods of immobilization and mineral N retention, which alter the relation between MSY and N losses. Rotational systems use N more efficiently than continuous systems with equivalent biomass yield as immobilization protects mineral N from leaching losses. These results highlight dynamic soil C–N cycle responses to harvest strategy that influence a range of functional characteristics, including N retention, leaching, and biomass yield

Critical random forests

Let $F(N,m)$ denote a random forest on a set of $N$ vertices, chosen uniformly from all forests with $m$ edges. Let $F(N,p)$ denote the forest obtained by conditioning the Erdos-Renyi graph $G(N,p)$ to be acyclic. We describe scaling limits for the largest components of $F(N,p)$ and $F(N,m)$, in the critical window $p=N^{-1}+O(N^{-4/3})$ or $m=N/2+O(N^{2/3})$. Aldous described a scaling limit for the largest components of $G(N,p)$ within the critical window in terms of the excursion lengths of a reflected Brownian motion with time-dependent drift. Our scaling limit for critical random forests is of a similar nature, but now based on a reflected diffusion whose drift depends on space as well as on time

A Stochastic Model for the Species Abundance Problem in an Ecological Community

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical expression for the marginalized stationary distribution. Our solution is found in excellent agreement with numerical simulations and compares rather well with observational data from tropical forests.Comment: 4 pages, 3 figures, submitted to PR

A L\'evy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index

The main tool for stochastic calculus with respect to a multidimensional process $B$ with small H\"older regularity index is rough path theory. Once $B$ has been lifted to a rough path, a stochastic calculus -- as well as solutions to stochastic differential equations driven by $B$ -- follow by standard arguments. Although such a lift has been proved to exist by abstract arguments \cite{LyoVic07}, a first general, explicit construction has been proposed in \cite{Unt09,Unt09bis} under the name of Fourier normal ordering. The purpose of this short note is to convey the main ideas of the Fourier normal ordering method in the particular case of the iterated integrals of lowest order of fractional Brownian motion with arbitrary Hurst index.Comment: 20 page