Emergent properties of heterogeneous decomposition networks

Abstract

Organic matter respiration in natural ecosystems is controlled by a network of biologically, physically, and chemically driven processes. Often it is important to estimate total carbon flux from a degradation system or the decay of mass in the system as a function of time. Historically, mass dynamics are predicted by a compartmental model consisting of various degradation processes. This approach provides a complete picture of mass in the model system, but includes extra information unnecessary for modeling overall mass dynamics. Furthermore, these models quickly become highly parameterized and are kept tangible by reducing the number of processes and system states. This thesis suggests a different approach. I allow the degradation system to be inherently complex, but only consider a simple projection of the system necessary to characterize mass dynamics. Because decomposing organic matter is often described as a heterogeneous continuum which transforms and degrades over a wide range of rates, I model degradation as a network consisting of a large, quasi-continuum of states. The retention of carbon in the network is then estimated by using an eigenvalue projection to calculate the impulse response of the degradation system. For a continuous network, the impulse response can be expressed as a Laplace transform of an "exit rate function." I then pose and solve an inverse problem in order to identify the rates of exit of carbon from decomposing plant matter from across North America. Analysis of the calculated exit rate functions and their associated decay data suggest that plant matter decomposition can often be mathematically approximated by a continuum of parallel processes. Within this approximation, the solution of the inverse problem yields the discovery that exit rate functions are on average lognormal. This result suggests that the overall mass dynamics of complex decay networks often collapse to just two parameters: the mean and the variance of the order of magnitude of exit rates from the network. These parameters are then used to assess the effects of climate and litter chemistry on organic carbon turnover and on rate heterogeneity. I also use observed patterns to explain the effect of natural selection in microbial communities on degradation network kinetics.