Unsteady State Solutions For Two Diffusion Processes And Their Ecological Significances

Diffusion equation is one of the most widely used equations in ecological studies.In many cases,analysis based on the equilibrium solution under assumed steady state condition cannot reflect the real ecological processes accurately,which may lead to mispresentation of ecology principles and misinterpretations to observation data.In this dissertation research,the structural dynamics of the size-frequency distribution of trees in natural forests and the diffusive fractionation of carbon isotopes during soil respiration were analyzed with the diffusion equations.To get the general analytical solutions of the two ecological processes under non-steady state,the second-order partial differential diffusion equation was first reduced to a first-order linear partial differential equation and a first-order linear ordinary differential equation based on their specific characteristics,then the constraint and the boundary conditions of the two models were determined according to the actual situations,and finally the characteristics of the solutions and their ecological significances were analyzed.For the size-frequency distribution dynamics of trees in natural forests,the traditional approach which used the birth rate as the boundary condition of structured population dynamics was abandoned,and a new restriction condition which based on the principle of resources conservation was provided.The intrinsic periodicity of forest size-frequency distribution dynamics was found which reconciled the variant and invariant properties of forest size structure on different spatial scales,which challenged the extensions of WBE's metabolic scaling theory on forest community level,such as the invariant power-law distribution of tree diameters and the converging tendency of forest size structure.The conclusions from this study were supported by our own Chinese mangrove community survey data,the forest inventory database of United States,and the Gentry's global forest transect survey dataset.For the carbon isotope fractionation during soil respiration,the fluxes of ¹³CO₂ and¹²CO₂ in the soil-atmosphere diffusion system were described using a set of diffusion equations.Under non-steady-state conditions,diffusive fractionation which was caused by the different concentration gradient variation and different diffusion coefficient of the two isotopologues,which led to a converging pattern for the?¹³C values of effluxed CO₂with the increase of CO₂ efflux rate,was proved to be the main reason for the observed?¹³C variations of soil effluxed CO₂.Thus previous studies that emphasized the biological influences and attributed the?¹³C variations of soil effluxed CO₂ to the shifting of contributing sources should be seriously reexamined.The conclusion was supported by both my own experiment data and the data from the literature.